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@article{Helander2015a,
abstract = {Recent progress in the gyrokinetic theory of stellarator microinstabilities$\backslash$nand turbulence simulations is summarized. The simulations have been$\backslash$ncarried out using two different gyrokinetic codes, the global particle-in-cell$\backslash$ncode EUTERPE and the continuum code GENE, which operates in the geometry$\backslash$nof a flux tube or a flux surface but is local in the radial direction.$\backslash$nIon-temperature-gradient (ITG) and trapped-electron modes are studied$\backslash$nand compared with their counterparts in axisymmetric tokamak geometry.$\backslash$nSeveral interesting differences emerge. Because of the more complicated$\backslash$nstructure of the magnetic field, the fluctuations are much less evenly$\backslash$ndistributed over each flux surface in stellarators than in tokamaks.$\backslash$nInstead of covering the entire outboard side of the torus, ITG turbulence$\backslash$nis localized to narrow bands along the magnetic field in regions$\backslash$nof unfavourable curvature, and the resulting transport depends on$\backslash$nthe normalized gyroradius rho* even in radially local simulations.$\backslash$nTrapped-electron modes can be significantly more stable than in typical$\backslash$ntokamaks, because of the spatial separation of regions with trapped$\backslash$nparticles from those with bad magnetic curvature. Preliminary non-linear$\backslash$nsimulations in flux-tube geometry suggest differences in the turbulence$\backslash$nlevels in Wendelstein 7-X and a typical tokamak.},
author = {Helander, P. and Bird, T. and Jenko, F. and Kleiber, R. and Plunk, G. G. and Proll, J. H.E. and Riemann, J. and Xanthopoulos, P.},
doi = {10.1088/0029-5515/55/5/053030},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Helander et al. - 2015 - Advances in stellarator gyrokinetics.pdf:pdf},
issn = {17414326},
journal = {Nucl. Fusion},
keywords = {confinement,gyrokinetics,stellarators},
number = {5},
title = {{Advances in stellarator gyrokinetics}},
volume = {55},
year = {2015}
}
@article{Umansky2005,
author = {Umansky, M.V. and Rognlien, T.D. and Xu, X.Q.},
doi = {10.1016/j.jnucmat.2004.10.021},
issn = {00223115},
journal = {J. Nucl. Mater.},
keywords = {edge modeling},
month = {mar},
pages = {266--270},
title = {{Simulation of turbulence in the divertor region of tokamak edge plasma}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022311504007561},
volume = {337-339},
year = {2005}
}
@article{Search1979,
author = {Search, Home and Journals, Collections and Contact, About and Iopscience, My and Address, I P},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Search et al. - 1979 - Low-Z impurity transport in tokamaks LOW-Z IMPURITY TRANSPORT IN TOKAMAKS.pdf:pdf},
journal = {Contract},
title = {{Low-Z impurity transport in tokamaks LOW-Z IMPURITY TRANSPORT IN TOKAMAKS *}},
volume = {607},
year = {1979}
}
@article{Miller1998a,
author = {Miller, R. L. and Chu, M. S. and Greene, J. M. and Lin-Liu, Y. R. and Waltz, R. E.},
doi = {10.1063/1.872666},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Miller et al. - 1998 - Noncircular, finite aspect ratio, local equilibrium model.pdf:pdf},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {4},
pages = {973},
title = {{Noncircular, finite aspect ratio, local equilibrium model}},
url = {http://link.aip.org/link/PHPAEN/v5/i4/p973/s1{\&}Agg=doi},
volume = {5},
year = {1998}
}
@book{White2009a,
abstract = {Fluid mechanics, the study of how fluids behave and interact under various forces and in various applied situationswhether in the liquid or gaseous state or bothis introduced and comprehensively covered in this widely adopted text. Fully revised and updated with the addition of a new chapter on biofluid mechanics, Fluid Mechanics, Fourth Edition is suitable for both a first or second course in fluid mechanics at the graduate or advanced undergraduate level. The leading advanced general text on fluid mechanics, Fluid Mechanics, 4e guides students from the fundamentals to the analysis and application of fluid mechanics, including compressible flow and such diverse applications as hydraulics and aerodynamics. Updates to several chapters and sections, including Boundary Layers, Turbulence, Geophysical Fluid Dynamics, Thermodynamics and Compressibility. Fully revised and updated chapter on Computational Fluid Dynamics. New chapter on Biofluid Mechanics by Professor Portonovo Ayyaswamy, the Asa Whitney Professor of Dynamical Engineering at the University of Pennsylvania. New Visual Resources appendix provides a list of fluid mechanics films available for viewing online. Additional worked-out examples and end-of-chapter problems. Updated online Solutions Manual for adopting instructors.},
archivePrefix = {arXiv},
arxivId = {1003.3921v1},
author = {White, Frank M.},
doi = {10.1146/annurev.fluid.36.050802.122132},
eprint = {1003.3921v1},
isbn = {978-0-07-352934-9},
issn = {19326203},
pages = {887},
pmid = {21448459},
title = {{Fluid Mechanics}},
year = {2009}
}
@article{Hornsby2017,
author = {Hornsby, W. A. and Angioni, C. and Fable, E. and Manas, P. and McDermott, R. and Peeters, A. G. and Barnes, M. and Parra, F.},
doi = {10.1088/1741-4326/aa5aa1},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hornsby et al. - 2017 - On the effect of neoclassical flows on intrinsic momentum in ASDEX Upgrade Ohmic L-mode plasmas.pdf:pdf},
issn = {17414326},
journal = {Nucl. Fusion},
keywords = {intrinsic rotation,tokamak,turbulence},
number = {4},
publisher = {IOP Publishing},
title = {{On the effect of neoclassical flows on intrinsic momentum in ASDEX Upgrade Ohmic L-mode plasmas}},
volume = {57},
year = {2017}
}
@article{Parra2014a,
abstract = {Self-consistent equations for intrinsic rotation in tokamaks with small poloidal magnetic field {\$}B{\_}p{\$} compared to the total magnetic field {\$}B{\$} are derived. The model gives the momentum redistribution due to turbulence, collisional transport and energy injection. Intrinsic rotation is determined by the balance between the momentum redistribution and the turbulent diffusion and convection. Two different turbulence regimes are considered: turbulence with characteristic perpendicular lengths of the order of the ion gyroradius, {\$}\backslashrho{\_}i{\$}, and turbulence with characteristic lengths of the order of the poloidal gyroradius, {\$}(B/B{\_}p) \backslashrho{\_}i{\$}. Intrinsic rotation driven by gyroradius scale turbulence is mainly due to the effect of neoclassical corrections and of finite orbit widths on turbulent momentum transport, whereas for the intrinsic rotation driven by poloidal gyroradius scale turbulence, the slow variation of turbulence characteristics in the radial and poloidal directions and the turbulent particle acceleration can be become as important as the neoclassical and finite orbit width effects. The magnetic drift is shown to be indispensable for the intrinsic rotation driven by the slow variation of turbulence characteristics and the turbulent particle acceleration. The equations are written in a form easily implementable in a flux tube code, and the effect of the radial variation of the turbulence is included without having to resort to a global gyrokinetic formalism.},
archivePrefix = {arXiv},
arxivId = {1407.1286},
author = {Parra, Felix I and Barnes, Michael},
doi = {10.1088/0741-3335/57/4/045002},
eprint = {1407.1286},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
keywords = {gyrokinetics,in colour only in,rotation,some figures may appear,the online journal,tokamak,turbulence},
pages = {83},
title = {{Intrinsic rotation in tokamaks. Theory}},
url = {http://arxiv.org/abs/1407.1286},
volume = {045002},
year = {2014}
}
@article{Kiviniemi2006a,
abstract = {A direct implicit ion polarization gyrokinetic full f particle-in-cell approach is implemented with kinetic electrons in global tokamak transport simulations. The method is applicable for calculations of rapid transients and steep gradients in the plasma, which is made feasible by recording the charge density change by the ion polarization drift together with the particle advancing. The code has been successfully validated against the linear and nonlinear predictions of the unstable mode growth rates and frequencies and their turbulent saturation level. A first global validation of the neoclassical radial electric field in the presence of turbulence for a heated collisional tokamak plasma is obtained. The neoclassical radial electric field together with the related geodesic acoustic mode oscillations is found to regulate the turbulence and heat and particle diffusion levels in a large aspect ratio tokamak at low plasma current},
author = {Kiviniemi, T. P. and Heikkinen, J. A. and Janhunen, S. and Henriksson, S. V.},
doi = {10.1088/0741-3335/48/5A/S32},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Kiviniemi et al. - 2006 - Full f gyrokinetic simulation of FT-2 tokamak plasma.pdf:pdf},
issn = {07413335},
journal = {Plasma Phys. Control. Fusion},
number = {5 A},
title = {{Full f gyrokinetic simulation of FT-2 tokamak plasma}},
volume = {48},
year = {2006}
}
@article{Doerk2012,
author = {Doerk, H},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Doerk - 2012 - Gyrokinetic Simulation of Microtearing Turbulence Dissertation.pdf:pdf},
pages = {1--262},
title = {{Gyrokinetic Simulation of Microtearing Turbulence Dissertation}},
year = {2012}
}
@article{Lee2009,
author = {Lee, D. K. and Peng, Y. K. M.},
doi = {10.1017/S0022377800023023},
issn = {0022-3778},
journal = {J. Plasma Phys.},
month = {mar},
number = {01},
pages = {161},
title = {{An approach to rapid plasma shape diagnostics in tokamaks}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022377800023023},
volume = {25},
year = {2009}
}
@article{Lovelace1986,
abstract = {A general theory is developed for relativistic, steady, axisymmetric, ideal magnetohydrodynamic flows around a black hole or a rotating magnetized star. The theory leads to an autonomous second-order partial differential equation - a Grad-Shafranov equation - for the magnetic flux function $\psi$(r,z). One limit of this equation gives the familiar Grad-Shafranov equation which describes the equilibrium of axisymmetric fusion plasmas. Another limit gives the equation describing general nonmagnetic flows of matter with angular momentum. A further limit gives the "pulsar equation" of Scharlemann, Wagoner, and Michel for relativistic plasma flows around an aligned, rotating, magnetized neutron star. Applications of the theory are made to thin, magnetized disks around a Schwarzschild black hole and around an aligned, rotating, magnetized star.},
author = {Lovelace, R V E and Mehanian, C and Mobarry, C M and Sulkanen, M E},
doi = {10.1086/191132},
issn = {00670049},
journal = {Astrophys. J. Suppl. Ser.},
pages = {1--37},
title = {{Theory of Axisymmetric Magnetohydrodynamic Flows: Disks}},
volume = {62},
year = {1986}
}
@article{Ludwig1998,
author = {Ludwig, G. O. and Andrade, M. C. R.},
doi = {10.1063/1.872900},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {6},
pages = {2274},
title = {{External inductance of large to ultralow aspect-ratio tokamak plasmas}},
url = {http://link.aip.org/link/PHPAEN/v5/i6/p2274/s1{\&}Agg=doi},
volume = {5},
year = {1998}
}
@article{Tatsuno2009,
abstract = {Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.},
author = {Tatsuno, T. and Dorland, W. and Schekochihin, A. A. and Plunk, G. G. and Barnes, M. and Cowley, S. C. and Howes, G. G.},
doi = {10.1103/PhysRevLett.103.015003},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Tatsuno et al. - 2009 - Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence.pdf:pdf},
journal = {Phys. Rev. Lett.},
title = {{Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence}},
url = {http://www.mendeley.com/research/nonlinear-phase-mixing-phasespace-cascade-entropy-gyrokinetic-plasma-turbulence},
year = {2009}
}
@article{Cerfon2010,
author = {Cerfon, Antoine J. and Freidberg, Jeffrey P.},
doi = {10.1063/1.3328818},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {3},
pages = {032502},
title = {{“One size fits all” analytic solutions to the Grad–Shafranov equation}},
url = {http://link.aip.org/link/PHPAEN/v17/i3/p032502/s1{\&}Agg=doi},
volume = {17},
year = {2010}
}
@article{Smartphones2003,
author = {Smartphones, Based},
doi = {10.1007/SpringerReference_28001},
isbn = {3032783534},
number = {August},
pages = {1--19},
title = {{User Manual}},
volume = {2015},
year = {2003}
}
@article{Federspiel2014,
abstract = {This thesis focuses on measurements of toroidal rotation and impurity profiles in im- proved plasma scenarios and in the presence of MHD activity. These experiments were performed on TCV, the Tokamak {\`{a}} Configuration Variable in Lausanne. In TCV, plasma rotation is measured by the charge exchange recombination spec- troscopy diagnostic (CXRS). The CXRS is associated with a low power diagnostic neutral beam injector (DNBI) that provides CX emission from the hot plasma core, without perturbing the plasma with additional torque. The beam is observed transver- sally by the CXRS diagnostic so that local ion temperature, density and intrinsic ve- locity measurements are obtained. During this work, a pre-existing CXRS diagnostic was improved and automated. The three systems composing the present day CXRS2013 diagnostic cover the entire TCV radial midplane with up to 80 measurement locations separated by around 7mm with a time resolution ranging from 2-30ms. The main upgrades concerned the installation of new sensitive cameras, the overhaul of the toroidal HFS system, the extended-chord configuration and the automation of the acquisition and analysis processes. These new CXRS capabilities permitted the investigation of more complex scenarios featuring low intensity and/or fast events, like the low density electron internal transport barriers (eITBs) and the sawtooth (ST) instability discussed in this work. For the first time, a comparison between rotation profiles measured over several saw- tooth events and across a “canonical” sawtooth cycle has been undertaken in limited L-mode plasmas in this thesis, in order to identify the effect of the various ST phases on the rotation profile, and thus momentum transport. It is shown that the main ST effect on momentum is not simply a rotation profile flattening, as might be con- jectured from their effect on electron temperature and density (consistent with a ST reconnection model), but results appear more complicated. The averaged rotation profiles obtained with the upgraded CXRS diagnostic show that ST restrict the max- imum attainable |vϕ,max| and that, in the plasma core, inside the q=1 surface, the rotation profiles are flattened and almost always display a small co-current contribu- tion. It is this effect that results in the 1/Ip scaling observed in TCV limited L-mode plasmas. The co-current core contribution is identified to be related to the ST crash, whilst, during the quiescent ramp of the sawtooth period, a plasma recoil outside the mixing radius is observed. A high degree of momentum conservation, up to 80-90{\%}, is measured, suggesting that a supplementary torque accompanying the ST crash is not required to explain the experimental observations. This study demonstrates the importance of including fast perturbating effects such as MHD modes in momentum transport models to build a complete picture, since they are likely to generate strong and rapid fluxes inside the plasma. Extensive work on transport barriers has been performed to better understand the formation and characteristics of eITBs on TCV, using, for the first time, toroidal and poloidal rotation measurements. During this work, the poloidal rotation, Er and the E × B shearing rate have been derived systematically from the asymmetry of the toroidal rotation measurements at the HFS and LFS. Since the position of the CXRS diagnostic view is at Z=0cm, two scenarios, a central barrier and a strong off-axis eITB, similar to previous targets investigated at Z=21cm, were developed to facilitate CXRS analysis during this thesis. The effect on the barrier strength and on the rota- tion profiles of several parameters, such as the central and total power, Ohmic current perturbations and MHD activity is investigated for both targets. The barrier strength increases with cnt-CD applied on axis, higher total power and negative Ohmic per- turbations. Indeed, for the strong co-CD off-axis eITB, a barrier in Te at 7keV and ne with a 23cm barrier width, confinement factor HRLW = 5.4 and |R/LTe| = 45 was achieved. No special dependence is found between the experimental |$\omega$? E×B| ∝ 104s−1 and the confinement factor HRLW or the maximum |R/LTe|, confirming that on TCV, the barrier improvement is not linked to higher |$\omega$? E×B| values. The experimental E×B shearing rates were compared with the growth rate of the most unstable mode for these discharges (TEM) obtained with the GENE code. The growth rate is found always one order of magnitude larger than the measured E × B shearing rates, confirming that the E×B shearing rate is not the cause of the formation of eITBs on TCV. This result supports previous theoretical studies concluding that the reversed shear profile is mainly responsible for the eITB formation. The comparison between the experimental ion temperature profiles and the results obtained with a quasi-linear model applied to TCV eITBs has shown some discrepancies. The |R/LTi|/|R/LTe| ratios measured at the barrier position are much lower than expected from the model, and no ion barrier is observed in these discharges. The installation of a new NB heating in 2015 will allow direct heating of the ion channel and may elucidate these discrepancies.},
author = {Federspiel, Lucia Isabel and Schneider, O. and Duval, B. and Sauter, O. and Camenen, Y. and Lister, J. B. and McDermott, R.},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Federspiel et al. - 2014 - Rotation and Impurity Studies in the presence of MHD activity and Internal Transport Barriers on TCV PAR.pdf:pdf},
title = {{Rotation and Impurity Studies in the presence of MHD activity and Internal Transport Barriers on TCV PAR}},
volume = {6050},
year = {2014}
}
@article{LoDestro1994,
author = {LoDestro, L. L. and Pearlstein, L. D.},
doi = {10.1063/1.870464},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {1},
pages = {90},
title = {{On the Grad–Shafranov equation as an eigenvalue problem, with implications for q solvers}},
url = {http://link.aip.org/link/PHPAEN/v1/i1/p90/s1{\&}Agg=doi},
volume = {1},
year = {1994}
}
@article{Sanchez2010a,
abstract = {In this paper, we report on simulations that have recently been carried out using the EUTERPE gyrokinetic code. The scaling of the code has been studied up to 20 000 processing elements. Linear and nonlinear simulations of ion temperature-gradient instabilities have been carried out in screw-pinch geometry, and the results are compared with those previously obtained using the TORB code, finding a good agreement. The influence of a finite {\$}beta{\$} on the growth rates of instabilities and on the zonal flows in a screw-pinch has also been studied. The results are compared with previous ones.},
author = {Sanchez, Edilberto and Kleiber, Ralf and Hatzky, Roman and Soba, Alejandro and S{\'{a}}ez, Xavier and Castejon, Francisco and Cela, Jose M.},
doi = {10.1109/TPS.2010.2051339},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Sanchez et al. - 2010 - Linear and nonlinear simulations using the EUTERPE gyrokinetic code.pdf:pdf},
issn = {00933813},
journal = {IEEE Trans. Plasma Sci.},
keywords = {Plasma confinement,plasma stability,simulation},
number = {9 PART 1},
pages = {2119--2128},
title = {{Linear and nonlinear simulations using the EUTERPE gyrokinetic code}},
volume = {38},
year = {2010}
}
@article{Nave2010,
abstract = {Using the unique capability of JET to monotonically change the amplitude of the magnetic field ripple, without modifying other relevant equilibrium conditions, the effect of the ripple on the angular rotation frequency of the plasma column was investigated under the conditions of no external momentum input. The ripple amplitude was varied from 0.08{\%} to 1.5{\%} in Ohmic and ion-cyclotron radio-frequency (ICRF) heated plasmas. In both cases the ripple causes counterrotation, indicating a strong torque due to nonambipolar transport of thermal ions and in the case of ICRF also fast ions.},
author = {Nave, M. F. F. and Johnson, T. and Eriksson, L.-G. and Cromb{\'{e}}, K. and Giroud, C. and Mayoral, M.-L. and Ongena, J. and Salmi, A. and Tala, T. and Tsalas, M.},
doi = {10.1103/PhysRevLett.105.105005},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Nave et al. - 2010 - Influence of Magnetic Field Ripple on the Intrinsic Rotation of Tokamak Plasmas.pdf:pdf},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
number = {10},
pages = {105005},
title = {{Influence of Magnetic Field Ripple on the Intrinsic Rotation of Tokamak Plasmas}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.105.105005{\%}5Cnhttp://prl.aps.org/abstract/PRL/v105/i10/e105005{\%}5Cnhttp://prl.aps.org/pdf/PRL/v105/i10/e105005},
volume = {105},
year = {2010}
}
@article{Kadomtsev1965,
author = {Kadomtsev, B.B.},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Kadomtsev - 1965 - Plasma turbulence.pdf:pdf},
number = {1965},
title = {{Plasma turbulence}},
url = {http://books.google.com/books?id=FIkkNjLPDWAC},
year = {1965}
}
@techreport{Landremann2016,
author = {Landremann, Matt},
title = {{SFINCS User Manual}},
year = {2016}
}
@article{Xi2012,
author = {Xi, P. W. and Xu, X. Q. and Wang, X. G. and Xia, T. Y.},
doi = {10.1063/1.4751256},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {9},
pages = {092503},
title = {{Influence of equilibrium shear flow on peeling-ballooning instability and edge localized mode crash}},
url = {http://link.aip.org/link/PHPAEN/v19/i9/p092503/s1{\&}Agg=doi},
volume = {19},
year = {2012}
}
@article{Charlton1984,
author = {Charlton, L. a. and Wieland, R. M. and Neilson, G. H.},
doi = {10.1063/1.864830},
issn = {00319171},
journal = {Phys. Fluids},
number = {7},
pages = {1738},
title = {{Equilibrium modeling of ISX-B tokamak discharges}},
url = {http://link.aip.org/link/PFLDAS/v27/i7/p1738/s1{\&}Agg=doi},
volume = {27},
year = {1984}
}
@article{Howes2006a,
abstract = {Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of astrophysical plasmas, including accretion disks, the solar wind, and the interstellar and intracluster medium. On small scales, this turbulence is often expected to consist of highly anisotropic fluctuations with frequencies small compared to the ion cyclotron frequency. For a number of applications, the small scales are also collisionless, so a kinetic treatment of the turbulence is necessary. We show that this anisotropic turbulence is well described by a low-frequency expansion of the kinetic theory called gyrokinetics. This paper is the first in a series to examine turbulent astrophysical plasmas in the gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations and explore the linear properties of gyrokinetics as a prelude to nonlinear simulations. The linear dispersion relation for gyrokinetics is obtained, and its solutions are compared to those of hot-plasma kinetic theory. These results are used to validate the performance of the gyrokinetic simulation code GS2 in the parameter regimes relevant for astrophysical plasmas. New results on global energy conservation in gyrokinetics are also derived. We briefly outline several of the problems to be addressed by future nonlinear simulations, including particle heating by turbulence in hot accretion flows and in the solar wind, the magnetic and electric field power spectra in the solar wind, and the origin of small-scale density fluctuations in the interstellar medium.},
archivePrefix = {arXiv},
arxivId = {astro-ph/0511812},
author = {Howes, G. G. and Cowley, S. C. and Dorland, W. and Hammett, G. W. and Quataert, E. and Schekochihin, a. a.},
doi = {10.1086/506172},
eprint = {0511812},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Howes et al. - 2006 - Astrophysical Gyrokinetics Basic Equations and Linear Theory.pdf:pdf},
isbn = {0004-637X},
issn = {15384357},
journal = {Astrophys. J.},
number = {1},
pages = {590--614},
primaryClass = {astro-ph},
title = {{Astrophysical Gyrokinetics: Basic Equations and Linear Theory}},
url = {http://stacks.iop.org/0004-637X/651/i=1/a=590},
volume = {651},
year = {2006}
}
@article{Hornsby2018,
abstract = {Non-linear, radially global, turbulence simulations of ASDEX Upgrade (AUG) plasmas are performed and the nonlinear generated intrinsic flow shows agreement with the intrinsic flow gradients measured in the core of Ohmic L-mode plasmas at nominal parameters. Simulations utilising the kinetic electron model show hollow intrinsic flow profiles as seen in a predominant number of experiments performed at similar plasma parameters. In addition, significantly larger flow gradients are seen than in a previous flux-tube analysis (Hornsby et al Nucl. Fusion (2017)). Adiabatic electron model simulations can show a flow profile with opposing sign in the gradient with respect to a kinetic electron simulation, implying a reversal in the sign of the residual stress due to kinetic electrons. The shaping of the intrinsic flow is strongly determined by the density gradient profile. The sensitivity of the residual stress to variations in density profile curvature is calculated and seen to be significantly stronger than to neoclassical flows (Hornsby et al Nucl. Fusion (2017)). This variation is strong enough on its own to explain the large variations in the intrinsic flow gradients seen in some AUG experiments. Analysis of the symmetry breaking properties of the turbulence shows that profile shearing is the dominant mechanism in producing a finite parallel wave-number, with turbulence gradient effects contributing a smaller portion of the parallel wave-vector.},
archivePrefix = {arXiv},
arxivId = {arXiv:1801.10600v1},
author = {Hornsby, W A and Angioni, C and Lu, Z X and Fable, E and Erofeev, I and Mcdermott, R and Medvedeva, A and Lebschy, A and Peeters, A G},
doi = {10.1088/1741-4326/aab22f},
eprint = {arXiv:1801.10600v1},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hornsby et al. - 2018 - Global gyrokinetic simulations of intrinsic rotation in ASDEX Upgrade Ohmic L-mode plasmas. Global gyrokinetic s.pdf:pdf},
issn = {17414326},
keywords = {PACS numbers:},
number = {2017},
pages = {1--24},
title = {{Global gyrokinetic simulations of intrinsic rotation in ASDEX Upgrade Ohmic L-mode plasmas. Global gyrokinetic simulations of intrinsic rotation in ASDEX Upgrade Ohmic L-mode plasmas.2}},
url = {https://arxiv.org/pdf/1801.10600.pdf},
year = {2018}
}
@misc{TheMendeleySupportTeam2011,
abstract = {A quick introduction to Mendeley. Learn how Mendeley creates your personal digital library, how to organize and annotate documents, how to collaborate and share with colleagues, and how to generate citations and bibliographies.},
address = {London},
author = {{The Mendeley Support Team}},
booktitle = {Mendeley Deskt.},
keywords = {Mendeley,how-to,user manual},
pages = {1--16},
publisher = {Mendeley Ltd.},
title = {{Getting Started with Mendeley}},
url = {http://www.mendeley.com},
year = {2011}
}
@article{Myra2002,
author = {Myra, J. R. and D'Ippolito, D. a. and Xu, X. Q.},
doi = {10.1063/1.1467929},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {1637},
title = {{Drift wave instability near a magnetic separatrix}},
url = {http://link.aip.org/link/PHPAEN/v9/i5/p1637/s1{\&}Agg=doi},
volume = {9},
year = {2002}
}
@article{Fenstermacher2013,
author = {Fenstermacher, M.E. and Xu, X.Q. and Joseph, I. and Lanctot, M.J. and Lasnier, C.J. and Meyer, W.H. and Tobias, B. and Zeng, L. and a.W. Leonard and Osborne, T.H.},
doi = {10.1016/j.jnucmat.2013.01.065},
issn = {00223115},
journal = {J. Nucl. Mater.},
month = {jul},
pages = {S346--S350},
title = {{Fast pedestal, SOL and divertor measurements from DIII-D to validate BOUT++ nonlinear ELM simulations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022311513000731},
volume = {438},
year = {2013}
}
@article{Hartwig2011,
author = {Hartwig, Zachary S and Podpaly, Yuri a},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hartwig, Podpaly - 2011 - Magnetic Fusion Energy Formulary.pdf:pdf},
journal = {World},
number = {November},
title = {{Magnetic Fusion Energy Formulary}},
year = {2011}
}
@article{Hitchcock,
author = {Hitchcock, D A and Hazeltine, R D and Spies, G O and Rij, W I Van and Meier, H K and Connor, J W and Hastie, R J and Chen, L and Hazeltine, R D and Ware, A A and Jr, C O Beasley and Mccune, J E and Taylor, J B and Hastie, R J},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hitchcock et al. - Unknown - Recursive derivation of drift-kinetic equation.pdf:pdf},
title = {{Recursive derivation of drift-kinetic equation}},
volume = {77}
}
@article{Parra2010b,
abstract = {We derive a self-consistent equation for the turbulent transport of toroidal angular momentum in tokamaks in the low flow ordering that only requires solving gyrokinetic Fokker-Planck and quasineutrality equations correct to second order in an expansion on the gyroradius over scale length. We also show that according to our orderings the long wavelength toroidal rotation and the long wavelength radial electric field satisfy the neoclassical relation that gives the toroidal rotation as a function of the radial electric field and the radial gradients of pressure and temperature. Thus, the radial electric field can be solved for once the toroidal rotation is calculated from the transport of toroidal angular momentum. Unfortunately, even though this methodology only requires a gyrokinetic model correct to second order in gyroradius over scale length, current gyrokinetic simulations are only valid to first order. To overcome this difficulty, we exploit the smallish ratio B(p)/B, where B is the total magnetic field and B(p) is its poloidal component. When B(p)/B is small, the usual first order gyrokinetic equation provides solutions that are accurate enough to employ for our expression for the transport of toroidal angular momentum. We show that current delta f and full f simulations only need small corrections to achieve this accuracy. Full f simulations, however, are still unable to determine the long wavelength, radial electric field from the quasineutrality equation.},
author = {Parra, Felix I. and Catto, Peter J.},
doi = {10.1088/0741-3335/52/4/045004},
issn = {07413335},
journal = {Plasma Phys. Control. Fusion},
title = {{Turbulent transport of toroidal angular momentum in low flow gyrokinetics}},
year = {2010}
}
@article{Hinton1976,
author = {Hinton, F L and Hazeltine, R D},
journal = {Rev. Mod. Phys.},
keywords = {Review,neoclassical classical transport drift kinetic equ,plasma transport},
mendeley-tags = {Review,plasma transport},
number = {2},
pages = {239--308},
title = {{Theory of Plasma Transport in Toroidal Confinements Systems}},
volume = {48},
year = {1976}
}
@article{Xue-qiao2001,
author = {Xue-qiao, Xu},
doi = {10.1088/1009-0630/3/5/006},
issn = {1009-0630},
journal = {Plasma Sci. Technol.},
month = {oct},
number = {5},
pages = {959--964},
title = {{The BOUT Project; Validation and Benchmark of BOUT Code and Experimental Diagnostic Tools for Fusion Boundary Turbulence}},
url = {http://stacks.iop.org/1009-0630/3/i=5/a=006?key=crossref.c0c1f7a94b9328a1e038d4221310d0a5},
volume = {3},
year = {2001}
}
@article{SalarElahi2009,
author = {{Salar Elahi}, a. and Ghoranneviss, M. and Emami, M.},
doi = {10.1007/s10894-009-9207-0},
issn = {0164-0313},
journal = {J. Fusion Energy},
keywords = {grad,multipole moments method {\'{a}},shafranov equation,tokamak {\'{a}} plasma position,{\'{a}}},
month = {jun},
number = {4},
pages = {385--389},
title = {{Comparative Measurements of Plasma Position Using Multipole Moments Method and Analytical Solution of Grad–Shafranov Equation in IR-T1 Tokamak}},
url = {http://link.springer.com/10.1007/s10894-009-9207-0},
volume = {28},
year = {2009}
}
@article{Litvinenko2010,
author = {Litvinenko, Yuri E.},
doi = {10.1063/1.3456519},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {7},
pages = {074502},
title = {{A similarity reduction of the Grad–Shafranov equation}},
url = {http://link.aip.org/link/PHPAEN/v17/i7/p074502/s1{\&}Agg=doi},
volume = {17},
year = {2010}
}
@article{Guo2010,
abstract = {A dispersion relation of the geodesic acoustic mode with the effect of impurity ions is systematically derived It is found that the frequency of the geodesic acoustic mode for a plasma with impurity ions is lower than that without impurity ions, which are mainly due to the polarization of impurity ions It is also found that the damping rate of the mode increases with the increase in effective charge in the small effective charge limit due to the polarization currents of impurity ions, and decreases in the large effective charge limit mainly due to the effect of the curvature drift of impurity ions A maximum damping rate is found in the intermediate effective charge regime (C) 2010 American Institute of Physics [doi:10.1063/1.3493631]},
author = {Guo, Wenfeng and Wang, Shaojie and Li, Jiangang},
doi = {10.1063/1.3493631},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Guo, Wang, Li - 2010 - Effect of impurity ions on the geodesic acoustic mode.pdf:pdf},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {11},
title = {{Effect of impurity ions on the geodesic acoustic mode}},
volume = {17},
year = {2010}
}
@article{Idomura2014,
abstract = {A long time ion temperature gradient driven turbulence simulation over a confinement time is performed using the full-f gyrokinetic Eulerian code GT5D. The convergence of steady temperature and rotation profiles is examined, and it is shown that the profile relaxation can be significantly accelerated when the simulation is initialized with linearly unstable temperature profiles. In the steady state, the temperature profile and the ion heat diffusivity are self-consistently determined by the power balance condition, while the intrinsic rotation profile is sustained by complicated momentum transport processes without momentum input. The steady turbulent momentum transport is characterized by bursty non-diffusive fluxes, and the resulting turbulent residual stress is consistent with the profile shear stress theory [Y. Camenen et al., ``Consequences of profile shearing on toroidal momentum transport,'' Nucl. Fusion 51, 073039 (2011)] in which the residual stress depends not only on the profile shear and the rad...},
author = {Idomura, Yasuhiro},
doi = {10.1063/1.4867180},
isbn = {9781632663108},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {2},
title = {{Full-f gyrokinetic simulation over a confinement time}},
volume = {21},
year = {2014}
}
@article{Xu2013,
author = {Xu, X. Q. and Xi, P. W. and Dimits, a. and Joseph, I. and Umansky, M. V. and Xia, T. Y. and Gui, B. and Kim, S. S. and Park, G. Y. and Rhee, T. and Jhang, H. and Diamond, P. H. and Dudson, B. and Snyder, P. B.},
doi = {10.1063/1.4801746},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {056113},
title = {{Gyro-fluid and two-fluid theory and simulations of edge-localized-modes}},
url = {http://link.aip.org/link/PHPAEN/v20/i5/p056113/s1{\&}Agg=doi},
volume = {20},
year = {2013}
}
@article{Stacey2008,
author = {Stacey, W. M.},
doi = {10.1063/1.3039946},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {12},
pages = {122505},
title = {{Applications of the Miller equilibrium to extend tokamak computational models}},
url = {http://link.aip.org/link/PHPAEN/v15/i12/p122505/s1{\&}Agg=doi},
volume = {15},
year = {2008}
}
@article{Isavnin2011,
abstract = {The Grad-Shafranov reconstruction is a method of estimating the orientation (invariant axis) and cross section of magnetic flux ropes using the data from a single spacecraft. It can be applied to various magnetic structures such as magnetic clouds (MCs) and flux ropes embedded in the magnetopause and in the solar wind. We develop a number of improvements of this technique and show some examples of the reconstruction procedure of interplanetary coronal mass ejections (ICMEs) observed at 1 AU by the STEREO, Wind, and ACE spacecraft during the minimum following Solar Cycle 23. The analysis is conducted not only for ideal localized ICME events but also for non-trivial cases of magnetic clouds in fast solar wind. The Grad-Shafranov reconstruction gives reasonable results for the sample events, although it possesses certain limitations, which need to be taken into account during the interpretation of the model results.},
author = {Isavnin, A and Kilpua, E K J and Koskinen, H E J},
journal = {Sol. Phys.},
pages = {205--219},
title = {{Grad-Shafranov Reconstruction of Magnetic Clouds: Overview and Improvements}},
volume = {273},
year = {2011}
}
@article{Chang1982,
abstract = {The effect of finite‐aspect ratio on the impurity contribution to neoclassical ion thermal conductivity is studied. A simple modification to the pure‐ion case is obtained with the assumption that the single heavy impurity species is in the Pfirsch–Schl{\"{u}}ter regime. It is found that the impurity contribution is larger than the usual approximation: Z eff times the pure ion thermal conductivity.},
author = {Chang, C. S. and Hinton, F. L.},
doi = {10.1063/1.863934},
isbn = {doi:10.1063/1.863934},
issn = {00319171},
journal = {Phys. Fluids},
number = {1493},
pages = {3314},
title = {{Effect of impurity particles on the finite-aspect ratio neoclassical ion thermal conductivity in a tokamak}},
url = {http://scitation.aip.org/content/aip/journal/pof1/29/10/10.1063/1.865847},
volume = {25},
year = {1982}
}
@article{Xu1991,
author = {Xu, X. Q. and Rosenbluth, M. N.},
doi = {10.1063/1.859650},
issn = {08998221},
journal = {Phys. Fluids B Plasma Phys.},
number = {8},
pages = {1807},
title = {{Unified theory of ballooning instabilities and temperature gradient-driven trapped ion modes}},
url = {http://link.aip.org/link/PFBPEI/v3/i8/p1807/s1{\&}Agg=doi},
volume = {3},
year = {1991}
}
@article{Belli2012,
abstract = {The complete linearized Fokker–Planck collision operator has been implemented in the drift-kinetic code NEO (Belli and Candy 2008 Plasma Phys. Control. Fusion 50 095010) for the calculation of neoclassical transport coefficients and flows. A key aspect of this work is the development of a fast numerical algorithm for treatment of the field particle operator. This Eulerian algorithm can accurately treat the disparate velocity scales that arise in the case of multi-species plasmas. Specifically, a Legendre series expansion in $\xi$ (the cosine of the pitch angle) is combined with a novel Laguerre spectral method in energy to ameliorate the rapid numerical precision loss that occurs for traditional Laguerre spectral methods. We demonstrate the superiority of this approach to alternative spectral and finite-element schemes. The physical accuracy and limitations of more commonly used model collision operators, such as the Connor and Hirshman–Sigmar operators, are studied, and the effects on neoclassical impurity poloidal flows and neoclassical transport for experimental parameters are explored. (Some figures may appear in colour only in the online journal)},
author = {Belli, E. A. and Candy, J.},
doi = {10.1088/0741-3335/54/1/015015},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Belli, Candy - 2012 - Full linearized Fokker-Planck collisions in neoclassical transport simulations.pdf:pdf},
issn = {07413335},
journal = {Plasma Phys. Control. Fusion},
number = {1},
title = {{Full linearized Fokker-Planck collisions in neoclassical transport simulations}},
volume = {54},
year = {2012}
}
@article{Search1999,
author = {Search, Home and Journals, Collections and Contact, About and Iopscience, My and Phys, Plasma and Address, I P},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Search et al. - 1999 - Contact us My IOPscience Numerical simulation of ion cyclotron waves in tokamak plasmas Numerical simulation of i.pdf:pdf},
pages = {0--34},
title = {{Contact us My IOPscience Numerical simulation of ion cyclotron waves in tokamak plasmas Numerical simulation of ion cyclotron waves in tokamak plasmas}},
volume = {1},
year = {1999}
}
@book{Yoshizawa,
author = {Yoshizawa, Akira},
title = {{Plasma and fluid turbulence}}
}
@book{Stillwell,
author = {Stillwell, John},
title = {{Elements of Number Theory}}
}
@article{Callen2009a,
abstract = {A comprehensive transport equation for the evolution of toroidal rotation in tokamak plasmas is developed self-consistently from the two-fluid momentum equations taking account of the constraints imposed by faster time scale processes. The resultant plasma toroidal rotation equation includes the effects of collision-induced perpendicular viscosities, anomalous transport due to microturbulence},
author = {Callen, J.D. and a.J. Cole and Hegna, C.C.},
doi = {10.1088/0029-5515/49/8/085021},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Callen, Cole, Hegna - 2009 - Toroidal rotation in tokamak plasmas.pdf:pdf},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {8},
pages = {085021},
title = {{Toroidal rotation in tokamak plasmas}},
volume = {49},
year = {2009}
}
@article{Abel2008,
abstract = {A new analytically and numerically manageable model collision operator is developed specifically for turbulence simulations. The like-particle collision operator includes both pitch-angle scattering and energy diffusion and satisfies the physical constraints required for collision operators: it conserves particles, momentum, and energy, obeys Boltzmann's H -theorem (collisions cannot decrease entropy), vanishes on a Maxwellian, and efficiently dissipates small-scale structure in the velocity space. The process of transforming this collision operator into the gyroaveraged form for use in gyrokinetic simulations is detailed. The gyroaveraged model operator is shown to have more suitable behavior at small scales in phase space than previously suggested models. Model operators for electron-ion and ion-electron collisions are also presented. {\textcopyright} 2008 American Institute of Physics.},
archivePrefix = {arXiv},
arxivId = {arXiv:0808.1300v1},
author = {Abel, I G and Barnes, Michael and Cowley, S C},
doi = {10.1063/1.3046067},
eprint = {arXiv:0808.1300v1},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Abel, Barnes, Cowley - 2008 - Linearized model Fokker-Planck collision operators for gyrokinetic simulations. I. Theory.pdf:pdf},
issn = {1070664X},
journal = {arXiv Prepr. arXiv {\ldots}},
number = {2008},
pages = {1--11},
title = {{Linearized model Fokker-Planck collision operators for gyrokinetic simulations. I. Theory}},
url = {http://arxiv.org/abs/0808.1300},
volume = {122509},
year = {2008}
}
@article{Turner2010,
author = {Turner, William J},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Turner - 2010 - A Brief Introduction to Proofs.pdf:pdf},
pages = {1--9},
title = {{A Brief Introduction to Proofs}},
year = {2010}
}
@article{Lapenta2003,
abstract = {A new class of solitonlike solutions is derived for the Grad-Shafranov (GS) equations. A mathematical analogy between the GS equation for MHD equilibria and the cubic Schr{\"{o}}dinger equation for nonlinear wave propagation forms the basis to derive the new class of solutions. The solitonlike solutions are considered for their possible relevance to astrophysics and solar physics problems. We discuss how a solitonlike solution can be generated by a repetitive process of magnetic arcade stretching and plasmoid formation induced by the differential rotation of the solar photosphere or of an accretion disk.},
archivePrefix = {arXiv},
arxivId = {astro-ph/0303448},
author = {Lapenta, Giovanni},
doi = {10.1103/PhysRevLett.90.135005},
eprint = {0303448},
journal = {Phys. Rev. Lett.},
pages = {135005},
pmid = {12689299},
primaryClass = {astro-ph},
title = {{Soliton-Like Solutions of the Grad-Shafranov Equation}},
volume = {90},
year = {2003}
}
@article{G??rcan2007,
abstract = {A novel mechanism for the generation and amplification of intrinsic rotation at the low-mode to high-mode transition is presented. The mechanism is one where the net parallel flow is accelerated by turbulence. A preferential direction of acceleration results from the breaking of k(parallel to)-{\textgreater}-k(parallel to) symmetry by sheared ExB flow. It is shown that the equilibrium pressure gradient contributes a piece of the parallel Reynolds stress, which is nonzero for vanishing parallel flow, and so can accelerate the plasma, driving net intrinsic rotation. Rotation drive, transport, and fluctuation dynamics are treated self-consistently. (c) 2007 American Institute of Physics.},
author = {G??rcan, ?? D. and Diamond, P. H. and Hahm, T. S. and Singh, R.},
doi = {10.1063/1.2717891},
isbn = {1070-664X},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {4},
title = {{Intrinsic rotation and electric field shear}},
volume = {14},
year = {2007}
}
@article{Smith2004,
author = {Smith, D. R. and Reiman, a. H.},
doi = {10.1063/1.1763576},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {8},
pages = {3752},
title = {{Analytic, high-$\beta$ solutions of the helical Grad–Shafranov equation}},
url = {http://link.aip.org/link/PHPAEN/v11/i8/p3752/s1{\&}Agg=doi},
volume = {11},
year = {2004}
}
@article{Burrell1997,
abstract = {One of the scientific success stories of fusion research over the past decade is the development of the E×B shear stabilization model to explain the formation of transport barriers in magnetic confinement devices. This model was originally developed to explain the transport barrier formed at the plasma edge in tokamaks after the L (low) to H (high) transition. This concept has the universality needed to explain the edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines. More recently, this model has been applied to explain the further confinement improvement from H (high) mode to VH (very high) mode seen in some tokamaks, where the edge transport barrier becomes wider. Most recently, this paradigm has been applied to the core transport barriers formed in plasmas with negative or low magnetic shear in the plasma core. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to a higher energy state with reduced turbulence and transport when an additional source of free energy is applied to it. The transport decrease that is associated with E×B velocity shear effects also has significant practical consequences for fusion research. The fundamental physics involved in transport reduction is the effect of E×B shear on the growth, radial extent, and phase correlation of turbulent eddies in the plasma. The same fundamental transport reduction process can be operational in various portions of the plasma because there are a number of ways to change the radial electric field Er. An important theme in this area is the synergistic effect of E×B velocity shear and magnetic shear. Although the E×B velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of E×B velocity shear and facilitate turbulence stabilization. Considerable experimental work has been done to test this picture of E×B velocity shear effects on turbulence; the experimental results are generally consistent with the basic theoretical models. {\textcopyright} 1997 American Institute of Physics.},
author = {Burrell, K. H.},
doi = {doi:10.1063/1.872367},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Burrell - 1997 - Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices.pdf:pdf},
isbn = {1070664X},
issn = {1070664X},
journal = {Phys. Plasmas},
keywords = {Drift Shear,Review,paper},
mendeley-tags = {Drift Shear,Review,paper},
number = {5},
pages = {1499--1518},
title = {{Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices}},
url = {http://pop.aip.org/resource/1/phpaen/v4/i5/p1499{\_}s1},
volume = {4},
year = {1997}
}
@article{Zheng1996,
author = {Zheng, S. B. and Wootton, a. J. and Solano, Emilia R.},
doi = {10.1063/1.871772},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {3},
pages = {1176},
title = {{Analytical tokamak equilibrium for shaped plasmas}},
url = {http://link.aip.org/link/PHPAEN/v3/i3/p1176/s1{\&}Agg=doi},
volume = {3},
year = {1996}
}
@article{Ida2014,
author = {Ida, K. and Rice, J.E.},
doi = {10.1088/0029-5515/54/4/045001},
issn = {0029-5515},
journal = {Nucl. Fusion},
keywords = {Review,intrinsic torque,momentum and turbulent transport,non-diffusive momentum transport,plasma rotation,residual stress,reynolds stress,spontaneous rotation,tokamak},
mendeley-tags = {Review,momentum and turbulent transport,plasma rotation},
number = {4},
pages = {045001},
title = {{Rotation and momentum transport in tokamaks and helical systems}},
url = {http://stacks.iop.org/0029-5515/54/i=4/a=045001?key=crossref.b8c8c6e201805bfdef142a1ccc5ca6c7},
volume = {54},
year = {2014}
}
@article{Appl1993,
abstract = {An analytic model for a stationary force-free relativistic magnetized jet is presented. The asymptotic Grad-Schluter-Shafranov equation is solved for a nonlinear current distribution, covering both diffuse and sharp pinches. The jet structure is characterized by a current-carrying core and a current-free envelope. The core radius Rc is related to the poloidal jet velocity up and the light cylinder RL by Rc = upRL. The Poynting flux is concentrated at the core radius. The rest frame magnetic field in the core is essentially parallel to the axis, and toroidal in the envelope. Self-confinement and confinement by external pressure is considered. It is shown how the form and the strength of the current determine the shape and the profile of the jet. The propagation of a jet is treated as a sequence of quasi-equilibria along the jet's path. The jet is mostly confined by its current, only close to the nucleus pressure might be relevant.},
author = {Appl, Stefan and Camenzind, Max},
journal = {Astron. Astrophys.},
title = {{The structure of relativistic MHD jets: a solution to the nonlinear Grad-Shafranov equation}},
volume = {274},
year = {1993}
}
@article{Callen2009,
abstract = {A comprehensive transport equation for the evolution of toroidal rotation in tokamak plasmas is developed self-consistently from the two-fluid momentum equations taking account of the constraints imposed by faster time scale processes. The resultant plasma toroidal rotation equation includes the effects of collision-induced perpendicular viscosities, anomalous transport due to microturbulence},
author = {Callen, J.D. and a.J. Cole and Hegna, C.C.},
doi = {10.1088/0029-5515/49/8/085021},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Callen, Cole, Hegna - 2009 - Toroidal rotation in tokamak plasmas.pdf:pdf},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {8},
pages = {085021},
title = {{Toroidal rotation in tokamak plasmas}},
volume = {49},
year = {2009}
}
@article{Tronko2013a,
author = {Tronko, Natalia},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Tronko - 2013 - Exact conservation laws for Gyrokinetic Vlasov-Poisson.pdf:pdf},
title = {{Exact conservation laws for Gyrokinetic Vlasov-Poisson}},
year = {2013}
}
@article{Chang1982a,
abstract = {The effect of finite‐aspect ratio on the impurity contribution to neoclassical ion thermal conductivity is studied. A simple modification to the pure‐ion case is obtained with the assumption that the single heavy impurity species is in the Pfirsch–Schl{\"{u}}ter regime. It is found that the impurity contribution is larger than the usual approximation: Z eff times the pure ion thermal conductivity.},
author = {Chang, C. S. and Hinton, F. L.},
doi = {10.1063/1.863934},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Chang, Hinton - 1982 - Effect of impurity particles on the finite-aspect ratio neoclassical ion thermal conductivity in a tokamak.pdf:pdf},
isbn = {doi:10.1063/1.863934},
issn = {00319171},
journal = {Phys. Fluids},
number = {1493},
pages = {3314},
title = {{Effect of impurity particles on the finite-aspect ratio neoclassical ion thermal conductivity in a tokamak}},
url = {http://scitation.aip.org/content/aip/journal/pof1/29/10/10.1063/1.865847},
volume = {25},
year = {1982}
}
@article{Callen2010,
abstract = {An H-mode edge pedestal plasma transport benchmarking exercise was undertaken for a single DIII-D pedestal. Transport modelling codes used include 1.5D interpretive (ONETWO, GTEDGE), 1.5D predictive (ASTRA) and 2D ones (SOLPS, UEDGE). The particular DIII-D discharge considered is 98889, which has a typical low density pedestal. Profiles for the edge plasma are obtained from Thomson and charge-exchange recombination data averaged over the last 20{\%} of the average 33.53 ms repetition time between type I edge localized modes. The modelled density of recycled neutrals is largest in the divertor X-point region and causes the edge plasma source rate to vary by a factor {\~{}}102 on the separatrix. Modelled poloidal variations in the densities and temperatures on flux surfaces are small on all flux surfaces up to within about 2.6 mm ($\rho$N {\textgreater} 0.99) of the mid-plane separatrix. For the assumed Fick's-diffusion-type laws, the radial heat and density fluxes vary poloidally by factors of 2–3 in the pedestal region; they are largest on the outboard mid-plane where flux surfaces are compressed and local radial gradients are largest. Convective heat flows are found to be small fractions of the electron (10{\%}) and ion (25{\%}) heat flows in this pedestal. Appropriately averaging the transport fluxes yields interpretive 1.5D effective diffusivities that are smallest near the mid-point of the pedestal. Their 'transport barrier' minima are about 0.3 (electron heat), 0.15 (ion heat) and 0.035 (density) m2 s−1. Electron heat transport is found to be best characterized by electron-temperature-gradient-induced transport at the pedestal top and paleoclassical transport throughout the pedestal. The effective ion heat diffusivity in the pedestal has a different profile from the neoclassical prediction and may be smaller than it. The very small effective density diffusivity may be the result of an inward pinch flow nearly balancing a diffusive outward radial density flux. The inward ion pinch velocity and density diffusion coefficient are determined by a new interpretive analysis technique that uses information from the force balance (momentum conservation) equations; the paleoclassical transport model provides a plausible explanation of these new results. Finally, the measurements and additional modelling needed to facilitate better pedestal plasma transport modelling are discussed.},
author = {Callen, J.D. and Groebner, R.J. and Osborne, T.H. and Canik, J.M. and Owen., L.W. and a.Y. Pankin and Rafiq, T. and Rognlien, T.D. and Stacey, W.M.},
doi = {10.1088/0029-5515/50/6/064004},
isbn = {0029-5515},
issn = {0029-5515},
journal = {Nucl. Fusion},
keywords = {nuclear fusion,paper},
mendeley-tags = {nuclear fusion,paper},
pages = {064004},
title = {{Analysis of pedestal plasma transport}},
volume = {50},
year = {2010}
}
@article{Rice2007,
abstract = {Parametric scalings of the intrinsic (spontaneous, with no external momentum input) toroidal rotation observed on a large number of tokamaks have been combined with an eye towards revealing the underlying mechanism(s) and extrapolation to future devices. The intrinsic rotation velocity has been found to increase with plasma stored energy or pressure in JET, Alcator C-Mod, Tore Supra, DIII-D, JT-60U and TCV, and to decrease with increasing plasma current in some of these cases. Use of dimensionless parameters has led to a roughly unified scaling with M A ∝ $\beta$ N , although a variety of Mach numbers works fairly well; scalings of the intrinsic rotation velocity with normalized gyro-radius or collisionality show no correlation. Whether this suggests the predominant role of MHD phenomena such as ballooning transport over turbulent processes in driving the rotation remains an open question. For an ITER discharge with $\beta$ N = 2.6, an intrinsic rotation Alfven Mach number of M A 0.02 may be expected from the above deduced scaling, possibly high enough to stabilize resistive wall modes without external momentum input. PACS numbers: 52.30.-q, 52.55.Fa},
author = {Rice, J E and Ince-Cushman, A and Degrassie, J S and Eriksson, L.-G and Sakamoto, Y and Scarabosio, A and Bortolon, A and Burrell, K H and Duval, B P and Fenzi-Bonizec, C and Greenwald, M J and Groebner, R J and Hoang, G T and Koide, Y and Marmar, E S and Pochelon, A and Podpaly, Y},
doi = {10.1088/0029-5515/47/11/025},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Rice et al. - 2007 - Inter-machine comparison of intrinsic toroidal rotation in tokamaks.pdf:pdf},
isbn = {0029-5515},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {47},
pages = {1618--1624},
title = {{Inter-machine comparison of intrinsic toroidal rotation in tokamaks}},
url = {http://iopscience.iop.org/0029-5515/47/11/025},
volume = {47},
year = {2007}
}
@article{Dong1994,
author = {Dong, J. Q. and Horton, W. and Dorland, W.},
doi = {10.1063/1.870942},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/1.870942.pdf:pdf},
issn = {1070-664X},
journal = {Phys. Plasmas},
number = {11},
pages = {3635--3640},
title = {{Isotope scaling and $\eta$ {\textless}sub{\textgreater} {\textless}i{\textgreater}i{\textless}/i{\textgreater} {\textless}/sub{\textgreater} mode with impurities in tokamak plasmas}},
url = {http://aip.scitation.org/doi/10.1063/1.870942},
volume = {1},
year = {1994}
}
@article{Li2011,
abstract = {The gyrokinetic linearized exact Fokker-Planck collision operator is obtained in a form suitable for plasma gyrokinetic equations, for arbitrary mass ratio. The linearized Fokker-Planck operator includes both the test-particle and field-particle contributions, and automatically conserves particles, momentum, and energy, while ensuring non-negative entropy production. Finite gyroradius effects in both field-particle and test-particle terms are evaluated. When implemented in gyrokinetic simulations, these effects can be precomputed. The field-particle operator at each time step requires the evaluation of a single two-dimensional integral, and is not only more accurate, but appears to be less expensive to evaluate than conserving model operators.},
author = {Li, B and Ernst, D R},
doi = {10.1103/PhysRevLett.106.195002},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Li, Ernst - 2011 - Gyrokinetic fokker-planck collision operator.pdf:pdf},
isbn = {1079-7114 (Electronic)$\backslash$r0031-9007 (Linking)},
issn = {00319007},
journal = {Phys. Rev. Lett.},
number = {19},
pmid = {21668167},
title = {{Gyrokinetic fokker-planck collision operator}},
url = {https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.106.195002},
volume = {106},
year = {2011}
}
@article{Hua1993,
author = {Hua, D. D. and Xu, X. Q. and Fowler, T. K.},
doi = {10.1063/1.860509},
issn = {08998221},
journal = {Phys. Fluids B Plasma Phys.},
number = {3},
pages = {1036},
title = {{Erratum: ‘‘Ion-temperature-gradient modes in noncircular tokamak geometry'' [Phys. Fluids B 4, 3216 (1992)]}},
url = {http://link.aip.org/link/PFBPEI/v5/i3/p1036/s1{\&}Agg=doi},
volume = {5},
year = {1993}
}
@article{Xu1991b,
author = {Xu, X. Q. and Rosenbluth, M. N.},
doi = {10.1063/1.859862},
issn = {08998221},
journal = {Phys. Fluids B Plasma Phys.},
number = {3},
pages = {627},
title = {{Numerical simulation of ion-temperature-gradient-driven modes}},
url = {http://link.aip.org/link/PFBPEI/v3/i3/p627/s1{\&}Agg=doi},
volume = {3},
year = {1991}
}
@article{Nave2014a,
author = {Nave, M F F and Bernardo, J and Coelho, R and Czarnecka, A and Ferreira, J and Figueiredo, A and Giroud, C and Hillesheim, J and Parail, V and Salmi, A and Voitsekhovitch, I and Zastrow, K-d and Contributors, J E T and Consortium, Eurofusion and Centre, Culham Science and Spectrometer, X-ray Crystal},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Nave et al. - 2014 - Measuring Intrinsic Rotation in the JET tokamak.pdf:pdf},
number = {633053},
pages = {633053},
title = {{Measuring Intrinsic Rotation in the JET tokamak}},
volume = {1},
year = {2014}
}
@article{Nakata2017,
abstract = {Impacts of isotope ion mass on trapped-electron-mode (TEM)-driven turbulence and zonal flows in magnetically confined fusion plasmas are investigated. Gyrokinetic simulations of TEM-driven turbulence in three-dimensional magnetic configuration of helical plasmas with hydrogen isotope ions and real-mass kinetic electrons are realized for the first time, and the linear and the nonlinear nature of the isotope and collisional effects on the turbulent transport and zonal-flow generation are clarified. It is newly found that combined effects of the collisional TEM stabilization by the isotope ions and the associated increase in the impacts of the steady zonal flows at the near-marginal linear stability lead to the significant transport reduction with the opposite ion mass dependence in comparison to the conventional gyro-Bohm scaling. The universal nature of the isotope effects on the TEM-driven turbulence and zonal flows is verified for a wide variety of toroidal plasmas, e.g., axisymmetric tokamak and non-axisymmetric helical or stellarator systems.},
author = {Nakata, Motoki and Nunami, Masanori and Sugama, Hideo and Watanabe, Tomo Hiko},
doi = {10.1103/PhysRevLett.118.165002},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Nakata et al. - 2017 - Isotope Effects on Trapped-Electron-Mode Driven Turbulence and Zonal Flows in Helical and Tokamak Plasmas.pdf:pdf},
journal = {Phys. Rev. Lett.},
title = {{Isotope Effects on Trapped-Electron-Mode Driven Turbulence and Zonal Flows in Helical and Tokamak Plasmas}},
url = {http://www.mendeley.com/research/isotope-effects-trappedelectronmode-driven-turbulence-zonal-flows-helical-tokamak-plasmas},
year = {2017}
}
@article{Kadomtsev1971,
abstract = {The review is devoted to the discussion of the role of trapped particles for equilibrium, diffusion and stability of plamas in toroidal magnetic devices. The motion of single particles in a toroidal magnetic field, the neoclassical transport processes due to the trapping of particles and trapped-particle instabilities in toroidal geometry are discussed. The correspondence between the neoclassical theory of diffusion, the turbulent transport processes due to the instabilities and the existing experimental Tokamak data is discussed.},
author = {Kadomtsev, B.B. and Pogutse, O.P. and {B.B. KADOMTSEV}, O.P. POGUTSE and Kadomtsev, B.B. and Pogutse, O.P. and {B.B. KADOMTSEV}, O.P. POGUTSE and Kadomtsev, B.B. and Pogutse, O.P. and {B.B. KADOMTSEV}, O.P. POGUTSE and Kadomtsev, B.B. and Pogutse, O.P.},
doi = {10.1088/0029-5515/11/1/010},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {1},
pages = {67--92},
title = {{Trapped particles in toroidal magnetic systems}},
url = {http://stacks.iop.org/0029-5515/11/i=1/a=010?key=crossref.efefb73e27dfcc555a67d6f1a6efb7fa},
volume = {11},
year = {1971}
}
@article{Sugama2009,
abstract = {Linearized model collision operators for multiple ion species plasmas are presented that conserve particles, momentum, and energy and satisfy adjointness relations and Boltzmann's H-theorem even for collisions between different particle species with unequal temperatures. The modelcollision operators are also written in the gyrophase-averaged form that can be applied to the gyrokineticequation. Balance equations for the turbulententropy density, the energy of electromagneticfluctuations, the turbulenttransport fluxes of particle and heat, and the collisional dissipation are derived from the gyrokineticequation including the collision term and Maxwell equations. It is shown that, in the steady turbulence, the entropy produced by the turbulenttransport fluxes is dissipated in part by collisions in the nonzonal-mode region and in part by those in the zonal-mode region after the nonlinear entropy transfer from nonzonal to zonal modes.},
author = {Sugama, H. and Watanabe, T. H. and Nunami, M.},
doi = {10.1063/1.3257907},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {11},
pages = {112503},
title = {{Linearized model collision operators for multiple ion species plasmas and gyrokinetic entropy balance equations}},
volume = {16},
year = {2009}
}
@article{Parra2014c,
abstract = {Self-consistent equations for intrinsic rotation in tokamaks with small poloidal magnetic field {\$}B{\_}p{\$} compared to the total magnetic field {\$}B{\$} are derived. The model gives the momentum redistribution due to turbulence, collisional transport and energy injection. Intrinsic rotation is determined by the balance between the momentum redistribution and the turbulent diffusion and convection. Two different turbulence regimes are considered: turbulence with characteristic perpendicular lengths of the order of the ion gyroradius, {\$}\backslashrho{\_}i{\$}, and turbulence with characteristic lengths of the order of the poloidal gyroradius, {\$}(B/B{\_}p) \backslashrho{\_}i{\$}. Intrinsic rotation driven by gyroradius scale turbulence is mainly due to the effect of neoclassical corrections and of finite orbit widths on turbulent momentum transport, whereas for the intrinsic rotation driven by poloidal gyroradius scale turbulence, the slow variation of turbulence characteristics in the radial and poloidal directions and the turbulent particle acceleration can be become as important as the neoclassical and finite orbit width effects. The magnetic drift is shown to be indispensable for the intrinsic rotation driven by the slow variation of turbulence characteristics and the turbulent particle acceleration. The equations are written in a form easily implementable in a flux tube code, and the effect of the radial variation of the turbulence is included without having to resort to a global gyrokinetic formalism.},
archivePrefix = {arXiv},
arxivId = {1407.1286},
author = {Parra, Felix I and Barnes, Michael},
doi = {10.1088/0741-3335/57/4/045002},
eprint = {1407.1286},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(7).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(13).pdf:pdf},
isbn = {0029-5515$\backslash$n1741-4326},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
keywords = {gyrokinetics,in colour only in,rotation,some figures may appear,the online journal,tokamak,turbulence},
month = {apr},
number = {4},
pages = {045002},
publisher = {IOP Publishing},
title = {{Intrinsic rotation in tokamaks: theory}},
url = {http://arxiv.org/abs/1407.1286 http://stacks.iop.org/0741-3335/57/i=4/a=045002?key=crossref.4aae68333c11be380fb621050a6b489a},
volume = {57},
year = {2015}
}
@article{Lao1992,
author = {Lao, L. L. and Taylor, T. S. and Chu, M. S. and Chan, V. S. and Ferron, J. R. and Strait, E. J.},
doi = {10.1063/1.860438},
issn = {08998221},
journal = {Phys. Fluids B Plasma Phys.},
number = {1},
pages = {232},
title = {{Effects of current profile on the ideal ballooning mode}},
url = {http://link.aip.org/link/PFBPEI/v4/i1/p232/s1{\&}Agg=doi},
volume = {4},
year = {1992}
}
@article{Ghendrih2001,
abstract = {Chapter 8 Fluctuations in the Edge Plasma},
author = {Ghendrih, Philippe},
doi = {10.1088/0741-3335/43/2/702},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Ghendrih - 2001 - The Plasma Boundary of Magnetic Fusion Devices.pdf:pdf},
isbn = {0750305592},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
number = {2},
pages = {223--224},
pmid = {11957383},
title = {{The Plasma Boundary of Magnetic Fusion Devices}},
url = {http://stacks.iop.org/0741-3335/43/i=2/a=702?key=crossref.697b1e31667aa5230930cad92b5e0e4f},
volume = {43},
year = {2001}
}
@article{Rice2007,
abstract = {Parametric scalings of the intrinsic (spontaneous, with no external momentum input) toroidal rotation observed on a large number of tokamaks have been combined with an eye towards revealing the underlying mechanism(s) and extrapolation to future devices. The intrinsic rotation velocity has been found to increase with plasma stored energy or pressure in JET, Alcator C-Mod, Tore Supra, DIII-D, JT-60U and TCV, and to decrease with increasing plasma current in some of these cases. Use of dimensionless parameters has led to a roughly unified scaling with M A ∝ {\$}\beta{\$} N , although a variety of Mach numbers works fairly well; scalings of the intrinsic rotation velocity with normalized gyro-radius or collisionality show no correlation. Whether this suggests the predominant role of MHD phenomena such as ballooning transport over turbulent processes in driving the rotation remains an open question. For an ITER discharge with {\$}\beta{\$} N = 2.6, an intrinsic rotation Alfven Mach number of M A 0.02 may be expected from the above deduced scaling, possibly high enough to stabilize resistive wall modes without external momentum input. PACS numbers: 52.30.-q, 52.55.Fa},
author = {Rice, J E and Ince-Cushman, A and Degrassie, J S and Eriksson, L.-G and Sakamoto, Y and Scarabosio, A and Bortolon, A and Burrell, K H and Duval, B P and Fenzi-Bonizec, C and Greenwald, M J and Groebner, R J and Hoang, G T and Koide, Y and Marmar, E S and Pochelon, A and Podpaly, Y},
doi = {10.1088/0029-5515/47/11/025},
isbn = {0029-5515},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {47},
pages = {1618--1624},
title = {{Inter-machine comparison of intrinsic toroidal rotation in tokamaks}},
url = {http://iopscience.iop.org/0029-5515/47/11/025},
volume = {47},
year = {2007}
}
@article{Myra2000,
author = {Myra, J. R. and D'Ippolito, D. a. and Xu, X. Q. and Cohen, R. H.},
doi = {10.1063/1.874125},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {6},
pages = {2290},
title = {{Resistive X-point modes in tokamak boundary plasmas}},
url = {http://link.aip.org/link/PHPAEN/v7/i6/p2290/s1{\&}Agg=doi},
volume = {7},
year = {2000}
}
@article{Parra2014b,
abstract = {Self-consistent equations for intrinsic rotation in tokamaks with small poloidal magnetic field {\$}B{\_}p{\$} compared to the total magnetic field {\$}B{\$} are derived. The model gives the momentum redistribution due to turbulence, collisional transport and energy injection. Intrinsic rotation is determined by the balance between the momentum redistribution and the turbulent diffusion and convection. Two different turbulence regimes are considered: turbulence with characteristic perpendicular lengths of the order of the ion gyroradius, {\$}\backslashrho{\_}i{\$}, and turbulence with characteristic lengths of the order of the poloidal gyroradius, {\$}(B/B{\_}p) \backslashrho{\_}i{\$}. Intrinsic rotation driven by gyroradius scale turbulence is mainly due to the effect of neoclassical corrections and of finite orbit widths on turbulent momentum transport, whereas for the intrinsic rotation driven by poloidal gyroradius scale turbulence, the slow variation of turbulence characteristics in the radial and poloidal directions and the turbulent particle acceleration can be become as important as the neoclassical and finite orbit width effects. The magnetic drift is shown to be indispensable for the intrinsic rotation driven by the slow variation of turbulence characteristics and the turbulent particle acceleration. The equations are written in a form easily implementable in a flux tube code, and the effect of the radial variation of the turbulence is included without having to resort to a global gyrokinetic formalism.},
archivePrefix = {arXiv},
arxivId = {1407.1286},
author = {Parra, Felix I and Barnes, Michael},
doi = {10.1088/0741-3335/57/4/045002},
eprint = {1407.1286},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(7).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(13).pdf:pdf},
isbn = {0029-5515$\backslash$n1741-4326},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
keywords = {gyrokinetics,in colour only in,rotation,some figures may appear,the online journal,tokamak,turbulence},
pages = {83},
title = {{Intrinsic rotation in tokamaks. Theory}},
url = {http://arxiv.org/abs/1407.1286},
volume = {045002},
year = {2014}
}
@article{Dickinson2013,
abstract = {Microtearing modes (MTMs) are unstable in the shallow gradient region just inside the top of the$\backslash$r pedestal in the spherical tokamak experiment MAST, and may play an important role in the pedestal$\backslash$r evolution. The linear properties of these instabilities are compared with MTMs deeper inside the$\backslash$r core, and further detailed investigations in s ? ? geometry expose the basic drive mechanism, which$\backslash$r is not well described by existing theories. In particular, the growth rate of the dominant edge MTM$\backslash$r does not peak at a finite collision frequency, as frequently reported for MTMs further into the$\backslash$r core. Our study suggests that the edge MTM is driven by a collisionless trapped particle mechanism$\backslash$r that is sensitive to magnetic drifts. This drive is enhanced in the outer region of MAST at high$\backslash$r magnetic shear and high trapped particle fraction. Observations of similar modes in conventional$\backslash$r aspect ratio devices suggest this drive mechanism may be somewhat ubiquitous towards the edge of$\backslash$r current day and future hot tokamaks.},
archivePrefix = {arXiv},
arxivId = {1209.3695v1},
author = {Dickinson, D and Roach, C M and Saarelma, S and Scannell, R and Kirk, A and Wilson, H R},
doi = {10.1088/0741-3335/55/7/074006},
eprint = {1209.3695v1},
isbn = {9781632663108},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
month = {jul},
number = {7},
pages = {074006},
title = {{Microtearing modes at the top of the pedestal}},
url = {http://stacks.iop.org/0741-3335/55/i=7/a=074006?key=crossref.496a42c42d84b5e6b024c71687efd4c8},
volume = {55},
year = {2013}
}
@article{Sydora2008,
author = {Sydora, Richard D},
doi = {10.1007/978-3-540-74686-7},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Sydora - 2008 - Computational Many-Particle Physics.pdf:pdf},
isbn = {978-3-540-74685-0},
pages = {191--219},
title = {{Computational Many-Particle Physics}},
url = {http://link.springer.com/10.1007/978-3-540-74686-7},
volume = {739},
year = {2008}
}
@article{Kiviniemi2006,
abstract = {A direct implicit ion polarization gyrokinetic full f particle-in-cell approach is implemented with kinetic electrons in global tokamak transport simulations. The method is applicable for calculations of rapid transients and steep gradients in the plasma, which is made feasible by recording the charge density change by the ion polarization drift together with the particle advancing. The code has been successfully validated against the linear and nonlinear predictions of the unstable mode growth rates and frequencies and their turbulent saturation level. A first global validation of the neoclassical radial electric field in the presence of turbulence for a heated collisional tokamak plasma is obtained. The neoclassical radial electric field together with the related geodesic acoustic mode oscillations is found to regulate the turbulence and heat and particle diffusion levels in a large aspect ratio tokamak at low plasma current},
author = {Kiviniemi, T P and Heikkinen, J A and Janhunen, S and Henriksson, S V and {T P Kiviniemi} and {J A Heikkinen} and {S Janhunen} and {S V Henriksson}},
journal = {Plasma Phys. Control. Fusion},
keywords = {Presentation,full gyrokinetics},
mendeley-tags = {Presentation,full gyrokinetics},
number = {5A},
pages = {A327},
title = {{Full f gyrokinetic simulation of FT-2 tokamak plasma}},
url = {file:////media/DATOS/BIBLIOTECA/Journals/Kiviniemi{\_}ppcf6{\_}5A{\_}S32.pdf},
year = {2006}
}
@article{Merz2012,
abstract = {Plasma microinstabilities, which can be described in the framework of the linear gyrokinetic equations, are routinely computed in the context of stability analyses and transport predictions for magnetic confinement fusion experiments. The GENE code, which solves the gyrokinetic equations, has been coupled to the SLEPc package for an efficient iterative, matrix-free, and parallel computation of rightmost eigenvalues. This setup is presented, including the preconditioner which is necessary for the newly implemented Jacobi–Davidson solver. The fast computation of instabilities at a single parameter set is exploited to make parameter scans viable, that is to compute the solution at many points in the parameter space. Several issues related to parameter scans are discussed, such as an efficient parallelization over parameter sets and subspace recycling.},
author = {Merz, F. and Kowitz, C. and Romero, E. and Roman, J.E. and Jenko, F.},
doi = {10.1016/j.cpc.2011.12.018},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Merz et al. - 2012 - Multi-dimensional gyrokinetic parameter studies based on eigenvalue computations.pdf:pdf},
issn = {00104655},
journal = {Comput. Phys. Commun.},
keywords = {Eigenvalue computation,GENE code,Gyrokinetic equations,Parameter scans},
month = {apr},
number = {4},
pages = {922--930},
title = {{Multi-dimensional gyrokinetic parameter studies based on eigenvalue computations}},
url = {http://www.sciencedirect.com/science/article/pii/S0010465511004061},
volume = {183},
year = {2012}
}
@article{Barnes2009b,
abstract = {A new analytically and numerically manageable model collision operator is developed specifically for turbulence simulations. The like-particle collision operator includes both pitch-angle scattering and energy diffusion and satisfies the physical constraints required for collision operators: it conserves particles, momentum and energy, obeys Boltzmann's H-theorem (collisions cannot decrease entropy), vanishes on a Maxwellian, and efficiently dissipates small-scale structure in the velocity space. The process of transforming this collision operator into the gyroaveraged form for use in gyrokinetic simulations is detailed. The gyroaveraged model operator is shown to have more suitable behavior at small scales in phase space than previously suggested models. A model operator for electron-ion collisions is also presented.},
archivePrefix = {arXiv},
arxivId = {0808.1300},
author = {Barnes, M. and Abel, I. G. and Dorland, W. and Ernst, D. R. and Hammett, G. W. and Ricci, P. and Rogers, B. N. and Schekochihin, A. A. and Tatsuno, T.},
doi = {10.1063/1.3155085},
eprint = {0808.1300},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Barnes et al. - 2009 - Linearized model fokker-planck collision operators for gyrokinetic simulations. II. Numerical implementation and.pdf:pdf},
isbn = {1070-664X},
issn = {1070-664X},
journal = {Phys. Plasmas},
month = {jul},
number = {7},
pages = {072107},
title = {{Linearized model Fokker–Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests}},
url = {http://aip.scitation.org/doi/10.1063/1.3155085},
volume = {16},
year = {2009}
}
@article{Catto2009,
abstract = {We first consider gyrokinetic quasineutrality limitations when evaluating the axisymmetric radial electric field in a non-turbulent tokamak by an improved examination of intrinsic ambipolarity. We next prove that the background ions in a pedestal of poloidal ion gyroradius scale must be Maxwellian and nearly isothermal in Pfirsch-Schluter and banana regime tokamak plasmas, and then consider zonal flow behaviour in a pedestal. Finally, we focus on a simplifying procedure for our transport time scale hybrid gyrokinetic-fluid treatment that removes the limitations of gyrokinetic quasineutrality and remains valid in the pedestal.},
author = {Catto, Peter J. and Parra, Felix I. and Kagan, Grigory and Simakov, Andrei N.},
doi = {10.1088/0029-5515/49/9/095026},
issn = {00295515},
journal = {Nucl. Fusion},
title = {{Limitations, insights and improvements to gyrokinetics}},
year = {2009}
}
@misc{Of,
archivePrefix = {arXiv},
arxivId = {NIHMS150003},
author = {Of, Rofessor},
booktitle = {ASA Refresh. Courses Anesthesiol.},
doi = {10.1109/TDEI.2009.5211872},
eprint = {NIHMS150003},
isbn = {1070-9878},
issn = {10709878},
pmid = {24335434},
title = {{H l u a}}
}
@article{Howard2014a,
author = {Howard, N. T. and White, A. E. and Greenwald, M. and Holland, C. and Candy, J. and Rice, J. E.},
doi = {10.1088/0741-3335/56/12/124004},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Howard et al. - 2014 - Impurity transport, turbulence transitions and intrinsic rotation in Alcator C-Mod plasmas(2).pdf:pdf},
isbn = {0741-3335$\backslash$r1361-6587},
issn = {13616587},
journal = {Plasma Phys. Control. Fusion},
keywords = {Gyrokinetics,Impurity transport,Intrinsic rotation},
number = {12},
title = {{Impurity transport, turbulence transitions and intrinsic rotation in Alcator C-Mod plasmas}},
volume = {56},
year = {2014}
}
@article{Atanasiu2004a,
abstract = {Two families of exact analytical solutions of the GradShafranov equation are presented by specifying the highest polynomial dependence of the plasma current density on the flux function $\Psi$ in such a way that the GradShafranov equation becomes a linear inhomogeneous differential equation. Both the pressure profile and the poloidal current profile each have two free parameters. X-points can be represented by superposition of solutions. Examples of the exact equilibrium solution are given for both a D-shaped plasma and a toroidally diverted plasma.},
author = {Atanasiu, C V and Günter, S and Lackner, K and Miron, I G},
doi = {10.1063/1.1756167},
issn = {1070664X},
journal = {Phys. Plasmas},
pages = {3510},
title = {{Analytical solutions to the Grad–Shafranov equation}},
volume = {11},
year = {2004}
}
@article{Abel2013,
abstract = {This paper presents a complete theoretical framework for studying turbulence and transport in rapidly rotating tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio $\epsilon$ = $\rho$i/$\alpha$ of the gyroradius to the equilibrium scale length. Proceeding order by order in this expansion, a set of coupled multiscale equations is developed. They describe an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the interplay between the equilibrium and the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equilibrium is obtained from the generalized Grad-Shafranov equation for a rotating plasma, determining the magnetic flux function from the mean pressure and velocity profiles of the plasma. The slow (resistive-timescale) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the 'high-flow' gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local (in space) cascade of the free energy of the fluctuations (i.e. there is no turbulence spreading). Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical and fluctuating corrections to the equilibrium Maxwellian act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived from the transport equations. Total energy, thermal, kinetic and magnetic, is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating and the equilibration of interspecies temperature differences. This equilibration is found to include both turbulent and collisional contributions. Finally, this framework is condensed, in the low-Mach-number limit, to a more concise set of equations suitable for numerical implementation.},
archivePrefix = {arXiv},
arxivId = {1209.4782},
author = {Abel, I G and Plunk, G G and Wang, E and Barnes, M and Cowley, S C and Dorland, W and Schekochihin, A A},
doi = {10.1088/0034-4885/76/11/116201},
eprint = {1209.4782},
isbn = {0034-4885; 1361-6633},
issn = {0034-4885},
journal = {Reports Prog. Phys.},
number = {11},
pages = {116201},
pmid = {24169038},
title = {{Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows}},
url = {http://stacks.iop.org/0034-4885/76/i=11/a=116201?key=crossref.7a15042d852eab7bfb7236cdc739a923},
volume = {76},
year = {2013}
}
@article{Guazzotto2007,
author = {Guazzotto, L. and Freidberg, J. P.},
doi = {10.1063/1.2803759},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {11},
pages = {112508},
title = {{A family of analytic equilibrium solutions for the Grad–Shafranov equation}},
url = {http://link.aip.org/link/PHPAEN/v14/i11/p112508/s1{\&}Agg=doi},
volume = {14},
year = {2007}
}
@article{Hawryluk1979,
abstract = {Low-Z impurity transport in tokamaks was simulated with a one-dimensional impurity transport model including both neoclassical and anomalous transports. The neoclassical fluxes are due to collisions between the background plasma and impurity ions as well as to collisions between the various ionization states. The evaluation of the neoclassical fluxes takes into account the different collisionality regimes of the background plasma and the impurity ions. A limiter scrape-off model is used to define the boundary condition for the impurity ions in the plasma periphery. To account for the spectroscopic measurements of power radiated by the lower ionization states, fluxes due to anomalous transport are included. The sensitivities of the results to uncertainties in rate coefficients and plasma parameters in the periphery are investigated. The implications of the transport model for spectroscopic evaluation of impurity concentrations, impurity fluxes, and radiated power from line emission measurements are discussed.},
author = {Hawryluk, R. J. and Suckewer, S. and Hirshman, S. P.},
doi = {10.1088/0029-5515/19/5/005},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {5},
pages = {607--632},
title = {{Low-Z impurity transport in tokamaks}},
url = {http://iopscience.iop.org/0029-5515/19/5/005},
volume = {19},
year = {1979}
}
@article{Lapillonne2010a,
author = {Lapillonne, X.},
doi = {10.5075/epfl-thesis-4684},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Lapillonne - 2010 - Local and Global Eulerian Gyrokinetic Simulations of Microturbulence in Realistic Geometry with Applications to the.pdf:pdf},
title = {{Local and Global Eulerian Gyrokinetic Simulations of Microturbulence in Realistic Geometry with Applications to the TCV Tokamak}},
volume = {4684},
year = {2010}
}
@article{Schekochihin2009,
abstract = {We present a theoretical framework for plasma turbulence in astrophysical plasmas (solar wind, interstellar medium, galaxy clusters, accretion disks). The key assumptions are that the turbulence is anisotropic with respect to the mean magnetic field and frequencies are low compared to the ion cyclotron frequency. The energy injected at the outer scale scale has to be converted into heat, which ultimately cannot be done without collisions. A KINETIC CASCADE develops that brings the energy to collisional scales both in space and velocity. Its nature depends on the physics of plasma fluctuations. In each of the physically distinct scale ranges, the kinetic problem is systematically reduced to a more tractable set of equations. In the "inertial range" above the ion gyroscale, the kinetic cascade splits into a cascade of Alfvenic fluctuations, which are governed by the RMHD equations at both the collisional and collisionless scales, and a passive cascade of compressive fluctuations, which obey a linear kinetic equation along the moving field lines associated with the Alfvenic component. In the "dissipation range" between the ion and electron gyroscales, there are again two cascades: the kinetic-Alfven-wave (KAW) cascade governed by two fluid-like Electron RMHD equations and a passive phase-space cascade of ion entropy fluctuations. The latter cascade brings the energy of the inertial-range fluctuations that was damped by collisionless wave-particle interaction at the ion gyroscale to collisional scales in the phase space and leads to ion heating. The KAW energy is similarly damped at the electron gyroscale and converted into electron heat. Kolmogorov-style scaling relations are derived for these cascades. Astrophysical and space-physical applications are discussed in detail.},
archivePrefix = {arXiv},
arxivId = {0704.0044},
author = {Schekochihin, A. A. and Cowley, S. C. and Dorland, W. and Hammett, G. W. and Howes, G. G. and Quataert, E. and Tatsuno, T.},
doi = {10.1088/0067-0049/182/1/310},
eprint = {0704.0044},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Schekochihin et al. - 2009 - ASTROPHYSICAL GYROKINETICS KINETIC AND FLUID TURBULENT CASCADES IN MAGNETIZED WEAKLY COLLISIONAL PLASMAS.pdf:pdf},
isbn = {0067-0049},
issn = {0067-0049},
journal = {Astrophys. J. Suppl. Ser.},
keywords = {MHD,Magnetic fields,Methods: analytical,Plasmas,Turbulence},
month = {may},
number = {1},
pages = {310--377},
title = {{ASTROPHYSICAL GYROKINETICS: KINETIC AND FLUID TURBULENT CASCADES IN MAGNETIZED WEAKLY COLLISIONAL PLASMAS}},
url = {http://stacks.iop.org/0067-0049/182/i=1/a=310?key=crossref.b30249850b64484ce0479cdbb4bb0cc2},
volume = {182},
year = {2009}
}
@article{Barnes2013,
author = {Barnes, M. and Parra, F. I. and Lee, J. P. and Belli, E. a. and Nave, M. F. F. and White, a. E.},
doi = {10.1103/PhysRevLett.111.055005},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
keywords = {PRL,filomena},
mendeley-tags = {PRL,filomena},
number = {5},
pages = {055005},
title = {{Intrinsic Rotation Driven by Non-Maxwellian Equilibria in Tokamak Plasmas}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.111.055005},
volume = {111},
year = {2013}
}
@article{Guo1994,
author = {Guo, S. C. and Romanelli, F.},
doi = {10.1063/1.870759},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {1101},
title = {{Stability analysis of the ion-temperature-gradient-driven mode in noncircular tokamak geometry}},
url = {http://link.aip.org/link/PHPAEN/v1/i5/p1101/s1{\&}Agg=doi},
volume = {1},
year = {1994}
}
@article{Popovich2010a,
author = {Popovich, P. and Umansky, M. V. and Carter, T. a. and Friedman, B.},
doi = {10.1063/1.3500283},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {10},
pages = {102107},
title = {{Analysis of plasma instabilities and verification of the BOUT code for the Large Plasma Device}},
url = {http://link.aip.org/link/PHPAEN/v17/i10/p102107/s1{\&}Agg=doi},
volume = {17},
year = {2010}
}
@article{Parker2016,
abstract = {Transfer of free energy from large to small velocity-space scales by phase mixing leads to Landau damping in a linear plasma. In a turbulent drift-kinetic plasma, this transfer is statistically nearly canceled by an inverse transfer from small to large velocity-space scales due to "anti-phase-mixing" modes excited by a stochastic form of plasma echo. Fluid moments (density, velocity, temperature) are thus approximately energetically isolated from the higher moments of the distribution function, so phase mixing is ineffective as a dissipation mechanism when the plasma collisionality is small.},
archivePrefix = {arXiv},
arxivId = {1603.06968},
author = {Parker, J. T. and Highcock, E. G. and Schekochihin, A. A. and Dellar, P. J.},
doi = {10.1063/1.4958954},
eprint = {1603.06968},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Parker et al. - 2016 - Suppression of phase mixing in drift-kinetic plasma turbulence.pdf:pdf},
issn = {1070-664X},
journal = {Phys. Plasmas},
month = {jul},
number = {7},
pages = {070703},
title = {{Suppression of phase mixing in drift-kinetic plasma turbulence}},
url = {http://aip.scitation.org/doi/10.1063/1.4958954},
volume = {23},
year = {2016}
}
@article{White2009,
author = {White, R. L. and Hazeltine, R. D.},
doi = {10.1063/1.3267211},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {12},
pages = {123101},
title = {{Symmetry analysis of the Grad–Shafranov equation}},
url = {http://link.aip.org/link/PHPAEN/v16/i12/p123101/s1{\&}Agg=doi},
volume = {16},
year = {2009}
}
@article{Rogers2007,
abstract = {Linear and nonlinear gyrokinetic simulations of collisionless magnetic reconnection in the presence of a strong guide field are presented. A periodic slab system is considered with a sinusoidally varying reconnecting magnetic field component. The linear growth rates of the tearing mode in both the large and small Delta'regimes are compared to kinetic and fluid theory calculations. In the nonlinear regime, focusing on the limit of large Delta', the nonlinear reconnection rates in the gyrokinetic simulations are found to be comparable to those obtained from a two-fluid model. In contrast to the fluid system, however, for Ti {\textgreater}{\textgreater} Te and very small initial perturbation amplitudes, the reconnection in the gyrokinetic system saturates in the early nonlinear phase. This saturation can be overcome if the simulation is seeded initially with sufficient random noise.},
author = {Rogers, B. N. and Kobayashi, S. and Ricci, P. and Dorland, W. and Drake, J. and Tatsuno, T.},
doi = {10.1063/1.2774003},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Rogers et al. - 2007 - Gyrokinetic simulations of collisionless magnetic reconnection.pdf:pdf},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {9},
pages = {092110},
title = {{Gyrokinetic simulations of collisionless magnetic reconnection}},
url = {http://scitation.aip.org/content/aip/journal/pop/14/9/10.1063/1.2774003},
volume = {14},
year = {2007}
}
@article{Fattorini2012a,
author = {Fattorini, L and Fredriksen, {\AA} and P{\'{e}}cseli, H L and Riccardi, C and Trulsen, J K},
doi = {10.1088/0741-3335/54/8/085017},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Fattorini et al. - 2012 - Turbulent transport in a toroidal magnetized plasma.pdf:pdf},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
keywords = {paper,ppcf},
mendeley-tags = {paper,ppcf},
number = {8},
pages = {085017},
title = {{Turbulent transport in a toroidal magnetized plasma}},
url = {http://stacks.iop.org/0741-3335/54/i=8/a=085017?key=crossref.8d6d8d6a568eacd47a6574ed4b2b85c6},
volume = {54},
year = {2012}
}
@article{Kinsey1995,
author = {Kinsey, Jon and Singer, Clifford and Djemil, Toufik and Cox, Dennis and Bateman, Glenn},
doi = {10.1063/1.871433},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {3},
pages = {811},
title = {{Systematic comparison of a theory-based transport model with a multi-tokamak profile database}},
url = {http://link.aip.org/link/PHPAEN/v2/i3/p811/s1{\&}Agg=doi},
volume = {2},
year = {1995}
}
@article{Agren2006,
abstract = {In addition to the standard set (epsilon,mu,p(phi)) of three invariants in axisymmetric tori, there exists a fourth independent radial drift invariant I-r. For confined particles, the net radial drift has to be zero, whereby the drift orbit average I-r= of the gyro center radial Clebsch coordinate is constant. To lowest order in the banana width, the radial invariant is the gyro center radial coordinate r(0)(x,v), and to this order the gyro center moves on a magnetic flux surface. The gyro center orbit projected on the (r,z) plane determines the radial invariant and first order banana width corrections to I-r are calculated. The radial drift invariant exists for trapped as well as passing particles. The new invariant is applied to construct Vlasov equilibria, where the magnetic field satisfies a generalized Grad-Shafranov equation with a poloidal plasma current and a bridge to ideal magnetohydrodynamic equilibria is found. For equilibria with sufficiently small banana widths and radial drift excursions, the approximation I-r approximate to r(0)(x,v) can be used for the equilibrium state. (c) 2006 American Institute of Physics.},
author = {Ågren, O and Moiseenko, V E},
doi = {10.1063/1.2195419},
issn = {1070664X},
journal = {Phys. Plasmas},
pages = {052501},
title = {{Four motional invariants in axisymmetric tori equilibria}},
volume = {13},
year = {2006}
}
@article{Cowley,
archivePrefix = {arXiv},
arxivId = {arXiv:1209.4782v4},
author = {Cowley, S C and Dorland, W and Schekochihin, A A},
eprint = {arXiv:1209.4782v4},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Cowley, Dorland, Schekochihin - Unknown - Multiscale Gyrokinetics for Rotating Tokamak Plasmas Fluctuations , Transport and Energy Flow.pdf:pdf},
title = {{Multiscale Gyrokinetics for Rotating Tokamak Plasmas : Fluctuations , Transport and Energy Flows arXiv : 1209 . 4782v4 [ physics . plasm-ph ] 2 Dec 2013}}
}
@article{Peeters2011a,
abstract = {Toroidal momentum transport mechanisms are reviewed and put in a broader perspective. The generation of a finite momentum flux is closely related to the breaking of symmetry (parity) along the field. The symmetry argument allows for the systematic identification of possible transport mechanisms. Those that appear to lowest order in the normalized Larmor radius (the diagonal part, Coriolis pinch, E x B shearing, particle flux, and up-down asymmetric equilibria) are reasonably well understood. At higher order, expected to be of importance in the plasma edge, the theory is still under development.},
author = {Peeters, A.G. and Angioni, C. and Bortolon, A. and Camenen, Y. and Casson, F.J. and Duval, B. and Fiederspiel, L. and Hornsby, W.A. and Idomura, Y. and Hein, T. and Kluy, N. and Mantica, P. and Parra, F.I. and Snodin, A.P. and Szepesi, G. and Strintzi, D. and Tala, T. and Tardini, G. and de Vries, P. and Weiland, J.},
doi = {10.1088/0029-5515/51/9/094027},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(8).pdf:pdf},
isbn = {0029-5515$\backslash$n1741-4326},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {9},
pages = {094027},
title = {{Overview of toroidal momentum transport}},
url = {http://stacks.iop.org/0029-5515/51/i=9/a=094027?key=crossref.6b7a20b81ecf225fc48a5b4e8cfb0324},
volume = {51},
year = {2011}
}
@book{LANDAU1980,
abstract = {A lucid presentation of statistical physics and thermodynamics which develops from the general principles to give a large number of applications of the theory.},
author = {LANDAU, L. D. and LIFSHITZ, E. M.},
booktitle = {Stat. Phys.},
isbn = {9780750633727},
pages = {544},
title = {{COURSE OF THEORETICAL PHYSICS Volume 5, STATISTICAL PHYSICS Part 1}},
year = {1980}
}
@book{Frisch,
author = {Frisch, Uriel},
title = {{Turbulence}}
}
@book{Chen1984,
abstract = {This complete introduction to plasma physics and controlled fusion by one of the pioneering scientists in this expanding field offers both a simple and intuitive discussion of the basic concepts of this subject and an insight into the challenging problems of current research. In a wholly lucid manner the work covers single-particle motions, fluid equations for plasmas, wave motions, diffusion and resistivity, Landau damping, plasma instabilities and nonlinear problems. For students, this outstanding text offers a painless introduction to this important field; for teachers, a large collection of problems; and for researchers, a concise review of the fundamentals as well as original treatments of a number of topics never before explained so clearly. This revised edition contains new material on kinetic effects, including Bernstein waves and the plasma dispersion function, and on nonlinear wave equations and solitons.},
author = {Chen, Francis F.},
doi = {10.1063/1.2814568},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Chen - 1984 - Introduction to Plasma Physics and Controlled Fusion.pdf:pdf},
isbn = {9781441932013},
issn = {07413335},
pages = {421},
title = {{Introduction to Plasma Physics and Controlled Fusion}},
url = {http://books.google.com.hk/books?id=WYM3cgAACAAJ},
year = {1984}
}
@book{StephenB.Pope,
author = {Pope, Stephen B.},
title = {{Turbulent Flows-Cambridge University Press (2000).pdf}}
}
@article{Jensen1977a,
author = {Jensen, R. V. and Post, D. E. and Grasberger, W. H. and Tarter, C. B. and Lokke, W. A.},
doi = {10.1088/0029-5515/17/6/007},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Jensen et al. - 1977 - Calculations of impurity radiation and its effects on tokamak experiments.pdf:pdf},
issn = {17414326},
journal = {Nucl. Fusion},
number = {6},
pages = {1187--1196},
title = {{Calculations of impurity radiation and its effects on tokamak experiments}},
volume = {17},
year = {1977}
}
@article{Casati2012,
abstract = {The development of a quasi-linear gyrokinetic transport model for tokamak plasmas, ultimately designed to provide physically comprehensive predictions of the time evolution of the thermodynamic relevant quantities, is a task that requires tight links among theoretical, experimental and numerical studies. The framework of the model here proposed, which operates a reduction of complexity on the nonlinear self-organizing plasma dynamics, allows in fact multiple validations of the current understanding of the tokamak micro-turbulence. The main outcomes of this work stem from the fundamental steps involved by the formulation of such a reduced transport model, namely: (1) the verification of the quasi-linear plasma response against the nonlinearly computed solution, (2) the improvement of the turbulent saturation model through an accurate validation of the nonlinear codes against the turbulence measurements, (3) the integration of the quasi-linear model within an integrated transport solver.},
archivePrefix = {arXiv},
arxivId = {arXiv:1204.3254v1},
author = {Casati, Alessandro},
eprint = {arXiv:1204.3254v1},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Casati - 2012 - A quasi-linear gyrokinetic transport model for tokamak plasmas.pdf:pdf},
journal = {arXiv:1204.3254},
title = {{A quasi-linear gyrokinetic transport model for tokamak plasmas}},
url = {http://arxiv.org/abs/1204.3254{\%}5Cnhttp://www.arxiv.org/pdf/1204.3254.pdf},
year = {2012}
}
@article{Xu1991a,
author = {Xu, X. Q. and Rosenbluth, M. N.},
doi = {10.1063/1.859746},
issn = {08998221},
journal = {Phys. Fluids B Plasma Phys.},
number = {2},
pages = {363},
title = {{Tearing modes in tokamaks with lower hybrid current drive}},
url = {http://link.aip.org/link/PFBPEI/v3/i2/p363/s1{\&}Agg=doi},
volume = {3},
year = {1991}
}
@article{Barnes2011,
abstract = {Scaling laws for ion temperature gradient driven turbulence in magnetized toroidal plasmas are derived and compared with direct numerical simulations. Predicted dependences of turbulence fluctuation amplitudes, spatial scales, and resulting heat fluxes on temperature gradient and magnetic field line pitch are found to agree with numerical results in both the driving and inertial ranges. Evidence is provided to support the critical balance conjecture that parallel streaming and nonlinear perpendicular decorrelation times are comparable at all spatial scales, leading to a scaling relationship between parallel and perpendicular spatial scales. This indicates that even strongly magnetized plasma turbulence is intrinsically three dimensional.},
archivePrefix = {arXiv},
arxivId = {1104.4514},
author = {Barnes, M. and Parra, F. I. and Schekochihin, A. A.},
doi = {10.1103/PhysRevLett.107.115003},
eprint = {1104.4514},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Barnes, Parra, Schekochihin - 2011 - Critically balanced ion temperature gradient turbulence in fusion plasmas.pdf:pdf},
issn = {00319007},
journal = {Phys. Rev. Lett.},
number = {11},
pages = {3--6},
title = {{Critically balanced ion temperature gradient turbulence in fusion plasmas}},
volume = {107},
year = {2011}
}
@article{Parra2011a,
abstract = {A low flow, delta f gyrokinetic formulation to obtain the intrinsic rotation profiles is presented. The momentum conservation equation in the low-flow ordering contains new terms, neglected in previous first-principles formulations, that may explain the intrinsic rotation observed in tokamaks in the absence of external sources of momentum. The intrinsic rotation profile depends on the density and temperature profiles and on the up-down asymmetry.},
author = {Parra, Felix I. FI Felix I. Felix I and Barnes, Michael and Catto, Peter J.},
doi = {10.1088/0029-5515/51/11/113001},
issn = {0029-5515},
journal = {Nucl. Fusion},
keywords = {Intrinsic rotation},
number = {11},
pages = {113001},
title = {{Sources of intrinsic rotation in the low-flow ordering}},
url = {http://iopscience.iop.org/0029-5515/51/11/113001{\%}5Cnhttp://stacks.iop.org/0029-5515/51/i=11/a=113001?key=crossref.a710252cd7b3479cfe2d86cefbaafcf4},
volume = {51},
year = {2011}
}
@article{Terry2003,
author = {Terry, J. L. and Zweben, S. J. and Hallatschek, K. and LaBombard, B. and Maqueda, R. J. and Bai, B. and Boswell, C. J. and Greenwald, M. and Kopon, D. and Nevins, W. M. and Pitcher, C. S. and Rogers, B. N. and Stotler, D. P. and Xu, X. Q.},
doi = {10.1063/1.1564090},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {1739},
title = {{Observations of the turbulence in the scrape-off-layer of Alcator C-Mod and comparisons with simulation}},
url = {http://link.aip.org/link/PHPAEN/v10/i5/p1739/s1{\&}Agg=doi},
volume = {10},
year = {2003}
}
@article{Barnes2009a,
abstract = {A new analytically and numerically manageable model collision operator is developed specifically for turbulence simulations. The like-particle collision operator includes both pitch-angle scattering and energy diffusion and satisfies the physical constraints required for collision operators: it conserves particles, momentum and energy, obeys Boltzmann's H-theorem (collisions cannot decrease entropy), vanishes on a Maxwellian, and efficiently dissipates small-scale structure in the velocity space. The process of transforming this collision operator into the gyroaveraged form for use in gyrokinetic simulations is detailed. The gyroaveraged model operator is shown to have more suitable behavior at small scales in phase space than previously suggested models. A model operator for electron-ion collisions is also presented.},
archivePrefix = {arXiv},
arxivId = {0808.1300},
author = {Barnes, M. and Abel, I. G. and Dorland, W. and Ernst, D. R. and Hammett, G. W. and Ricci, P. and Rogers, B. N. and Schekochihin, A. A. and Tatsuno, T.},
doi = {10.1063/1.3155085},
eprint = {0808.1300},
isbn = {1070-664X},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {7},
title = {{Linearized model fokker-planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests}},
volume = {16},
year = {2009}
}
@article{Hua2009,
author = {Hứa, Minh-đức},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hứa - 2009 - Plasma rotation in the MAST and JET tokamaks.pdf:pdf},
journal = {Plasma Phys.},
keywords = {JET,MAST,plasma rotation,thesis},
mendeley-tags = {JET,MAST,plasma rotation,thesis},
number = {December},
title = {{Plasma rotation in the MAST and JET tokamaks}},
year = {2009}
}
@article{Search1989,
author = {Search, Home and Journals, Collections and Contact, About and Iopscience, My and Phys, Plasma and Address, I P},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Search et al. - 1989 - Contact us My IOPscience Models of plasma transport based on microturbulence.pdf:pdf},
journal = {Plasma Phys.},
keywords = {anomalous transport,microinstabilities,qi-mode,scaling laws,trapped electron mode},
title = {{Contact us My IOPscience Models of plasma transport based on microturbulence}},
volume = {1535},
year = {1989}
}
@article{Jackson2015,
abstract = {The CHEASE code (Cubic Hermite Element Axisymmetric Static Equilibrium) solves the Grad-Shafranov equation for toroidal MHD equilibria using a Hermite bicubic finite element discretization with pressure, current profiles and plasma boundaries specified by analytical forms or sets of experimental data points. Moreover, CHEASE allows the automatic generation of pressure profiles marginally stable to ballooning modes or with a prescribed fraction of bootstrap current. The code provides equilibrium quantities for several stability and global wave propagation codes.},
archivePrefix = {arXiv},
arxivId = {arXiv:1205.2509v1},
author = {Jackson, Adrian and Hein, Joachim and Roach, Colin},
doi = {10.1109/TPDS.2014.2351826},
eprint = {arXiv:1205.2509v1},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Jackson, Hein, Roach - 2015 - Optimising Performance through Unbalanced Decompositions.pdf:pdf},
isbn = {1045-9219},
issn = {10459219},
journal = {IEEE Trans. Parallel Distrib. Syst.},
keywords = {Benchmark testing,Computational modeling,Indexes,Layout,Load modeling,Mathematical model,Plasmas},
number = {10},
pages = {2863--2873},
title = {{Optimising Performance through Unbalanced Decompositions}},
volume = {26},
year = {2015}
}
@article{Cowley,
author = {Cowley, Steven C.},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Cowley - Unknown - From ITER time-scales to gyro-kinetics.pdf:pdf},
journal = {Gyro-kinetics Lect.},
title = {{From ITER time-scales to gyro-kinetics}}
}
@book{Rudin,
author = {Rudin, Walter},
title = {{Principles of Mathematical Analysis}}
}
@article{Suzuki1993,
abstract = {Summary form only given. For controls and stability of an axisymmetric toroidal plasma, such as a tokamak or a reversed field pinch. The authors have developed the code-solving Grad-Shafranov (GS) equation as a free boundary condition including external poloidal coil currents. Using the flux function of a toroidal field proposed by M. Suzuki et al. (1992), the authors analyzed the toroidal equilibrium of a reversed field pinch configuration, including finite pressure gradient and external poloidal coil currents. Calculated results on the toroidal effect on the F-{\&}theta; curve and the RFP equilibrium with a poloidal divertor are presented},
author = {Suzuki, M and Hotta, E},
doi = {10.1109/PLASMA.1993.593084},
isbn = {0780313607},
issn = {07309244},
journal = {Int. Conf. Plasma Sci. ICOPS},
title = {{Toroidal equilibrium analysis of an axisymmetric plasma}},
year = {1993}
}
@article{Gorler2009,
author = {Görler, T.},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Görler - 2009 - Multiscale Effects in Plasma Microturbulence.pdf:pdf},
journal = {Dissertation},
pages = {152},
title = {{Multiscale Effects in Plasma Microturbulence}},
year = {2009}
}
@article{Parra2014,
abstract = {Self-consistent equations for intrinsic rotation in tokamaks with small poloidal magnetic field {\$}B{\_}p{\$} compared to the total magnetic field {\$}B{\$} are derived. The model gives the momentum redistribution due to turbulence, collisional transport and energy injection. Intrinsic rotation is determined by the balance between the momentum redistribution and the turbulent diffusion and convection. Two different turbulence regimes are considered: turbulence with characteristic perpendicular lengths of the order of the ion gyroradius, {\$}\backslashrho{\_}i{\$}, and turbulence with characteristic lengths of the order of the poloidal gyroradius, {\$}(B/B{\_}p) \backslashrho{\_}i{\$}. Intrinsic rotation driven by gyroradius scale turbulence is mainly due to the effect of neoclassical corrections and of finite orbit widths on turbulent momentum transport, whereas for the intrinsic rotation driven by poloidal gyroradius scale turbulence, the slow variation of turbulence characteristics in the radial and poloidal directions and the turbulent particle acceleration can be become as important as the neoclassical and finite orbit width effects. The magnetic drift is shown to be indispensable for the intrinsic rotation driven by the slow variation of turbulence characteristics and the turbulent particle acceleration. The equations are written in a form easily implementable in a flux tube code, and the effect of the radial variation of the turbulence is included without having to resort to a global gyrokinetic formalism.},
archivePrefix = {arXiv},
arxivId = {1407.1286},
author = {Parra, Felix I and Barnes, Michael},
doi = {10.1088/0741-3335/57/4/045002},
eprint = {1407.1286},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
keywords = {gyrokinetics,in colour only in,rotation,some figures may appear,the online journal,tokamak,turbulence},
pages = {83},
title = {{Turbulent transport in rotating tokamak plasmas}},
url = {http://arxiv.org/abs/1407.1286},
volume = {045002},
year = {2014}
}
@article{Merz2008,
author = {Merz, Florian},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Merz - 2008 - Gyrokinetic Simulation of Multimode Plasma Turbulence.pdf:pdf},
journal = {PhD Thesis},
title = {{Gyrokinetic Simulation of Multimode Plasma Turbulence}},
year = {2008}
}
@article{Xu2003,
author = {Xu, X. Q. and Nevins, W. M. and Rognlien, T. D. and Bulmer, R. H. and Greenwald, M. and Mahdavi, a. and Pearlstein, L. D. and Snyder, P.},
doi = {10.1063/1.1566032},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {1773},
title = {{Transitions of turbulence in plasma density limits}},
url = {http://link.aip.org/link/PHPAEN/v10/i5/p1773/s1{\&}Agg=doi},
volume = {10},
year = {2003}
}
@article{Beer2000,
author = {Beer, M A and Cowley, S C and Hammett, G W and Beer, M A and Cowley, S C and Hammett, G W},
doi = {10.1063/1.871232},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Beer et al. - 2000 - Field-aligned coordinates for nonlinear simulations of tokamak turbulence Field-aligned coordinates for nonlinear s.pdf:pdf},
number = {1995},
title = {{Field-aligned coordinates for nonlinear simulations of tokamak turbulence Field-aligned coordinates for nonlinear simulations of tokamak turbulence}},
volume = {2687},
year = {2000}
}
@article{Mauriya2014,
author = {Mauriya, A and Barnes, M and Nave, M F F and Parra, F},
number = {1995},
pages = {112503},
title = {{Implementation of Multiple Species Collisional Operator in Gyro-Kinetic Code GS2}},
volume = {128},
year = {2014}
}
@article{Hirshman1976,
abstract = {An analytically tractable approximation is developed for the linearized Fokker – Planck collision operator describing a plasma nearly in thermal equilibrium. This approximate operator preserves the symmetry properties of the exact collision integral which imply the physical ...},
author = {Hirshman, S P and Sigmar, D J},
doi = {10.1063/1.861356},
isbn = {1070-6631},
issn = {00319171},
journal = {Phys. Fluids},
number = {10},
pages = {1532},
title = {{Approximate Fokker–Planck collision operator for transport theory applications}},
url = {http://link.aip.org/link/PFLDAS/v19/i10/p1532/s1{\&}Agg=doi{\%}5Cnpapers2://publication/doi/10.1063/1.861356},
volume = {19},
year = {1976}
}
@article{Martin2007,
author = {Martín, P. and Castro, E. and Haines, M. G.},
doi = {10.1063/1.2727455},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {052502},
title = {{Collisional diffusion in toroidal plasmas with elongation and triangularity}},
url = {http://link.aip.org/link/PHPAEN/v14/i5/p052502/s1{\&}Agg=doi},
volume = {14},
year = {2007}
}
@article{Nadjafikhah2011,
abstract = {The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose the Grad-Shafranov equation which may illustrate the reciprocal advantage of this interaction between plasma physics and symmetry techniques. A symmetry classification of the Grad-Shafranov equation with two arbitrary functions F(u) and G(u) of the unknown variable u=u(x,t) is given. The optimal system of one-dimensional subalgebras is performed. This latter provides a process for building new solutions for the equation.},
archivePrefix = {arXiv},
arxivId = {1105.1497},
author = {Nadjafikhah, Mehdi and Kabi-Nejad, Parastoo},
eprint = {1105.1497},
journal = {Phys. Plasmas},
pages = {9},
title = {{Lie symmetry analysis of the Grad-Shafranov equation}},
volume = {16},
year = {2011}
}
@article{Sanchez2010,
abstract = {In this paper, we report on simulations that have recently been carried out using the EUTERPE gyrokinetic code. The scaling of the code has been studied up to 20 000 processing elements. Linear and nonlinear simulations of ion temperature-gradient instabilities have been carried out in screw-pinch geometry, and the results are compared with those previously obtained using the TORB code, finding a good agreement. The influence of a finite {\$}beta{\$} on the growth rates of instabilities and on the zonal flows in a screw-pinch has also been studied. The results are compared with previous ones.},
author = {Sanchez, Edilberto and Kleiber, Ralf and Hatzky, Roman and Soba, Alejandro and S{\'{a}}ez, Xavier and Castejon, Francisco and Cela, Jose M.},
doi = {10.1109/TPS.2010.2051339},
issn = {00933813},
journal = {IEEE Trans. Plasma Sci.},
keywords = {Plasma confinement,plasma stability,simulation},
number = {9 PART 1},
pages = {2119--2128},
title = {{Linear and nonlinear simulations using the EUTERPE gyrokinetic code}},
volume = {38},
year = {2010}
}
@article{Brambilla2003,
author = {Brambilla, Marco},
doi = {10.1063/1.1600736},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {9},
pages = {3674},
title = {{Iterative solution of the Grad–Shafranov equation in symmetric magnetic coordinates}},
url = {http://link.aip.org/link/PHPAEN/v10/i9/p3674/s1{\&}Agg=doi},
volume = {10},
year = {2003}
}
@article{Braginskii1965,
abstract = {Toroidal momentum transport mechanisms are reviewed and put in a broader perspective. The generation of a finite momentum flux is closely related to the breaking of symmetry (parity) along the field. The symmetry argument allows for the systematic identification of possible transport mechanisms. Those that appear to lowest order in the normalized Larmor radius (the diagonal part, Coriolis pinch, E x B shearing, particle flux, and up-down asymmetric equilibria) are reasonably well understood. At higher order, expected to be of importance in the plasma edge, the theory is still under development.},
archivePrefix = {arXiv},
arxivId = {1407.1286},
author = {Anderson, Oscar a. and Baker, William R. and Bratenahl, Alexander and Furth, H.P. and Ise, John and Kunkel, W.B. and Stone, John M. and Barnes, Michael and Parra, Felix I. F.I. and Lee, J. P. and Belli, E. a. and Nave, M. F. F. and White, a. E. and Smartphones, Based and Braginskii, S. I. and Engineering, Nuclear and Hegna, C.C. C and Callen, Co-authors J D and Cole, a.J. J and Ida, K. and Rice, J.E. and Peeters, A.G. and Angioni, C. and Bortolon, A. and Camenen, Y. and Casson, F.J. J. and Duval, B. and Fiederspiel, L. and Hornsby, W.a. and Idomura, Yasuhiro and Hein, T. and Kluy, N. and Mantica, P. and Parra, Felix I. F.I. and a.P. Snodin and Szepesi, Gabor and Strintzi, D. and Tala, Tuomas and Tardini, G. and de Vries, P. C. and Weiland, J. and Barnes, Michael and Casson, F.J. J. and Barnes, Michael and Parra, Felix I. F.I. and Braginskii, S. I. and Callen, J.D. and Cole, a.J. J and Hegna, C.C. C and Peeters, A.G. and Angioni, C. and Bortolon, A. and Camenen, Y. and Casson, F.J. J. and Duval, B. and Fiederspiel, L. and Hornsby, W.a. and Idomura, Yasuhiro and Hein, T. and Kluy, N. and Mantica, P. and Parra, Felix I. F.I. and a.P. Snodin and Szepesi, Gabor and Strintzi, D. and Tala, Tuomas and Tardini, G. and de Vries, P. C. and Weiland, J. and Scott, B and Smirnov, J and Tynan, G R and Yu, J H and Yan, Z and Xu, M and Diamond, P H and Holland, C and Mu, S H},
doi = {10.1007/SpringerReference_28001},
eprint = {1407.1286},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Braginskii - 1965 - Transport processes in a plasma.pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Unknown - Unknown - Radu Balescu-Transport processes in plasmas.djvu:djvu;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma.pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(2).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(3).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(4).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(5).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(6).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(7).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(8).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(9).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(10).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(11).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(12).pdf:pdf;:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Anderson et al. - 2010 - Study and use of rotating plasma(13).pdf:pdf},
isbn = {0029-5515$\backslash$n1741-4326},
issn = {0029-5515},
journal = {Nucl. Fusion},
keywords = {QC Physics,TK Electrical engineering. Electronics Nuclear eng,gyrokinetics,in colour only in,intrinsic torque,non-diffusive momentum transport,residual stress,reynolds stress,rotation,some figures may appear,spontaneous rotation,the online journal,tokamak,turbulence},
number = {5},
pages = {205},
title = {{Study and use of rotating plasma}},
url = {http://dx.doi.org/10.1088/0029-5515/51/9/094027{\%}5Cnhttp://stacks.iop.org/0029-5515/51/i=9/a=094027?key=crossref.6b7a20b81ecf225fc48a5b4e8cfb0324 http://webcat.warwick.ac.uk/record=b2521720{~}S15 http://arxiv.org/abs/1407.1286 http://stacks.iop.org/0029-5515/5},
volume = {2015},
year = {2010}
}
@article{Parra2010,
abstract = {We derive a self-consistent equation for the turbulent transport of toroidal angular momentum in tokamaks in the low flow ordering that only requires solving gyrokinetic Fokker-Planck and quasineutrality equations correct to second order in an expansion on the gyroradius over scale length. We also show that according to our orderings the long wavelength toroidal rotation and the long wavelength radial electric field satisfy the neoclassical relation that gives the toroidal rotation as a function of the radial electric field and the radial gradients of pressure and temperature. Thus, the radial electric field can be solved for once the toroidal rotation is calculated from the transport of toroidal angular momentum. Unfortunately, even though this methodology only requires a gyrokinetic model correct to second order in gyroradius over scale length, current gyrokinetic simulations are only valid to first order. To overcome this difficulty, we exploit the smallish ratio B(p)/B, where B is the total magnetic field and B(p) is its poloidal component. When B(p)/B is small, the usual first order gyrokinetic equation provides solutions that are accurate enough to employ for our expression for the transport of toroidal angular momentum. We show that current delta f and full f simulations only need small corrections to achieve this accuracy. Full f simulations, however, are still unable to determine the long wavelength, radial electric field from the quasineutrality equation.},
author = {Parra, F. I. and Catto, P. J.},
doi = {10.1088/0741-3335/52/4/045004},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Parra, Catto - 2010 - Turbulent transport of toroidal angular momentum in low flow gyrokinetics.pdf:pdf},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
title = {{Turbulent transport of toroidal angular momentum in low flow gyrokinetics}},
url = {//000275748400006},
volume = {52},
year = {2010}
}
@article{Sagdeev2003,
author = {Sagdeev, R Z and Meiss, J D},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Sagdeev, Meiss - 2003 - Drift kinetic equation and neoclassical transport theory.pdf:pdf},
title = {{Drift kinetic equation and neoclassical transport theory}},
year = {2003}
}
@article{Nave2014,
author = {Nave, M F F and Bernardo, J and Coelho, R and Czarnecka, A and Ferreira, J and Figueiredo, A and Giroud, C and Hillesheim, J and Parail, V and Salmi, A and Voitsekhovitch, I and Zastrow, K-d and Contributors, J E T and Consortium, Eurofusion and Centre, Culham Science and Spectrometer, X-ray Crystal},
number = {633053},
pages = {633053},
title = {{Measuring Intrinsic Rotation in the JET tokamak}},
volume = {1},
year = {2014}
}
@article{Degtyarev1985,
author = {Degtyarev, L.M. and Drozdov, V.V.},
doi = {10.1016/0167-7977(85)90002-4},
issn = {01677977},
journal = {Comput. Phys. Reports},
month = {jun},
number = {7},
pages = {341--387},
title = {{An inverse variable technique in the MHD-equilibrium problem}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0167797785900024},
volume = {2},
year = {1985}
}
@article{Rampp2012,
abstract = {To achieve real-time control of fusion plasmas, the flux distribution and derived quantities have to be calculated within the time of the machine control cycyle, which in the case of the ASDEX-Upgrade experiment can be as small as 1 ms. To this end we have developed a fast numerical solver for the Grad-Shafranov equation, which allows exploitation of the parallel capabilities of modern multicore processors. Our implementation, termed CPEC (Garching parallel equilibrium code), is based entirely on open-source software components. For a numerical grid of size 3264, our new code requires only 0.04ms (0.11ms for 64128) for a single call of the Grad-Shafranov solver using a standard Intel Xeon quad-core CPU (3.2GHz). We also show the first GPEC benchmark results obtained on the Intel Sandy Bridge eight-core server processor and demonstrate the relevance of the new solver for application in plasma equilibrium codes.},
author = {Rampp, M and Preuss, R and Fischer, R},
journal = {Fusion Sci.},
keywords = {grad shafranov equation,parallel solver,real},
pages = {409--418},
title = {{A Parallel Grad-Shafranov Solver for Real-Time Control of Tokamak Plasmas}},
volume = {62},
year = {2012}
}
@article{Blum2009,
abstract = {The problem of equilibrium of a plasma in a Tokamak is a free boundary problemdescribed by the Grad-Shafranov equation in axisymmetric configurations. The right hand side of this equation is a non linear source, which represents the toroidal component of the plasma current density. This paper deals with the real time identification of this non linear source from experimental measurements. The proposed method is based on a fixed point algorithm, a finite element resolution, a reduced basis method and a least-square optimization formulation.},
archivePrefix = {arXiv},
arxivId = {0909.1646},
author = {Blum, Jacques and Boulbe, C{\'{e}}dric and Faugeras, Blaise},
doi = {10.1088/1742-6596/135/1/012019},
eprint = {0909.1646},
journal = {Physics (College. Park. Md).},
pages = {420--429},
title = {{Real-Time Equilibrium Reconstruction in a Tokamak}},
volume = {135},
year = {2009}
}
@article{Citrin2014,
abstract = {References from the article Ion temperature profile stiffness: non-linear gyrokinetic simulations and comparison with experiment},
archivePrefix = {arXiv},
arxivId = {arXiv:1303.2217v2},
author = {Citrin, J. and Jenko, F. and Mantica, P. and Told, D. and Bourdelle, C. and Dumont, R. and Garcia, J. and Haverkort, J. W. and Hogeweij, G. M.D. and Johnson, T. and Pueschel, M. J.},
doi = {10.1088/0029-5515/54/2/023008},
eprint = {arXiv:1303.2217v2},
issn = {00295515},
journal = {Nucl. Fusion},
title = {{Ion temperature profile stiffness: Non-linear gyrokinetic simulations and comparison with experiment}},
year = {2014}
}
@article{Reference1,
abstract = {We have developed an enhanced Littrow configuration extended cavity diode laser (ECDL) that can be tuned without changing the direction of the output beam. The output of a conventional Littrow ECDL is reflected from a plane mirror fixed parallel to the tuning diffraction grating. Using a free-space Michelson wavemeter to measure the laser wavelength, we can tune the laser over a range greater than 10 nm without any alteration of alignment.},
author = {Hawthorn, C J and Weber, K P and Scholten, R E},
journal = {Rev. Sci. Instrum.},
month = {dec},
number = {12},
pages = {4477--4479},
title = {{Littrow Configuration Tunable External Cavity Diode Laser with Fixed Direction Output Beam}},
url = {http://link.aip.org/link/?RSI/72/4477/1},
volume = {72},
year = {2001}
}
@article{Sun2013a,
author = {Sun, Y. and Shaing, K. C. and Liang, Y. and Casper, T. and Loarte, A. and Shen, B. and Wan, B.},
doi = {10.1088/0029-5515/53/9/093010},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Sun et al. - 2013 - Intrinsic plasma rotation determined by neoclassical toroidal plasma viscosity in tokamaks.pdf:pdf},
issn = {00295515},
journal = {Nucl. Fusion},
number = {9},
pages = {8--10},
title = {{Intrinsic plasma rotation determined by neoclassical toroidal plasma viscosity in tokamaks}},
volume = {53},
year = {2013}
}
@article{Idomura2014,
abstract = {A long time ion temperature gradient driven turbulence simulation over a confinement time is performed using the full-f gyrokinetic Eulerian code GT5D. The convergence of steady temperature and rotation profiles is examined, and it is shown that the profile relaxation can be significantly accelerated when the simulation is initialized with linearly unstable temperature profiles. In the steady state, the temperature profile and the ion heat diffusivity are self-consistently determined by the power balance condition, while the intrinsic rotation profile is sustained by complicated momentum transport processes without momentum input. The steady turbulent momentum transport is characterized by bursty non-diffusive fluxes, and the resulting turbulent residual stress is consistent with the profile shear stress theory [Y. Camenen et al., “Consequences of profile shearing on toroidal momentum transport,” Nucl. Fusion 51, 073039 (2011)] in which the residual stress depends not only on the profile shear and the rad...},
author = {Idomura, Yasuhiro},
doi = {10.1063/1.4867180},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Idomura - 2014 - Full-f gyrokinetic simulation over a confinement time.pdf:pdf},
isbn = {9781632663108},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {2},
title = {{Full-f gyrokinetic simulation over a confinement time}},
volume = {21},
year = {2014}
}
@article{Howes2010,
abstract = {The ion-to-electron heating ratio due to the dissipation of Alfv{\'{e}}nic turbulence in astrophysical plasmas is calculated based on a cascade model for turbulence in weakly collisional plasmas. Conditions for validity of this model are discussed, a prescription for the turbulent heating is presented and it is applied to predict turbulent heating in accretion discs and the interstellar medium.},
author = {Howes, G. G.},
doi = {10.1111/j.1745-3933.2010.00958.x},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Howes - 2010 - A prescription for the turbulent heating of astrophysical plasmas.pdf:pdf},
issn = {17453925},
journal = {Mon. Not. R. Astron. Soc. Lett.},
month = {nov},
number = {1},
pages = {L104--L108},
title = {{A prescription for the turbulent heating of astrophysical plasmas}},
url = {http://www.mendeley.com/research/prescription-turbulent-heating-astrophysical-plasmas https://academic.oup.com/mnrasl/article-lookup/doi/10.1111/j.1745-3933.2010.00958.x},
volume = {409},
year = {2010}
}
@article{Calvo2012,
abstract = {Recently, the electrostatic gyrokinetic Hamiltonian and change of coordinates have been computed to order {\"{I}}µ 2 in general magnetic geometry. Here {\"{I}}µ is the gyrokinetic expansion parameter, the gyroradius over the macroscopic scale length. Starting from these results, the long-wavelength limit of the gyrokinetic Fokker{\^{a}}€“Planck and quasineutrality equations is taken for tokamak geometry. Employing the set of equations derived in the present paper, it is possible to calculate the long-wavelength components of the distribution functions and of the poloidal electric field to order {\"{I}}µ 2 . These higher order pieces contain both neoclassical and turbulent contributions, and constitute one of the necessary ingredients (the other is given by the short-wavelength components up to second order) that will eventually enter a complete model for the radial transport of toroidal angular momentum in a tokamak in the low flow ordering. Finally, we provide an explicit and detailed proof that the system consisting of second-order gyrokinetic Fokker{\^{a}}€“Planck and quasineutrality equations leaves the long-wavelength radial electric field undetermined; that is, the turbulent tokamak is intrinsically ambipolar.},
archivePrefix = {arXiv},
arxivId = {arXiv:1204.1509v3},
author = {Calvo, Iv{\'{a}}n and Parra, Felix I},
doi = {10.1088/0741-3335/54/11/115007},
eprint = {arXiv:1204.1509v3},
isbn = {9781622769810},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
number = {11},
pages = {115007},
title = {{Long-wavelength limit of gyrokinetics in a turbulent tokamak and its intrinsic ambipolarity}},
url = {http://stacks.iop.org/0741-3335/54/i=11/a=115007?key=crossref.61b77d1f18e024d06015a12c19feec5c},
volume = {54},
year = {2012}
}
@article{Myra2000a,
author = {Myra, J.R. and D'Ippolito, D.a. and Xu, X.Q. and Cohen, R.H.},
doi = {10.1002/1521-3986(200006)40:3/4<352::AID-CTPP352>3.3.CO;2-T},
issn = {08631042},
journal = {Contrib. to Plasma Phys.},
month = {jun},
number = {3-4},
pages = {352--361},
title = {{MHD and Fluid Instabilities at the Plasma Edge in the Presence of a Separatrix and X-Point}},
url = {http://doi.wiley.com/10.1002/1521-3986{\%}28200006{\%}2940{\%}3A3{\%}2F4{\%}3C352{\%}3A{\%}3AAID-CTPP352{\%}3E3.3.CO{\%}3B2-T},
volume = {40},
year = {2000}
}
@article{Parra2011,
abstract = {A low flow, delta f gyrokinetic formulation to obtain the intrinsic rotation profiles is presented. The momentum conservation equation in the low-flow ordering contains new terms, neglected in previous first-principles formulations, that may explain the intrinsic rotation observed in tokamaks in the absence of external sources of momentum. The intrinsic rotation profile depends on the density and temperature profiles and on the up-down asymmetry.},
author = {Parra, Felix I. FI Felix I. Felix I and Barnes, Michael and Catto, Peter J.},
doi = {10.1088/0029-5515/51/11/113001},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Parra, Barnes, Catto - 2011 - Sources of intrinsic rotation in the low-flow ordering.pdf:pdf},
issn = {0029-5515},
journal = {Nucl. Fusion},
keywords = {Intrinsic rotation},
number = {11},
pages = {113001},
title = {{Sources of intrinsic rotation in the low-flow ordering}},
url = {http://iopscience.iop.org/0029-5515/51/11/113001{\%}5Cnhttp://stacks.iop.org/0029-5515/51/i=11/a=113001?key=crossref.a710252cd7b3479cfe2d86cefbaafcf4},
volume = {51},
year = {2011}
}
@book{Shibata2016,
author = {Shibata, Yoshihiro and Suzuki, Yukihito},
doi = {10.1007/978-4-431-56457-7},
isbn = {978-4-431-56455-3},
number = {November},
title = {{Mathematical Fluid Dynamics, Present and Future}},
url = {http://link.springer.com/10.1007/978-4-431-56457-7},
volume = {183},
year = {2016}
}
@article{Lapillonne2010,
abstract = {Two global gyrokinetic codes are benchmarked against each other by comparing simulation results in the case of ion temperature gradient driven turbulence, in the adiabatic electron response limit. The two codes are the Eulerian code GENE and the Lagrangian particle-in-cell code ORB5 which solve the gyrokinetic equations. Linear results are presented, including growth rates, real frequencies, and mode structure comparisons. Nonlinear simulations without sources are carried out with particular attention to considering the same initial conditions, showing identical linear phase and first nonlinear burst. Very good agreement is also achieved between simulations obtained using a Krook-type heat source, which enables to reach a quasisteady state and thus to compare the heat diffusivity traces over a statistically meaningful time interval. For these nonlinear results, the radial zonal flow structure and shearing rate profile are also discussed. The very detailed comparisons presented may serve as reference for b...},
author = {Lapillonne, X. and McMillan, B. F. and G{\"{o}}rler, T. and Brunner, S. and Dannert, T. and Jenko, F. and Merz, F. and Villard, L.},
doi = {10.1063/1.3518118},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Lapillonne et al. - 2010 - Nonlinear quasisteady state benchmark of global gyrokinetic codes.pdf:pdf},
isbn = {1070664X},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {11},
pages = {1--10},
title = {{Nonlinear quasisteady state benchmark of global gyrokinetic codes}},
volume = {17},
year = {2010}
}
@article{Umansky2011,
author = {Umansky, M. V. and Popovich, P. and Carter, T. a. and Friedman, B. and Nevins, W. M.},
doi = {10.1063/1.3567033},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {055709},
title = {{Numerical simulation and analysis of plasma turbulence the Large Plasma Device}},
url = {http://link.aip.org/link/PHPAEN/v18/i5/p055709/s1{\&}Agg=doi},
volume = {18},
year = {2011}
}
@article{Reference2,
abstract = {We present a review of the use of diode lasers in atomic physics with an extensive list of references. We discuss the relevant characteristics of diode lasers and explain how to purchase and use them. We also review the various techniques that have been used to control and narrow the spectral outputs of diode lasers. Finally we present a number of examples illustrating the use of diode lasers in atomic physics experiments. Review of Scientific Instruments is copyrighted by The American Institute of Physics.},
author = {Wieman, Carl E and Hollberg, Leo},
journal = {Rev. Sci. Instrum.},
keywords = {Diode Laser},
month = {jan},
number = {1},
pages = {1--20},
title = {{Using Diode Lasers for Atomic Physics}},
url = {http://link.aip.org/link/?RSI/62/1/1},
volume = {62},
year = {1991}
}
@article{Gorler2008a,
abstract = {Gyrokinetic turbulence simulations covering both electron and ion spatio-temporal scales self-consistently are presented. It is found that for experimentally realistic transport levels at long wavelengths, electron temperature gradient modes may yield substantial or even dominant high-wavenumber contributions to the electron heat flux. It is investigated in which way this behavior is reflected in several experimentally accessible quantities as, for instance, density or frequency spectra.},
author = {G{\"{o}}rler, T. and Jenko, F.},
doi = {10.1063/1.3006086},
issn = {1070664X},
journal = {Phys. Plasmas},
title = {{Multiscale features of density and frequency spectra from nonlinear gyrokinetics}},
year = {2008}
}
@article{Nave2017,
author = {Nave, M.F.F. and Kirov, K. and Bernardo, J. and Brix, M. and Ferreira, J. and Giroud, C. and Hawkes, N. and Hellsten, T. and Jonsson, T. and Mailloux, J. and Ongena, J. and Parra, F.},
doi = {10.1088/1741-4326/aa4e54},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Nave et al. - 2017 - The effect of lower hybrid waves on JET plasma rotation.pdf:pdf},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {3},
pages = {034002},
publisher = {IOP Publishing},
title = {{The effect of lower hybrid waves on JET plasma rotation}},
url = {http://stacks.iop.org/0029-5515/57/i=3/a=034002?key=crossref.823f5eaf46efcd88a84da52c5e3bb35a},
volume = {57},
year = {2017}
}
@article{Fulop2009a,
abstract = {Impurity particle transport in tokamaks is studied using an electrostatic fluid model for main ion and impurity temperature gradient (ITG) mode and trapped electron (TE) mode turbulence in the collisionless limit and neoclassical theory. The impurity flux and impurity density peaking factor obtained from a self-consistent treatment of impurity transport are compared and contrasted with the results of the often used trace impurity approximation. Comparisons between trace and self-consistent turbulent impurity transport are performed for ITER-like profiles. It is shown that for small impurity concentrations the trace impurity limit is adequate if the plasma is dominated by ITG turbulence. However, in case of TE mode dominated plasmas the contribution from impurity modes may be significant, and therefore a self-consistent treatment may be needed. {\textcopyright} 2009 American Institute of Physics.},
author = {F{\"{u}}l{\"{o}}p, T. and Nordman, H.},
doi = {10.1063/1.3083299},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/F{\"{u}}l{\"{o}}p, Nordman - 2009 - Turbulent and neoclassical impurity transport in tokamak plasmas.pdf:pdf},
isbn = {1070-664X},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {3},
title = {{Turbulent and neoclassical impurity transport in tokamak plasmas}},
volume = {16},
year = {2009}
}
@article{Krommes2015,
abstract = {{\textless}p{\textgreater} In honour of the 50th anniversary of the influential review/monograph on plasma turbulence by B. B. Kadomtsev as well as the seminal works of T. H. Dupree and J. Weinstock on resonance-broadening theory, an introductory tutorial is given about some highlights of the statistical–dynamical description of turbulent plasmas and fluids, including the ideas of nonlinear incoherent noise, coherent damping, and self-consistent dielectric response. The statistical closure problem is introduced. Incoherent noise and coherent damping are illustrated with a solvable model of passive advection. Self-consistency introduces turbulent polarization effects that are described by the dielectric function {\textless}inline-formula{\textgreater} {\textless}alternatives{\textgreater} {\textless}inline-graphic href="S0022377815000756{\_}inline1" mime-subtype="gif" type="simple"/{\textgreater} {\textless}tex-math{\textgreater}{\$}{\{}\backslashmathcal{\{}D{\}}{\}}{\$}{\textless}/tex-math{\textgreater} {\textless}/alternatives{\textgreater} {\textless}/inline-formula{\textgreater} . Dupree's method of using {\textless}inline-formula{\textgreater} {\textless}alternatives{\textgreater} {\textless}inline-graphic href="S0022377815000756{\_}inline2" mime-subtype="gif" type="simple"/{\textgreater} {\textless}tex-math{\textgreater}{\$}{\{}\backslashmathcal{\{}D{\}}{\}}{\$}{\textless}/tex-math{\textgreater} {\textless}/alternatives{\textgreater} {\textless}/inline-formula{\textgreater} to estimate the saturation level of turbulence is described; then it is explained why a more complete theory that includes nonlinear noise is required. The general theory is best formulated in terms of Dyson equations for the covariance {\textless}inline-formula{\textgreater} {\textless}alternatives{\textgreater} {\textless}inline-graphic href="S0022377815000756{\_}inline3" mime-subtype="gif" type="simple"/{\textgreater} {\textless}tex-math{\textgreater}{\$}C{\$}{\textless}/tex-math{\textgreater} {\textless}/alternatives{\textgreater} {\textless}/inline-formula{\textgreater} and an infinitesimal response function {\textless}inline-formula{\textgreater} {\textless}alternatives{\textgreater} {\textless}inline-graphic href="S0022377815000756{\_}inline4" mime-subtype="gif" type="simple"/{\textgreater} {\textless}tex-math{\textgreater}{\$}R{\$}{\textless}/tex-math{\textgreater} {\textless}/alternatives{\textgreater} {\textless}/inline-formula{\textgreater} , which subsumes {\textless}inline-formula{\textgreater} {\textless}alternatives{\textgreater} {\textless}inline-graphic href="S0022377815000756{\_}inline5" mime-subtype="gif" type="simple"/{\textgreater} {\textless}tex-math{\textgreater}{\$}{\{}\backslashmathcal{\{}D{\}}{\}}{\$}{\textless}/tex-math{\textgreater} {\textless}/alternatives{\textgreater} {\textless}/inline-formula{\textgreater} . An important example is the direct-interaction approximation (DIA). It is shown how to use Novikov's theorem to develop an {\textless}inline-formula{\textgreater} {\textless}alternatives{\textgreater} {\textless}inline-graphic href="S0022377815000756{\_}inline6" mime-subtype="gif" type="simple"/{\textgreater} {\textless}tex-math{\textgreater}{\$}\backslashboldsymbol{\{}x{\}}{\$}{\textless}/tex-math{\textgreater} {\textless}/alternatives{\textgreater} {\textless}/inline-formula{\textgreater} -space approach to the DIA that is complementary to the original {\textless}inline-formula{\textgreater} {\textless}alternatives{\textgreater} {\textless}inline-graphic href="S0022377815000756{\_}inline7" mime-subtype="gif" type="simple"/{\textgreater} {\textless}tex-math{\textgreater}{\$}\backslashboldsymbol{\{}k{\}}{\$}{\textless}/tex-math{\textgreater} {\textless}/alternatives{\textgreater} {\textless}/inline-formula{\textgreater} -space approach of Kraichnan. A dielectric function is defined for arbitrary quadratically nonlinear systems, including the Navier–Stokes equation, and an algorithm for determining the form of {\textless}inline-formula{\textgreater} {\textless}alternatives{\textgreater} {\textless}inline-graphic href="S0022377815000756{\_}inline8" mime-subtype="gif" type="simple"/{\textgreater} {\textless}tex-math{\textgreater}{\$}{\{}\backslashmathcal{\{}D{\}}{\}}{\$}{\textless}/tex-math{\textgreater} {\textless}/alternatives{\textgreater} {\textless}/inline-formula{\textgreater} in the DIA is sketched. The independent insights of Kadomtsev and Kraichnan about the problem of the DIA with random Galilean invariance are described. The mixing-length formula for drift-wave saturation is discussed in the context of closures that include nonlinear noise (shielded by {\textless}inline-formula{\textgreater} {\textless}alternatives{\textgreater} {\textless}inline-graphic href="S0022377815000756{\_}inline9" mime-subtype="gif" type="simple"/{\textgreater} {\textless}tex-math{\textgreater}{\$}{\{}\backslashmathcal{\{}D{\}}{\}}{\$}{\textless}/tex-math{\textgreater} {\textless}/alternatives{\textgreater} {\textless}/inline-formula{\textgreater} ). The role of {\textless}inline-formula{\textgreater} {\textless}alternatives{\textgreater} {\textless}inline-graphic href="S0022377815000756{\_}inline10" mime-subtype="gif" type="simple"/{\textgreater} {\textless}tex-math{\textgreater}{\$}R{\$}{\textless}/tex-math{\textgreater} {\textless}/alternatives{\textgreater} {\textless}/inline-formula{\textgreater} in the calculation of the symmetry-breaking (zonostrophic) instability of homogeneous turbulence to the generation of inhomogeneous mean flows is addressed. The second-order cumulant expansion and the stochastic structural stability theory are also discussed in that context. Various historical research threads are mentioned and representative entry points to the literature are given. Some outstanding conceptual issues are enumerated. {\textless}/p{\textgreater}},
author = {Krommes, John A.},
doi = {10.1017/S0022377815000756},
issn = {14697807},
journal = {J. Plasma Phys.},
title = {{A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev's Plasma Turbulence and the resonance-broadening theory of Dupree and Weinstock}},
year = {2015}
}
@article{Burby2015a,
abstract = {We present a formulation of collisional gyrokinetic theory with exact conservation laws for energy and canonical toroidal momentum. Collisions are accounted for by a nonlinear gyrokinetic Landau operator. Gyroaveraging and linearization do not destroy the operator's conservation properties. Just as in ordinary kinetic theory, the conservation laws for collisional gyrokinetic theory are selected by the limiting collisionless gyrokinetic theory.},
archivePrefix = {arXiv},
arxivId = {1503.07185},
author = {Burby, J. W. and Brizard, A. J. and Qin, H.},
doi = {10.1063/1.4935124},
eprint = {1503.07185},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Burby, Brizard, Qin - 2015 - Energetically consistent collisional gyrokinetics.pdf:pdf},
issn = {1070-664X},
journal = {Phys. Plasmas},
month = {oct},
number = {10},
pages = {100707},
title = {{Energetically consistent collisional gyrokinetics}},
url = {http://aip.scitation.org/doi/10.1063/1.4935124},
volume = {22},
year = {2015}
}
@article{Xu1993a,
author = {Xu, X. Q. and Rosenbluth, M. N. and Diamond, P. H.},
doi = {10.1063/1.860968},
issn = {08998221},
journal = {Phys. Fluids B Plasma Phys.},
number = {7},
pages = {2206},
title = {{Electron-temperature-gradient-driven instability in tokamak boundary plasma}},
url = {http://link.aip.org/link/PFBPEI/v5/i7/p2206/s1{\&}Agg=doi},
volume = {5},
year = {1993}
}
@article{Parra2008,
abstract = {We present a new recursive procedure to find a full f electrostatic gyrokinetic equation correct to first order in an expansion of gyroradius over magnetic field characteristic length. The procedure provides new insights into the limitations of the gyrokinetic quasineutrality equation. We find that the ion distribution function must be known at least to second order in gyroradius over characteristic length to calculate the long wavelength components of the electrostatic potential self-consistently. Moreover, using the example of a steady-state $\theta$-pinch, we prove that the quasineutrality equation fails to provide the axisymmetric piece of the potential even with a distribution function correct to second order. We also show that second order accuracy is enough if a more convenient moment equation is used instead of the quasineutrality equation. These results indicate that the gyrokinetic quasineutrality equation is not the most effective procedure to find the electrostatic potential if the long wavelength components are to be retained in the analysis.},
author = {Parra, Felix I. and Catto, Peter J.},
doi = {10.1088/0741-3335/50/6/065014},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Parra, Catto - 2008 - Limitations of gyrokinetics on transport time scales.pdf:pdf},
issn = {07413335},
journal = {Plasma Phys. Control. Fusion},
number = {6},
title = {{Limitations of gyrokinetics on transport time scales}},
volume = {50},
year = {2008}
}
@article{Idomura2016,
abstract = {A new hybrid kinetic electron model is developed for electrostatic full-f gyrokinetic simulations of the ion temperature gradient driven trapped electron mode (ITG-TEM) turbulence at the ion scale. In the model, a full kinetic electron model is applied to the full-f gyrokinetic equation, the multi-species linear Fokker-Planck collision operator, and an axisymmetric part of the gyrokinetic Poisson equation, while in a non-axisymmetric part of the gyrokinetic Poisson equation, turbulent fluctuations are determined only by kinetic trapped electrons responses. By using this approach, the so-called $\omega$Hmode is avoided with keeping important physics such as the ITG-TEM, the neoclassical transport, the ambipolar condition, and particle trapping and detrapping processes. The model enables full-f gyrokinetic simulations of ITG-TEM turbulence with a reasonable computational cost. Comparisons between flux driven ITG turbulence simulations with kinetic and adiabatic electrons are presented. Although the similar ion temperature gradients with nonlinear upshift from linear critical gradients are sustained in quasi-steady states, parallel flows and radial electric fields are qualitatively different with kinetic electrons.},
author = {Idomura, Y.},
doi = {10.1016/j.jcp.2016.02.057},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Idomura - 2016 - A new hybrid kinetic electron model for full- f gyrokinetic simulations.pdf:pdf},
issn = {00219991},
journal = {J. Comput. Phys.},
keywords = {Full-f model,Gyrokinetics,Ion temperature gradient mode,Kinetic electrons,Neoclassical transport,Trapped electron mode},
month = {may},
pages = {511--531},
title = {{A new hybrid kinetic electron model for full- f gyrokinetic simulations}},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0021999116001297},
volume = {313},
year = {2016}
}
@article{Balbus,
author = {Balbus, Steven},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Balbus - Unknown - Derivation of the Kinetic Drift Equation.pdf:pdf},
pages = {1--8},
title = {{Derivation of the Kinetic Drift Equation}}
}
@article{Xia2013,
author = {Xia, T. Y. and Xu, X. Q.},
doi = {10.1063/1.4801006},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {052102},
title = {{Five-field simulations of peeling-ballooning modes using BOUT++ code}},
url = {http://link.aip.org/link/PHPAEN/v20/i5/p052102/s1{\&}Agg=doi},
volume = {20},
year = {2013}
}
@article{Snyder2004,
author = {Snyder, P.B and Wilson, H.R and Ferron, J.R and Lao, L.L and a.W Leonard and Mossessian, D and Murakami, M and Osborne, T.H and a.D Turnbull and Xu, X.Q},
doi = {10.1088/0029-5515/44/2/014},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {feb},
number = {2},
pages = {320--328},
title = {{ELMs and constraints on the H-mode pedestal: peeling–ballooning stability calculation and comparison with experiment}},
url = {http://stacks.iop.org/0029-5515/44/i=2/a=014?key=crossref.89835c4cb4068995f80cd693912eebc5},
volume = {44},
year = {2004}
}
@article{Hirshman1976a,
abstract = {An analytically tractable approximation is developed for the linearized Fokker – Planck collision operator describing a plasma nearly in thermal equilibrium. This approximate operator preserves the symmetry properties of the exact collision integral which imply the physical ...},
author = {Hirshman, S. P. and Sigmar, D. J.},
doi = {10.1063/1.861356},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hirshman, Sigmar - 1976 - Approximate Fokker–Planck collision operator for transport theory applications.pdf:pdf},
isbn = {1070-6631},
issn = {00319171},
journal = {Phys. Fluids},
number = {10},
pages = {1532},
title = {{Approximate Fokker–Planck collision operator for transport theory applications}},
url = {http://scitation.aip.org/content/aip/journal/pof1/19/10/10.1063/1.861356},
volume = {19},
year = {1976}
}
@article{Zakharov1999a,
author = {Zakharov, L. E. and Pletzer, a.},
doi = {10.1063/1.873756},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {12},
pages = {4693},
title = {{Theory of perturbed equilibria for solving the Grad–Shafranov equation}},
url = {http://link.aip.org/link/PHPAEN/v6/i12/p4693/s1{\&}Agg=doi},
volume = {6},
year = {1999}
}
@article{Roumeliotis1993,
abstract = {We have constructed a new class of exact, nonlinear solutions to the Grad-Shafranov equation, representing force-free magnetic fields with translational symmetry. These exact solutions are pertinent to the study of magnetic structures in the solar corona that are subjected to photospheric shearing motions.},
author = {Roumeliotis, George},
journal = {Phys. Rev. B},
pages = {2--7},
title = {{A new class of exact, nonlinear solutions to the Grad-Shafranov equation}},
volume = {84},
year = {1993}
}
@article{Gourdain2004,
author = {Gourdain, P.-a. and Leboeuf, J.-N.},
doi = {10.1063/1.1776174},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {9},
pages = {4372},
title = {{Contour dynamics method for solving the Grad–Shafranov equation with applications to high beta equilibria}},
url = {http://link.aip.org/link/PHPAEN/v11/i9/p4372/s1{\&}Agg=doi},
volume = {11},
year = {2004}
}
@article{Shea2003,
abstract = {The NRL Plasma Formulary has been the mini-Bible of plasma physicists for the past 25 years. It is an eclectic compilation of mathematical and scientific formulas, and contains physical parameters pertinent to a variety of plasma regimes, ranging from laboratory devices to astrophysical objects.},
author = {Shea, J.J.},
doi = {10.1109/MEI.2003.1178121},
isbn = {9781234126070},
issn = {0883-7554},
journal = {IEEE Electr. Insul. Mag.},
number = {1},
pages = {52--52},
title = {{A plasma formulary for physics, technology, and astrophysics [Book Review]}},
url = {http://ieeexplore.ieee.org/document/1178121/},
volume = {19},
year = {2003}
}
@article{Jensen1977,
author = {Jensen, RV and Post, DE and Grasberger, WH and Tarter, C.B. and Lokke, W.A.},
doi = {10.1088/0029-5515/17/6/007},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {6},
pages = {1187--1196},
title = {{Calculations of impurity radiation and its effects on tokamak experiments}},
url = {http://iopscience.iop.org/0029-5515/17/6/007{\%}5Cnhttp://stacks.iop.org/0029-5515/17/i=6/a=007?key=crossref.0640ae1384ecc0e2293701a7fa60d9ca},
volume = {17},
year = {1977}
}
@article{Reference3,
abstract = {Operating a laser diode in an extended cavity which provides frequency-selective feedback is a very effective method of reducing the laser's linewidth and improving its tunability. We have developed an extremely simple laser of this type, built from inexpensive commercial components with only a few minor modifications. A 780{\~{}}nm laser built to this design has an output power of 80{\~{}}mW, a linewidth of 350{\~{}}kHz, and it has been continuously locked to a Doppler-free rubidium transition for several days.},
author = {Arnold, A S and Wilson, J S and Boshier, M G},
journal = {Rev. Sci. Instrum.},
month = {mar},
number = {3},
pages = {1236--1239},
title = {{A Simple Extended-Cavity Diode Laser}},
url = {http://link.aip.org/link/?RSI/69/1236/1},
volume = {69},
year = {1998}
}
@incollection{Bishop1995,
abstract = {This paper presents results from the first use of neural networks for the real-time feedback control of high temperature plasmas in a Tokamak fusion experiment. The Tokamak is currently the principal experimental device for research into the magnetic confinement approach to controlled fusion. In the Tokamak, hydrogen plasmas, at temperatures of up to 100 Million K, are confined by strong magnetic fields. Accurate control of the position and shape of the plasma boundary requires real-time feedback control of the magnetic field structure on a time-scale of a few tens of microseconds. Software simulations have demonstrated that a neural network approach can give significantly better performance than the linear technique currently used on most Tokamak experiments. The practical application of the neural network approach requires high-speed hardware, for which a fully parallel implementation of the multi-layer perceptron, using a hybrid of digital and analogue technology, has been developed.},
author = {Bishop, Christopher M and Haynes, P S and Smith, M E U and Todd, T N and Trotman, D L and Windsor, C G},
booktitle = {Neural Comput.},
editor = {Tesauro, Gerald and Touretzky, David S and Leen, Todd K},
keywords = {mathematical computing sciences not elsewhere clas},
number = {1},
pages = {1007--1013},
publisher = {Massachusetts Institute of Technology Press (MIT Press)},
title = {{Real-time control of a Tokamak plasma using neural networks}},
url = {http://eprints.aston.ac.uk/379/},
volume = {7},
year = {1995}
}
@article{Grandgirard2010a,
author = {Grandgirard, Virginie},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Grandgirard - 2010 - Gyrokinetic simulations of magnetic fusion plasmas Tutorial 3 Acknowledgements Yanick Sarazin Gyrokinetic codes.pdf:pdf},
keywords = {Presentation,gyrokinetics,simulations},
mendeley-tags = {Presentation,gyrokinetics,simulations},
title = {{Gyrokinetic simulations of magnetic fusion plasmas Tutorial 3 Acknowledgements : Yanick Sarazin Gyrokinetic codes}},
year = {2010}
}
@article{Callen2009b,
abstract = {A comprehensive transport equation for the evolution of toroidal rotation in tokamak plasmas is developed self-consistently from the two-fluid momentum equations taking account of the constraints imposed by faster time scale processes. The resultant plasma toroidal rotation equation includes the effects of collision-induced perpendicular viscosities, anomalous transport due to microturbulence},
author = {Callen, J.D. and Cole, A.J. and Hegna, C.C.},
doi = {10.1088/0029-5515/49/8/085021},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Callen, Cole, Hegna - 2009 - Toroidal rotation in tokamak plasmas.pdf:pdf},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {8},
pages = {085021},
title = {{Toroidal rotation in tokamak plasmas}},
url = {http://stacks.iop.org/0029-5515/49/i=8/a=085021?key=crossref.29df5e8761b945da7ff663d65e783f2e},
volume = {49},
year = {2009}
}
@article{TenBarge2013,
abstract = {The dissipation of turbulence in the weakly collisional solar wind plasma is governed by unknown kinetic mechanisms. Two candidates have been suggested to play an important role in the dissipation, collisionless damping via wave-particle interactions and dissipation in small-scale current sheets. High resolution spacecraft measurements of the turbulent magnetic energy spectrum provide important constraints on the dissipation mechanism. The limitations of popular fluid and hybrid numerical schemes for simulation of the dissipation of solar wind turbulence are discussed, and instead a three-dimensional kinetic approach is recommended. We present a three-dimensional nonlinear gyrokinetic simulation of solar wind turbulence at electron scales that quantitatively reproduces the exponential form of the turbulent magnetic energy spectrum measured in the solar wind. A weakened cascade model that accounts for nonlocal interactions and collisionless Landau damping also quantitatively agrees with the observed exponential form. These results establish that a turbulent cascade of kinetic Alfv{\'{e}}n waves that is terminated by collisionless Landau damping is sufficient to explain the observed magnetic energy spectrum in the dissipation range of solar wind turbulence.},
author = {TenBarge, J. M. and Howes, G. G. and Dorland, W.},
doi = {10.1088/0004-637X/774/2/139},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/TenBarge, Howes, Dorland - 2013 - COLLISIONLESS DAMPING AT ELECTRON SCALES IN SOLAR WIND TURBULENCE.pdf:pdf},
isbn = {10.1088/0004-637X/774/2/139},
issn = {0004-637X},
journal = {Astrophys. J.},
keywords = {plasmas,solar wind,turbulence},
month = {aug},
number = {2},
pages = {139},
title = {{COLLISIONLESS DAMPING AT ELECTRON SCALES IN SOLAR WIND TURBULENCE}},
url = {http://stacks.iop.org/0004-637X/774/i=2/a=139?key=crossref.d21031dcf7dda821c69a731d514af695},
volume = {774},
year = {2013}
}
@article{Hu2013,
author = {Hu, Qiang and Farrugia, C. J. and Osherovich, V. a. and M{\"{o}}stl, C. and Szabo, a. and Ogilvie, K. W. and Lepping, R. P.},
doi = {10.1007/s11207-013-0259-y},
issn = {0038-0938},
journal = {Sol. Phys.},
month = {mar},
number = {1},
pages = {275--291},
title = {{Effect of Electron Pressure on the Grad–Shafranov Reconstruction of Interplanetary Coronal Mass Ejections}},
url = {http://link.springer.com/10.1007/s11207-013-0259-y},
volume = {284},
year = {2013}
}
@article{Hirshman1985,
author = {Hirshman, S. P. and Weitzner, H.},
doi = {10.1063/1.864998},
issn = {00319171},
journal = {Phys. Fluids},
number = {4},
pages = {1207},
title = {{A convergent spectral representation for three-dimensional inverse magnetohydrodynamic equilibria}},
url = {http://link.aip.org/link/PFLDAS/v28/i4/p1207/s1{\&}Agg=doi},
volume = {28},
year = {1985}
}
@article{Sonnerup2006,
author = {Sonnerup, Bengt U. {\"{O}}. and Hasegawa, Hiroshi and Teh, Wai-Leong and Hau, Lin-Ni},
doi = {10.1029/2006JA011717},
issn = {0148-0227},
journal = {J. Geophys. Res.},
number = {A9},
pages = {A09204},
title = {{Grad-Shafranov reconstruction: An overview}},
url = {http://doi.wiley.com/10.1029/2006JA011717},
volume = {111},
year = {2006}
}
@article{Howes2011,
abstract = {A three-dimensional, nonlinear gyrokinetic simulation of plasma turbulence resolving scales from the ion to electron gyroradius with a realistic mass ratio is presented, where all damping is provided by resolved physical mechanisms. The resulting energy spectra are quantitatively consistent with a magnetic power spectrum scaling of k−2.8 as observed in in situ spacecraft measurements of the “dissipation range” of solar wind turbulence. Despite the strongly nonlinear nature of the turbulence, the linear kinetic Alfv{\'{e}}n wave mode quantitatively describes the polarization of the turbulent fluctuations. The collisional ion heating is measured at subion-Larmor radius scales, which provides evidence of the ion entropy cascade in an electromagnetic turbulence simulation.},
author = {Howes, G. G. and Tenbarge, J. M. and Dorland, W. and Quataert, E. and Schekochihin, A. A. and Numata, R. and Tatsuno, T.},
doi = {10.1103/PhysRevLett.107.035004},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Howes et al. - 2011 - Gyrokinetic simulations of solar wind turbulence from ion to electron scales.pdf:pdf},
journal = {Phys. Rev. Lett.},
title = {{Gyrokinetic simulations of solar wind turbulence from ion to electron scales}},
url = {http://www.mendeley.com/research/gyrokinetic-simulations-solar-wind-turbulence-ion-electron-scales},
year = {2011}
}
@article{Ltitjens1996,
author = {Ltitjens, H and B, A and Sauter, O},
doi = {10.1016/0010-4655(96)00046-X},
issn = {00104655},
journal = {Comput. Phys. Commun.},
keywords = {ballooning modes,bootstrap current,coordinates,cubic hermite finite elements,equilibrium,grad shafranov equation,local interchange modes,magnetohydrodynamics,mapping magnetic flux,mhd,plasma physics},
pages = {219--260},
title = {{The CHEASE code for toroidal MHD equilibria}},
volume = {97},
year = {1996}
}
@article{Heikkinen2007,
author = {Heikkinen, J A and Janhunen, S J and Kiviniemi, T P and Leerink, S and Ogando, F},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Heikkinen et al. - 2007 - Kinetic Simulation of Sheared Flows in Tokamaks.pdf:pdf},
number = {d},
pages = {2044},
title = {{Kinetic Simulation of Sheared Flows in Tokamaks}},
year = {2007}
}
@article{Itagaki2006,
author = {Itagaki, Masafumi and Fukunaga, Takaaki},
doi = {10.1016/j.enganabound.2006.04.003},
issn = {09557997},
journal = {Eng. Anal. Bound. Elem.},
keywords = {axisymmetric problem,eigenvalue,grad,nuclear fusion,polynomial expansion,shafranov equation,singularity},
month = {sep},
number = {9},
pages = {746--757},
title = {{Boundary element modelling to solve the Grad–Shafranov equation as an axisymmetric problem}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0955799706000725},
volume = {30},
year = {2006}
}
@article{Zhu2010,
abstract = {A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: A finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity {\$}v{\$} with {\$}N{\$} grid points (where {\$}N+1{\$} quantities are conserved, corresponding to an energy invariant and {\$}N{\$} entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.},
author = {Zhu, Jian Zhou and Hammett, Gregory W.},
doi = {10.1063/1.3514141},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Zhu, Hammett - 2010 - Gyrokinetic statistical absolute equilibrium and turbulence.pdf:pdf},
journal = {Phys. Plasmas},
title = {{Gyrokinetic statistical absolute equilibrium and turbulence}},
url = {http://www.mendeley.com/research/gyrokinetic-statistical-absolute-equilibrium-turbulence},
year = {2010}
}
@article{Liu2012,
author = {Liu, Z. X. and Xia, T. Y. and Xu, X. Q. and Gao, X. and Hughes, J. W. and Liu, S. C. and Ding, S. Y. and Li, J. G.},
doi = {10.1063/1.4757220},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {10},
pages = {102502},
title = {{ELMy H-mode linear simulation with 3-field model on experimental advanced superconducting tokamak using BOUT++}},
url = {http://link.aip.org/link/PHPAEN/v19/i10/p102502/s1{\&}Agg=doi},
volume = {19},
year = {2012}
}
@article{Srinivasan2004,
author = {Srinivasan, R. and Chaturvedi, S. and Deshpande, S.P.},
doi = {10.1016/j.fusengdes.2004.03.001},
issn = {09203796},
journal = {Fusion Eng. Des.},
keywords = {divertor configuration,poloidal field,rapid optimization scheme},
month = {jul},
number = {3},
pages = {269--278},
title = {{Rapid optimization scheme for Poloidal Field design of tokamak with divertor configuration}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0920379604000110},
volume = {70},
year = {2004}
}
@article{Atanasiu2004,
author = {Atanasiu, C. V. and Günter, S. and Lackner, K. and Miron, I. G.},
doi = {10.1063/1.1756167},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {7},
pages = {3510},
title = {{Analytical solutions to the Grad–Shafranov equation}},
url = {http://link.aip.org/link/PHPAEN/v11/i7/p3510/s1{\&}Agg=doi},
volume = {11},
year = {2004}
}
@article{Dudson2009,
author = {Dudson, B.D. and Umansky, M.V. and Xu, X.Q. and Snyder, P.B. and Wilson, H.R.},
doi = {10.1016/j.cpc.2009.03.008},
issn = {00104655},
journal = {Comput. Phys. Commun.},
month = {sep},
number = {9},
pages = {1467--1480},
publisher = {Elsevier B.V.},
title = {{BOUT++: A framework for parallel plasma fluid simulations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0010465509001040},
volume = {180},
year = {2009}
}
@article{Kammerer2008,
abstract = {When performing linear gyrokinetic simulations, it is found that various types of microinstabilities, which are usually considered as strictly separated, can actually be transformed into each other via continuous variations of the plasma parameters. This behavior can be explained in terms of so-called exceptional points, which have their origin in the non-Hermiticity of the linear gyrokinetic operator and also occur in many other branches of physics. As a consequence, in large regions of parameter space, the designation of unstable modes should be done very carefully or even be avoided altogether.},
author = {Kammerer, M. and Merz, F. and Jenko, F.},
doi = {10.1063/1.2909618},
issn = {1070-664X},
journal = {Phys. Plasmas},
month = {may},
number = {5},
pages = {052102},
title = {{Exceptional points in linear gyrokinetics}},
url = {http://aip.scitation.org/doi/10.1063/1.2909618},
volume = {15},
year = {2008}
}
@article{Beer1995a,
author = {Beer, M A and Cowley, S C and Hammett, G W},
doi = {10.1063/1.871232},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Beer, Cowley, Hammett - 1995 - Field-aligned coordinates for nonlinear simulations of tokamak turbulence.pdf:pdf},
journal = {Cit. Phys. Plasmas},
title = {{Field-aligned coordinates for nonlinear simulations of tokamak turbulence}},
url = {http://dx.doi.org/10.1063/1.871232 http://aip.scitation.org/toc/php/2/7},
volume = {2},
year = {1995}
}
@article{Braginskii1965,
abstract = {Self-consistent equations for intrinsic rotation in tokamaks with small poloidal magnetic field {\$}B{\_}p{\$} compared to the total magnetic field {\$}B{\$} are derived. The model gives the momentum redistribution due to turbulence, collisional transport and energy injection. Intrinsic rotation is determined by the balance between the momentum redistribution and the turbulent diffusion and convection. Two different turbulence regimes are considered: turbulence with characteristic perpendicular lengths of the order of the ion gyroradius, {\$}\backslashrho{\_}i{\$}, and turbulence with characteristic lengths of the order of the poloidal gyroradius, {\$}(B/B{\_}p) \backslashrho{\_}i{\$}. Intrinsic rotation driven by gyroradius scale turbulence is mainly due to the effect of neoclassical corrections and of finite orbit widths on turbulent momentum transport, whereas for the intrinsic rotation driven by poloidal gyroradius scale turbulence, the slow variation of turbulence characteristics in the radial and poloidal directions and the turbulent particle acceleration can be become as important as the neoclassical and finite orbit width effects. The magnetic drift is shown to be indispensable for the intrinsic rotation driven by the slow variation of turbulence characteristics and the turbulent particle acceleration. The equations are written in a form easily implementable in a flux tube code, and the effect of the radial variation of the turbulence is included without having to resort to a global gyrokinetic formalism.},
archivePrefix = {arXiv},
arxivId = {1407.1286},
author = {Ida, K. and Rice, J.E. and Peeters, A.G. and Angioni, C. and Bortolon, A. and Camenen, Y. and Casson, F.J. J. and Duval, B. and Fiederspiel, L. and Hornsby, W.a. and Idomura, Yasuhiro and Hein, T. and Kluy, N. and Mantica, P. and Parra, Felix I F.I. and a.P. Snodin and Szepesi, Gabor and Strintzi, D. and Tala, Tuomas and Tardini, G. and de Vries, P. C. and Weiland, J. and Barnes, Michael and Casson, F.J. J. and Barnes, Michael and Parra, Felix I F.I. and Braginskii, S. I. and Callen, J.D. and a.J. Cole and Hegna, C.C.},
doi = {10.1088/0029-5515/49/8/085021},
eprint = {1407.1286},
isbn = {0029-5515$\backslash$n1741-4326},
issn = {0029-5515},
journal = {Nucl. Fusion},
keywords = {QC Physics,TK Electrical engineering. Electronics Nuclear eng,gyrokinetics,in colour only in,intrinsic torque,non-diffusive momentum transport,residual stress,reynolds stress,rotation,some figures may appear,spontaneous rotation,the online journal,tokamak,turbulence},
number = {4},
pages = {045001},
title = {{Turbulent transport in rotating tokamak plasmas}},
url = {http://webcat.warwick.ac.uk/record=b2521720{~}S15 http://arxiv.org/abs/1407.1286 http://dx.doi.org/10.1088/0029-5515/51/9/094027{\%}5Cnhttp://stacks.iop.org/0029-5515/51/i=9/a=094027?key=crossref.6b7a20b81ecf225fc48a5b4e8cfb0324 http://stacks.iop.org/0029-5515/5},
volume = {045002},
year = {2014}
}
@article{Martin2005a,
author = {Martín, P. and Castro, E. and Haines, M. G.},
doi = {10.1063/1.2080587},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {10},
pages = {102505},
title = {{Conserved functions and extended Grad–Shafranov equation for low vorticity viscous plasmas with nonlinear flows}},
url = {http://link.aip.org/link/PHPAEN/v12/i10/p102505/s1{\&}Agg=doi},
volume = {12},
year = {2005}
}
@article{Rice2012,
abstract = {Ohmic energy confinement saturation is found to be closely related to core toroidal rotation reversals in Alcator C-Mod tokamakplasmas. Rotation reversals occur at a critical density, depending on the plasma current and toroidalmagnetic field, which coincides with the density separating the linear Ohmic confinement regime from the saturated Ohmic confinement regime. The rotation is directed co-current at low density and abruptly changes direction to counter-current when the energy confinement saturates as the density is increased. Since there is a bifurcation in the direction of the rotation at this critical density, toroidal rotation reversal is a very sensitive indicator in the determination of the regime change. The reversal and confinement saturation results can be unified, since these processes occur in a particular range of the collisionality.},
author = {Rice, J. E. and Greenwald, M. J. and Podpaly, Y. A. and Reinke, M. L. and Diamond, P. H. and Hughes, J. W. and Howard, N. T. and Ma, Y. and Cziegler, I. and Duval, B. P. and Ennever, P. C. and Ernst, D. and Fiore, C. L. and Gao, C. and Irby, J. H. and Marmar, E. S. and Porkolab, M. and Tsujii, N. and Wolfe, S. M.},
doi = {10.1063/1.3695213},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
title = {{Ohmic energy confinement saturation and core toroidal rotation reversal in Alcator C-Mod plasmas}},
volume = {19},
year = {2012}
}
@article{Parra2008a,
abstract = {We present a new recursive procedure to find a full f electrostatic gyrokinetic equation correct to first order in an expansion of gyroradius over magnetic field characteristic length. The procedure provides new insights into the limitations of the gyrokinetic quasineutrality equation. We find that the ion distribution function must be known at least to second order in gyroradius over characteristic length to calculate the long wavelength components of the electrostatic potential self-consistently. Moreover, using the example of a steady-state $\theta$-pinch, we prove that the quasineutrality equation fails to provide the axisymmetric piece of the potential even with a distribution function correct to second order. We also show that second order accuracy is enough if a more convenient moment equation is used instead of the quasineutrality equation. These results indicate that the gyrokinetic quasineutrality equation is not the most effective procedure to find the electrostatic potential if the long wavelength components are to be retained in the analysis.},
author = {Parra, Felix I. and Catto, Peter J.},
doi = {10.1088/0741-3335/50/6/065014},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Parra, Catto - 2008 - Limitations of gyrokinetics on transport time scales.pdf:pdf},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
month = {jun},
number = {6},
pages = {065014},
title = {{Limitations of gyrokinetics on transport time scales}},
url = {http://stacks.iop.org/0741-3335/50/i=6/a=065014?key=crossref.7023dfe4f622df6a2fa56874e69889d7},
volume = {50},
year = {2008}
}
@article{Solano2003,
abstract = {We review criticality theory as a prelude to consideration of criticality of the Grad-Shafranov equation. Novel criticality conditions of ODEs and PDEs are derived, easily evaluated. The possibility that transport barriers are associated with characteristics of the equilibrium equation is explored. We conjecture that equilibrium criticality permits the appearance of new solution branches: the high confinement branch has high poloidal flux gradient in a diamagnetic region of the plasma. Similarly, criticality may lead to loss of solution, which could be related to MHD instability and/or island formation},
archivePrefix = {arXiv},
arxivId = {physics/0308048},
author = {Solano, Emilia R},
doi = {10.1088/0741-3335/46/3/L02},
eprint = {0308048},
journal = {Plasma Phys. Control. Fusion},
pages = {6},
primaryClass = {physics},
title = {{Criticality of the Grad-Shafranov equation: transport barriers and fragile equilibria}},
volume = {46},
year = {2003}
}
@article{Ham2016,
author = {Ham, C. J. and Cowley, S. C. and Brochard, G. and Wilson, H. R.},
doi = {10.1103/PhysRevLett.116.235001},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Ham et al. - 2016 - Nonlinear Stability and Saturation of Ballooning Modes in Tokamaks.pdf:pdf},
issn = {10797114},
journal = {Phys. Rev. Lett.},
number = {23},
pages = {1--5},
title = {{Nonlinear Stability and Saturation of Ballooning Modes in Tokamaks}},
volume = {116},
year = {2016}
}
@article{Xi2013,
author = {Xi, P.W. and Xu, X.Q. and Xia, T.Y. and Nevins, W.M. and Kim, S.S.},
doi = {10.1088/0029-5515/53/11/113020},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {nov},
number = {11},
pages = {113020},
title = {{Impact of a large density gradient on linear and nonlinear edge-localized mode simulations}},
url = {http://stacks.iop.org/0029-5515/53/i=11/a=113020?key=crossref.a464f1835211e3400747b7ffe7f30d37},
volume = {53},
year = {2013}
}
@article{Feng1995,
author = {Feng, Y. and Wolle, B. and H{\"{u}}bner, K.},
doi = {10.1016/0010-4655(95)00013-6},
issn = {00104655},
journal = {Comput. Phys. Commun.},
month = {aug},
number = {2-3},
pages = {161--172},
title = {{New, simplified technique for calculating particle source rates due to neutral beam injection into tokamaks}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0010465595000136},
volume = {88},
year = {1995}
}
@article{Wang2012,
author = {Wang, E. and Xu, X. and Candy, J. and Groebner, R.J. and Snyder, P.B. and Chen, Y. and Parker, S.E. and Wan, W. and Lu, Gaimin and Dong, J.Q.},
doi = {10.1088/0029-5515/52/10/103015},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {oct},
number = {10},
pages = {103015},
title = {{Linear gyrokinetic analysis of a DIII-D H-mode pedestal near the ideal ballooning threshold}},
url = {http://stacks.iop.org/0029-5515/52/i=10/a=103015?key=crossref.876026a4473cf8363464122952671a52},
volume = {52},
year = {2012}
}
@article{Barnes2010,
abstract = {Many plasmas of interest to the astrophysical and fusion communities are weakly collisional. In such plasmas, small scales can develop in the distribution of particle velocities, potentially affecting observable quantities such as turbulent fluxes. Consequently, it is necessary to monitor velocity space resolution in gyrokinetic simulations. In this paper, we present a set of computationally efficient diagnostics for measuring velocity space resolution in gyrokinetic simulations and apply them to a range of plasma physics phenomena using the continuum gyrokinetic code GS2. For the cases considered here, it is found that the use of a collisionality at or below experimental values allows for the resolution of plasma dynamics with relatively few velocity space grid points. Additionally, we describe the implementation of an adaptive collision frequency, which can be used to improve velocity space resolution in the collisionless regime, where results are expected to be independent of collision frequency.},
archivePrefix = {arXiv},
arxivId = {0907.4413},
author = {Barnes, M. and Dorland, W. and Tatsuno, T.},
doi = {10.1063/1.3313348},
eprint = {0907.4413},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Barnes, Dorland, Tatsuno - 2010 - Resolving velocity space dynamics in continuum gyrokinetics.pdf:pdf},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {3},
pages = {1--13},
title = {{Resolving velocity space dynamics in continuum gyrokinetics}},
volume = {17},
year = {2010}
}
@article{Lao1981a,
abstract = {A variational method is developed to find approximate solutions to the Grad-Shafranov equaiton. The surfaces of the constant poloidal magnetic flux $\backslash$psi(R,Z) are obtained by solving a few ordinary differential equations, which are moments of the Grad-Shafranov equaiton, for the Fourier amplitudes of the inverse mapping R($\backslash$psi, $\backslash$theta) and Z($\backslash$psi, $\backslash$theta). Analytic properties and solutions of the moment equations are considered. Specific calculations using the Impurity Study Experiment (ISX-B) and the Engineering Test Facility (ETF)/International Tokamak Reactor (INTOR) geometries are performed numerically, and the results agree well with those calculated using standared two-dimensional equilibrium codes. The main advantage of the variational moment method is that it significantly reduces the computational time required to determine two-dimensional equilibria without sacrificing accuracy.},
author = {Lao, L. L. and Hirshman, S. P. and Wieland, R. M.},
doi = {10.1063/1.863562},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Lao, Hirshman, Wieland - 1981 - Variational Moment Solutions to the Grad-Shafranov Equation.pdf:pdf},
issn = {1070-6631},
journal = {Phys. Fluids},
number = {1981},
pages = {1431--1441},
title = {{Variational Moment Solutions to the Grad-Shafranov Equation}},
volume = {24},
year = {1981}
}
@book{Ruizhik1965,
abstract = {7th ed. Previous edition: 2000. The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom. - Fully searchable CD that puts information at your fingertips included with text - Most up to date listing of integrals, series and products - Provides accuracy and efficiency in work.},
archivePrefix = {arXiv},
arxivId = {arXiv:1011.1669v3},
author = {Ruizhik, Iosif Moiseevich and Geronimus, Yu V and Tseytlin, M Yu and Jeffrey, Alan},
booktitle = {Book},
doi = {10.1017/CBO9781107415324.004},
eprint = {arXiv:1011.1669v3},
isbn = {0080471110},
issn = {1098-6596},
pages = {1086},
pmid = {25246403},
title = {{Table of integrals, series, and products}},
year = {1965}
}
@article{Schekochihin2008,
abstract = {This paper describes a conceptual framework for understanding kinetic plasma turbulence as a generalized form of energy cascade in phase space. It is emphasized that conversion of turbulent energy into thermodynamic heat is only achievable in the presence of some (however small) degree of collisionality. The smallness of the collision rate is compensated for by the emergence of a small-scale structure in the velocity space. For gyrokinetic turbulence, a nonlinear perpendicular phase-mixing mechanism is identified and described as a turbulent cascade of entropyfluctuations simultaneously occurring at spatial scales smaller than the ion gyroscale and in velocity space. Scaling relations for the resulting fluctuation spectra are derived. An estimate for the collisional cutoff is provided. The importance of adequately modelling and resolving collisions in gyrokinetic simulations is briefly discussed, as well as the relevance of these results to understanding the dissipation-range turbulence in the solar wind and the electrostatic microturbulence in fusion plasmas.},
author = {Schekochihin, A. A. and Cowley, S. C. and Dorland, W. and Hammett, G. W. and Howes, G. G. and Plunk, G. G. and Quataert, E. and Tatsuno, T.},
doi = {10.1088/0741-3335/50/12/124024},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Schekochihin et al. - 2008 - Gyrokinetic turbulence A nonlinear route to dissipation through phase space.pdf:pdf},
journal = {Plasma Phys. Control. Fusion},
title = {{Gyrokinetic turbulence: A nonlinear route to dissipation through phase space}},
url = {http://www.mendeley.com/research/gyrokinetic-turbulence-nonlinear-route-dissipation-through-phase-space},
year = {2008}
}
@article{Yan2010,
abstract = {An azimuthally symmetric radially sheared azimuthal flow is driven by a nondiffusive, or residual, turbulent stress localized to a narrow annular region at the boundary of a cylindrical magnetized helicon plasma device. A no-slip condition, imposed by ion-neutral flow damping outside the annular region, combined with a diffusive stress arising from turbulent and collisional viscous damping in the central plasma region, leads to net plasma rotation in the absence of momentum input.},
author = {Yan, Z. and Xu, M. and Diamond, P. H. and Holland, C. and M{\"{u}}ller, S. H. and Tynan, G. R. and Yu, J. H.},
doi = {10.1103/PhysRevLett.104.065002},
isbn = {0031-9007},
issn = {00319007},
journal = {Phys. Rev. Lett.},
number = {6},
pages = {10--13},
pmid = {20366825},
title = {{Intrinsic rotation from a residual stress at the boundary of a cylindrical laboratory plasma}},
volume = {104},
year = {2010}
}
@article{Landreman2014,
abstract = {In this work, we examine the validity of several common simplifying assumptions used in numerical neoclassical calculations for nonaxisymmetric plasmas, both by using a new continuum drift-kinetic code and by considering analytic properties of the kinetic equation. First, neoclassical phenomena are computed for the LHD and W7-X stellarators using several versions of the drift-kinetic equation, including the commonly used incompressible-E × B-drift approximation and two other variants, corresponding to different effective particle trajectories. It is found that for electric fields below roughly one third of the resonant value, the different formulations give nearly identical results, demonstrating the incompressible E × B-drift approximation is quite accurate in this regime. However, near the electric field resonance, the models yield substantially different results. We also compare results for various collision operators, including the full linearized Fokker-Planck operator. At low collisionality, the radial transport driven by radial gradients is nearly identical for the different operators; while in other cases, it is found to be important that collisions conserve momentum.},
archivePrefix = {arXiv},
arxivId = {arXiv:1312.6058v3},
author = {Landreman, M. and Smith, H. M. and Moll{\'{e}}n, A. and Helander, P.},
doi = {10.1063/1.4870077},
eprint = {arXiv:1312.6058v3},
issn = {1070664X},
journal = {Phys. Plasmas},
title = {{Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas}},
year = {2014}
}
@article{Candy2011,
abstract = {()},
author = {Candy, J},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Candy - 2011 - GYRO Technical Guide.pdf:pdf},
pages = {1--73},
title = {{GYRO Technical Guide}},
url = {papers://31a1b09a-25a9-4e20-879d-491c4732424b/Paper/p2322},
year = {2011}
}
@article{Bateman1986a,
author = {Bateman, Glenn and Morris, R. N.},
doi = {10.1063/1.865929},
issn = {00319171},
journal = {Phys. Fluids},
number = {3},
pages = {753},
title = {{Saturated tearing modes in toroidal geometry}},
url = {http://link.aip.org/link/PFLDAS/v29/i3/p753/s1{\&}Agg=doi},
volume = {29},
year = {1986}
}
@book{Reif,
author = {Reif, Frederick},
title = {{Fundamentals of Statistical And Thermal Physics}}
}
@article{Plunk2014,
abstract = {We investigate the linear theory of the ion-temperature-gradient (ITG) mode, with the goal of developing a general understanding that may be applied to stellarators. We highlight the Wendelstein 7X (W7-X) device. Simple fluid and kinetic models that follow closely from existing literature are reviewed and two new first-principle models are presented and compared with results from direct numerical simulation. One model investigates the effect of regions of strong localized shear, which are generic to stellarator equilibria. These “shear spikes” are found to have a potentially significant stabilizing affect on the mode; however, the effect is strongest at short wavelengths perpendicular to the magnetic field, and it is found to be significant only for the fastest growing modes in W7-X. A second model investigates the long-wavelength limit for the case of negligible global magnetic shear. The analytic calculation reveals that the effect of the curvature drive enters at second order in the drift frequency, confirming conventional wisdom that the ITG mode is slab-like at long wavelengths. Using flux tube simulations of a zero-shear W7-X configuration, we observe a close relationship to an axisymmetric configuration at a similar parameter point. It is concluded that scale lengths of the equilibrium gradients constitute a good parameter space to characterize the ITG mode. Thus, to optimize the magnetic geometry for ITG mode stability, it may be fruitful to focus on local parameters, such as the magnitude of bad curvature, connection length, and local shear at locations of bad curvature (where the ITG mode amplitude peaks).},
archivePrefix = {arXiv},
arxivId = {arXiv:1312.2424v2},
author = {Plunk, G. G. and Helander, P. and Xanthopoulos, P. and Connor, J. W.},
doi = {10.1063/1.4868412},
eprint = {arXiv:1312.2424v2},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Plunk et al. - 2014 - Collisionless microinstabilities in stellarators. III. The ion-temperature-gradient mode.pdf:pdf},
issn = {1070-664X},
journal = {Phys. Plasmas},
month = {mar},
number = {3},
pages = {032112},
title = {{Collisionless microinstabilities in stellarators. III. The ion-temperature-gradient mode}},
url = {http://aip.scitation.org/doi/10.1063/1.4868412},
volume = {21},
year = {2014}
}
@article{Mostl2009,
abstract = {We present results on the geometry of a magnetic cloud (MC) on 23 May 2007 from a comprehensive analysis of Wind and STEREO observations. We first apply a Grad - Shafranov reconstruction to the STEREO-A plasma and magnetic field data, delivered by the PLASTIC and IMPACT instruments. We then optimize the resulting field map with the aid of observations by Wind, which were made at the very outer boundary of the cloud, at a spacecraft angular separation of 6. For the correct choice of reconstruction parameters such as axis orientation, interval and grid size, we find both a very good match between the predicted magnetic field at the position of Wind and the actual observations as well as consistent timing. We argue that the reconstruction captures almost the full extent of the cross-section of the cloud. The resulting shape transverse to the invariant axis consists of distorted ellipses and is slightly flattened in the direction of motion. The MC axis is inclined at 58 to the ecliptic with an axial field strength of 12 nT. We derive integrated axial fluxes and currents with increased precision, which we contrast with the results from linear force-free fitting. The helical geometry of the MC with almost constant twist (1.5 turns AU1) is not consistent with the linear force-free Lundquist model. We also find that the cloud is non-force-free J J {\textgreater}0.3) in about a quarter of the cloud cross sectional area, particularly in the back part which is interacting with the trailing high speed stream. Based on the optimized reconstruction we put forward preliminary guidelines for the improved use of single-spacecraft Grad - Shafranov reconstruction. The results also give us the opportunity to compare the CME direction inferred from STEREO/SECCHI observations by Mierla et al. Solar Phys. 252, 385, {\textless}CitationRef with the three-dimensional configuration of the MC at 1 AU. This yields an almost radial CME propagation from the Sun to the Earth.},
author = {M{\"{o}}stl, C and Farrugia, C J and Biernat, H K and Leitner, M and Kilpua, E K J and Galvin, A B and Luhmann, J G},
doi = {10.1007/s11207-009-9360-7},
issn = {00380938},
journal = {Sol. Phys.},
pages = {427--441},
title = {{Optimized Grad – Shafranov Reconstruction of a Magnetic Cloud Using STEREO-Wind Observations}},
volume = {256},
year = {2009}
}
@article{Highcock2012,
abstract = {The transport of heat that results from turbulence is a major factor limiting the temperature gradient, and thus the performance, of fusion devices. We use nonlinear simulations to show that a toroidal equilibrium scale sheared flow can completely suppress the turbulence across a wide range of flow gradient and temperature gradient values. We demonstrate the existence of a bifurcation across this range whereby the plasma may transition from a low flow gradient and tem- perature gradient state to a higher flow gradient and temperature gradient state. We show further that the maximum temperature gradient that can be reached by such a transition is limited by the existence, at high flow gradient, of subcritical turbulence driven by the parallel velocity gradient (PVG). We use linear simulations and analytic calculations to examine the properties of the transiently growing modes which give rise to this subcritical turbulence, and conclude that there may be a critical value of the ratio of the PVG to the suppressing perpendicular gradient of the velocity (in a tokamak this ratio is equal to q/ǫ where q is the magnetic safety factor and ǫ the inverse aspect ra- tio) below which the PVG is unable to drive subcritical turbulence. In light of this, we use nonlinear simulations to calculate, as a function of three parameters (the perpendicular flow shear, q/ǫ and the tempera- ture gradient), the surface within that parameter space which divides the regions where turbulence can and cannot be sustained: the zero- turbulence manifold. We are unable to conclude that there is in fact a critical value of q/ǫ below which PVG-driven turbulence is eliminated. Nevertheless, we demonstrate that at low values of q/ǫ, the maximum critical temperature gradient that can be reached without generating turbulence (and thus, we infer, the maximum temperature gradient that could be reached in the transport bifurcation) is dramatically in- creased. Thus, we anticipate that a fusion device for which, across a significant portion of the minor radius, the magnetic shear is low, the ratio q/ǫ is low and the toroidal flow shear is strong, will achieve high levels of energy confinement and thus high performance.},
archivePrefix = {arXiv},
arxivId = {arXiv:1207.4419v1},
author = {Highcock, Eg},
eprint = {arXiv:1207.4419v1},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Highcock - 2012 - The Zero Turbulence Manifold in Fusion Plasmas.pdf:pdf},
journal = {arXiv Prepr. arXiv1207.4419},
number = {April},
title = {{The Zero Turbulence Manifold in Fusion Plasmas}},
url = {http://arxiv.org/abs/1207.4419},
year = {2012}
}
@article{Gourdain2006,
author = {Gourdain, P.-a. and Leboeuf, J.-N. and Neches, R.Y.},
doi = {10.1016/j.jcp.2005.12.005},
issn = {00219991},
journal = {J. Comput. Phys.},
keywords = {beta,equilibrium,high,magnetohydrodynamics,multigrid,plasma,shafranov,tokamak,unity},
month = {jul},
number = {1},
pages = {275--299},
title = {{High-resolution magnetohydrodynamic equilibrium code for unity beta plasmas}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999105005528},
volume = {216},
year = {2006}
}
@article{Snyder2005,
author = {Snyder, P. B. and Wilson, H. R. and Xu, X. Q.},
doi = {10.1063/1.1873792},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {056115},
title = {{Progress in the peeling-ballooning model of edge localized modes: Numerical studies of nonlinear dynamics}},
url = {http://link.aip.org/link/PHPAEN/v12/i5/p056115/s1{\&}Agg=doi},
volume = {12},
year = {2005}
}
@article{McDevitt2009a,
abstract = {Starting from a phase space conserving gyrokinetic formulation, a systematic derivation of parallel momentum conservation uncovers a novel mechanism by which microturbulence may drive intrinsic rotation. This mechanism, which appears in the gyrokinetic formulation through the parallel nonlinearity, emerges due to charge separation induced by the polarization drift. The derivation and physical discussion of this mechanism will be pursued throughout this Letter.},
author = {McDevitt, C. J. and Diamond, P. H. and G{\"{u}}rcan, {\"{O}} D. and Hahm, T. S.},
doi = {10.1103/PhysRevLett.103.205003},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/McDevitt et al. - 2009 - Toroidal rotation driven by the polarization drift.pdf:pdf},
isbn = {0031-9007},
issn = {00319007},
journal = {Phys. Rev. Lett.},
number = {20},
pages = {1--4},
pmid = {20365987},
title = {{Toroidal rotation driven by the polarization drift}},
volume = {103},
year = {2009}
}
@book{LANDAU,
author = {LANDAU, L. D. and LIFSHITZ, E. M.},
title = {{Statistical Physics}}
}
@article{Camenen2010,
abstract = {A new mechanism has recently been proposed that generates a radial flux of parallel momentum in toroidal plasmas. Namely, by considering up-down asymmetric flux surfaces, the symmetry following the magnetic field can be broken and an additional contribution to the turbulent momentum flux arises, potentially changing the intrinsic rotation profile. These predictions are tested with specific experiments on TCV. The intrinsic toroidal rotation is observed to change by roughly a factor of two when changing the up-down asymmetry of the plasma. More precisely, the toroidal rotation gradient changes in the outer part of the plasma, where the flux surface asymmetry is the highest. The experiments were performed for all combinations of the toroidal magnetic field and plasma current directions, that affect the sign of the predicted up-down asymmetry flux. In each case the variation of the intrinsic rotation profile with the up-down asymmetry is observed in the direction predicted by the theory.},
author = {Camenen, Y. and Bortolon, A. and Duval, B. P. and Federspiel, L. and Peeters, A. G. and Casson, F. J. and Hornsby, W. A. and Karpushov, A. N. and Piras, F. and Sauter, O. and Snodin, A. P. and Szepesi, G. and Team, the TCV},
doi = {10.1088/0741-3335/52/12/124037},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Camenen et al. - 2010 - Experimental demonstration of an up-down asymmetry effect on intrinsic rotation in the TCV tokamak.pdf:pdf},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
number = {12},
pages = {124037},
title = {{Experimental demonstration of an up-down asymmetry effect on intrinsic rotation in the TCV tokamak}},
url = {http://iopscience.iop.org/0741-3335/52/12/124037{\%}5Cnhttp://iopscience.iop.org/0741-3335/52/12/124037/{\%}5Cnhttp://iopscience.iop.org/0741-3335/52/12/124037/pdf/0741-3335{\_}52{\_}12{\_}124037.pdf},
volume = {52},
year = {2010}
}
@article{Barnes2012,
abstract = {Scaling laws for the transport and heating of trace heavy ions in low-frequency, magnetized plasma turbulence are derived and compared with direct numerical simulations. The predicted dependences of turbulent fluxes and heating on ion charge and mass number are found to agree with numerical results for both stationary and differentially rotating plasmas. Heavy ion momentum transport is found to increase with mass, and heavy ions are found to be preferentially heated, implying a mass-dependent ion temperature for very weakly collisional plasmas and for partially-ionized heavy ions in strongly rotating plasmas.},
archivePrefix = {arXiv},
arxivId = {1207.5175},
author = {Barnes, M. and Parra, F. I. and Dorland, W.},
doi = {10.1103/PhysRevLett.109.185003},
eprint = {1207.5175},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Barnes, Parra, Dorland - 2012 - Turbulent transport and heating of trace heavy ions in hot magnetized plasmas.pdf:pdf},
issn = {00319007},
journal = {Phys. Rev. Lett.},
number = {18},
pages = {1--5},
title = {{Turbulent transport and heating of trace heavy ions in hot magnetized plasmas}},
volume = {109},
year = {2012}
}
@inproceedings{DeGrassie2007,
abstract = {In the absence of any auxiliary torque input, the DIII-D plasma consists of nonzero toroidal angular momentum, in other words, it rotates. This effect is commonly observed in tokamaks, being referred to as intrinsic rotation. Measurements of intrinsic rotation profiles have been made in DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)] H-mode discharges, with both Ohmic heating (OH) and electron cyclotron heating (ECH) in which there is no auxiliary torque. Recently, the H-mode data set has been extended with the newly configured DIII-D simultaneous co- and counter-directed neutral beam injection (NBI) capability resulting in control of the local torque deposition, where co and counter refer to the direction relative to the toroidal plasma current. Understanding intrinsic rotation is important for projection toward burning plasma performance where any NBI torque will be relatively small. The toroidal velocity is recognizably important regarding issues of stability and confinement. In DIII-D ECH H-modes the rotation profile is hollow, co-directed at large minor radius and depressed, or actually counter-directed, nearer the magnetic axis. This profile varies with the ECH power deposition profile to some extent. In contrast, OH H-modes have a relatively flat co-directed rotation profile. There is a scaling of the DIII-D intrinsic toroidal velocity with W/I-p, as seen in intrinsic rotation in Alcator C-Mod [J. Rice, Nucl. Fusion 39, 1175 (1999)], where W is the total plasma thermal energy and I-p is the magnitude of the toroidal plasma current. This common scaling resulted in a dimensionless similarity experiment between DIII-D and Alcator C-Mod on intrinsic rotation, obtaining a single spatial point match in the toroidal velocity normalized to the ion thermal velocity. The balanced NBI capability in DIII-D is a useful tool to push scaling studies to higher values of the plasma normalized energy, notwithstanding the details of torque deposition for co-NBI versus counter-NBI. There are theories which address intrinsic rotation, both extensions of neoclassical theory and related to turbulent transport. At this time, the comparisons with theory are qualitative. (C) 2007 American Institute of Physics.},
author = {DeGrassie, J. S. and Rice, J. E. and Burrell, K. H. and Groebner, R. J. and Solomon, W. M.},
booktitle = {Phys. Plasmas},
doi = {10.1063/1.2539055},
issn = {1070664X},
number = {5},
title = {{Intrinsic rotation in DIII-D}},
volume = {14},
year = {2007}
}
@book{Dhaeseleer1991,
abstract = {2nd rev. ed. Examples of stiff equations -- Stability analysis for explicit RK methods -- Stability function of implicit RK-methods -- Order stars -- Construction of implicit Runge-Kutta methods -- Diagonally implicit RK methods -- Rosenbrock-type methods -- Implementation of implicit Runge-Kutta methods -- Extrapolation methods -- Numerical experiments -- Contractivity for linear problems -- B-stability and Contractivity -- Positive quadrature formulas and B-stable RK-methods -- Existence and uniqueness of IRK solutions -- B-convergence -- Stability of multistep methods -- "Nearly" A-stable multistep methods -- Generalized multistep methods -- Order stars on Riemann surfaces -- Experiments with multistep codes -- One-leg methods and G-stability -- Convergence for linear problems -- Convergence for nonlinear problems -- Algebraic stability of general linear methods -- Solving index 1 problems -- Multistep methods -- Epsilon expansions for exact and RK solutions -- Rosenbrock methods -- Extrapolation methods -- Quasilinear problems -- The index and various examples -- Index reduction methods -- Multistep methods for index 2 DAE -- Runge-Kutta methods for index 2 DAE -- Order conditions for index 2 DAE -- Half-explicit methods for index 2 systems -- Computation of multibody mechanisms -- Symplectic methods for constrained Hamiltonian systems.},
author = {D'haeseleer, William Denis and Hitchon, William Nicholas Guy and Callen, James D. and Shohet, J. Leon},
doi = {10.1007/978-3-642-75595-8},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/D'haeseleer et al. - 1991 - Flux Coordinates and Magnetic Field Structure.pdf:pdf},
isbn = {978-3-642-75597-2},
issn = {00104655},
title = {{Flux Coordinates and Magnetic Field Structure}},
url = {http://link.springer.com/10.1007/978-3-642-75595-8},
year = {1991}
}
@article{Finkelstein2002,
abstract = {This chapter discusses the structure of proteins molecule. The “living conditions”, structure-stabilizing interactions and overall architecture of proteins provide the basis for classifying proteins as (1) fibrous proteins, (2) membrane proteins and (3) water-soluble globular proteins. The function of fibrous proteins is mostly structural. They form microfilaments and microtubules, as well as fibrils, hair, silk and other shielding textures; they reinforce membranes and maintain the structure of cells and tissues. Fibrous proteins are often very large. Fibrous proteins often form enormous aggregates; their spatial structure is mostly highly regular, which iscomposed of huge secondary-structure blocks, and reinforced by interactions among adjacent polypeptide chains. The primary structure of fibrous proteins is also characterized by high regularity and periodicity, which ensures the formation of vast regular secondary structures. Some typical representatives of fibrous proteins are $\beta$-structural proteins like silk fibroin, $\alpha$-structural fibrous proteins, and collagen. The chapter explains how the helices associate. Fibrous proteins are often structurally simple owing to the periodicity of their primary structure and secondary structure as well.},
author = {Finkelstein, Alexei V. and Ptitsyn, Oleg B. and Finkelstein, Alexei V. and Ptitsyn, Oleg B.},
doi = {10.1016/B978-012256781-0/50013-5},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Finkelstein et al. - 2002 - – Lecture 11.pdf:pdf},
isbn = {9780122567810},
journal = {Protein Phys.},
pages = {127--134},
title = {{– Lecture 11}},
year = {2002}
}
@article{Wang2010,
author = {Wang, W X and Ethier, S and Klasky, S and Adams, M and Hahm, T S and Rewoldt, G and Lee, W W and Tang, W M and Diamond, P H},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Wang et al. - 2010 - Non-Diffusive Momentum Transport and Intrinsic Rotation in Tokamaks.pdf:pdf},
keywords = {-diffusive momentum transport and,intrinsic rotation in},
title = {{Non-Diffusive Momentum Transport and Intrinsic Rotation in Tokamaks}},
year = {2010}
}
@article{Asif2011,
author = {Asif, Muhammad},
doi = {10.4236/jmp.2011.21002},
issn = {2153-1196},
journal = {J. Mod. Phys.},
keywords = {plasma internal energy,toroidal elliptic plasmas},
number = {01},
pages = {5--7},
title = {{Plasma Internal Energy for Toroidal Elliptic Plasmas with Triangularity}},
url = {http://www.scirp.org/journal/PaperDownload.aspx?DOI=10.4236/jmp.2011.21002},
volume = {02},
year = {2011}
}
@article{Peeters2011,
abstract = {Toroidal momentum transport mechanisms are reviewed and put in a broader perspective. The generation of a finite momentum flux is closely related to the breaking of symmetry (parity) along the field. The symmetry argument allows for the systematic identification of possible transport mechanisms. Those that appear to lowest order in the normalized Larmor radius (the diagonal part, Coriolis pinch, E x B shearing, particle flux, and up-down asymmetric equilibria) are reasonably well understood. At higher order, expected to be of importance in the plasma edge, the theory is still under development.},
author = {Peeters, A.G. and Angioni, C. and Bortolon, A. and Camenen, Y. and Casson, F.J. and Duval, B. and Fiederspiel, L. and Hornsby, W.a. and Idomura, Yasuhiro and Hein, T. and Kluy, N. and Mantica, P. and Parra, F.I. and a.P. Snodin and Szepesi, Gabor and Strintzi, D. and Tala, Tuomas and Tardini, G. and de Vries, P. C. and Weiland, J.},
doi = {10.1088/0029-5515/51/9/094027},
isbn = {0029-5515$\backslash$n1741-4326},
issn = {0029-5515},
journal = {Nucl. Fusion},
keywords = {QC Physics,TK Electrical engineering. Electronics Nuclear eng},
number = {9},
pages = {094027},
title = {{Overview of toroidal momentum transport}},
url = {http://dx.doi.org/10.1088/0029-5515/51/9/094027{\%}5Cnhttp://stacks.iop.org/0029-5515/51/i=9/a=094027?key=crossref.6b7a20b81ecf225fc48a5b4e8cfb0324},
volume = {51},
year = {2011}
}
@article{0741-3335-54-7-074006,
abstract = {Understanding the origin of rotation in ion cyclotron resonance frequency (ICRF) heated plasmas is important for predictions for burning plasmas sustained by alpha particles, being characterized by a large population of fast ions and no external momentum input. The angular velocity of the plasma column has been measured in JET H-mode plasmas with pure ICRF heating both for the standard low toroidal magnetic ripple configuration, of about ∼0.08{\%} and, for increased ripple values up to 1.5{\%} (Nave et al 2010 Phys. Rev. Lett. 105 [http://dx.doi.org/10.1103/PhysRevLett.105.105005] 105005 ). These new JET rotation data were compared with the multi-machine scaling of Rice et al (2007 Nucl. Fusion 47 [http://dx.doi.org/10.1088/0029-5515/47/11/025] 1618 ) for the Alfv{\'{e}}n–Mach number and with the scaling for the velocity change from L-mode into H-mode. The JET data do not fit well any of these scalings that were derived for plasmas that are co-rotating with respect to the plasma current. With the standard low ripple configuration, JET plasmas with large ICRF heating power and normalized beta, $\beta$ N ≈ 1.3, have a very small co-current rotation, with Alfv{\'{e}}n–Mach numbers significantly below those given by the rotation scaling of Rice et al (2007 Nucl. Fusion 47 [http://dx.doi.org/10.1088/0029-5515/47/11/025] 1618 ). In some cases the plasmas are actually counter-rotating. No significant difference between the H-mode and L-mode rotation is observed. Typically the H-mode velocities near the edge are lower than those in L-modes. With ripple values larger than the standard JET value, between 1{\%} and 1.5{\%}, H-mode plasmas were obtained where both the edge and the core counter-rotated.},
author = {Nave, M F F and Eriksson, L-G and Giroud, C and Johnson, T J and Kirov, K and Mayoral, M-L and Noterdaeme, J-M and Ongena, J and Saibene, G and Sartori, R and Rimini, F and Tala, T and de Vries, P and Zastrow, K-D and Contributors, JET-EFDA},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Nave et al. - 2012 - JET intrinsic rotation studies in plasmas with a high normalized beta and varying toroidal field ripple.pdf:pdf},
journal = {Plasma Phys. Control. Fusion},
number = {7},
pages = {74006},
title = {{JET intrinsic rotation studies in plasmas with a high normalized beta and varying toroidal field ripple}},
url = {http://stacks.iop.org/0741-3335/54/i=7/a=074006},
volume = {54},
year = {2012}
}
@article{Dif-Pradalier2011,
abstract = {Treatment of binary Coulomb collisions when the full gyrokinetic distribution function is evolved is discussed here. A spectrum of different collision operators is presented, differing through both the physics that can be addressed and the numerics they are based on. Eulerian-like (semi-Lagrangian) and particle in cell (PIC) (Monte-Carlo) schemes are successfully cross-compared, and a detailed confrontation to neoclassical theory is shown. {\textcopyright} 2011 American Institute of Physics.},
author = {Dif-Pradalier, G. and Diamond, P. H. and Grandgirard, V. and Sarazin, Y. and Abiteboul, J. and Garbet, X. and Ghendrih, Ph and Latu, G. and Strugarek, A. and Ku, S. and Chang, C. S.},
doi = {10.1063/1.3592652},
issn = {1070664X},
journal = {Phys. Plasmas},
title = {{Neoclassical physics in full distribution function gyrokinetics}},
year = {2011}
}
@article{Xu2009,
author = {Xu, X.Q. and Belli, E. and Bodi, K. and Candy, J. and Chang, C.S. and Cohen, R.H. and Colella, P. and a.M. Dimits and Dorr, M.R. and Gao, Z. and Hittinger, J.a. and Ko, S. and Krasheninnikov, S. and McKee, G.R. and Nevins, W.M. and Rognlien, T.D. and Snyder, P.B. and Suh, J. and Umansky, M.V.},
doi = {10.1088/0029-5515/49/6/065023},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {jun},
number = {6},
pages = {065023},
title = {{Dynamics of kinetic geodesic-acoustic modes and the radial electric field in tokamak neoclassical plasmas}},
url = {http://stacks.iop.org/0029-5515/49/i=6/a=065023?key=crossref.6538691b1b97f7f1856a35a609a09445},
volume = {49},
year = {2009}
}
@article{Krebs2017,
abstract = {A self-regulating magnetic flux pumping mechanism in tokamaks that maintains the core safety factor at {\$}q\backslashapprox 1{\$}, thus preventing sawteeth, is analyzed in nonlinear 3D magnetohydrodynamic simulations using the M3D-C{\$}{\^{}}1{\$} code. In these simulations, the most important mechanism responsible for the flux pumping is that a saturated {\$}(m=1,n=1){\$} quasi-interchange instability generates an effective negative loop voltage in the plasma center via a dynamo effect. It is shown that sawtoothing is prevented in the simulations if {\$}\backslashbeta{\$} is sufficiently high to provide the necessary drive for the {\$}(m=1,n=1){\$} instability that generates the dynamo loop voltage. The necessary amount of dynamo loop voltage is determined by the tendency of the current density profile to centrally peak which, in our simulations, is controlled by the peakedness of the applied heat source profile.},
archivePrefix = {arXiv},
arxivId = {1706.06672},
author = {Krebs, I. and Jardin, S. C. and G{\"{u}}nter, S. and Lackner, K. and Hoelzl, M. and Strumberger, E. and Ferraro, N.},
doi = {10.1063/1.4990704},
eprint = {1706.06672},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Krebs et al. - 2017 - Magnetic flux pumping in 3D nonlinear magnetohydrodynamic simulations.pdf:pdf},
issn = {10897674},
journal = {Phys. Plasmas},
month = {oct},
number = {10},
pages = {102511},
title = {{Magnetic flux pumping in 3D nonlinear magnetohydrodynamic simulations}},
url = {http://aip.scitation.org/doi/10.1063/1.4990704},
volume = {24},
year = {2017}
}
@article{Basiuk2003,
author = {Basiuk, V and Artaud, J.F and Imbeaux, F and Litaudon, X and B coulet, A and Eriksson, L.-G and Hoang, G.T and Huysmans, G and Mazon, D and Moreau, D and Peysson, Y},
doi = {10.1088/0029-5515/43/9/305},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {sep},
number = {9},
pages = {822--830},
title = {{Simulations of steady-state scenarios for Tore Supra using the CRONOS code}},
url = {http://stacks.iop.org/0029-5515/43/i=9/a=305?key=crossref.e674eeeb2d94e114edc592193d4cf46c},
volume = {43},
year = {2003}
}
@article{Bourdelle2015,
author = {Bourdelle, C. and Citrin, J. and Baiocchi, B. and Casati, A. and Cottier, P. and Garbet, X. and Imbeaux, F.},
doi = {10.1088/0741-3335/58/1/014036},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Bourdelle et al. - 2015 - Core turbulent transport in tokamak plasmas Bridging theory and experiment with QuaLiKiz.pdf:pdf},
issn = {13616587},
journal = {Plasma Phys. Control. Fusion},
keywords = {modeling,tokamak,turbulence},
number = {1},
pages = {14036},
publisher = {IOP Publishing},
title = {{Core turbulent transport in tokamak plasmas: Bridging theory and experiment with QuaLiKiz}},
url = {http://dx.doi.org/10.1088/0741-3335/58/1/014036},
volume = {58},
year = {2015}
}
@article{Garbet2010,
abstract = {This overview is an assessment of the gyrokinetic framework and simulations to compute turbulent transport in fusion plasmas. It covers an introduction to the gyrokinetic theory, the principal numerical techniques which are being used to solve the gyrokinetic equations, fundamentals in gyrokinetic turbulence and the main results which have been brought by simulations with regard to transport in fusion devices and fluctuation measurements.},
author = {Garbet, X. and Idomura, Y. and Villard, L. and Watanabe, T.H.},
doi = {10.1088/0029-5515/50/4/043002},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Garbet et al. - 2010 - Gyrokinetic simulations of turbulent transport.pdf:pdf},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {4},
pages = {043002},
title = {{Gyrokinetic simulations of turbulent transport}},
volume = {50},
year = {2010}
}
@article{Abel2013a,
abstract = {This paper presents a complete theoretical framework for plasma turbulence and transport in tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio of the gyroradius to the equilibrium scale length. Proceeding order-by-order in this expansion, a framework for plasma turbulence is developed. It comprises an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equillibrium is obtained from the Grad-Shafranov equation for a rotating plasma and the slow (resistive) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the high-flow gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local cascade of free energy. Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical corrections and the fluctuations act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived. Total energy is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating, and the equilibration of mean temperatures. Finally, this framework is condensed, in the low-Mach-number limit, to a concise set of equations suitable for numerical implementation.},
archivePrefix = {arXiv},
arxivId = {1209.4782},
author = {Abel, I. G. and Plunk, G. G. and Wang, E. and Barnes, M. and Cowley, S. C. and Dorland, W. and Schekochihin, A. A.},
doi = {10.1088/0034-4885/76/11/116201},
eprint = {1209.4782},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Abel et al. - 2013 - Multiscale gyrokinetics for rotating tokamak plasmas Fluctuations, transport and energy flows.pdf:pdf},
isbn = {0034-4885; 1361-6633},
issn = {00344885},
journal = {Reports Prog. Phys.},
number = {11},
pmid = {24169038},
title = {{Multiscale gyrokinetics for rotating tokamak plasmas: Fluctuations, transport and energy flows}},
volume = {76},
year = {2013}
}
@article{Kotschenreuther2017,
abstract = {The first high fidelity gyrokinetic simulations of the energy losses in the transport barriers of large tokamaks in pursuit of fusion gain are presented. These simulations calculate the turbulent energy losses with an extensive treatment of relevant physical effects—fully kinetic, non-linear, electromagnetic—inclusive of all major plasma species, and in equilibria with relevant shape and local bootstrap current for fusion-relevant cases. We find that large plasmas with a small normalized gyroradius lie in an unexpected regime of enhanced losses that can prevent the projected energy gain. Our simulations are qualitatively consistent with recent experiments on JET with an ITER-like wall. Interestingly and very importantly, the simulations predict parameter regimes of reduced transport that are quite fusion-favorable.},
author = {Kotschenreuther, M. and Hatch, D. R. and Mahajan, S. and Valanju, P. and Zheng, L. and Liu, X.},
doi = {10.1088/1741-4326/aa6416},
issn = {17414326},
journal = {Nucl. Fusion},
title = {{Pedestal transport in H-mode plasmas for fusion gain}},
year = {2017}
}
@article{Valentini2008,
abstract = {The understanding of the small-scale termination of the turbulent energy cascade in collisionless plasmas is nowadays one of the outstanding problems in space physics. In the absence of collisional viscosity, the dynamics at small scales is presumably kinetic in nature; the identification of the physical mechanism which replaces energy dissipation and establishes the link between macroscopic and microscopic scales would open a new scenario in the study of turbulent heating in space plasmas. We present a numerical analysis of kinetic effects along the turbulent energy cascade in solar-wind plasmas which provides an effective unified interpretation of a wide set of spacecraft observations and shows that, simultaneously with an increase in the ion perpendicular temperature, strong bursts of electrostatic activity in the form of ion-acoustic turbulence are produced together with accelerated beams in the ion distribution function.},
author = {Valentini, F. and Veltri, P. and Califano, F. and Mangeney, A.},
doi = {10.1103/PhysRevLett.101.025006},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Valentini et al. - 2008 - Cross-scale effects in solar-wind turbulence.pdf:pdf},
journal = {Phys. Rev. Lett.},
title = {{Cross-scale effects in solar-wind turbulence}},
url = {http://www.mendeley.com/research/crossscale-effects-solarwind-turbulence},
year = {2008}
}
@article{Jenko2001,
abstract = {One of the central physics issues currently targeted by nonlinear gyrokinetic simulations is the role of finite-$\beta$ effects. The latter change the MHD equilibrium, introduce new dynamical space and time scales, alter and enlarge the zoo of electrostatic microinstabilities and saturation mechanisms, and lead to turbulent transport along fluctuating magnetic field lines. It is shown that the electromagnetic effects on primarily electrostatic microinstabilities are generally weakly or moderately stabilizing. However, the saturation of these modes and hence the determination of the transport level in the quasi-stationary turbulent state can be dominated by nonlinear electromagnetic effects and yield surprising results. Despite this, the induced transport is generally electrostatic in nature well below the ideal ballooning limit.},
author = {Jenko, F. and Dorland, W.},
doi = {10.1088/0741-3335/43/12A/310},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Jenko, Dorland - 2001 - Nonlinear electromagnetic gyrokinetic simulations of tokamak plasmas.pdf:pdf},
isbn = {0741-3335},
issn = {0741-3335},
journal = {Plasma Phys. Control. fusion},
pages = {A141},
title = {{Nonlinear electromagnetic gyrokinetic simulations of tokamak plasmas}},
url = {http://iopscience.iop.org/0741-3335/43/12A/310},
volume = {43},
year = {2001}
}
@article{Boley1984,
author = {Boley, C.D.},
doi = {10.1016/0022-3115(84)90339-8},
issn = {00223115},
journal = {J. Nucl. Mater.},
keywords = {-d time-dependent plasma transport,1,by the 3-d monte,carlo neutral transport code,code whist,contains the best available,degas,fusion,in conjunction with the,in the proposed reactor,including a selection of,limiter,neutrals,plasma,tfcx has been modeled,the distribution of neutrals,the former code,the latter code,treatment of neutral-particle physics,wall reflection models,which has been run},
month = {dec},
pages = {127--130},
title = {{Transport of neutral atoms and molecules in TFCX}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0022311584903398},
volume = {128-129},
year = {1984}
}
@article{Lao1985,
author = {Lao, L. L. and Greene, J. M. and Wang, T. S. and Helton, F. J. and Zawadzki, E. M.},
doi = {10.1063/1.865056},
issn = {00319171},
journal = {Phys. Fluids},
number = {3},
pages = {869},
title = {{Three-dimensional toroidal equilibria and stability by a variational spectral method}},
url = {http://link.aip.org/link/PFLDAS/v28/i3/p869/s1{\&}Agg=doi},
volume = {28},
year = {1985}
}
@article{Lee2014a,
archivePrefix = {arXiv},
arxivId = {arXiv:1301.4260v1},
author = {Lee, Jungpyo and Parra, Felix I. and Barnes, Michael},
doi = {10.1088/0029-5515/54/2/022002},
eprint = {arXiv:1301.4260v1},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Lee, Parra, Barnes - 2014 - Turbulent momentum pinch of diamagnetic flows in a tokamak.pdf:pdf},
issn = {00295515},
journal = {Nucl. Fusion},
keywords = {momentum pinch,rotation,tokamak},
number = {2},
title = {{Turbulent momentum pinch of diamagnetic flows in a tokamak}},
volume = {54},
year = {2014}
}
@article{Bourdelle2015,
author = {Bourdelle, C and Citrin, J and Baiocchi, B and Casati, A and Cottier, P and Garbet, X and Imbeaux, F},
doi = {10.1088/0741-3335/58/1/014036},
issn = {13616587},
journal = {Plasma Phys. Control. Fusion},
keywords = {modeling,tokamak,turbulence},
number = {1},
pages = {14036},
publisher = {IOP Publishing},
title = {{Core turbulent transport in tokamak plasmas: Bridging theory and experiment with QuaLiKiz}},
url = {http://dx.doi.org/10.1088/0741-3335/58/1/014036},
volume = {58},
year = {2015}
}
@article{Rognlien2005,
author = {Rognlien, T.D. and Umansky, M.V. and Xu, X.Q. and Cohen, R.H. and LoDestro, L.L.},
doi = {10.1016/j.jnucmat.2004.10.023},
issn = {00223115},
journal = {J. Nucl. Mater.},
keywords = {edge transport,neutral transport simulation,non-diffusive transport,plasma turbulence,uedge},
month = {mar},
pages = {327--331},
title = {{Simulation of plasma fluxes to material surfaces with self-consistent edge turbulence and transport for tokamaks}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022311504007615},
volume = {337-339},
year = {2005}
}
@article{Shi2005,
author = {Shi, Bingren},
doi = {10.1063/1.2140227},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {12},
pages = {122504},
title = {{Analytic description of high poloidal beta equilibrium with a natural inboard poloidal field null}},
url = {http://link.aip.org/link/PHPAEN/v12/i12/p122504/s1{\&}Agg=doi},
volume = {12},
year = {2005}
}
@article{Search1971,
author = {Search, Home and Journals, Collections and Contact, About and Iopscience, My and Address, I P},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Search et al. - 1971 - Trapped particles in toroidal magnetic systems TRAPPED PARTICLES IN TOROIDAL MAGNETIC SYSTEMS.pdf:pdf},
title = {{Trapped particles in toroidal magnetic systems TRAPPED PARTICLES IN TOROIDAL MAGNETIC SYSTEMS}},
volume = {67},
year = {1971}
}
@article{Grad1958,
author = {Grad, Harold and Rubin, Hanan},
doi = {10.1016/0891-3919(58)90139-6},
issn = {08913919},
journal = {J. Nucl. Energy},
month = {sep},
number = {3-4},
pages = {284--285},
title = {{Hydromagnetic equilibria and force-free fields}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0891391958901396},
volume = {7},
year = {1958}
}
@article{Sorbom2015,
abstract = {The affordable, robust, compact (ARC) reactor is the product of a conceptual design study aimed at reducing the size, cost, and complexity of a combined fusion nuclear science facility (FNSF) and demonstration fusion Pilot power plant. ARC is a ∼200-250 MWe tokamak reactor with a major radius of 3.3 m, a minor radius of 1.1 m, and an on-axis magnetic field of 9.2 T. ARC has rare earth barium copper oxide (REBCO) superconducting toroidal field coils, which have joints to enable disassembly. This allows the vacuum vessel to be replaced quickly, mitigating first wall survivability concerns, and permits a single device to test many vacuum vessel designs and divertor materials. The design point has a plasma fusion gain of Q{\textless}inf{\textgreater}p{\textless}/inf{\textgreater} ≈ 13.6, yet is fully non-inductive, with a modest bootstrap fraction of only ∼63{\%}. Thus ARC offers a high power gain with relatively large external control of the current profile. This highly attractive combination is enabled by the ∼23 T peak field on coil achievable with newly available REBCO superconductor technology. External current drive is provided by two innovative inboard RF launchers using 25 MW of lower hybrid and 13.6 MW of ion cyclotron fast wave power. The resulting efficient current drive provides a robust, steady state core plasma far from disruptive limits. ARC uses an all-liquid blanket, consisting of low pressure, slowly flowing fluorine lithium beryllium (FLiBe) molten salt. The liquid blanket is low-risk technology and provides effective neutron moderation and shielding, excellent heat removal, and a tritium breeding ratio ≥ 1.1. The large temperature range over which FLiBe is liquid permits an output blanket temperature of 900 K, single phase fluid cooling, and a high efficiency helium Brayton cycle, which allows for net electricity generation when operating ARC as a Pilot power plant.},
archivePrefix = {arXiv},
arxivId = {1409.3540},
author = {Sorbom, B. N. and Ball, J. and Palmer, T. R. and Mangiarotti, F. J. and Sierchio, J. M. and Bonoli, P. and Kasten, C. and Sutherland, D. A. and Barnard, H. S. and Haakonsen, C. B. and Goh, J. and Sung, C. and Whyte, D. G.},
doi = {10.1016/j.fusengdes.2015.07.008},
eprint = {1409.3540},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Sorbom et al. - 2015 - ARC A compact, high-field, fusion nuclear science facility and demonstration power plant with demountable magnets.pdf:pdf},
isbn = {9781479982646},
issn = {09203796},
journal = {Fusion Eng. Des.},
title = {{ARC: A compact, high-field, fusion nuclear science facility and demonstration power plant with demountable magnets}},
year = {2015}
}
@article{Callen2011,
author = {Callen, J.D.},
doi = {10.1088/0029-5515/51/9/094026},
issn = {0029-5515},
journal = {Nucl. Fusion},
language = {en},
month = {sep},
number = {9},
pages = {094026},
publisher = {IOP Publishing},
title = {{Effects of 3D magnetic perturbations on toroidal plasmas}},
url = {http://iopscience.iop.org/article/10.1088/0029-5515/51/9/094026},
volume = {51},
year = {2011}
}
@article{Boedo2003,
author = {Boedo, J. a. and Rudakov, D. L. and Moyer, R. a. and McKee, G. R. and Colchin, R. J. and Schaffer, M. J. and Stangeby, P. G. and West, W. P. and Allen, S. L. and Evans, T. E. and Fonck, R. J. and Hollmann, E. M. and Krasheninnikov, S. and Leonard, a. W. and Nevins, W. and Mahdavi, M. a. and Porter, G. D. and Tynan, G. R. and Whyte, D. G. and Xu, X.},
doi = {10.1063/1.1563259},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {1670},
title = {{Transport by intermittency in the boundary of the DIII-D tokamak}},
url = {http://link.aip.org/link/PHPAEN/v10/i5/p1670/s1{\&}Agg=doi},
volume = {10},
year = {2003}
}
@article{Xu2008,
author = {Xu, X.},
doi = {10.1103/PhysRevE.78.016406},
issn = {1539-3755},
journal = {Phys. Rev. E},
month = {jul},
number = {1},
pages = {016406},
title = {{Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.78.016406},
volume = {78},
year = {2008}
}
@article{Stangeby2000,
author = {Stangeby, Peter C},
isbn = {750305592},
title = {{The plasma boundary of magnetic fusion devices}},
url = {http://physics.technion.ac.il/{~}plasma/publications/ebooks/books2/djvu{\_}library/Plasma/MHD abd Fusion/Stangeby P. The Plasma Boundary of Magnetic Fusion Devices (ISBN 0750305592)(IoP, 2000)(715s).pdf},
year = {2000}
}
@article{Idouakass2018,
author = {Idouakass, M and Gravier, E and Lesur, M and M{\'{e}}dina, J and R{\'{e}}veill{\'{e}}, T and Drouot, T and Garbet, X and Sarazin, Y},
doi = {10.1063/1.5026381},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Idouakass et al. - 2018 - Impurity density gradient influence on trapped particle modes.pdf:pdf},
issn = {10897674},
journal = {Cit. Phys. Plasmas},
title = {{Impurity density gradient influence on trapped particle modes}},
url = {https://doi.org/10.1063/1.5026381{\%}0Ahttp://aip.scitation.org/toc/php/25/6},
volume = {25},
year = {2018}
}
@book{Fulop2009,
author = {F{\"{u}}l{\"{o}}p, T. and Nordman, H.},
booktitle = {Phys. Plasmas},
doi = {10.1063/1.3083299},
isbn = {1070-664X},
issn = {1070664X},
keywords = {Neoclassical Transport theory,pustzai,sweden,thesis,turbulence},
mendeley-tags = {Neoclassical Transport theory,pustzai,sweden,thesis,turbulence},
number = {3},
pages = {1--8},
title = {{Turbulent and neoclassical impurity transport in tokamak plasmas}},
volume = {16},
year = {2009}
}
@article{Hirshman1994,
author = {Hirshman, S. P. and Lee, D. K. and Levinton, F. M. and Batha, S. H. and Okabayashi, M. and Wieland, R. M.},
doi = {10.1063/1.870625},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {7},
pages = {2277},
title = {{Equilibrium reconstruction of the safety factor profile in tokamaks from motional Stark effect data}},
url = {http://link.aip.org/link/PHPAEN/v1/i7/p2277/s1{\&}Agg=doi},
volume = {1},
year = {1994}
}
@article{Shestakov2003a,
author = {a.I. Shestakov and Cohen, R.H. and Crotinger, J.a. and LoDestro, L.L. and Tarditi, a. and Xu, X.Q.},
doi = {10.1016/S0021-9991(02)00063-3},
issn = {00219991},
journal = {J. Comput. Phys.},
month = {mar},
number = {2},
pages = {399--426},
title = {{Self-consistent modeling of turbulence and transport}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999102000633},
volume = {185},
year = {2003}
}
@article{Throumoulopoulos1986,
abstract = {The Grad-Shafranov equation which determines the ideal axisymmetric hydromagnetic plasma equilibrium is transformed to a general curvilinear orthogonal system by the conformal mapping method. For the physical problems of plasma equilibrium, transformations which take into account the symmetry conditions and the constraints of several plasma configurations are investigated. For a number of such transformations the linear Grad-Shafranov equation is solved using the method of separation of variables. Old solutions are recovered and new analytic solutions in spherical, prolate and oblate spheroidal co-ordinates are deduced from which compact toroidal equilibria are derived. A formula for the average beta value of the determined equilibria is derived and the interval in which it lies is determined.},
author = {Throumoulopoulos, G N and Pantis, G},
doi = {10.1088/0029-5515/26/11/005},
issn = {00295515},
journal = {Nucl. Fusion},
pages = {1501--1506},
title = {{The Grad-Shafranov equation under a conformal mapping transformation: Analytic solutions with emphasis on compact toroidal configurations}},
volume = {26},
year = {1986}
}
@article{Belli2017,
abstract = {{\textcopyright} 2017 IOP Publishing Ltd Printed in the UK.In this work, we explore both the potential improvements and pitfalls that arise when using advanced collision models in gyrokinetic simulations of plasma microinstabilities. Comparisons are made between the simple-but-standard electron Lorentz operator and specific variations of the advanced Sugama operator. The Sugama operator describes multi-species collisions including energy diffusion, momentum and energy conservation terms, and is valid for arbitrary wavelength. We report scans over collision frequency for both low and high ks modes, with relevance for multiscale simulations that couple ion and electron scale physics. The influence of the ionion collision terms-not retained in the electron Lorentz model-on the damping of zonal flows is also explored. Collision frequency scans for linear and nonlinear simulations of ion-temperature-gradient instabilities including impurity ions are presented. Finally, implications for modeling turbulence in the highly collisional edge are discussed.},
author = {Belli, E. A. and Candy, J.},
doi = {10.1088/1361-6587/aa5c94},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Belli, Candy - 2017 - Implications of advanced collision operators for gyrokinetic simulation.pdf:pdf},
issn = {13616587},
journal = {Plasma Phys. Control. Fusion},
keywords = {appear in colour only,collisions,gyrokinetic,in the online journal,some fi gures may,tokamak,turbulence},
number = {4},
publisher = {IOP Publishing},
title = {{Implications of advanced collision operators for gyrokinetic simulation}},
volume = {59},
year = {2017}
}
@article{Proll2013,
abstract = {Microinstabilities exhibit a rich variety of behavior in stellarators due to the many degrees of freedom in the magnetic geometry. It has recently been found that certain stellarators (quasi-isodynamic ones with maximum-J geometry) are partly resilient to trapped-particle instabilities, because fast-bouncing particles tend to extract energy from these modes near marginal stability. In reality, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here, the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with the National Compact Stellarator Experiment and the DIII-D tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, ion-temperature-gradient modes, trapped-electron modes, and mixed-type instabilities are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilizing in the energy budget. These results suggest that imperfectly optimized stellarators can retain most of the stabilizing properties predicted for perfect maximum-J configurations. {\textcopyright} 2013 Euratom.},
archivePrefix = {arXiv},
arxivId = {arXiv:1311.3127v2},
author = {Proll, J. H. E. and Xanthopoulos, P. and Helander, P.},
doi = {10.1063/1.4846835},
eprint = {arXiv:1311.3127v2},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Proll, Xanthopoulos, Helander - 2013 - Collisionless microinstabilities in stellarators. II. Numerical simulations.pdf:pdf},
isbn = {1070-664X; 1089-7674},
issn = {1070-664X},
journal = {Phys. Plasmas},
month = {dec},
number = {12},
pages = {122506},
title = {{Collisionless microinstabilities in stellarators. II. Numerical simulations}},
url = {http://aip.scitation.org/doi/10.1063/1.4846835},
volume = {20},
year = {2013}
}
@book{Meyer,
author = {Meyer, Richard E.},
title = {{Introduction to mathematical fluid dynamics}}
}
@article{Maeyama2015,
abstract = {{\textcopyright} 2015 American Physical Society.Multiscale gyrokinetic turbulence simulations with the real ion-to-electron mass ratio and $\beta$ value are realized for the first time, where the $\beta$ value is given by the ratio of plasma pressure to magnetic pressure and characterizes electromagnetic effects on microinstabilities. Numerical analysis at both the electron scale and the ion scale is used to reveal the mechanism of their cross-scale interactions. Even with the real-mass scale separation, ion-scale turbulence eliminates electron-scale streamers and dominates heat transport, not only of ions but also of electrons. Suppression of electron-scale turbulence by ion-scale eddies, rather than by long-wavelength zonal flows, is also demonstrated by means of direct measurement of nonlinear mode-to-mode coupling. When the ion-scale modes are stabilized by finite-$\beta$ effects, the contribution of the electron-scale dynamics to the turbulent transport becomes non-negligible and turns out to enhance ion-scale turbulent transport. Damping of the ion-scale zonal flows by electron-scale turbulence is responsible for the enhancement of ion-scale transport.},
author = {Maeyama, S. and Idomura, Y. and Watanabe, T. H. and Nakata, M. and Yagi, M. and Miyato, N. and Ishizawa, A. and Nunami, M.},
doi = {10.1103/PhysRevLett.114.255002},
issn = {10797114},
journal = {Phys. Rev. Lett.},
title = {{Cross-scale interactions between electron and ion scale turbulence in a tokamak plasma}},
year = {2015}
}
@misc{Wesson,
author = {Wesson, John},
title = {{Tokamaks}}
}
@article{Cowley1991,
author = {Cowley, S. C. and Kulsrud, R. M. and Sudan, R.},
doi = {10.1063/1.859913},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Cowley, Kulsrud, Sudan - 1991 - Considerations of ion-temperature-gradient-driven turbulence.pdf:pdf},
issn = {08998221},
journal = {Phys. Fluids B Plasma Phys.},
number = {10},
pages = {2767},
title = {{Considerations of ion-temperature-gradient-driven turbulence}},
url = {http://scitation.aip.org/content/aip/journal/pofb/3/10/10.1063/1.859913},
volume = {3},
year = {1991}
}
@article{Dorland,
author = {Dorland, W and College, Imperial},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Dorland, College - Unknown - Gyrokinetic Simulations of Tokamak Microturbulence Gyrokinetics is Maturing Rapidly.pdf:pdf},
title = {{Gyrokinetic Simulations of Tokamak Microturbulence Gyrokinetics is Maturing Rapidly}}
}
@article{Gao2010,
author = {Gao, Zhe},
doi = {10.1063/1.3481464},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {9},
pages = {092503},
title = {{Plasma shaping effects on the geodesic acoustic mode in the large orbit drift width limit}},
url = {http://link.aip.org/link/PHPAEN/v17/i9/p092503/s1{\&}Agg=doi},
volume = {17},
year = {2010}
}
@article{Marjan2012,
author = {Marjan, Alireza Seife and Sobhanian, Samad},
doi = {10.1186/2251-7235-6-34},
issn = {2251-7235},
journal = {J. Theor. Appl. Phys.},
keywords = {25-xz,28,52,52-s,55-s,current density,elongation,g-s equation,magnetic field,pacs,triangularity},
number = {1},
pages = {34},
title = {{A new form of Grad-Shafranov equation for a tokomak with an elongated cross section}},
url = {http://www.jtaphys.com/content/6/1/34},
volume = {6},
year = {2012}
}
@article{Jenko2000,
abstract = {Collisionless electron-temperature-gradient-driven (ETG) turbulence in toroidal geometry is studied via nonlinear numerical simulations. To this aim, two massively parallel, fully gyrokinetic Vlasov codes are used, both including electromagnetic effects. Somewhat surprisingly, and unlike in the analogous case of ion-temperature-gradient-driven (ITG) turbulence, we find that the turbulent electron heat flux is significantly underpredicted by simple mixing length estimates in a certain parameter regime (ŝ{\~{}}1, low $\alpha$). This observation is directly linked to the presence of radially highly elongated vortices (``streamers'') which lead to very effective cross-field transport. The simulations therefore indicate that ETG turbulence is likely to be relevant to magnetic confinement fusion experiments.},
author = {Jenko, F and Dorland, W and Kotschenreuther, M and Rogers, B N},
doi = {10.1063/1.874014},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {1904},
pmid = {11136051},
title = {{Electron temperature gradient driven turbulence}},
url = {http://adsabs.harvard.edu/cgi-bin/nph-data{\_}query?bibcode=2000PhPl....7.1904J{\&}link{\_}type=ABSTRACT{\%}5Cnpapers2://publication/doi/10.1063/1.874014{\%}5Cnhttp://link.aip.org/link/PHPAEN/v7/i5/p1904/s1{\&}Agg=doi},
volume = {7},
year = {2000}
}
@article{Howard2014,
author = {Howard, N T and White, a E and Greenwald, M and Holland, C and Candy, J and Rice, J E},
doi = {10.1088/0741-3335/56/12/124004},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Howard et al. - 2014 - Impurity transport, turbulence transitions and intrinsic rotation in Alcator C-Mod plasmas.pdf:pdf},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
keywords = {gyrokinetics,impurity transport,in colour only in,intrinsic rotation,neutral beams to achieve,of neutral beams into,placing limits on the,some figures may appear,some high performance scenarios,the core,the online journal,use of},
pages = {124004},
title = {{Impurity transport, turbulence transitions and intrinsic rotation in Alcator C-Mod plasmas}},
url = {http://stacks.iop.org/0741-3335/56/i=12/a=124004?key=crossref.66d7139b1428ea2448f900b3295a1a05},
volume = {56},
year = {2014}
}
@article{Duval2007,
abstract = {Carbon ion velocity profiles are measured in TCV with a charge exchange diagnostic using a negligibly perturbing diagnostic neutral beam. These 'intrinsic' rotation profiles are measured up to the plasma edge in the toroidal and poloidal directions for both limited and diverted plasma configurations in Ohmic plasmas and in the presence of strong second harmonic electron cyclotron heating (ECH). Absolute toroidal velocities are shown to scale with peak ion temperature and inversely with plasma current. The plasma edge rotation is always small in limited configurations but evolves smoothly with the core density for diverted configurations. A strong intrinsic rotation builds up in the plasma core in the counter-current direction for limited configurations but is observed in the co-current direction for diverted plasmas. Unexpectedly, above a given density threshold, the rotation profile reverses to the co-current direction for limited configurations (and surprisingly, in the counter-current direction for diverted configurations). This threshold density is found to depend on plasma current, the presence of ECH and the magnetic topology. Poloidal velocity measurements are used to deduce the radial electric field change across the transition. A strong dependence of the rotation profile on plasma triangularity is reported and possible physics models for these observations are discussed. The origin of the momentum drive, its reversal and its magnitude are not yet clearly understood even for these relatively 'simple' experimental configurations. },
author = {Duval, B.{\~{}}P. and Bortolon, A and Karpushov, A and Pitts, R.{\~{}}A. and Pochelon, A and Scarabosio, A and {the TCV Team}},
doi = {10.1088/0741-3335/49/12B/S18},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
keywords = {paper,ppcf},
mendeley-tags = {paper,ppcf},
pages = {195},
title = {{Bulk plasma rotation in the TCV tokamak in the absence of external momentum input}},
url = {http://cdsads.u-strasbg.fr/abs/2007PPCF...49..195D},
volume = {49},
year = {2007}
}
@article{Callen2009a,
abstract = {A comprehensive transport equation for the evolution of toroidal rotation in tokamak plasmas is developed self-consistently from the two-fluid momentum equations taking account of the constraints imposed by faster time scale processes. The resultant plasma toroidal rotation equation includes the effects of collision-induced perpendicular viscosities, anomalous transport due to microturbulence},
author = {Callen, J.D. and a.J. Cole and Hegna, C.C.},
doi = {10.1088/0029-5515/49/8/085021},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {8},
pages = {085021},
title = {{Toroidal rotation in tokamak plasmas}},
volume = {49},
year = {2009}
}
@article{Staebler2005,
author = {Staebler, G. M. and Kinsey, J. E. and Waltz, R. E.},
doi = {10.1063/1.2044587},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Staebler, Kinsey, Waltz - 2005 - Gyro-Landau fluid equations for trapped and passing particles.pdf:pdf},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {10},
pages = {1--24},
title = {{Gyro-Landau fluid equations for trapped and passing particles}},
volume = {12},
year = {2005}
}
@article{Search1997,
author = {Search, Home and Journals, Collections and Contact, About and Iopscience, My and Address, I P},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Search et al. - 1997 - Poloidal Distribution of Impurities.pdf:pdf},
pages = {1--6},
title = {{Poloidal Distribution of Impurities}},
volume = {577},
year = {1997}
}
@article{Dudson2011,
author = {Dudson, B D and Xu, X Q and Umansky, M V and Wilson, H R and Snyder, P B},
doi = {10.1088/0741-3335/53/5/054005},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
month = {may},
number = {5},
pages = {054005},
title = {{Simulation of edge localized modes using BOUT++}},
url = {http://stacks.iop.org/0741-3335/53/i=5/a=054005?key=crossref.6672cb1fd223386594806af78de3b8ba},
volume = {53},
year = {2011}
}
@book{JohnDa,
author = {Jackson, John David},
title = {{Classical electrodynamics}}
}
@article{Belli2006,
abstract = {Advanced numerical algorithms for gyrokinetic simulations are explored for$\backslash$nmore eective studies of plasma turbulent transport. The gyrokinetic equations$\backslash$ndescribe the dynamics of particles in 5-dimensional phase space, averaging$\backslash$nover the fast gyromotion, and provide a foundation for studying plasma microturbulence$\backslash$nin fusion devices and in astrophysical plasmas. Several algorithms for Eulerian/$\backslash$ncontinuum gyrokinetic solvers are compared. An iterative implicit scheme$\backslash$nbased on numerical approximations of the plasma response is developed. This$\backslash$nmethod reduces the long time needed to set-up implicit arrays, yet still has larger$\backslash$ntime step advantages similar to a fully implicit method. Various model preconditioners$\backslash$nand iteration schemes, including Krylov-based solvers, are explored. An$\backslash$nAlternating Direction Implicit algorithm is also studied and is surprisingly found$\backslash$nto yield a severe stability restriction on the time step. Overall, an iterative Krylov$\backslash$nalgorithm might be the best approach for extensions of core tokamak gyrokinetic$\backslash$nsimulations to edge kinetic formulations and may be particularly useful for studies$\backslash$nof large-scale ExB shear eects.$\backslash$nThe eects of $\backslash$nux surface shape on the gyrokinetic stability and transport of$\backslash$ntokamak plasmas are studied using the nonlinear GS2 gyrokinetic code with analytic$\backslash$nequilibria based on interpolations of representative JET-like shapes. High$\backslash$nshaping is found to be a stabilizing in$\backslash$nuence on both the linear ITG instability and$\backslash$nnonlinear ITG turbulence. A scaling of the heat $\backslash$nux with elongation of   1:5$\backslash$nor 2 (depending on the triangularity) is observed, which is consistent with previous$\backslash$ngyro$\backslash$nuid simulations. Thus, the GS2 turbulence simulations are explaining a$\backslash$nsignicant fraction, but not all, of the empirical elongation scaling. The remainder$\backslash$nof the scaling may come from (1) the edge boundary conditions for core turbulence,$\backslash$nand (2) the larger Dimits nonlinear critical temperature gradient shift due$\backslash$nto the enhancement of zonal $\backslash$nows with shaping, which is observed with the GS2$\backslash$nsimulations.$\backslash$nFinally, a local linear trial function-based gyrokinetic code is developed to aid$\backslash$nin fast scoping studies of gyrokinetic linear stability. This code is successfully$\backslash$nbenchmarked with the full GS2 code in the collisionless, electrostatic limit, as well$\backslash$nas in the more general electromagnetic description with higher-order Hermite basis$\backslash$nfunctions.},
author = {Belli, Emily Ann},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Belli - 2006 - Studies of Numerical Algorithms for Gyrokinetics and the Effects of Shaping on Plasma Turbulence.pdf:pdf},
number = {June},
pages = {319},
title = {{Studies of Numerical Algorithms for Gyrokinetics and the Effects of Shaping on Plasma Turbulence}},
url = {http://www.princeton.edu/{~}ebelli/thesis.final.pdf},
year = {2006}
}
@article{Search1999a,
author = {Search, Home and Journals, Collections and Contact, About and Iopscience, My and Address, I P},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Search et al. - 1999 - Scalings for tokamak energy confinement34.pdf:pdf},
title = {{Scalings for tokamak energy confinement[34]}},
volume = {1999},
year = {1999}
}
@techreport{Barnesa,
author = {Barnes, Michael},
number = {1},
title = {{GS3 notes}}
}
@article{Duval2007a,
abstract = {Carbon ion velocity profiles are measured in TCV with a charge exchange diagnostic using a negligibly perturbing diagnostic neutral beam. These 'intrinsic' rotation profiles are measured up to the plasma edge in the toroidal and poloidal directions for both limited and diverted plasma configurations in Ohmic plasmas and in the presence of strong second harmonic electron cyclotron heating (ECH). Absolute toroidal velocities are shown to scale with peak ion temperature and inversely with plasma current. The plasma edge rotation is always small in limited configurations but evolves smoothly with the core density for diverted configurations. A strong intrinsic rotation builds up in the plasma core in the counter-current direction for limited configurations but is observed in the co-current direction for diverted plasmas. Unexpectedly, above a given density threshold, the rotation profile reverses to the co-current direction for limited configurations (and surprisingly, in the counter-current direction for diverted configurations). This threshold density is found to depend on plasma current, the presence of ECH and the magnetic topology. Poloidal velocity measurements are used to deduce the radial electric field change across the transition. A strong dependence of the rotation profile on plasma triangularity is reported and possible physics models for these observations are discussed. The origin of the momentum drive, its reversal and its magnitude are not yet clearly understood even for these relatively 'simple' experimental configurations. },
archivePrefix = {arXiv},
arxivId = {astro-ph/0610810},
author = {Duval, B. P. and Bortolon, A. and Karpushov, A. and Pitts, R. A. and Pochelon, A. and Scarabosio, A.},
doi = {10.1088/0741-3335/49/12B/S18},
eprint = {0610810},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Duval et al. - 2007 - Bulk plasma rotation in the TCV tokamak in the absence of external momentum input.pdf:pdf},
issn = {07413335},
journal = {Plasma Phys. Control. Fusion},
number = {12 B},
primaryClass = {astro-ph},
title = {{Bulk plasma rotation in the TCV tokamak in the absence of external momentum input}},
volume = {49},
year = {2007}
}
@article{Batishchev1996,
author = {Batishchev, O. V. and Xu, X. Q. and Byers, J. a. and Cohen, R. H. and Krasheninnikov, S. I. and Rognlien, T. D. and Sigmar, D. J.},
doi = {10.1063/1.871615},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {9},
pages = {3386},
title = {{Kinetic effects on particle and heat fluxes in detached plasmas}},
url = {http://link.aip.org/link/PHPAEN/v3/i9/p3386/s1{\&}Agg=doi},
volume = {3},
year = {1996}
}
@article{Bhattacharyya2000,
author = {Bhattacharyya, S. N.},
doi = {10.1063/1.1319334},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {12},
pages = {4805},
title = {{The diocotron spectrum of a toroidal non-neutral plasma}},
url = {http://link.aip.org/link/PHPAEN/v7/i12/p4805/s1{\&}Agg=doi},
volume = {7},
year = {2000}
}
@article{Hesslow2017,
abstract = {We analyze the dynamics of fast electrons in plasmas containing partially ionized impurity atoms, where the screening effect of bound electrons must be included. We derive analytical expressions for the deflection and slowing-down frequencies, and show that they are increased significantly compared to the results obtained with complete screening, already at subrelativistic electron energies. Furthermore, we show that the modifications to the deflection and slowing down frequencies are of equal importance in describing the runaway current evolution. Our results greatly affect fast-electron dynamics and have important implications, e.g., for the efficacy of mitigation strategies for runaway electrons in tokamak devices, and energy loss during relativistic breakdown in atmospheric discharges.},
archivePrefix = {arXiv},
arxivId = {1705.08638},
author = {Hesslow, L. and Embr{\'{e}}us, O. and Stahl, A. and Dubois, T. C. and Papp, G. and Newton, S. L. and F{\"{u}}l{\"{o}}p, T.},
doi = {10.1103/PhysRevLett.118.255001},
eprint = {1705.08638},
issn = {10797114},
journal = {Phys. Rev. Lett.},
number = {25},
pages = {1--5},
title = {{Effect of Partially Screened Nuclei on Fast-Electron Dynamics}},
volume = {118},
year = {2017}
}
@article{Rognlien2002,
author = {Rognlien, T.D. and Xu, X.Q. and a.C. Hindmarsh},
doi = {10.1006/jcph.2001.6944},
issn = {00219991},
journal = {J. Comput. Phys.},
keywords = {edge plasma,krylov,lence,newton,parallel computation,plasma transport,plasma turbu-},
month = {jan},
number = {1},
pages = {249--268},
title = {{Application of Parallel Implicit Methods to Edge-Plasma Numerical Simulations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S002199910196944X},
volume = {175},
year = {2002}
}
@article{Parra2010a,
abstract = {Full f electrostatic gyrokinetic formulations employ two gyrokinetic equations, one for ions and the other for electrons, and quasineutrality to obtain the ion and electron distribution functions and the electrostatic potential. We demonstrate with several examples that the long wavelength radial electric field obtained with full f approaches is extremely sensitive to errors in the ion and electron density since small deviations in density give rise to large, nonphysical deviations in the conservation of toroidal angular momentum. For typical tokamak values, a relative error of 10(-7) in the ion or electron densities is enough to obtain the incorrect toroidal rotation. Based on the insights gained with the examples considered, three simple tests to check transport of toroidal angular momentum in full f simulations are proposed. (C) 2010 American Institute of Physics. [doi:10.1063/1.3327127]},
author = {Parra, Felix I. and Catto, Peter J.},
doi = {10.1063/1.3327127},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Parra, Catto - 2010 - Transport of momentum in full f gyrokinetics.pdf:pdf},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {1--12},
title = {{Transport of momentum in full f gyrokinetics}},
volume = {17},
year = {2010}
}
@article{Wang2005,
author = {Wang, Shaojie and Yu, Jun},
doi = {10.1063/1.1924554},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {6},
pages = {062501},
title = {{An exact solution of the Grad–Shafranov–Helmhotz equation with central current density reversal}},
url = {http://link.aip.org/link/PHPAEN/v12/i6/p062501/s1{\&}Agg=doi},
volume = {12},
year = {2005}
}
@article{Plunk2017,
abstract = {In the complex 3D magnetic fields of stellarators, ion-temperature-gradient turbulence is shown to have two distinct saturation regimes, as revealed by petascale numerical simulations, and explained by a simple turbulence theory. The first regime is marked by strong zonal flows, and matches previous observations in tokamaks. The newly observed second regime, in contrast, exhibits small- scale quasi-two-dimensional turbulence, negligible zonal flows, and, surprisingly, a weaker heat flux scaling. Our findings suggest that key details of the magnetic geometry control turbulence in stellarators.},
archivePrefix = {arXiv},
arxivId = {1703.03257},
author = {Plunk, G. G. and Xanthopoulos, P. and Helander, P.},
doi = {10.1103/PhysRevLett.118.105002},
eprint = {1703.03257},
issn = {10797114},
journal = {Phys. Rev. Lett.},
title = {{Distinct Turbulence Saturation Regimes in Stellarators}},
year = {2017}
}
@article{VanMilligen2014,
abstract = {This work explores the potential of an information-theoretical causality detection method for unravelling the relation between fluctuating variables in complex non-linear systems. The method is tested on some simple though non-linear models, and guidelines for the choice of analysis parameters are established. Then, measurements from magnetically confined fusion plasmas are analysed. The selected data bear relevance to the all-important spontaneous confinement transitions often observed in fusion plasmas, fundamental for the design of an economically attractive fusion reactor. It is shown how the present method is capable of clarifying the interaction between fluctuating quantities such as the turbulence amplitude, turbulent flux and zonal flow amplitude, and uncovers several interactions that were missed by traditional methods.},
archivePrefix = {arXiv},
arxivId = {arXiv:1309.7769v3},
author = {van Milligen, B.Ph. and Birkenmeier, G. and Ramisch, M. and Estrada, T. and Hidalgo, C. and Alonso, A.},
doi = {10.1088/0029-5515/54/2/023011},
eprint = {arXiv:1309.7769v3},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/van Milligen et al. - 2014 - Causality detection and turbulence in fusion plasmas.pdf:pdf},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {feb},
number = {2},
pages = {023011},
title = {{Causality detection and turbulence in fusion plasmas}},
url = {http://stacks.iop.org/0029-5515/54/i=2/a=023011?key=crossref.a2f4a785ef8ab8cee8def5297190438f},
volume = {54},
year = {2014}
}
@article{Dannert2005,
author = {Dannert, Tilman},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Dannert - 2005 - Gyrokinetische Simulation von Plasmaturbulenz mit gefangenen Teilchen und elektromagnetischen Gyrokinetische Simulation.pdf:pdf},
title = {{Gyrokinetische Simulation von Plasmaturbulenz mit gefangenen Teilchen und elektromagnetischen Gyrokinetische Simulation von Plasmaturbulenz mit gefangenen Teilchen und elektromagnetischen Effekten}},
year = {2005}
}
@article{Banon2012,
author = {Ba{\~{n}}{\'{o}}n, Alejando and Supervisor, Navarro and Carati, Daniele},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Ba{\~{n}}{\'{o}}n, Supervisor, Carati - 2012 - Gyrokinetic Large Eddy Simulations.pdf:pdf},
title = {{Gyrokinetic Large Eddy Simulations}},
year = {2012}
}
@book{Lebedev1972,
author = {Lebedev, N N},
booktitle = {English},
title = {{Special functions and their applications}},
url = {http://books.google.com/books?hl=en{\&}lr={\&}id=po-6Yxz851MC{\&}oi=fnd{\&}pg=PA1{\&}dq=Special+functions+and+their+applications{\&}ots=w6c8g-XuYf{\&}sig=TxVq2jr2Nbrn64f0aE-KIwYAOYs{\%}5Cnhttp://books.google.com/books?hl=en{\&}lr={\&}id=po-6Yxz851MC{\&}oi=fnd{\&}pg=PA1{\&}dq=Special+functions+},
year = {1972}
}
@article{To2009,
author = {To, I Nvitation and Ubmission, P Rovide A S and Ydney, O N S and Uture, S T Ransport F},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/To et al. - 2009 - T Ransport B Lueprint for Nsw With a Focus on S Ydney M Etropolitan a Rea.pdf:pdf},
title = {{T Ransport B Lueprint for Nsw With a Focus on S Ydney M Etropolitan a Rea}},
year = {2009}
}
@article{Dimits2000,
abstract = {The predictions of gyrokinetic and gyrofluid simulations of ion-temperature-gradient (ITG) instability and turbulence in tokamak plasmas as well as some tokamak plasma thermal transport models, which have been widely used for predicting the performance of the proposed International Thermonuclear Experimental Reactor (ITER) tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 1, p. 3], are compared. These comparisons provide information on effects of differences in the physics content of the various models and on the fusion-relevant figures of merit of plasma performance predicted by the models. Many of the comparisons are undertaken for a simplified plasma model and geometry which is an idealization of the plasma conditions and geometry in a Doublet III-D [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high confinement (H-mode) experiment. Most of the models show good agreements in their predictions and assumptions for the linear growth rates and frequencies. There are some differences associated with different equilibria. However, there are significant differences in the transport levels between the models. The causes of some of the differences are examined in some detail, with particular attention to numerical convergence in the turbulence simulations (with respect to simulation mesh size, system size and, for particle-based simulations, the particle number). The implications for predictions of fusion plasma performance are also discussed. (C) 2000 American Institute of Physics. [S1070-664X(00)03703-4]},
author = {Dimits, a. M. and Bateman, G. and Beer, M. a. and Cohen, B. I. and Dorland, W. and Hammett, G. W. and Kim, C. and Kinsey, J. E. and Kotschenreuther, M. and Kritz, a. H. and Lao, L. L. and Mandrekas, J. and Nevins, W. M. and Parker, S. E. and Redd, a. J. and Shumaker, D. E. and Sydora, R. and Weiland, J.},
doi = {10.1063/1.873896},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Dimits et al. - 2000 - Comparisons and physics basis of tokamak transport models and turbulence simulations.pdf:pdf},
isbn = {1070664X},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {3},
pages = {969},
title = {{Comparisons and physics basis of tokamak transport models and turbulence simulations}},
url = {http://scitation.aip.org/content/aip/journal/pop/7/3/10.1063/1.873896},
volume = {7},
year = {2000}
}
@article{Rodrigues2004,
author = {Rodrigues, Paulo and Bizarro, João P. S.},
doi = {10.1063/1.1625372},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {1},
pages = {186},
title = {{Asymptotic, closed integral solutions for the reconstruction of Grad–Shafranov equilibria in axisymmetric, large-aspect-ratio toroidal plasmas}},
url = {http://link.aip.org/link/PHPAEN/v11/i1/p186/s1{\&}Agg=doi},
volume = {11},
year = {2004}
}
@article{Miller1998,
author = {Miller, R L and Chu, M S and Greene, J M and Waltz, R E},
doi = {10.1063/1.872666},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Miller et al. - 1998 - Noncircular, finite aspect ratio, local equilibrium model.pdf:pdf},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {4},
pages = {973},
title = {{Noncircular, finite aspect ratio, local equilibrium model}},
url = {http://link.aip.org/link/PHPAEN/v5/i4/p973/s1{\&}Agg=doi},
volume = {5},
year = {1998}
}
@techreport{Eq,
author = {Barnes, Michael},
number = {7},
pages = {1--4},
title = {lowflow notes}
}
@article{Hauff2009,
author = {Hauff, Thilo},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hauff - 2009 - Transport of Energetic Particles in Turbulent Plasmas.pdf:pdf},
title = {{Transport of Energetic Particles in Turbulent Plasmas}},
year = {2009}
}
@article{Xu1995,
author = {Xu, X. Q. and Cohen, R. H. and Crotinger, J. a. and Shestakov, a. I.},
doi = {10.1063/1.871420},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {3},
pages = {686},
title = {{Fluid simulations of nonlocal dissipative drift-wave turbulence}},
url = {http://link.aip.org/link/PHPAEN/v2/i3/p686/s1{\&}Agg=doi},
volume = {2},
year = {1995}
}
@misc{Helander2002a,
abstract = {This is a textbook on theoretical plasma physics, which is the science of extremely hot gases which make up most of the universe and which are used extensively in fusion energy research. This book treats a topic at the heart of this subject, so-called transport theory, which predicts the electrical and thermal properties of the plasma. It is the most comprehensive book in its field, and is directed at graduate students in physics and professional research physicists, in particular fusion energy scientists and space physicists.},
author = {Helander, Per and Sigmar, Dieter J.},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Helander, Sigmar - 2002 - Collisional transport in magnetized plasmas.pdf:pdf},
isbn = {0521807980},
pages = {1----292},
title = {{Collisional transport in magnetized plasmas}},
year = {2002}
}
@article{Stacey2014,
author = {Stacey, Weston M. and Grierson, Brian a.},
doi = {10.1088/0029-5515/54/7/073021},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Stacey, Grierson - 2014 - Interpretation of rotation and momentum transport in the DIII-D edge plasma and comparison with neoclassical t.pdf:pdf},
issn = {0029-5515},
journal = {Nucl. Fusion},
keywords = {in colour only in,intrinsic rotation,momentum transport,rotation,some figures may appear,the online journal},
number = {7},
pages = {073021},
title = {{Interpretation of rotation and momentum transport in the DIII-D edge plasma and comparison with neoclassical theory}},
url = {http://stacks.iop.org/0029-5515/54/i=7/a=073021?key=crossref.9cc742f1e7e6f393867073d73db294a6},
volume = {54},
year = {2014}
}
@article{Puschel2009,
abstract = {This thesis details findings related to the effects of magnetic field fluctuations on the properties of microturbulent transport in fusion plasmas. To this end, direct numerical analyses and supporting analytical investigations are performed. Primarily, the gyrokinetic turbulence code Gene is employed to obtain the re- sults presented here – the derivation of its basic equations is outlined, along with its most important numerical features. Examples for contributions to its devel- opment are given in a detailed study of the effects of multiple (hyper-)diffusion terms on Gene simulations, as well as in an overview of data visualization tools. The rest of the thesis is focussed on physical scenarios. Advances are presented in electromagnetic simulations with so-called Cyclone Base Case parameters: Linearly, the subdominant and stable behavior of Kinetic Ballooning Modes (KBMs) is studied, along with mode interactions and trans- formations. The nonlinearly accessible range of the plasma pressure is extended significantly, showing for the first time examples of KBM turbulence. Multiple analyses concerning the transport levels at high pressure are performed, including quasilinear models and zonal flow studies. To augment these results, a second operation point is chosen in the Trapped Electron Mode regime which displays different physical behavior in multiple aspects. The aforementioned simulations are analyzed to solidify a test particle based model for the magnetic transport, to study the nature of changes to the magnetic geometry due to fluctuations of themagnetic field, and to investigate the behavior of fast ions as they are subjected to electromagnetic fields. Additionally, effects of realistic geometry on simulations at finite plasma pressure are discussed. Finally, two astrophysical scenarios are analyzed in the context of microturbulent heat transport levels. In the case of evaporating cold gas clouds immersed inmuch hotter material, such transport may have a significant impact on the standard model for these objects.},
author = {P{\"{u}}schel, Moritz Johannes},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/P{\"{u}}schel - 2009 - Electromagnetic Effects in Gyrokinetic Simulations of Plasma Turbulence.pdf:pdf},
title = {{Electromagnetic Effects in Gyrokinetic Simulations of Plasma Turbulence}},
year = {2009}
}
@article{Search1999,
author = {Search, Home and Journals, Collections and Contact, About and Iopscience, My and Phys, Plasma and Address, I P},
pages = {0--34},
title = {{Contact us My IOPscience Numerical simulation of ion cyclotron waves in tokamak plasmas Numerical simulation of ion cyclotron waves in tokamak plasmas}},
volume = {1},
year = {1999}
}
@article{Pataki2013a,
author = {Pataki, Andras and Cerfon, Antoine J. and Freidberg, Jeffrey P. and Greengard, Leslie and O'Neil, Michael},
doi = {10.1016/j.jcp.2013.02.045},
issn = {00219991},
journal = {J. Comput. Phys.},
month = {jun},
pages = {28--45},
publisher = {Elsevier Inc.},
title = {{A fast, high-order solver for the Grad–Shafranov equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999113001721},
volume = {243},
year = {2013}
}
@book{Bittencourt,
author = {Bittencourt},
isbn = {9781475740301},
title = {{Fundamentals of plasma physics}}
}
@article{Howes2006,
abstract = {Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of astrophysical plasmas, including accretion disks, the solar wind, and the interstellar and intracluster medium. On small scales, this turbulence is often expected to consist of highly anisotropic fluctuations with frequencies small compared to the ion cyclotron frequency. For a number of applications, the small scales are also collisionless, so a kinetic treatment of the turbulence is necessary. We show that this anisotropic turbulence is well described by a low-frequency expansion of the kinetic theory called gyrokinetics. This paper is the first in a series to examine turbulent astrophysical plasmas in the gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations and explore the linear properties of gyrokinetics as a prelude to nonlinear simulations. The linear dispersion relation for gyrokinetics is obtained, and its solutions are compared to those of hot-plasma kinetic theory. These results are used to validate the performance of the gyrokinetic simulation code GS2 in the parameter regimes relevant for astrophysical plasmas. New results on global energy conservation in gyrokinetics are also derived. We briefly outline several of the problems to be addressed by future nonlinear simulations, including particle heating by turbulence in hot accretion flows and in the solar wind, the magnetic and electric field power spectra in the solar wind, and the origin of small-scale density fluctuations in the interstellar medium.},
archivePrefix = {arXiv},
arxivId = {astro-ph/0511812},
author = {Howes, Gregory G. and Cowley, Steven C. and Dorland, William and Hammett, Gregory W. and Quataert, Eliot and Schekochihin, Alexander A.},
doi = {10.1086/506172},
eprint = {0511812},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Howes et al. - 2006 - Astrophysical Gyrokinetics Basic Equations and Linear Theory.pdf:pdf},
issn = {0004-637X},
journal = {Astrophys. J.},
month = {nov},
number = {1},
pages = {590--614},
primaryClass = {astro-ph},
title = {{Astrophysical Gyrokinetics: Basic Equations and Linear Theory}},
url = {http://stacks.iop.org/0004-637X/651/i=1/a=590},
volume = {651},
year = {2006}
}
@article{Fulton2014,
abstract = {Gyrokinetic simulations of electrostatic driftwave instabilities in a tokamak edge have been carried out to study the turbulent transport in the pedestal of an H-mode plasma. The simulations use annulus geometry and focus on two radial regions of a DIII-D experiment: the pedestal top with a mild pressure gradient and the middle of the pedestal with a steep pressure gradient. A reactive trapped electron instability with a typical ballooning mode structure is excited by trapped electrons in the pedestal top. In the middle of the pedestal, the electrostatic instability exhibits an unusual mode structure, which peaks at the poloidal angle $\theta$=±$\pi$/2. The simulations find that this unusual mode structure is due to the steep pressure gradients in the pedestal but not due to the particular DIII-D magnetic geometry. Realistic DIII-D geometry appears to have a stabilizing effect on the instability when compared to a simple circular tokamak geometry.},
author = {Fulton, D. P. and Lin, Z. and Holod, I. and Xiao, Y.},
doi = {10.1063/1.4871387},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Fulton et al. - 2014 - Microturbulence in DIII-D tokamak pedestal. I. Electrostatic instabilities.pdf:pdf},
issn = {1070-664X},
journal = {Phys. Plasmas},
month = {apr},
number = {4},
pages = {042110},
title = {{Microturbulence in DIII-D tokamak pedestal. I. Electrostatic instabilities}},
url = {http://aip.scitation.org/doi/10.1063/1.4871387},
volume = {21},
year = {2014}
}
@article{Shestakov2003,
author = {a.I. Shestakov and Cohen, R.H. and Crotinger, J.a. and LoDestro, L.L. and Tarditi, a. and Xu, X.Q.},
doi = {10.1016/S0021-9991(03)00047-0},
issn = {00219991},
journal = {J. Comput. Phys.},
month = {mar},
number = {1},
pages = {360},
title = {{Corrigendum to: Self-consistent modeling of turbulence and transport [J. Comput. Phys. 185 (2003) 399–426]}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999103000470},
volume = {186},
year = {2003}
}
@article{Petty2005,
author = {Petty, C C and Politzer, P a and Lin-Liu, Y R},
doi = {10.1088/0741-3335/47/7/008},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
month = {jul},
number = {7},
pages = {1077--1100},
title = {{Direct measurement of neoclassical currents using motional Stark effect polarimetry}},
url = {http://stacks.iop.org/0741-3335/47/i=7/a=008?key=crossref.24b20ebff6d486860e9d757bedd0578b},
volume = {47},
year = {2005}
}
@article{Hazeltine1973,
abstract = {A drift kinetic equation is derived which contains higher order effects. The upper bound appropriate to the drift ordering is only imposed so that the result is quite general and can be reduced to previous drift equations. The differential geometry of the magnetic field enters only trivially and a single recursion suffices to obtain the desired result.},
author = {Hazeltine, R D},
doi = {10.1088/0032-1028/15/1/009},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hazeltine - 1973 - Recursive derivation of drift-kinetic equation.pdf:pdf},
issn = {0032-1028},
journal = {Plasma Phys.},
number = {1},
pages = {77--80},
title = {{Recursive derivation of drift-kinetic equation}},
url = {http://stacks.iop.org/0032-1028/15/i=1/a=009?key=crossref.0e8ea9f4bfee5a31b84cb048242ab2fc},
volume = {15},
year = {1973}
}
@article{BanonNavarro2011,
abstract = {In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a (strongly) local, forward (from large to small scales) cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large-eddy-simulation techniques for gyrokinetics.},
archivePrefix = {arXiv},
arxivId = {1008.3974},
author = {{Ba{\~{n}}{\'{o}}n Navarro}, A. and Morel, P. and Albrecht-Marc, M. and Carati, D. and Merz, F. and G{\"{o}}rler, T. and Jenko, F.},
doi = {10.1103/PhysRevLett.106.055001},
eprint = {1008.3974},
isbn = {0031-9007$\backslash$n1079-7114},
issn = {00319007},
journal = {Phys. Rev. Lett.},
title = {{Free energy cascade in gyrokinetic turbulence}},
year = {2011}
}
@article{Dorland2001,
author = {Dorland, W and College, Imperial},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Dorland, College - 2001 - Gyrokinetic Turbulence Simulations.pdf:pdf},
title = {{Gyrokinetic Turbulence Simulations}},
year = {2001}
}
@article{Guzdar2005,
abstract = {When a tokamak plasma makes a transition into the good or the high confinement H mode, the edge density and pressure steepen and develop a very sharp pressure pedestal. Prediction of the height and width of this pressure profile has been actively pursued so as to provide a reliable extrapolation to future burning plasma devices. The double-Beltrami two-fluid equilibria of Mahajan and Yoshida [Phys. Plasmas 7, 635 (2000)] are invoked and extended to derive scalings for the edge pedestal width and height with plasma parameters: these scalings come out in agreement with the established semiempirical scalings. The theory predictions are also compared with limited published H-mode data and the agreement is found to be very encouraging.},
author = {Guzdar, P. N. and Mahajan, S. M. and Yoshida, Z.},
doi = {10.1063/1.1852468},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Guzdar, Mahajan, Yoshida - 2005 - A theory for the pressure pedestal in high (H) mode tokamak discharges.pdf:pdf},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {3},
pages = {1--6},
title = {{A theory for the pressure pedestal in high (H) mode tokamak discharges}},
volume = {12},
year = {2005}
}
@article{Itagaki2004,
author = {Itagaki, Masafumi and Kamisawada, Jun-ichi and Oikawa, Shun-ichi},
doi = {10.1088/0029-5515/44/3/008},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {mar},
number = {3},
pages = {427--437},
title = {{Boundary-only integral equation approach based on polynomial expansion of plasma current profile to solve the Grad–Shafranov equation}},
url = {http://stacks.iop.org/0029-5515/44/i=3/a=008?key=crossref.5d9c5e49f59f17c9fb7b3c1086c4492f},
volume = {44},
year = {2004}
}
@article{Beer1995,
abstract = {Turbulence in tokamaks is characterized by long parallel wavelengths and short perpendicular wavelengths. A coordinate system for nonlinear fluid, gyrokinetic ‘‘Vlasov,'' or particle simulations is presented that exploits the elongated nature of the turbulence by resolving the minimum necessary simulation volume: a long thin twisting flux tube. It is very similar to the ballooning representation, although periodicity constraints can be incorporated in a manner that allows E×B nonlinearities to be evaluated efficiently with fast Fourier transforms (FFT's). If the parallel correlation length is very long, however, enforcing periodicity can introduce artificial correlations, so periodicity should not necessarily be enforced in the poloidal angle at $\theta$=±$\pi$. This method is applied to high resolution three‐dimensional simulations of toroidal ion temperature gradient (ITG) driven turbulence, which predict fluctuation spectra and ion heat transport similar to experimental measurements.},
author = {Beer, M. A. and Cowley, S. C. and Hammett, G. W.},
doi = {10.1063/1.871232},
issn = {1070-664X},
journal = {Phys. Plasmas},
keywords = {COORDINATES,CORRELATION LENGTH,FOURIER TRANSFORMATION,PLASMA MICROINSTABILITIES,PLASMA SIMULATION,TOKAMAK DEVICES,TRANSPORT THEORY,TURBULENCE},
month = {aug},
number = {7},
pages = {2687--2700},
publisher = {American Institute of Physics},
title = {{Field‐aligned coordinates for nonlinear simulations of tokamak turbulence}},
url = {http://aip.scitation.org/doi/10.1063/1.871232},
volume = {2},
year = {1995}
}
@article{Parra2010c,
abstract = {Full f electrostatic gyrokinetic formulations employ two gyrokinetic equations, one for ions and the other for electrons, and quasineutrality to obtain the ion and electron distribution functions and the electrostatic potential. We demonstrate with several examples that the long wavelength radial electric field obtained with full f approaches is extremely sensitive to errors in the ion and electron density since small deviations in density give rise to large, nonphysical deviations in the conservation of toroidal angular momentum. For typical tokamak values, a relative error of 10(-7) in the ion or electron densities is enough to obtain the incorrect toroidal rotation. Based on the insights gained with the examples considered, three simple tests to check transport of toroidal angular momentum in full f simulations are proposed. (C) 2010 American Institute of Physics. [doi:10.1063/1.3327127]},
author = {Parra, Felix I. and Catto, Peter J.},
doi = {10.1063/1.3327127},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Parra, Catto - 2010 - Transport of momentum in full f gyrokinetics.pdf:pdf},
issn = {1070-664X},
journal = {Phys. Plasmas},
month = {may},
number = {5},
pages = {056106},
title = {{Transport of momentum in full f gyrokinetics}},
url = {http://aip.scitation.org/doi/10.1063/1.3327127},
volume = {17},
year = {2010}
}
@article{Hirshman1990,
author = {Hirshman, S.P. and Schwenn, U. and N{\"{u}}hrenberg, J.},
doi = {10.1016/0021-9991(90)90259-4},
issn = {00219991},
journal = {J. Comput. Phys.},
month = {apr},
number = {2},
pages = {396--407},
title = {{Improved radial differencing for three-dimensional magnetohydrodynamic equilibrium calculations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0021999190902594},
volume = {87},
year = {1990}
}
@article{Krommes2012,
abstract = {Nonlinear gyrokinetics is the major formalism used for both the analytical and numerical descriptions of low-frequency microturbulence in magnetized plasmas. Its derivation from noncanonical Lagrangian methods and field-theoretic variational principles is summarized. Basic properties of gyrokinetic physics are discussed, including polarization and the concept of the gyrokinetic vacuum, equilibrium statistical mechanics, and the two fundamental constituents of gyrokinetic turbulence, namely drift waves and zonal flows. Numerical techniques are described briefly, and illustrative simulation results are presented. Advanced topics include the transition to turbulence, the nonlinear saturation of turbulence by coupling to damped gyrokinetic eigenmodes, phase-space cascades, subcritical turbulence, and momentum conservation.},
author = {Krommes, John a.},
doi = {10.1146/annurev-fluid-120710-101223},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Krommes - 2012 - The Gyrokinetic Description of Microturbulence in Magnetized Plasmas.pdf:pdf},
issn = {0066-4189},
journal = {Annu. Rev. Fluid Mech.},
keywords = {drift waves,entropy cascade,gyrokinetic,noncanonical lagrangian methods,simulations,zonal flows},
number = {1},
pages = {175--201},
title = {{The Gyrokinetic Description of Microturbulence in Magnetized Plasmas}},
volume = {44},
year = {2012}
}
@article{Solano2004,
author = {Solano, Emilia R},
doi = {10.1088/0741-3335/46/3/L02},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
month = {mar},
number = {3},
pages = {L7--L13},
title = {{Criticality of the Grad–Shafranov equation: transport barriers and fragile equilibria}},
url = {http://stacks.iop.org/0741-3335/46/i=3/a=L02?key=crossref.b6553295f3cbc19fb9ff4e7270945364},
volume = {46},
year = {2004}
}
@article{Reference1,
abstract = {We have developed an enhanced Littrow configuration extended cavity diode laser (ECDL) that can be tuned without changing the direction of the output beam. The output of a conventional Littrow ECDL is reflected from a plane mirror fixed parallel to the tuning diffraction grating. Using a free-space Michelson wavemeter to measure the laser wavelength, we can tune the laser over a range greater than 10 nm without any alteration of alignment.},
author = {Hawthorn, C J and Weber, K P and Scholten, R E},
journal = {Rev. Sci. Instrum.},
month = {dec},
number = {12},
pages = {4477--4479},
title = {{Littrow Configuration Tunable External Cavity Diode Laser with Fixed Direction Output Beam}},
url = {http://link.aip.org/link/?RSI/72/4477/1},
volume = {72},
year = {2001}
}
@article{Miller1998,
abstract = {A tokamak equilibrium model, local to a flux surface, is introduced which is completely described in terms of nine parameters including aspect ratio, elongation, triangularity, and safety factor. By allowing controlled variation of each of these nine parameters, the model is particularly suitable for localized stability studies such as those carried out using the ballooning mode representation of the gyrokinetic equations.},
author = {Miller, R. L. and Chu, M. S. and Greene, J. M. and Lin-Liu, Y. R. and Waltz, R. E.},
doi = {10.1063/1.872666},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Miller et al. - 1998 - Noncircular, finite aspect ratio, local equilibrium model.pdf:pdf},
issn = {1070-664X},
journal = {Phys. Plasmas},
number = {4},
pages = {973--978},
title = {{Noncircular, finite aspect ratio, local equilibrium model}},
url = {http://aip.scitation.org/doi/10.1063/1.872666},
volume = {5},
year = {1998}
}
@article{Xu2007,
author = {Xu, X.Q and Xiong, Z and Dorr, M.R and Hittinger, J.a and Bodi, K and Candy, J and Cohen, B.I and Cohen, R.H and Colella, P and Kerbel, G.D and Krasheninnikov, S and Nevins, W.M and Qin, H and Rognlien, T.D and Snyder, P.B and Umansky, M.V},
doi = {10.1088/0029-5515/47/8/011},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {aug},
number = {8},
pages = {809--816},
title = {{Edge gyrokinetic theory and continuum simulations}},
url = {http://stacks.iop.org/0029-5515/47/i=8/a=011?key=crossref.9476829b713daed4fe0a85d7fe3c85d6},
volume = {47},
year = {2007}
}
@article{Lee2014,
author = {Lee, J. P. and Barnes, M. and Parra, F. I. and Belli, E. A. and Candy, J.},
doi = {10.1063/1.4872322},
issn = {10897674},
journal = {Phys. Plasmas},
number = {5},
pages = {13--21},
title = {{The effect of diamagnetic flows on turbulent driven ion toroidal rotation}},
url = {http://dx.doi.org/10.1063/1.4872322},
volume = {21},
year = {2014}
}
@article{Casson2011,
abstract = {Small scale turbulence in a magnetically confined fusion plasma drives energy and particle transport which determine the confinement. The plasma in a tokamak experiment has a toroidal rotation which may be driven externally, but can also arise spontaneously from turbulent momentum transport. This thesis investigates the interaction between turbulence and rotation via nonlinear numerical simulations, which use the gyrokinetic description in the frame that corotates with the plasma. A local gyrokinetic code is extended to include both the centrifugal force, and the stabilising effect of sheared equilibrium flow. Sheared flow perpendicular to the magnetic field suppresses the turbulence, and also breaks a symmetry of the local model. The resulting asymmetry creates a turbulent residual stress which can counteract diffusive momentum transport and contribute to spontaneous rotation. The competition between symmetry breaking and turbulence suppression results in a maximum in the nondiffusive momentum flux at intermediate shearing rates. Whilst this component of the momentum transport is driven by the sheared flow, it is also found to be suppressed by the shearing more strongly than the thermal transport. The direction of the residual stress reverses for negative magnetic shear, but also persists at zero magnetic shear. The parallel component of the centrifugal force traps particles on the outboard side of the plasma, which destabilises trapped particle driven modes. The perpendicular component of the centrifugal force appears as a centrifugal drift which modifies the phase relation between density and electric field perturbations, and is stabilising for both electron and ion driven instabilities. For ion temperature gradient dominated turbulence, an increased fraction of slow trapped electrons enhances the convective particle pinch, suggesting increased density peaking for strongly rotating plasmas. Heavy impurities feel the centrifugal force more strongly, therefore the effects of rotation are significant for impurities even when the bulk ion Mach number is low. For ion driven modes, rotation results in a strong impurity convection inward, whilst a more moderate convection outward is found for electron driven modes.},
archivePrefix = {arXiv},
arxivId = {1007.3390},
author = {Casson, F. J.},
eprint = {1007.3390},
keywords = {QC Physics},
number = {March},
title = {{Turbulent transport in rotating tokamak plasmas}},
url = {http://webcat.warwick.ac.uk/record=b2521720{~}S15},
year = {2011}
}
@article{PLUNK2010,
abstract = {Two-dimensional gyrokinetics is a simple paradigm for the study of kinetic magnetised plasma turbulence. In this paper, we present a comprehensive theoretical framework for this turbulence. We study both the inverse and direct cascades (the ‘dual cascade'), driven by a homogeneous and isotropic random forcing. The key characteristic length of gyrokinetics, the Larmor radius, divides scales into two physically distinct ranges. For scales larger than the Larmor radius, we derive the familiar Charney–Hasegawa–Mima equation from the gyrokinetic system, and explain its relationship to gyrokinetics. At scales smaller than the Larmor radius, a dual cascade occurs in phase space (two dimensions in position space plus one dimension in velocity space) via a nonlinear phase-mixing process. We show that at these sub-Larmor scales, the turbulence is self-similar and exhibits power-law spectra in position and velocity space. We propose a Hankel-transform formalism to characterise velocity-space spectra. We derive the exact relations for third-order structure functions, analogous to Kolmogorov's four-fifths and Yaglom's four-thirds laws and valid at both long and short wavelengths. We show how the general gyrokinetic invariants are related to the particular invariants that control the dual cascade in the long- and short-wavelength limits. We describe the full range of cascades from the fluid to the fully kinetic range.},
archivePrefix = {arXiv},
arxivId = {arXiv:0904.0243v4},
author = {PLUNK, G. G. and COWLEY, S. C. and SCHEKOCHIHIN, A. A. and TATSUNO, T.},
doi = {10.1017/S002211201000371X},
eprint = {arXiv:0904.0243v4},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/PLUNK et al. - 2010 - Two-dimensional gyrokinetic turbulence.pdf:pdf},
isbn = {0022-1120},
issn = {0022-1120},
journal = {J. Fluid Mech.},
keywords = {kinetic theory,plasmas,turbulence theory},
month = {dec},
pages = {407--435},
title = {{Two-dimensional gyrokinetic turbulence}},
url = {http://www.journals.cambridge.org/abstract{\_}S002211201000371X},
volume = {664},
year = {2010}
}
@book{Ben-Naim2007,
abstract = {Ever since I heard the word “entropy” for the first time, I was fascinated with its mysterious nature. I vividly recall my first encounter with entropy and with the Second Law of Thermo- dynamics. It was more than forty years ago. I remember the hall, the lecturer, even the place where I sat; in the first row, facing the podium where the lecturer stood.},
author = {Ben-Naim, Arieh},
doi = {10.1142/6261},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Ben-Naim - 2007 - Entropy Demystified.pdf:pdf},
isbn = {978-981-270-052-0},
issn = {1557-7988},
pmid = {19897091},
title = {{Entropy Demystified}},
url = {http://www.worldscientific.com/worldscibooks/10.1142/6261},
year = {2007}
}
@article{McCarthy1999,
author = {{Mc Carthy}, P. J.},
doi = {10.1063/1.873630},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {9},
pages = {3554},
title = {{Analytical solutions to the Grad–Shafranov equation for tokamak equilibrium with dissimilar source functions}},
url = {http://link.aip.org/link/PHPAEN/v6/i9/p3554/s1{\&}Agg=doi},
volume = {6},
year = {1999}
}
@article{Howard2016,
abstract = {Validation of nonlinear gyrokinetic simulations of L-and I-mode plasmas on Alcator C-Mod Physics of Plasmas 24, 056104 (2017); 10.1063/1.4977466 Validation metrics for turbulent plasma transport Physics of Plasmas 23, 060901 (2016); 10.1063/1.4954151 The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence Physics of Plasmas 23, 062518 (2016); 10.1063/1.4954905 Quantitative comparison of electron temperature fluctuations to nonlinear gyrokinetic simulations in C-Mod Ohmic L-mode discharges Physics of Plasmas 23, 042303 (2016); 10.1063/1.4945620 Multi-scale gyrokinetic simulation of Alcator C-Mod tokamak discharges Physics of Plasmas 21, 032308 (2014); 10.1063/1.4869078 To better understand the role of cross-scale coupling in experimental conditions, a series of multi-scale gyrokinetic simulations were performed on Alcator C-Mod, L-mode plasmas. These simula-tions, performed using all experimental inputs and realistic ion to electron mass ratio ((m i /m e) 1=2 ¼ 60.0), simultaneously capture turbulence at the ion (k h q s {\$} Oð1:0Þ) and electron-scales (k h q e {\$} Oð1:0Þ). Direct comparison with experimental heat fluxes and electron profile stiffness indi-cates that Electron Temperature Gradient (ETG) streamers and strong cross-scale turbulence cou-pling likely exist in both of the experimental conditions studied. The coupling between ion and electron-scales exists in the form of energy cascades, modification of zonal flow dynamics, and the effective shearing of ETG turbulence by long wavelength, Ion Temperature Gradient (ITG) turbu-lence. The tightly coupled nature of ITG and ETG turbulence in these realistic plasma conditions is shown to have significant implications for the interpretation of experimental transport and fluctua-tions. Initial attempts are made to develop a " rule of thumb " based on linear physics, to help predict when cross-scale coupling plays an important role and to inform future modeling of experimental dis-charges. The details of the simulations, comparisons with experimental measurements, and implica-tions for both modeling and experimental interpretation are discussed. Published by AIP Publishing.},
author = {Howard, N. T. and Holland, C. and White, A. E. and Greenwald, M. and Candy, J. and Creely, A. J.},
doi = {10.1063/1.4946028},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Howard et al. - 2016 - Multi-scale gyrokinetic simulations Comparison with experiment and implications for predicting turbulence and tra.pdf:pdf},
issn = {1070-664X},
journal = {Phys. Plasmas},
month = {may},
number = {5},
pages = {056109},
title = {{Multi-scale gyrokinetic simulations: Comparison with experiment and implications for predicting turbulence and transport}},
url = {http://aip.scitation.org/doi/10.1063/1.4946028},
volume = {23},
year = {2016}
}
@article{Hatch2015,
abstract = {The gyrokinetic G ENE code is used to study the inter-ELM H-mode pedestal profile evolution for an ASDEX Upgrade discharge. Density gradient driven trapped electron modes are the dominant pedestal instability during the early density-buildup phase. Nonlinear simulations produce particle transport levels consistent with experimental expectations. Later inter-ELM phases appear to be simultaneously constrained by electron temperature gradient (ETG) and kinetic ballooning mode (KBM) turbulence. The electron temperature gradient achieves a critical value early in the ELM cycle, concurrent with the appearance of both microtearing modes and ETG modes. Nonlinear ETG simulations demonstrate that the profiles lie at a nonlinear critical gradient. The nominal profiles are stable to KBM, but moderate increases in ? are sufficient to surpass the KBM threshold. Certain aspects of the dynamics support the premise of KBM-constrained pedestal evolution; the density and temperature profiles separately undergo large changes, but in a manner that keeps the pressure profile constant and near the KBM limit.},
author = {Hatch, D. R. and Told, D. and Jenko, F. and Doerk, H. and Dunne, M. G. and Wolfrum, E. and Viezzer, E. and Pueschel, M. J.},
doi = {10.1088/0029-5515/55/6/063028},
issn = {17414326},
journal = {Nucl. Fusion},
title = {{Gyrokinetic study of ASDEX Upgrade inter-ELM pedestal profile evolution}},
year = {2015}
}
@article{Ling1985,
author = {Ling, K.M. and Jardin, S.C.},
doi = {10.1016/0021-9991(85)90165-2},
issn = {00219991},
journal = {J. Comput. Phys.},
month = {may},
number = {3},
pages = {300--335},
title = {{The Princeton spectral equilibrium code: PSEC}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0021999185901652},
volume = {58},
year = {1985}
}
@article{Myra2000b,
author = {Myra, J. R. and D'Ippolito, D. a. and Xu, X. Q. and Cohen, R. H.},
doi = {10.1063/1.1314623},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {11},
pages = {4622},
title = {{Resistive modes in the edge and scrape-off layer of diverted tokamaks}},
url = {http://link.aip.org/link/PHPAEN/v7/i11/p4622/s1{\&}Agg=doi},
volume = {7},
year = {2000}
}
@article{Hua1992,
author = {Hua, D. D. and Xu, X. Q. and Fowler, T. K.},
doi = {10.1063/1.860377},
issn = {08998221},
journal = {Phys. Fluids B Plasma Phys.},
number = {10},
pages = {3216},
title = {{Ion-temperature-gradient modes in noncircular tokamak geometry}},
url = {http://link.aip.org/link/PFBPEI/v4/i10/p3216/s1{\&}Agg=doi},
volume = {4},
year = {1992}
}
@article{Wong2005,
abstract = {An efficient method is described for deriving the drift-kinetic equation. A maximal ordering is invoked: the ordering parameter ϵ⪡1 is formally taken to be proportional to m/e, subject to the proviso that the parallel electric field E‖ ∼ ϵ. Electric drifts can be of the order of particle thermal velocities. The drift-kinetic equation is derived up to second order in ϵ, and is in a form such that the phase-space volume following the particle phase-space trajectories is preserved. The mean density, mean velocity, momentum flow tensor, and the presure tensor are evaluated in terms of the electromagnetic fields and the velocity moments of the drift-kinetic distribution function . The moments of the drift-kinetic equation reproduce the corresponding moments of the Vlasov equation up to order ϵ2. A consistent set of fluid-kinetic equations is formulated, with the fluid-like perpendicular motion described by the perpendicular component of the momentum equation. The drift-kinetic equation describes the parallel motion, and the solution is required to evaluate the velocity moments necessary to close the set of equations.},
author = {Wong, H. Vernon},
doi = {10.1063/1.2116867},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Wong - 2005 - Nonlinear finite-Larmor-radius drift-kinetic equation.pdf:pdf},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {11},
pages = {1--19},
title = {{Nonlinear finite-Larmor-radius drift-kinetic equation}},
volume = {12},
year = {2005}
}
@article{Search1981,
author = {Search, Home and Journals, Collections and Contact, About and Iopscience, My and Address, I P},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Search et al. - 1981 - Neoclassical transport of impurities in tokamak plasmas REVIEW PAPER NEOCLASSICAL TRANSPORT OF IMPURITIES United.pdf:pdf},
title = {{Neoclassical transport of impurities in tokamak plasmas REVIEW PAPER NEOCLASSICAL TRANSPORT OF IMPURITIES United States of America}},
volume = {1079},
year = {1981}
}
@article{Morley2015,
abstract = {The Academic Phrasebank is an invaluable academic writing resource whatever stage of your career you are at. Equally useful for writers of English as a second language and native speakers, for researchers who want to improve their academic writing and students who need assistance writing up their thesis or dissertation.},
author = {Morley, John},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Morley - 2015 - The Academic Phrasebank An Academic Writing Resource for Students and Researchers.pdf:pdf},
pages = {139},
title = {{The Academic Phrasebank: An Academic Writing Resource for Students and Researchers}},
year = {2015}
}
@article{Stacey2009,
author = {Stacey, W. M. and Bae, Cheonho},
doi = {10.1063/1.3177613},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {8},
pages = {082501},
title = {{Representation of the plasma fluid equations in “Miller equilibrium” analytical flux surface geometry}},
url = {http://link.aip.org/link/PHPAEN/v16/i8/p082501/s1{\&}Agg=doi},
volume = {16},
year = {2009}
}
@article{McKee2009,
author = {McKee, G.R. and Gohil, P. and Schlossberg, D.J. and Boedo, J.a. and Burrell, K.H. and DeGrassie, J.S. and Groebner, R.J. and Moyer, R.a. and Petty, C.C. and Rhodes, T.L. and Schmitz, L. and Shafer, M.W. and Solomon, W.M. and Umansky, M. and Wang, G. and a.E. White and Xu, X.},
doi = {10.1088/0029-5515/49/11/115016},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {nov},
number = {11},
pages = {115016},
title = {{Dependence of the L- to H-mode power threshold on toroidal rotation and the link to edge turbulence dynamics}},
url = {http://stacks.iop.org/0029-5515/49/i=11/a=115016?key=crossref.a241f03da91762ed5215eb7a498ab741},
volume = {49},
year = {2009}
}
@article{Cohen2007,
author = {Cohen, R.H and LaBombard, B and Ryutov, D.D and Terry, J. L and Umansky, M.V and Xu, X.Q and Zweben, S},
doi = {10.1088/0029-5515/47/7/012},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {jul},
number = {7},
pages = {612--625},
title = {{Theory and fluid simulations of boundary-plasma fluctuations}},
url = {http://stacks.iop.org/0029-5515/47/i=7/a=012?key=crossref.0d3241b8b3d7c976145e55beb8e055c1},
volume = {47},
year = {2007}
}
@article{McDevitt2009,
abstract = {Starting from a phase space conserving gyrokinetic formulation, a systematic derivation of parallel momentum conservation uncovers a novel mechanism by which microturbulence may drive intrinsic rotation. This mechanism, which appears in the gyrokinetic formulation through the parallel nonlinearity, emerges due to charge separation induced by the polarization drift. The derivation and physical discussion of this mechanism will be pursued throughout this Letter.},
author = {McDevitt, C J and Diamond, P H and Gurcan, O D and Hahm, T S},
doi = {10.1103/PhysRevLett.103.205003},
isbn = {0031-9007},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
keywords = {PRL,paper,plasma,plasma rotation,reversal,tokamaks,wave turbulence},
mendeley-tags = {PRL,paper,plasma rotation},
number = {20},
pages = {--},
pmid = {20365987},
title = {{Toroidal Rotation Driven by the Polarization Drift}},
volume = {103},
year = {2009}
}
@article{Xia2013a,
author = {Xia, T.Y. and Xu, X.Q. and Xi, P.W.},
doi = {10.1088/0029-5515/53/7/073009},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {jul},
number = {7},
pages = {073009},
title = {{Six-field two-fluid simulations of peeling–ballooning modes using BOUT++}},
url = {http://stacks.iop.org/0029-5515/53/i=7/a=073009?key=crossref.e285e3a00110042b6896b8574dc50054},
volume = {53},
year = {2013}
}
@article{Xu2000,
author = {Xu, X. Q. and Cohen, R. H. and Rognlien, T. D. and Myra, J. R.},
doi = {10.1063/1.874044},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {1951},
title = {{Low-to-high confinement transition simulations in divertor geometry}},
url = {http://link.aip.org/link/PHPAEN/v7/i5/p1951/s1{\&}Agg=doi},
volume = {7},
year = {2000}
}
@article{Xu2010,
author = {Xu, X.Q. and Bodi, K. and Cohen, R.H. and Krasheninnikov, S. and Rognlien, T.D.},
doi = {10.1088/0029-5515/50/6/064003},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {jun},
number = {6},
pages = {064003},
title = {{TEMPEST simulations of the plasma transport in a single-null tokamak geometry}},
url = {http://stacks.iop.org/0029-5515/50/i=6/a=064003?key=crossref.24b40b5b63109f9391b68a7a2a624cc7},
volume = {50},
year = {2010}
}
@article{Beskin2008,
abstract = {The goal of this presentation is in paying attention to the 1D cylindrical version of the Grad-Shafranov (GS) equation. In our opinion, this approach is more rich than classical self-similar ones, and more suitable for astrophysical jets we observe. In particular, it allows us describing the central (and, hence, the most energetic) part of the flow.},
archivePrefix = {arXiv},
arxivId = {0802.0142},
author = {Beskin, V S and Nokhrina, E E},
doi = {10.1142/S0218271808013352},
eprint = {0802.0142},
journal = {worldscinetcom},
keywords = {agn,gs equation,jets,yso},
pages = {1731--1742},
title = {{On the Cylindrical Grad-Shafranov Equation}},
year = {2008}
}
@article{Grandgirard2016,
abstract = {This paper addresses non-linear gyrokinetic simulations of ion temperature gradient (ITG) turbulence in tokamak plasmas. The electrostatic GYSELA code is one of the few international 5D gyrokinetic codes able to perform global, full-f and flux-driven simulations. Its has also the numerical originality of being based on a semi-Lagrangian (SL) method. This reference paper for the GYSELA code presents a complete description of its multi-ion species version including: (i) numerical scheme, (ii) high level of parallelism up to 500k cores and (iii) conservation law properties.},
author = {Grandgirard, V. and Abiteboul, J. and Bigot, J. and Cartier-Michaud, T. and Crouseilles, N. and Dif-Pradalier, G. and Ehrlacher, Ch and Esteve, D. and Garbet, X. and Ghendrih, Ph and Latu, G. and Mehrenberger, M. and Norscini, C. and Passeron, Ch and Rozar, F. and Sarazin, Y. and Sonnendr{\"{u}}cker, E. and Strugarek, A. and Zarzoso, D.},
doi = {10.1016/j.cpc.2016.05.007},
issn = {00104655},
journal = {Comput. Phys. Commun.},
title = {{A 5D gyrokinetic full-f global semi-Lagrangian code for flux-driven ion turbulence simulations}},
year = {2016}
}
@article{Zakharov1999,
author = {Zakharov, L E and Pletzer, A},
doi = {10.1063/1.873756},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {12},
pages = {4693},
title = {{Theory of perturbed equilibria for solving the Grad–Shafranov equation}},
url = {http://link.aip.org/link/PHPAEN/v6/i12/p4693/s1{\&}Agg=doi},
volume = {6},
year = {1999}
}
@article{Sun2013,
author = {Sun, Y. and Shaing, K.C. and Liang, Y. and Casper, T. and Loarte, A. and Shen, B. and Wan, B.},
doi = {10.1088/0029-5515/53/9/093010},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {9},
pages = {093010},
title = {{Intrinsic plasma rotation determined by neoclassical toroidal plasma viscosity in tokamaks}},
url = {http://stacks.iop.org/0029-5515/53/i=9/a=093010?key=crossref.1bcd7f7318780c6b0098b220ebb8543d},
volume = {53},
year = {2013}
}
@article{Tsui2009,
abstract = {The standard Grad-Shafranov equation for axisymmetric toroidal plasma equilibrium is customary expressed in cylindrical coordinates with toroidal contours, and through which benchmark equilibria are solved. An alternative approach to cast the Grad-Shafranov equation in spherical coordinates is presented. This equation, in spherical coordinates, is examined for toroidal solutions to describe low beta Solovev and high beta plasma equilibria in terms of elementary functions.},
archivePrefix = {arXiv},
arxivId = {0902.0272},
author = {Tsui, K H},
doi = {10.1063/1.3006340},
eprint = {0902.0272},
journal = {Phys. Plasmas},
pages = {112506},
title = {{Toroidal equilibria in spherical coordinates}},
volume = {15},
year = {2009}
}
@article{Rodrigues2005,
abstract = {Numerical Grad-Shafranov (GS) equilibria with negative current density in the plasma core are computed which do not impose any particularly chosen models for the pressure and current-density profiles. This flexibility allows the profiles to be tailored so that an island unfolds in the low-field side, even for elongated plasmas, thus sustaining the negative-current core against outward forces. Among other topological results, reversed GS equilibria are also shown to be necessarily non-nested, except for the cylindrical and other very special degenerate, hence structurally unstable cases.},
author = {Rodrigues, Paulo and Bizarro, Jo{\~{a}}o P S},
journal = {Phys. Rev. Lett.},
pages = {015001},
pmid = {16090623},
title = {{Grad-Shafranov equilibria with negative core toroidal current in Tokamak plasmas.}},
volume = {95},
year = {2005}
}
@article{Rice2007a,
abstract = {Parametric scalings of the intrinsic (spontaneous, with no external momentum input) toroidal rotation observed on a large number of tokamaks have been combined with an eye towards revealing the underlying mechanism(s) and extrapolation to future devices. The intrinsic rotation velocity has been found to increase with plasma stored energy or pressure in JET, Alcator C-Mod, Tore Supra, DIII-D, JT-60U and TCV, and to decrease with increasing plasma current in some of these cases. Use of dimensionless parameters has led to a roughly unified scaling with M A ∝ $\beta$ N , although a variety of Mach numbers works fairly well; scalings of the intrinsic rotation velocity with normalized gyro-radius or collisionality show no correlation. Whether this suggests the predominant role of MHD phenomena such as ballooning transport over turbulent processes in driving the rotation remains an open question. For an ITER discharge with $\beta$ N = 2.6, an intrinsic rotation Alfven Mach number of M A 0.02 may be expected from the above deduced scaling, possibly high enough to stabilize resistive wall modes without external momentum input. PACS numbers: 52.30.-q, 52.55.Fa},
author = {Rice, J E and Ince-Cushman, A and Degrassie, J S and Eriksson, L.-G and Sakamoto, Y and Scarabosio, A and Bortolon, A and Burrell, K H and Duval, B P and Fenzi-Bonizec, C and Greenwald, M J and Groebner, R J and Hoang, G T and Koide, Y and Marmar, E S and Pochelon, A and Podpaly, Y},
doi = {10.1088/0029-5515/47/11/025},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Rice et al. - 2007 - Inter-machine comparison of intrinsic toroidal rotation in tokamaks.pdf:pdf},
isbn = {0029-5515},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {47},
pages = {1618--1624},
title = {{Inter-machine comparison of intrinsic toroidal rotation in tokamaks}},
url = {http://iopscience.iop.org/0029-5515/47/11/025},
volume = {47},
year = {2007}
}
@article{Candy2016,
abstract = {We describe a new approach to solve the electromagnetic gyrokinetic equations which is optimized for accurate treatment of multispecies Fokker–Planck collisions including both pitch-angle and energy diffusion. The new algorithm is spectral/pseudospectral in four of the five phase space dimensions, and in the fieldline direction a novel 5th-order conservative upwind scheme is used to permit high-accuracy electromagnetic simulation even in the limit of very high plasma $\beta$ and vanishingly small perpendicular wavenumber, k⊥→0. To our knowledge, this is the first pseudospectral implementation of the collision operator in a gyrokinetic code. We show that the new solver agrees closely with GYRO in the limit of weak Lorentz collisions, but gives a significantly more realistic description of collisions at high collision frequency. The numerical methods are also designed to be efficient and scalable for multiscale simulations that treat ion-scale and electron–scale turbulence simultaneously.},
author = {Candy, J. and Belli, E. A. and Bravenec, R. V.},
doi = {10.1016/j.jcp.2016.07.039},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Candy, Belli, Bravenec - 2016 - A high-accuracy Eulerian gyrokinetic solver for collisional plasmas.pdf:pdf},
issn = {10902716},
journal = {J. Comput. Phys.},
keywords = {Continuum,Eulerian,Gyrokinetic},
pages = {73--93},
publisher = {Elsevier Inc.},
title = {{A high-accuracy Eulerian gyrokinetic solver for collisional plasmas}},
url = {http://dx.doi.org/10.1016/j.jcp.2016.07.039},
volume = {324},
year = {2016}
}
@article{Parra2012,
abstract = {The generation of intrinsic rotation by turbulence and neoclassical effects in tokamaks is considered. To obtain the complex dependences observed in experiments, it is necessary to have a model of the radial flux of momentum that redistributes the momentum within the tokamak in the absence of a preexisting velocity. When the lowest order gyrokinetic formulation is used, a symmetry of the model precludes this possibility, making small effects in the gyroradius over scale length expansion necessary. These effects that are usually small become important for momentum transport because the symmetry of the lowest order gyrokinetic formulation leads to the cancellation of the lowest order momentum flux. The accuracy to which the gyrokinetic equation needs to be obtained to retain all the physically relevant effects is discussed. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3699186]},
archivePrefix = {arXiv},
arxivId = {arXiv:1203.4958v1},
author = {Parra, F. I. and Barnes, M. and Calvo, I. and Catto, P. J.},
doi = {10.1063/1.3699186},
eprint = {arXiv:1203.4958v1},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Parra et al. - 2012 - Intrinsic rotation with gyrokinetic models.pdf:pdf},
issn = {1070-664X},
journal = {Phys. Plasmas},
number = {2012},
title = {{Intrinsic rotation with gyrokinetic models}},
url = {//000304831100076},
volume = {19},
year = {2012}
}
@article{Search,
author = {Search, Home and Journals, Collections and Contact, About and Iopscience, My and Address, I P},
title = {{Determination of current distribution in JET from soft X-ray measurements DETERMINATION OF CURRENT DISTRIBUTION IN JET FROM SOFT X-RAY MEASUREMENTS}},
volume = {703}
}
@article{Cheviakov2005,
abstract = {Dynamic plasma equilibrium systems, both in isotropic and anisotropic framework, possess infinite-dimensional Lie groups of point symmetries, which depend on solution topology and lead to construction of infinite families of new physical solutions. By performing the complete classification, we show that in the static isotropic case no infinite point symmetries arise, whereas static anisotropic plasma equilibria still possess a Lie group of symmetries depending on one free function defined on the set of magnetic field lines. The finite form of the symmetries is found and used to obtain new exact solutions. We demonstrate how anisotropic axially- and helically-symmetric equilibria are obtained using conventional Grad-Shafranov and JFKO equations. A recently developed multifunctional automated Maple-based software package for symmetry and conservation law analysis is presented and used in this work.},
archivePrefix = {arXiv},
arxivId = {math-ph/0510003},
author = {Cheviakov, Alexei F},
eprint = {0510003},
journal = {Arxiv Prepr. mathph0510003},
keywords = {exact so,grad shafranov equation,lie group,lutions,plasma equilibria,symbolic computations,symmetry},
pages = {22},
primaryClass = {math-ph},
title = {{Point symmetries of 3D static plasma equilibrium systems: comparison and applications}},
year = {2005}
}
@article{Hatch2010,
author = {Hatch, David R},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hatch - 2010 - Mode Analyses of Gyrokinetic Simulations of Plasma Microturbulence.pdf:pdf},
journal = {Engineering},
title = {{Mode Analyses of Gyrokinetic Simulations of Plasma Microturbulence}},
year = {2010}
}
@article{Falessi2018,
abstract = {A set of equations is derived describing the macroscopic transport of particles and energy in a thermonuclear plasma on the energy confinement time. The equations thus derived allow studying collisional and turbulent transport self-consistently, retaining the effect of magnetic field geometry without postulating any scale separation between the reference state and fluctuations. Previously, assuming scale separation, transport equations have been derived from kinetic equations by means of multiple-scale perturbation analysis and spatio-temporal averaging. In this work, the evolution equations for the moments of the distribution function are obtained following the standard approach; meanwhile, gyrokinetic theory has been used to explicitly express the fluctuation induced fluxes. In this way, equations for the transport of particles and energy up to the transport time scale can be derived using standard first order gyrokinetics.},
archivePrefix = {arXiv},
arxivId = {1710.07229},
author = {Falessi, Matteo Valerio and Zonca, Fulvio},
doi = {10.1063/1.5018175},
eprint = {1710.07229},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Falessi, Zonca - 2018 - Gyrokinetic theory for particle and energy transport in fusion plasmas.pdf:pdf},
issn = {10897674},
journal = {Phys. Plasmas},
number = {3},
title = {{Gyrokinetic theory for particle and energy transport in fusion plasmas}},
volume = {25},
year = {2018}
}
@article{Fenstermacher2005,
author = {Fenstermacher, M.E and Osborne, T.H and a.W Leonard and Snyder, P.B and Thomas, D.M and Boedo, J.a and Casper, T.a and Groebner, R.J and Groth, M and Kempenaars, M.a.H and Loarte, a and McKee, G.R and Meyer, W.M and Saibene, G and VanZeeland, M.a and Xu, X.Q and Zeng, L and Team, the Diii-D},
doi = {10.1088/0029-5515/45/12/004},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {dec},
number = {12},
pages = {1493--1502},
title = {{Structure, stability and ELM dynamics of the H-mode pedestal in DIII-D}},
url = {http://stacks.iop.org/0029-5515/45/i=12/a=004?key=crossref.f72f956175e1654536fa0da0c876484a},
volume = {45},
year = {2005}
}
@article{Ciolfi2010,
abstract = {We construct general relativistic models of stationary, strongly magnetized neutron stars. The magnetic field configuration, obtained by solving the relativistic Grad-Shafranov equation, is a generalization of the twisted torus model recently proposed in the literature; the stellar deformations induced by the magnetic field are computed by solving the perturbed Einstein's equations; stellar matter is modeled using realistic equations of state. We find that in these configurations the poloidal field dominates over the toroidal field and that, if the magnetic field is sufficiently strong during the first phases of the stellar life, it can produce large deformations.},
archivePrefix = {arXiv},
arxivId = {1003.2148},
author = {Ciolfi, R and Ferrari, V and Gualtieri, L},
eprint = {1003.2148},
journal = {Mon. Not. R. Astron. Soc.},
pages = {10},
title = {{Structure and deformations of strongly magnetized neutron stars with twisted torus configurations}},
volume = {406},
year = {2010}
}
@article{Xu2011,
author = {Xu, X.Q. and Dudson, B.D. and Snyder, P.B. and Umansky, M.V. and Wilson, H.R. and Casper, T.},
doi = {10.1088/0029-5515/51/10/103040},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {oct},
number = {10},
pages = {103040},
title = {{Nonlinear ELM simulations based on a nonideal peeling–ballooning model using the BOUT++ code}},
url = {http://stacks.iop.org/0029-5515/51/i=10/a=103040?key=crossref.5298d32f63131003e848e7f59f1878dd},
volume = {51},
year = {2011}
}
@article{Wang2004,
abstract = {It is found that, with a model current profile, the Grad-Shafranov equation can be reduced to the Helmholtz equation, which can describe a variety of equilibrium configurations. With the eigenvalue problem solved in the toroidal coordinate system, an analytical solution to the Grad-Shafranov equation is found. It is demonstrated that current reversal equilibrium configurations exist with finite radial gradient of plasma pressure and continuous current density, and that current density reversal is accompanied by pressure gradient reversal.},
author = {Wang, Shaojie},
journal = {Phys. Rev. Lett.},
pages = {155007},
pmid = {15524896},
title = {{Theory of tokamak equilibria with central current density reversal.}},
volume = {93},
year = {2004}
}
@article{Tatsuno2012,
abstract = {In magnetized plasmas, a turbulent cascade occurs in phase space at scales smaller than the thermal Larmor radius ("sub-Larmor scales") [Phys. Rev. Lett. 103, 015003 (2009)]. When the turbulence is restricted to two spatial dimensions perpendicular to the background magnetic field, two independent cascades may take place simultaneously because of the presence of two collisionless invariants. In the present work, freely decaying turbulence of two-dimensional electrostatic gyrokinetics is investigated by means of phenomenological theory and direct numerical simulations. A dual cascade (forward and inverse cascades) is observed in velocity space as well as in position space, which we diagnose by means of nonlinear transfer functions for the collisionless invariants. We find that the turbulence tends to a time-asymptotic state, dominated by a single scale that grows in time. A theory of this asymptotic state is derived in the form of decay laws. Each case that we study falls into one of three regimes (weakly collisional, marginal, and strongly collisional), determined by a dimensionless number D*, a quantity analogous to the Reynolds number. The marginal state is marked by a critical number D* = D0 that is preserved in time. Turbulence initialized above this value become increasingly inertial in time, evolving toward larger and larger D*; turbulence initialized below D0 become more and more collisional, decaying to progressively smaller D*.},
author = {Tatsuno, T. and Plunk, G. G. and Barnes, M. and Dorland, W. and Howes, G. G. and Numata, R.},
doi = {10.1063/1.4769029},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Tatsuno et al. - 2012 - Freely decaying turbulence in two-dimensional electrostatic gyrokinetics.pdf:pdf},
journal = {Phys. Plasmas},
title = {{Freely decaying turbulence in two-dimensional electrostatic gyrokinetics}},
url = {http://www.mendeley.com/research/freely-decaying-turbulence-twodimensional-electrostatic-gyrokinetics},
year = {2012}
}
@article{Wang2012a,
abstract = {Gyrokinetics for high-frequency modes in tokamaks is developed. It is found that the breakdown of the invariants by perturbed electromagnetic fields drives microinstability. The obtained diamagnetic frequency, omega*, is proportional to only the toroidal mode number rather than transverse mode numbers. Therefore, there is no nonadiabatic drive for axisymmetrical modes in gyrokinetics. Meanwhile, the conventional eikonal Ansatz breaks down for the axisymmetrical modes. The ion drift-cyclotron instability discovered in a mirror machine is found for the first time in the toroidal system. The growth rates are proportional to rho(i)/L-n, and the slope changes with magnetic curvature. In spherical torus, where magnetic curvature is greater than that of traditional tokamaks, instability poses a potential danger to such devices. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4737108]},
author = {Wang, Z. T. and Wang, L. and Long, L. X. and Dong, J. Q. and He, Zhixiong and Liu, Y. and Tang, C. J.},
doi = {10.1063/1.4737108},
issn = {1070664X},
journal = {Phys. Plasmas},
title = {{Gyrokinetics for high-frequency modes in tokamaks}},
year = {2012}
}
@article{Colyer2017,
abstract = {In electrostatic simulations of MAST plasma at electron-gyroradius scales, using the local flux-tube gyrokinetic code GS2 with adiabatic ions, we find that the long-time saturated electron heat flux (the level most relevant to energy transport) decreases as the electron collisionality decreases. At early simulation times, the heat flux "quasi-saturates" without any strong dependence on collisionality, and with the turbulence dominated by streamer-like radially elongated structures. However, the zonal fluctuation component continues to grow slowly until much later times, eventually leading to a new saturated state dominated by zonal modes and with the heat flux proportional to the collision rate, in approximate agreement with the experimentally observed collisionality scaling of the energy confinement in MAST. We outline an explanation of this effect based on a model of ETG turbulence dominated by zonal-nonzonal interactions and on an analytically derived scaling of the zonal-mode damping rate with the electron-ion collisionality. Improved energy confinement with decreasing collisionality is favourable towards the performance of future, hotter devices.},
archivePrefix = {arXiv},
arxivId = {1607.06752},
author = {Colyer, G. J. and Schekochihin, A. A. and Parra, F. I. and Roach, C. M. and Barnes, M. A. and Ghim, Y. C. and Dorland, W.},
doi = {10.1088/1361-6587/aa5f75},
eprint = {1607.06752},
issn = {13616587},
journal = {Plasma Phys. Control. Fusion},
pmid = {55002},
title = {{Collisionality scaling of the electron heat flux in ETG turbulence}},
year = {2017}
}
@article{VanWyk2016,
abstract = {Tokamak turbulence, driven by the ion-temperature gradient and occurring in the presence of flow shear, is investigated by means of local, ion-scale, electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A parameter scan in the local values of the ion-temperature gradient and flow shear is performed. It is demonstrated that the experimentally observed state is near the stability threshold and that this stability threshold is nonlinear: sheared turbulence is subcritical, i.e. the system is formally stable to small perturbations, but, given a large enough initial perturbation, it transitions to a turbulent state. A scenario for such a transition is proposed and supported by numerical results: close to threshold, the nonlinear saturated state and the associated anomalous heat transport are dominated by long-lived coherent structures, which drift across the domain, have finite amplitudes, but are not volume filling; as the system is taken away from the threshold into the more unstable regime, the number of these structures increases until they overlap and a more conventional chaotic state emerges. Whereas this appears to represent a new scenario for transition to turbulence in tokamak plasmas, it is reminiscent of the behaviour of other subcritically turbulent systems, e.g. pipe flows and Keplerian magnetorotational accretion flows.},
archivePrefix = {arXiv},
arxivId = {1607.08173},
author = {{Van Wyk}, F. and Highcock, E. G. and Schekochihin, A. A. and Roach, C. M. and Field, A. R. and Dorland, W.},
doi = {10.1017/S0022377816001148},
eprint = {1607.08173},
isbn = {0022377816},
issn = {14697807},
journal = {J. Plasma Phys.},
keywords = {fusion plasma,plasma instabilities,plasma simulation},
number = {6},
title = {{Transition to subcritical turbulence in a tokamak plasma}},
volume = {82},
year = {2016}
}
@article{Beskin2004,
abstract = {My lecture is devoted to the analytical results available for a large class of axisymmetric stationary flows in the vicinity of compact astrophysical objects. First, the most general case is formulated corresponding to the axisymmetric stationary MHD flow in the Kerr metric. Then, I discuss the hydrodynamical version of the Grad-Shafranov equation. Although not so well-known as the full MHD one, it allows us to clarify the nontrivial structure of the Grad-Shafranov approach as well as to discuss the simplest version of the 3+1-split language - the most convenient one for the description of ideal flows in the vicinity of rotating black holes. Finally, I consider several examples that demonstrate how this approach can be used to obtain the quantitative description of the real transonic flows in the vicinity of rotating and moving black holes.},
archivePrefix = {arXiv},
arxivId = {astro-ph/0409076},
author = {Beskin, V S},
eprint = {0409076},
journal = {ArXiv Astrophys. eprints},
pages = {1--17},
primaryClass = {astro-ph},
title = {{Grad-Shafranov Approach To Axisymmetric Stationary Flows In Astrophysics}},
year = {2004}
}
@article{Kater1997,
abstract = {The problem of plasma equilibrium in a gravitational field is investigated analytically. For the two-dimensional problem, the system of ideal magnetohydrodynamic equations is reduced to a single nonlinear elliptic equation of the magnetic potential as a Grad-Shafranov-type equation. By specifying the arbitrary functions in this equation, the sinh-Poisson equation can be obtained. Using the B{\"{a}}cklund-transformation technique and Painlev{\'{e}} analysis, a set of exact solutions are obtained which adequately describe force-free models for solar flares and plane-parallel filaments of a diffuse magnetized plasma suspended horizontally in equilibrium in a uniform gravitational field.},
author = {Kater, A and Ibrahim, R S and Shamardan, A B and Callebaut, D K},
doi = {10.1093/imamat/58.1.51},
issn = {02724960},
journal = {IMA J. Appl. Math.},
pages = {51--69},
title = {{B{\"{a}}cklund transformations and Painlev{\'{e}} analysis: exact solutions for a Grad-Shafranov-type magnetohydrodynamic equilibrium}},
volume = {58},
year = {1997}
}
@article{Qin2007,
author = {Qin, H. and Cohen, R. H. and Nevins, W. M. and Xu, X. Q.},
doi = {10.1063/1.2472596},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {056110},
title = {{Geometric gyrokinetic theory for edge plasmas}},
url = {http://link.aip.org/link/PHPAEN/v14/i5/p056110/s1{\&}Agg=doi},
volume = {14},
year = {2007}
}
@article{Umansky2009,
author = {Umansky, M.V. and Xu, X.Q. and Dudson, B. and LoDestro, L.L. and Myra, J.R.},
doi = {10.1016/j.cpc.2008.12.012},
issn = {00104655},
journal = {Comput. Phys. Commun.},
keywords = {edge plasma turbulence},
month = {jun},
number = {6},
pages = {887--903},
publisher = {Elsevier B.V.},
title = {{Status and verification of edge plasma turbulence code BOUT}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0010465508004293},
volume = {180},
year = {2009}
}
@misc{Helander2002,
abstract = {This is a textbook on theoretical plasma physics, which is the science of extremely hot gases which make up most of the universe and which are used extensively in fusion energy research. This book treats a topic at the heart of this subject, so-called transport theory, which predicts the electrical and thermal properties of the plasma. It is the most comprehensive book in its field, and is directed at graduate students in physics and professional research physicists, in particular fusion energy scientists and space physicists.},
author = {Helander, Per and Sigmar, Dieter J.},
isbn = {0521807980},
pages = {1----292},
title = {{Collisional transport in magnetized plasmas}},
year = {2002}
}
@article{Callen2010a,
abstract = {An H-mode edge pedestal plasma transport benchmarking exercise was undertaken for a single DIII-D pedestal. Transport modelling codes used include 1.5D interpretive (ONETWO, GTEDGE), 1.5D predictive (ASTRA) and 2D ones (SOLPS, UEDGE). The particular DIII-D discharge considered is 98889, which has a typical low density pedestal. Profiles for the edge plasma are obtained from Thomson and charge-exchange recombination data averaged over the last 20{\%} of the average 33.53 ms repetition time between type I edge localized modes. The modelled density of recycled neutrals is largest in the divertor X-point region and causes the edge plasma source rate to vary by a factor {\~{}}102 on the separatrix. Modelled poloidal variations in the densities and temperatures on flux surfaces are small on all flux surfaces up to within about 2.6 mm ($\rho$N {\textgreater} 0.99) of the mid-plane separatrix. For the assumed Fick's-diffusion-type laws, the radial heat and density fluxes vary poloidally by factors of 2–3 in the pedestal region; they are largest on the outboard mid-plane where flux surfaces are compressed and local radial gradients are largest. Convective heat flows are found to be small fractions of the electron (10{\%}) and ion (25{\%}) heat flows in this pedestal. Appropriately averaging the transport fluxes yields interpretive 1.5D effective diffusivities that are smallest near the mid-point of the pedestal. Their 'transport barrier' minima are about 0.3 (electron heat), 0.15 (ion heat) and 0.035 (density) m2 s−1. Electron heat transport is found to be best characterized by electron-temperature-gradient-induced transport at the pedestal top and paleoclassical transport throughout the pedestal. The effective ion heat diffusivity in the pedestal has a different profile from the neoclassical prediction and may be smaller than it. The very small effective density diffusivity may be the result of an inward pinch flow nearly balancing a diffusive outward radial density flux. The inward ion pinch velocity and density diffusion coefficient are determined by a new interpretive analysis technique that uses information from the force balance (momentum conservation) equations; the paleoclassical transport model provides a plausible explanation of these new results. Finally, the measurements and additional modelling needed to facilitate better pedestal plasma transport modelling are discussed.},
author = {Callen, J. D. and Groebner, R. J. and Osborne, T. H. and Canik, J. M. and Owen., L. W. and Pankin, A. Y. and Rafiq, T. and Rognlien, T. D. and Stacey, W. M.},
doi = {10.1088/0029-5515/50/6/064004},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Callen et al. - 2010 - Analysis of pedestal plasma transport.pdf:pdf},
isbn = {0029-5515},
issn = {00295515},
journal = {Nucl. Fusion},
number = {6},
title = {{Analysis of pedestal plasma transport}},
volume = {50},
year = {2010}
}
@article{Miller1998b,
abstract = {A tokamak equilibrium model, local to a flux surface, is introduced which is completely described in terms of nine parameters including aspect ratio, elongation, triangularity, and safety factor. By allowing controlled variation of each of these nine parameters, the model is particularly suitable for localized stability studies such as those carried out using the ballooning mode representation of the gyrokinetic equations.},
author = {Miller, R. L. and Chu, M. S. and Greene, J. M. and Lin-Liu, Y. R. and Waltz, R. E.},
doi = {10.1063/1.872666},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Miller et al. - 1998 - Noncircular, finite aspect ratio, local equilibrium model.pdf:pdf},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {4},
pages = {973--978},
title = {{Noncircular, finite aspect ratio, local equilibrium model}},
volume = {5},
year = {1998}
}
@article{Ko2015,
abstract = {We study the impact of impurities on turbulence driven intrinsic rotation (via residual stress) in the context of the quasi-linear theory. A two-fluid formulation for main and impurity ions is employed to study ion temperature gradient modes in sheared slab geometry modified by the presence of impurities. An effective form of the parallel Reynolds stress is derived in the center of mass frame of a coupled main ion-impurity system. Analyses show that the contents and the radial profile of impurities have a strong influence on the residual stress. In particular, an impurity profile aligned with that of main ions is shown to cause a considerable reduction of the residual stress, which may lead to the reduction of turbulence driven intrinsic rotation.},
archivePrefix = {arXiv},
arxivId = {1504.08086},
author = {Ko, S. H. and Jhang, Hogun and Singh, R.},
doi = {10.1063/1.4927779},
eprint = {1504.08086},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Ko, Jhang, Singh - 2015 - A quasi-linear analysis of the impurity effect on turbulent momentum transport and residual stress.pdf:pdf},
journal = {arXiv Prepr.},
pages = {1--20},
title = {{A quasi-linear analysis of the impurity effect on turbulent momentum transport and residual stress}},
url = {http://arxiv.org/abs/1504.08086},
year = {2015}
}
@article{Diamond2005,
abstract = {A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, planetary zonal flows are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave–zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research.},
author = {Diamond, P. H. and Itoh, S. I. and Itoh, K. and Hahm, T. S.},
doi = {10.1088/0741-3335/47/5/R01},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Diamond et al. - 2005 - Zonal flows in plasma - A review.pdf:pdf},
isbn = {0741-3335 1361-6587},
issn = {07413335},
journal = {Plasma Phys. Control. Fusion},
number = {5},
title = {{Zonal flows in plasma - A review}},
volume = {47},
year = {2005}
}
@article{Snyder2002,
author = {Snyder, P. B. and Wilson, H. R. and Ferron, J. R. and Lao, L. L. and Leonard, a. W. and Osborne, T. H. and Turnbull, a. D. and Mossessian, D. and Murakami, M. and Xu, X. Q.},
doi = {10.1063/1.1449463},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {2037},
title = {{Edge localized modes and the pedestal: A model based on coupled peeling–ballooning modes}},
url = {http://link.aip.org/link/PHPAEN/v9/i5/p2037/s1{\&}Agg=doi},
volume = {9},
year = {2002}
}
@article{Plunk2010,
abstract = {Two-dimensional gyrokinetics is a simple paradigm for the study of kinetic magnetised plasma turbulence. In this paper, we present a comprehensive theoretical framework for this turbulence. We study both the inverse and direct cascades (the ‘dual cascade'), driven by a homogeneous and isotropic random forcing. The key characteristic length of gyrokinetics, the Larmor radius, divides scales into two physically distinct ranges. For scales larger than the Larmor radius, we derive the familiar Charney–Hasegawa–Mima equation from the gyrokinetic system, and explain its relationship to gyrokinetics. At scales smaller than the Larmor radius, a dual cascade occurs in phase space (two dimensions in position space plus one dimension in velocity space) via a nonlinear phase-mixing process. We show that at these sub-Larmor scales, the turbulence is self-similar and exhibits power-law spectra in position and velocity space. We propose a Hankel-transform formalism to characterise velocity-space spectra. We derive the exact relations for third-order structure functions, analogous to Kolmogorov's four-fifths and Yaglom's four-thirds laws and valid at both long and short wavelengths. We show how the general gyrokinetic invariants are related to the particular invariants that control the dual cascade in the long- and short-wavelength limits. We describe the full range of cascades from the fluid to the fully kinetic range.},
archivePrefix = {arXiv},
arxivId = {arXiv:0904.0243v4},
author = {Plunk, G. G. and Cowley, S. C. and Schekochihin, A. A. and Tatsuno, T.},
doi = {10.1017/S002211201000371X},
eprint = {arXiv:0904.0243v4},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/PLUNK et al. - 2010 - Two-dimensional gyrokinetic turbulence.pdf:pdf},
isbn = {0022-1120},
issn = {00221120},
journal = {J. Fluid Mech.},
keywords = {kinetic theory,plasmas,turbulence theory},
pages = {407--435},
title = {{Two-dimensional gyrokinetic turbulence}},
volume = {664},
year = {2010}
}
@article{Ko2015,
abstract = {We study the impact of impurities on turbulence driven intrinsic rotation (via residual stress) in the context of the quasi-linear theory. A two-fluid formulation for main and impurity ions is employed to study ion temperature gradient modes in sheared slab geometry modified by the presence of impurities. An effective form of the parallel Reynolds stress is derived in the center of mass frame of a coupled main ion-impurity system. Analyses show that the contents and the radial profile of impurities have a strong influence on the residual stress. In particular, an impurity profile aligned with that of main ions is shown to cause a considerable reduction of the residual stress, which may lead to the reduction of turbulence driven intrinsic rotation.},
archivePrefix = {arXiv},
arxivId = {1504.08086},
author = {Ko, S. H. and Jhang, Hogun and Singh, R.},
doi = {10.1063/1.4927779},
eprint = {1504.08086},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Ko, Jhang, Singh - 2015 - A quasi-linear analysis of the impurity effect on turbulent momentum transport and residual stress(2).pdf:pdf},
issn = {10897674},
journal = {Phys. Plasmas},
number = {8},
title = {{A quasi-linear analysis of the impurity effect on turbulent momentum transport and residual stress}},
volume = {22},
year = {2015}
}
@article{Reference2,
abstract = {We present a review of the use of diode lasers in atomic physics with an extensive list of references. We discuss the relevant characteristics of diode lasers and explain how to purchase and use them. We also review the various techniques that have been used to control and narrow the spectral outputs of diode lasers. Finally we present a number of examples illustrating the use of diode lasers in atomic physics experiments. Review of Scientific Instruments is copyrighted by The American Institute of Physics.},
author = {Wieman, Carl E and Hollberg, Leo},
journal = {Rev. Sci. Instrum.},
keywords = {Diode Laser},
month = {jan},
number = {1},
pages = {1--20},
title = {{Using Diode Lasers for Atomic Physics}},
url = {http://link.aip.org/link/?RSI/62/1/1},
volume = {62},
year = {1991}
}
@article{Martin2005,
author = {Martín, P. and Haines, M. G. and Castro, E.},
doi = {10.1063/1.1995587},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {8},
pages = {082506},
title = {{Current density and poloidal magnetic field for toroidal elliptic plasmas with triangularity}},
url = {http://link.aip.org/link/PHPAEN/v12/i8/p082506/s1{\&}Agg=doi},
volume = {12},
year = {2005}
}
@article{Popovich2010,
author = {Popovich, P. and Umansky, M. V. and Carter, T. a. and Friedman, B.},
doi = {10.1063/1.3527987},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {12},
pages = {122312},
title = {{Modeling of plasma turbulence and transport in the Large Plasma Device}},
url = {http://link.aip.org/link/PHPAEN/v17/i12/p122312/s1{\&}Agg=doi},
volume = {17},
year = {2010}
}
@article{Camenen2010,
abstract = {A new mechanism has recently been proposed that generates a radial flux of parallel momentum in toroidal plasmas. Namely, by considering up-down asymmetric flux surfaces, the symmetry following the magnetic field can be broken and an additional contribution to the turbulent momentum flux arises, potentially changing the intrinsic rotation profile. These predictions are tested with specific experiments on TCV. The intrinsic toroidal rotation is observed to change by roughly a factor of two when changing the up-down asymmetry of the plasma. More precisely, the toroidal rotation gradient changes in the outer part of the plasma, where the flux surface asymmetry is the highest. The experiments were performed for all combinations of the toroidal magnetic field and plasma current directions, that affect the sign of the predicted up-down asymmetry flux. In each case the variation of the intrinsic rotation profile with the up-down asymmetry is observed in the direction predicted by the theory.},
author = {Camenen, Y and Bortolon, A and Duval, B P and Federspiel, L and Peeters, A G and Casson, F J and Hornsby, W A and Karpushov, A N and Piras, F and Sauter, O and Snodin, A P and Szepesi, G and Team, the T C V},
doi = {10.1088/0741-3335/52/12/124037},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
number = {12},
pages = {124037},
title = {{Experimental demonstration of an up-down asymmetry effect on intrinsic rotation in the TCV tokamak}},
url = {http://iopscience.iop.org/0741-3335/52/12/124037{\%}5Cnhttp://iopscience.iop.org/0741-3335/52/12/124037/{\%}5Cnhttp://iopscience.iop.org/0741-3335/52/12/124037/pdf/0741-3335{\_}52{\_}12{\_}124037.pdf},
volume = {52},
year = {2010}
}
@article{Diaz2009,
archivePrefix = {arXiv},
arxivId = {arXiv:1309.7385v1},
author = {Diaz, F. Parra},
eprint = {arXiv:1309.7385v1},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Diaz - 2009 - Extension of gyrokinetics to transport time scales.pdf:pdf},
number = {2004},
title = {{Extension of gyrokinetics to transport time scales}},
year = {2009}
}
@book{Ziegel1987,
abstract = {Bridging the gap between physics and astronomy textbooks, this book provides step-by-step physical and mathematical development of fundamental astrophysical ...},
archivePrefix = {arXiv},
arxivId = {arXiv:1011.1669v3},
author = {Ziegel, Eric and Press, William and Flannery, Brian and Teukolsky, Saul and Vetterling, William},
booktitle = {Technometrics},
doi = {10.2307/1269484},
eprint = {arXiv:1011.1669v3},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Ziegel et al. - 1987 - Numerical Recipes The Art of Scientific Computing.pdf:pdf},
isbn = {0521431085},
issn = {00401706},
number = {4},
pages = {501},
pmid = {7879318},
title = {{Numerical Recipes: The Art of Scientific Computing}},
url = {http://www.jstor.org/stable/1269484?origin=crossref},
volume = {29},
year = {1987}
}
@article{Gourdain2004a,
author = {Gourdain, P.-a. and Leboeuf, J.-N.},
doi = {10.1063/1.1776174},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {9},
pages = {4372},
title = {{Contour dynamics method for solving the Grad–Shafranov equation with applications to high beta equilibria}},
url = {http://link.aip.org/link/PHPAEN/v11/i9/p4372/s1{\&}Agg=doi},
volume = {11},
year = {2004}
}
@article{Hammett2007,
author = {Hammett, Greg and Plasma, Princeton},
doi = {10.1063/1.859309},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hammett, Plasma - 2007 - The Ion Temperature Gradient ( ITG ) Instability.pdf:pdf},
journal = {Computing},
title = {{The Ion Temperature Gradient ( ITG ) Instability}},
year = {2007}
}
@book{Freidberg,
author = {Freidberg, Jeffrey P.},
title = {{Ideal MHD}}
}
@article{Berk1993,
author = {Berk, H.-L and Cohen, R.H and Ryutov, D.D and Tsidulko, Yu.A and Xu, X.Q},
doi = {10.1088/0029-5515/33/2/I07},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {feb},
number = {2},
pages = {263--282},
title = {{Electron temperature gradient induced instability in tokamak scrape-off layers}},
url = {http://stacks.iop.org/0029-5515/33/i=2/a=I07?key=crossref.0dd425ff9c2ceffe3f3ac85aa335d769},
volume = {33},
year = {1993}
}
@article{Goedbloed2004,
author = {Goedbloed, J. P.},
doi = {10.1063/1.1808453},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {12},
pages = {L81},
title = {{Variational principles for stationary one- and two-fluid equilibria of axisymmetric laboratory and astrophysical plasmas}},
url = {http://link.aip.org/link/PHPAEN/v11/i12/pL81/s1{\&}Agg=doi},
volume = {11},
year = {2004}
}
@article{Helander2015,
abstract = {Recent progress in the gyrokinetic theory of stellarator microinstabilities$\backslash$nand turbulence simulations is summarized. The simulations have been$\backslash$ncarried out using two different gyrokinetic codes, the global particle-in-cell$\backslash$ncode EUTERPE and the continuum code GENE, which operates in the geometry$\backslash$nof a flux tube or a flux surface but is local in the radial direction.$\backslash$nIon-temperature-gradient (ITG) and trapped-electron modes are studied$\backslash$nand compared with their counterparts in axisymmetric tokamak geometry.$\backslash$nSeveral interesting differences emerge. Because of the more complicated$\backslash$nstructure of the magnetic field, the fluctuations are much less evenly$\backslash$ndistributed over each flux surface in stellarators than in tokamaks.$\backslash$nInstead of covering the entire outboard side of the torus, ITG turbulence$\backslash$nis localized to narrow bands along the magnetic field in regions$\backslash$nof unfavourable curvature, and the resulting transport depends on$\backslash$nthe normalized gyroradius rho* even in radially local simulations.$\backslash$nTrapped-electron modes can be significantly more stable than in typical$\backslash$ntokamaks, because of the spatial separation of regions with trapped$\backslash$nparticles from those with bad magnetic curvature. Preliminary non-linear$\backslash$nsimulations in flux-tube geometry suggest differences in the turbulence$\backslash$nlevels in Wendelstein 7-X and a typical tokamak.},
author = {Helander, P. and Bird, T. and Jenko, F. and Kleiber, R. and Plunk, G.G. and Proll, J.H.E. and Riemann, J. and Xanthopoulos, P.},
doi = {10.1088/0029-5515/55/5/053030},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Helander et al. - 2015 - Advances in stellarator gyrokinetics.pdf:pdf},
issn = {0029-5515},
journal = {Nucl. Fusion},
keywords = {confinement,gyrokinetics,stellarators},
month = {may},
number = {5},
pages = {053030},
title = {{Advances in stellarator gyrokinetics}},
url = {http://stacks.iop.org/0029-5515/55/i=5/a=053030?key=crossref.ad83421976ebc2b3541651b6d4eedc8b},
volume = {55},
year = {2015}
}
@article{Cohen2013,
author = {Cohen, B. I. and Umansky, M. V. and Nevins, W. M. and Makowski, M. a. and Boedo, J. a. and Rudakov, D. L. and McKee, G. R. and Yan, Z. and Groebner, R. J. and Cohen, B. I. and Umansky, M. V. and Nevins, W. M. and Makowski, M. a. and Boedo, J. a.},
doi = {10.1063/1.4804638},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {055906},
title = {{Simulations of drift resistive ballooning L-mode turbulence in the edge plasma of the DIII-D tokamak}},
url = {http://link.aip.org/link/PHPAEN/v20/i5/p055906/s1{\&}Agg=doi},
volume = {20},
year = {2013}
}
@article{The2016,
author = {The, Catherine E},
doi = {10.1016/j.solener.2011.09.029.Publication},
title = {{The economics of advertising and privacy The MIT Faculty has made this article openly available . Please share how this access benefits you . Your story matters . Citation Publisher Version Accessed Citable Link Terms of Use Detailed Terms The Economics o}},
year = {2016}
}
@article{Calvo2012,
author = {Calvo, Iv{\'{a}}n and Parra, Felix I},
doi = {10.1088/0741-3335/54/11/115007},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
month = {nov},
number = {11},
pages = {115007},
title = {{Long-wavelength limit of gyrokinetics in a turbulent tokamak and its intrinsic ambipolarity}},
url = {http://stacks.iop.org/0741-3335/54/i=11/a=115007?key=crossref.61b77d1f18e024d06015a12c19feec5c},
volume = {54},
year = {2012}
}
@article{Cheviakov2007,
archivePrefix = {arXiv},
arxivId = {0708.4247},
author = {Cheviakov, Alexei F and Anco, Stephen C},
doi = {10.1016/j.physleta.2007.09.065},
eprint = {0708.4247},
journal = {Arxiv Prepr. arXiv07084247},
keywords = {conservation laws,exact solutions,grad shafranov,plasma equilibrium,symmetries},
pages = {1--19},
title = {{Symmetries, conservation laws and exact solutions of static plasma equilibrium systems in three dimensions}},
year = {2007}
}
@article{Gorler2008,
abstract = {Nonlinear gyrokinetic simulations of microturbulence simultaneously driven by electron temperature gradient modes, trapped electron modes, and ion temperature gradient modes are presented, covering both electron and ion spatiotemporal scales self-consistently. It is found that, for realistic ion heat (and particle) flux levels and in the presence of unstable electron temperature gradient modes, there tends to be a scale separation between electron and ion thermal transport. In contrast to the latter, the former may exhibit substantial or even dominant high-wave-number contributions.},
author = {G{\"{o}}rler, T. and Jenko, F.},
doi = {10.1103/PhysRevLett.100.185002},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/G{\"{o}}rler, Jenko - 2008 - Scale Separation between Electron and Ion Thermal Transport.pdf:pdf},
isbn = {0031-9007$\backslash$n1079-7114},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
number = {18},
pages = {185002},
pmid = {18518382},
title = {{Scale Separation between Electron and Ion Thermal Transport}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.100.185002},
volume = {100},
year = {2008}
}
@article{Team2009,
author = {Team, Gene Development},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Team - 2009 - The Gyrokinetic Plasma Turbulence Code Gene User Manual.pdf:pdf},
journal = {Power},
title = {{The Gyrokinetic Plasma Turbulence Code Gene : User Manual}},
year = {2009}
}
@article{Falchetto2008,
abstract = {A cross-comparison and verification of state-of-the-art European codes describing gradient-driven plasma turbulence in the core and edge regions of tokamaks, carried out within the EFDA Task Force on Integrated Tokamak Modelling, is presented. In the case of core ion temperature gradient (ITG) driven turbulence with adiabatic electrons (neglecting trapped particles), good/reasonable agreement is found between various gyrokinetic/gyrofluid codes. The main physical reasons for some deviations observed in nonlocal simulations are discussed. The edge simulations agree very well on collisionality scaling and acceptably well on beta scaling (below the MHD boundary) for cold-ion cases, also in terms of the non-linear mode structure.},
author = {Falchetto, G. L. and Scott, B. D. and Angelino, P. and Bottino, A. and Dannert, T. and Grandgirard, V. and Janhunen, S. and Jenko, F. and Jolliet, S. and Kendl, A. and McMillan, B. F. and Naulin, V. and Nielsen, A. H. and Ottaviani, M. and Peeters, A. G. and Pueschel, M. J. and Reiser, D. and Ribeiro, T. T. and Romanelli, M.},
doi = {10.1088/0741-3335/50/12/124015},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Falchetto et al. - 2008 - The European turbulence code benchmarking effort turbulence driven by thermal gradients in magnetically confin.pdf:pdf},
issn = {0741-3335},
journal = {Plasma Phys. Control. Fusion},
number = {12},
pages = {124015},
title = {{The European turbulence code benchmarking effort: turbulence driven by thermal gradients in magnetically confined plasmas}},
url = {http://stacks.iop.org/0741-3335/50/i=12/a=124015?key=crossref.acf097f0fd94ffbaf7374a9028c37749},
volume = {50},
year = {2008}
}
@article{Kotschenreuther1985,
author = {Kotschenreuther, M. and Hazeltine, R. D. and Morrison, P. J.},
doi = {10.1063/1.865200},
issn = {00319171},
journal = {Phys. Fluids},
number = {1},
pages = {294},
title = {{Nonlinear dynamics of magnetic islands with curvature and pressure}},
url = {http://link.aip.org/link/PFLDAS/v28/i1/p294/s1{\&}Agg=doi},
volume = {28},
year = {1985}
}
@article{Morley2017,
abstract = {The Academic Phrasebank is an invaluable academic writing resource whatever stage of your career you are at. Equally useful for writers of English as a second language and native speakers, for researchers who want to improve their academic writing and students who need assistance writing up their thesis or dissertation.},
author = {Morley, Hohn},
title = {{The Academic Phrasebank: an academic writing resource for students and researchers - Kindle edition by Dr. John Morley. Reference Kindle eBooks @ Amazon.com.}},
year = {2017}
}
@misc{Hazeltine1968,
abstract = {Detailed and authoritative, this graduate-level text examines the essential physics underlying international research in magnetic confinement fusion. It offers readable, thorough accounts of the fundamental concepts behind methods of confining plasma at or near thermonuclear conditions. 1992 edition.},
author = {Hazeltine, R. D. and Meiss, J. D.},
booktitle = {Sci. News},
doi = {10.2307/3953570},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hazeltine, Meiss - 1968 - Plasma Confinement Improved.pdf:pdf},
isbn = {9780486151038},
issn = {00368423},
number = {18},
pages = {438},
title = {{Plasma Confinement Improved}},
url = {http://www.jstor.org/stable/3953570?origin=crossref},
volume = {94},
year = {1968}
}
@article{Rice2000,
abstract = {Central toroidal rotation and impurity transport coefficients have been determined in Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] Ohmic high confinement mode (H-mode) plasmas from observations of x-ray emission following impurity injection. Rotation velocities up to 3 x 10(4) m/sec in the co-current direction have been observed in the center of the best Ohmic H-mode plasmas. Purely ohmic H-mode plasmas display many characteristics similar to ion cyclotron range of frequencies (ICRF) heated H-mode plasmas, including the scaling of the rotation velocity with plasma parameters and the formation of edge pedestals in the electron density and temperature profiles. Very long impurity confinement times (similar to 1 sec) are seen in edge localized mode-free (ELM-free) Ohmic H-modes and the inward impurity convection velocity profile has been determined to be close to the calculated neoclassical profile. (C) 2000 American Institute of Physics. [S1070-664X(00)91705-1].},
author = {Rice, J. E. and Goetz, J. A. and Granetz, R. S. and Greenwald, M. J. and Hubbard, A. E. and Hutchinson, I. H. and Marmar, E. S. and Mossessian, D. and Pedersen, T. S. and Snipes, J. A. and Terry, J. L. and Wolfe, S. M.},
doi = {10.1063/1.874004},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Rice et al. - 2000 - Impurity toroidal rotation and transport in Alcator C-Mod ohmic high confinement mode plasmas.pdf:pdf},
issn = {1070-664X},
journal = {Phys. Plasmas},
pages = {1825--1830},
title = {{Impurity toroidal rotation and transport in Alcator C-Mod ohmic high confinement mode plasmas}},
url = {//000086511000027},
volume = {7},
year = {2000}
}
@article{Anderson1958,
author = {Anderson, Oscar a. and Baker, William R. and Bratenahl, Alexander and Furth, H.P. and Ise, John and Kunkel, W.B. and Stone, John M.},
doi = {10.1016/0891-3919(58)90127-X},
issn = {08913919},
journal = {J. Nucl. Energy},
keywords = {paper,plasma rotation},
mendeley-tags = {paper,plasma rotation},
number = {3-4},
pages = {280},
title = {{Study and use of rotating plasma}},
volume = {7},
year = {1958}
}
@article{Abel2013b,
abstract = {In this paper, we extend the multiscale approach developed in [Abel et. al., Rep. Prog. Phys., submitted] by exploiting the scale separation between ions and the electrons. The gyrokinetic equation is expanded in powers of the electron to ion mass ratio, which provides a rigorous method for deriving the reduced electron model. We prove that ion-scale electromagnetic turbulence cannot change the magnetic topology, and argue that to lowest order the magnetic field lies on fluctuating flux surfaces. These flux surfaces are used to construct magnetic coordinates, and in these coordinates a closed system of equations for the electron response to ion-scale turbulence is derived. All fast electron timescales have been eliminated from these equations. We also use these magnetic surfaces to construct transport equations for electrons and for electron heat in terms of the reduced electron model.},
archivePrefix = {arXiv},
arxivId = {1210.1417},
author = {Abel, I. G. and Cowley, S. C.},
doi = {10.1088/1367-2630/15/2/023041},
eprint = {1210.1417},
isbn = {1367-2630},
issn = {13672630},
journal = {New J. Phys.},
title = {{Multiscale gyrokinetics for rotating tokamak plasmas: II. Reduced models for electron dynamics}},
year = {2013}
}
@article{Sugama2009a,
abstract = {Linearized model collision operators for multiple ion species plasmas are presented that conserve particles, momentum, and energy and satisfy adjointness relations and Boltzmann's H-theorem even for collisions between different particle species with unequal temperatures. The modelcollision operators are also written in the gyrophase-averaged form that can be applied to the gyrokineticequation. Balance equations for the turbulententropy density, the energy of electromagneticfluctuations, the turbulenttransport fluxes of particle and heat, and the collisional dissipation are derived from the gyrokineticequation including the collision term and Maxwell equations. It is shown that, in the steady turbulence, the entropy produced by the turbulenttransport fluxes is dissipated in part by collisions in the nonzonal-mode region and in part by those in the zonal-mode region after the nonlinear entropy transfer from nonzonal to zonal modes.},
author = {Sugama, H. and Watanabe, T. H. and Nunami, M.},
doi = {10.1063/1.3257907},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Sugama, Watanabe, Nunami - 2009 - Linearized model collision operators for multiple ion species plasmas and gyrokinetic entropy balance.pdf:pdf},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {11},
pages = {112503},
title = {{Linearized model collision operators for multiple ion species plasmas and gyrokinetic entropy balance equations}},
volume = {16},
year = {2009}
}
@article{Hinton1976a,
author = {Hinton, F L and Hazeltine, R D},
doi = {10.1103/RevModPhys.48.239},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hinton, Hazeltine - 1976 - Theory of Plasma Transport in Toroidal Confinements Systems.pdf:pdf},
journal = {Rev. Mod. Phys.},
keywords = {neoclassical classical transport drift kinetic equ},
number = {2},
pages = {239--308},
title = {{Theory of Plasma Transport in Toroidal Confinements Systems}},
volume = {48},
year = {1976}
}
@article{Sonnerup2010,
author = {Sonnerup, Bengt U. {\"{O}}. and Hasegawa, Hiroshi},
doi = {10.1029/2010JA015678},
issn = {0148-0227},
journal = {J. Geophys. Res.},
month = {nov},
number = {A11},
pages = {A11218},
title = {{On slowly evolving Grad-Shafranov equilibria}},
url = {http://doi.wiley.com/10.1029/2010JA015678},
volume = {115},
year = {2010}
}
@article{Xanthopoulos2006,
author = {Xanthopoulos, P. and Jenko, F.},
doi = {10.1063/1.2338818},
issn = {1070664X},
journal = {Phys. Plasmas},
title = {{Clebsch-type coordinates for nonlinear gyrokinetics in generic toroidal configurations}},
year = {2006}
}
@article{Xiong2008,
author = {Xiong, Z. and Cohen, R.H. and Rognlien, T.D. and Xu, X.Q.},
doi = {10.1016/j.jcp.2008.04.004},
issn = {00219991},
journal = {J. Comput. Phys.},
keywords = {constants-of-motion coordinates,finite volume,fokker,high-order scheme,planck collisions},
month = {jul},
number = {15},
pages = {7192--7205},
title = {{A high-order finite-volume algorithm for Fokker–Planck collisions in magnetized plasmas}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999108002052},
volume = {227},
year = {2008}
}
@article{Pataki2013,
author = {Pataki, Andras and Cerfon, Antoine J. and Freidberg, Jeffrey P. and Greengard, Leslie and O'Neil, Michael},
doi = {10.1016/j.jcp.2013.02.045},
issn = {00219991},
journal = {J. Comput. Phys.},
month = {jun},
pages = {28--45},
title = {{A fast, high-order solver for the Grad–Shafranov equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999113001721},
volume = {243},
year = {2013}
}
@article{Bovet2014,
abstract = {Suprathermal ion turbulent transport in magnetized plasmas is generally nondiffusive, ranging from subdiffusive to superdiffusive depending on the interplay of the turbulent structures and the suprathermal ion orbits. Here, we present time-resolved measurements of the cross-field suprathermal ion transport in a toroidal magnetized turbulent plasma. Measurements in the superdiffusive regime are characterized by a higher intermittency than in the subdiffusive regime. Using conditional averaging, we show that, when the transport is superdiffusive, suprathermal ions are transported by intermittent field-elongated turbulent structures that are radially propagating},
author = {Bovet, A. and Fasoli, A. and Furno, I.},
doi = {10.1103/PhysRevLett.113.225001},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Bovet, Fasoli, Furno - 2014 - Time-resolved measurements of suprathermal ion transport induced by intermittent plasma blob filaments.pdf:pdf},
journal = {Phys. Rev. Lett.},
title = {{Time-resolved measurements of suprathermal ion transport induced by intermittent plasma blob filaments}},
url = {http://www.mendeley.com/research/timeresolved-measurements-suprathermal-ion-transport-induced-intermittent-plasma-blob-filaments},
year = {2014}
}
@article{Lao1981,
author = {Lao, L. L.},
doi = {10.1063/1.863562},
issn = {00319171},
journal = {Phys. Fluids},
number = {8},
pages = {1431},
title = {{Variational moment solutions to the Grad–Shafranov equation}},
url = {http://link.aip.org/link/PFLDAS/v24/i8/p1431/s1{\&}Agg=doi},
volume = {24},
year = {1981}
}
@article{Furnish1999,
author = {Furnish, G. and Horton, W. and Kishimoto, Y. and LeBrun, M. and Tajima, T.},
doi = {10.1063/1.873366},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {4},
pages = {1227},
title = {{Global gyrokinetic simulation of tokamak transport}},
url = {http://link.aip.org/link/PHPAEN/v6/i4/p1227/s1{\&}Agg=doi},
volume = {6},
year = {1999}
}
@article{Gates2009,
author = {Gates, D.a. and Ahn, J. and Allain, J. and Andre, R. and Bastasz, R. and Bell, M. and Bell, R. and Belova, E. and Berkery, J. and Betti, R. and Bialek, J. and Biewer, T. and Bigelow, T. and Bitter, M. and Boedo, J. and Bonoli, P. and Boozer, a. and Brennan, D. and Breslau, J. and Brower, D. and Bush, C. and Canik, J. and Caravelli, G. and Carter, M. and Caughman, J. and Chang, C. and Choe, W. and Crocker, N. and Darrow, D. and Delgado-Aparicio, L. and Diem, S. and D'Ippolito, D. and Domier, C. and Dorland, W. and Efthimion, P. and Ejiri, a. and Ershov, N. and Evans, T. and Feibush, E. and Fenstermacher, M. and Ferron, J. and Finkenthal, M. and Foley, J. and Frazin, R. and Fredrickson, E. and Fu, G. and Funaba, H. and Gerhardt, S. and Glasser, a. and Gorelenkov, N. and Grisham, L. and Hahm, T. and Harvey, R. and Hassanein, a. and Heidbrink, W. and Hill, K. and Hillesheim, J. and Hillis, D. and Hirooka, Y. and Hosea, J. and Hu, B. and Humphreys, D. and Idehara, T. and Indireshkumar, K. and Ishida, a. and Jaeger, F. and Jarboe, T. and Jardin, S. and Jaworski, M. and Ji, H. and Jung, H. and Kaita, R. and Kallman, J. and Katsuro-Hopkins, O. and Kawahata, K. and Kawamori, E. and Kaye, S. and Kessel, C. and Kim, J. and Kimura, H. and Kolemen, E. and Krasheninnikov, S. and Krstic, P. and Ku, S. and Kubota, S. and Kugel, H. and {La Haye}, R. and Lao, L. and LeBlanc, B. and Lee, W. and Lee, K. and Leuer, J. and Levinton, F. and Liang, Y. and Liu, D. and Luhmann, N. and Maingi, R. and Majeski, R. and Manickam, J. and Mansfield, D. and Maqueda, R. and Mazzucato, E. and McCune, D. and McGeehan, B. and McKee, G. and Medley, S. and Menard, J. and Menon, M. and Meyer, H. and Mikkelsen, D. and Miloshevsky, G. and Mitarai, O. and Mueller, D. and Mueller, S. and Munsat, T. and Myra, J. and Nagayama, Y. and Nelson, B. and Nguyen, X. and Nishino, N. and Nishiura, M. and Nygren, R. and Ono, M. and Osborne, T. and Pacella, D. and Park, H. and Park, J. and Paul, S. and Peebles, W. and Penaflor, B. and Peng, M. and Phillips, C. and Pigarov, a. and Podesta, M. and Preinhaelter, J. and Ram, a. and Raman, R. and Rasmussen, D. and Redd, a. and Reimerdes, H. and Rewoldt, G. and Ross, P. and Rowley, C. and Ruskov, E. and Russell, D. and Ruzic, D. and Ryan, P. and Sabbagh, S. and Schaffer, M. and Schuster, E. and Scott, S. and Shaing, K. and Sharpe, P. and Shevchenko, V. and Shinohara, K. and Sizyuk, V. and Skinner, C. and Smirnov, a. and Smith, D. and Smith, S. and Snyder, P. and Solomon, W. and Sontag, a. and Soukhanovskii, V. and Stoltzfus-Dueck, T. and Stotler, D. and Strait, T. and Stratton, B. and Stutman, D. and Takahashi, R. and Takase, Y. and Tamura, N. and Tang, X. and Taylor, G. and Taylor, C. and Ticos, C. and Tritz, K. and Tsarouhas, D. and Turrnbull, a. and Tynan, G. and Ulrickson, M. and Umansky, M. and Urban, J. and Utergberg, E. and Walker, M. and Wampler, W. and Wang, J. and Wang, W. and Welander, a. and Whaley, J. and White, R. and Wilgen, J. and Wilson, R. and Wong, K. and Wright, J. and Xia, Z. and Xu, X. and Youchison, D. and Yu, G. and Yuh, H. and Zakharov, L. and Zemlyanov, D. and Zweben, S.},
doi = {10.1088/0029-5515/49/10/104016},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {oct},
number = {10},
pages = {104016},
title = {{Overview of results from the National Spherical Torus Experiment (NSTX)}},
url = {http://stacks.iop.org/0029-5515/49/i=10/a=104016?key=crossref.d93719ea43d3ccb911018c3f42de00ed},
volume = {49},
year = {2009}
}
@article{Gourgouliatos2010,
abstract = {Observations of clusters of galaxies show ubiquitous presence of X-ray cavities, presumably blown by the AGN jets. We consider magnetic field structures of these cavities. Stability requires that they contain both toroidal and poloidal magnetic fields, while realistic configurations should have vanishing magnetic field on the boundary. For axisymmetric configurations embedded in unmagnetized plasma, the continuity of poloidal and toroidal magnetic field components on the surface of the bubble then requires solving the elliptical Grad-Shafranov equation with both Dirichlet and Neumann boundary conditions. This leads to a double eigenvalue problem, relating the pressure gradients and the toroidal magnetic field to the radius of the bubble. We have found fully analytical stable solutions. This result is confirmed by numerical simulation. We present synthetic X-ray images and synchrotron emission profiles and evaluate the rotation measure for radiation traversing the bubble.},
archivePrefix = {arXiv},
arxivId = {1008.5353},
author = {Gourgouliatos, Konstantinos Nektarios and Braithwaite, Jonathan and Lyutikov, Maxim},
eprint = {1008.5353},
journal = {eprint arXiv10085353},
pages = {10},
title = {{Structure of magnetic fields in intracluster cavities}},
volume = {409},
year = {2010}
}
@article{Perkins2001,
abstract = {A mechanism is proposed and evaluated for driving rotation in tokamak plasmas by minority ion-cyclotron heating, even though this heating introduces negligible angular momentum. The mechanism has two elements: First, angular momentum transport is governed by a diffusion equation with a boundary condition at the separatrix. Second, Monte Carlo calculations show that ion-cyclotron energized particles will provide a torque density source which has a zero volume integral but separated positive and negative regions. With such a source, a solution of the diffusion equation predicts that ion-cyclotron heating will cause a rotational shear layer to develop. The corresponding jump in plasma rotation Delta Omega is found to be negative outwards when the ion-cyclotron surface lies on the low-field side of the magnetic axis and positive outwards with the resonance on the high-field side. The magnitude of the jump Delta Omega=(4q(max)WJ(2)*) (eBR(3)a(2)n(e)(2 pi)(2))(-1)(tau (M)/tau (E)) where $\backslash$J(2)*$\backslash$approximate to2-4 is a nondimensional rotation frequency calculated by the Monte Carlo ORBIT code [R. B. White and M. S. Chance, Phys. Fluids 27, 2455 (1984)]. For a no-slip boundary condition when the resonance lies on the low-field side of the magnetic axis, the sense of predicted axial rotation is co-current and overall agreement with experiment is good. When the resonance lies on the high-field side, the predicted rotation becomes countercurrent for a no-slip boundary while the observed rotation remains co-current. The rotational shear layer position is controllable and of sufficient magnitude to affect microinstabilities. (C) 2001 American Institute of Physics.},
author = {Perkins, F. W. and White, R. B. and Bonoli, P. T. and Chan, V. S.},
doi = {10.1063/1.1362535},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Perkins et al. - 2001 - Generation of plasma rotation in a tokamak by ion-cyclotron absorption of fast Alfven waves.pdf:pdf},
issn = {1070-664X},
journal = {Phys. Plasmas},
pages = {2181--2187},
title = {{Generation of plasma rotation in a tokamak by ion-cyclotron absorption of fast Alfven waves}},
url = {//wos},
volume = {8},
year = {2001}
}
@article{Throumoulopoulos2003,
abstract = {In the above entitled recent publication by Giovanni Lapenta Phys. Rev. Lett. Vol 90, 135005 (2003) it is claimed construction of a new class of solitonlike solutions for the Grad-Shafranov equation in plane geometry. It is proved here that, because of the mathematically erroneous choice nabla p= Psi 2 Psi nabla Psi for an analytic continuation of the poloidal magnetic flux-function Psi in the complex plane (p is the pressure), the cubic Schr"odinger equation considered by the author is irrelevant to the equilibrium problem and the Grad-Shafranov equation.},
archivePrefix = {arXiv},
arxivId = {physics/0307105},
author = {Throumoulopoulos, G N and Hizanidis, K and Tasso, H},
doi = {10.1103/PhysRevLett.92.249501},
eprint = {0307105},
journal = {Phys. Rev. Lett.},
pages = {3},
pmid = {15245139},
primaryClass = {physics},
title = {{Comment on "Solitonlike solutions of the Grad-Shafranov equation".}},
volume = {92},
year = {2003}
}
@article{Burby2015,
abstract = {We present a formulation of collisional gyrokinetic theory with exact conservation laws for energy and canonical toroidal momentum. Collisions are accounted for by a nonlinear gyrokinetic Landau operator. Gyroaveraging and linearization do not destroy the operator's conservation properties. Just as in ordinary kinetic theory, the conservation laws for collisional gyrokinetic theory are selected by the limiting collisionless gyrokinetic theory.},
archivePrefix = {arXiv},
arxivId = {1503.07185},
author = {Burby, J. W. and Brizard, A. J. and Qin, H.},
doi = {10.1063/1.4935124},
eprint = {1503.07185},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Burby, Brizard, Qin - 2015 - Energetically consistent collisional gyrokinetics.pdf:pdf},
issn = {10897674},
journal = {Phys. Plasmas},
number = {10},
title = {{Energetically consistent collisional gyrokinetics}},
volume = {22},
year = {2015}
}
@article{Hegna2010,
author = {Hegna, C C and Callen, Co-authors J D and Cole, a J},
journal = {Physics (College. Park. Md).},
keywords = {Presentation,plasma rotation},
mendeley-tags = {Presentation,plasma rotation},
title = {{Plasma Rotation in Tokamaks}},
year = {2010}
}
@article{Barnes,
author = {Barnes, Michael and Parra, Felix},
keywords = {Barnes,Parra,Presentation},
mendeley-tags = {Barnes,Parra,Presentation},
title = {{Intrinsic rotation in tokamaks Can we get large rotational shear for free ?}}
}
@article{Hatch2016,
abstract = {The first nonlinear gyrokinetic turbulence simulations that quantitatively reproduce$\backslash$r$\backslash$nexperimental transport levels in an H-mode pedestal are reported. In the JET-ILW (ITER-like$\backslash$r$\backslash$nwall) pedestal, the bulk of the transport in the steep gradient region is caused by the turbulence$\backslash$r$\backslash$ndriven by the microtearing mode (MTM). Kinetic ballooning modes are found to be in a$\backslash$r$\backslash$nsecond-stability regime. With contributions from the neoclassical and electron temperature$\backslash$r$\backslash$ngradient driven transport, the MTM mechanism reproduces, quantitatively, the experimental$\backslash$r$\backslash$npower balance across most of the pedestal.},
author = {Hatch, D. R. and Kotschenreuther, M. and Mahajan, S. and Valanju, P. and Jenko, F. and Told, D. and G{\"{i}}¿½rler, T. and Saarelma, S.},
doi = {10.1088/0029-5515/56/10/104003},
issn = {17414326},
journal = {Nucl. Fusion},
title = {{Microtearing turbulence limiting the JET-ILW pedestal}},
year = {2016}
}
@article{Gorler2016,
abstract = {Aiming to fill a corresponding lack of sophisticated test cases for global electromagnetic gyrokinetic codes, a new hierarchical benchmark is proposed. Starting from established test sets with adiabatic electrons, fully gyrokinetic electrons, and electrostatic fluctuations are taken into account before finally studying the global electromagnetic micro-instabilities. Results from up to five codes involving representatives from different numerical approaches as particle-in-cell methods, Eulerian and Semi-Lagrangian are shown. By means of spectrally resolved growth rates and frequencies and mode structure comparisons, agreement can be confirmed on ion-gyro-radius scales, thus providing confidence in the correct implementation of the underlying equations.},
author = {G{\"{o}}rler, T. and Tronko, N. and Hornsby, W. A. and Bottino, A. and Kleiber, R. and Norscini, C. and Grandgirard, V. and Jenko, F. and Sonnendr{\"{u}}cker, E.},
doi = {10.1063/1.4954915},
issn = {10897674},
journal = {Phys. Plasmas},
title = {{Intercode comparison of gyrokinetic global electromagnetic modes}},
year = {2016}
}
@article{Howes2008,
abstract = {This paper studies the turbulent cascade of magnetic energy in weakly collisional magnetized plasmas. A cascade model is presented, based on the assumptions of local nonlinear energy transfer in wavenumber space, critical balance between linear propagation and nonlinear interaction times, and the applicability of linear dissipation rates for the nonlinearly turbulent plasma. The model follows the nonlinear cascade of energy from the driving scale in the MHD regime, through the transition at the ion Larmor radius into the kinetic Alfven wave regime, in which the turbulence is dissipated by kinetic processes. The turbulent fluctuations remain at frequencies below the ion cyclotron frequency due to the strong anisotropy of the turbulent fluctuations, k{\_}parallel {\textless}{\textless} k{\_}perp (implied by critical balance). In this limit, the turbulence is optimally described by gyrokinetics; it is shown that the gyrokinetic approximation is well satisfied for typical slow solar wind parameters. Wave phase velocity measurements are consistent with a kinetic Alfven wave cascade and not the onset of ion cyclotron damping. The conditions under which the gyrokinetic cascade reaches the ion cyclotron frequency are established. Cascade model solutions imply that collisionless damping provides a natural explanation for the observed range of spectral indices in the dissipation range of the solar wind. The dissipation range spectrum is predicted to be an exponential fall off; the power-law behavior apparent in observations may be an artifact of limited instrumental sensitivity. The cascade model is motivated by a programme of gyrokinetic simulations of turbulence and particle heating in the solar wind.},
author = {Howes, G. G. and Cowley, S. C. and Dorland, W. and Hammett, G. W. and Quataert, E. and Schekochihin, A. A.},
doi = {10.1029/2007JA012665},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Howes et al. - 2008 - A model of turbulence in magnetized plasmas Implications for the dissipation range in the solar wind.pdf:pdf},
journal = {J. Geophys. Res. Sp. Phys.},
title = {{A model of turbulence in magnetized plasmas: Implications for the dissipation range in the solar wind}},
url = {http://www.mendeley.com/research/model-turbulence-magnetized-plasmas-implications-dissipation-range-solar-wind},
year = {2008}
}
@article{Xu1993,
author = {Xu, X. Q.},
doi = {10.1063/1.860836},
issn = {08998221},
journal = {Phys. Fluids B Plasma Phys.},
number = {10},
pages = {3641},
title = {{Fluid simulations of conducting-wall-driven turbulence in boundary plasmas}},
url = {http://link.aip.org/link/PFBPEI/v5/i10/p3641/s1{\&}Agg=doi},
volume = {5},
year = {1993}
}
@article{Abel2012,
abstract = {This paper presents a complete theoretical framework for plasma turbulence and transport in tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio of the gyroradius to the equilibrium scale length. Proceeding order-by-order in this expansion, a framework for plasma turbulence is developed. It comprises an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equillibrium is obtained from the Grad-Shafranov equation for a rotating plasma and the slow (resistive) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the high-flow gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local cascade of free energy. Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical corrections and the fluctuations act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived. Total energy is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating, and the equilibration of mean temperatures. Finally, this framework is condensed, in the low-Mach-number limit, to a concise set of equations suitable for numerical implementation.},
archivePrefix = {arXiv},
arxivId = {1209.4782},
author = {Abel, I. G. and Plunk, G. G. and Wang, E. and Barnes, M. and Cowley, S. C. and Dorland, W. and Schekochihin, A. A.},
doi = {10.1088/0034-4885/76/11/116201},
eprint = {1209.4782},
title = {{Multiscale Gyrokinetics for Rotating Tokamak Plasmas: Fluctuations, Transport and Energy Flows}},
url = {http://arxiv.org/abs/1209.4782{\%}0Ahttp://dx.doi.org/10.1088/0034-4885/76/11/116201},
year = {2012}
}
@article{Yushmanov1990,
abstract = {ABSTRACT. On the basis of an analysis of the ITER L-mode energy confinement database, two new scaling$\backslash$nexpressions for tokamak L-mode energy confinement are proposed, namely a power law scaling and an offset-linear$\backslash$nscaling. The analysis indicates that the present multiplicity of scaling expressions for the energy confinement time TE$\backslash$nin tokamaks (Goldston, Kaye, Odajima-Shimomura, Rebut-Lallia, etc.) is due both to the lack of variation of a key$\backslash$nparameter combination in the database, fs = 0.32 R a"075 k05 {\~{}} A aO25k05, and to variations in the dependence of$\backslash$nrE on the physical parameters among the different tokamaks in the database. By combining multiples of fs and another$\backslash$nfactor, fq = 1.56 a2 kB/RIp = qeng/3.2, which partially reflects the tokamak to tokamak variation of the dependence of$\backslash$nTE on q and therefore implicitly the dependence of TE on Ip and n,., the two proposed confinement scaling expressions$\backslash$ncan be transformed to forms very close to most of the common scaling expressions. To reduce the multiplicity of the$\backslash$nscalings for energy confinement, the database must be improved by adding new data with significant variations in fs,$\backslash$nand the physical reasons for the tokamak to tokamak variation of some of the dependences of the energy confinement$\backslash$ntime on tokamak parameters must be clarified.},
author = {Yushmanov, P. N. and Takizuka, T. and Riedel, K. S. and Kardaun, Ojwf and Cordey, J. G. and Kaye, S. M. and Post, D. E.},
doi = {10.1088/0029-5515/30/10/001},
isbn = {0029-5515},
issn = {0029-5515},
journal = {Nucl. Fusion},
pages = {1999--2006},
title = {{Scalings for Tokamak Energy Confinement}},
volume = {30},
year = {1990}
}
@article{Brizard2007,
abstract = {Nonlinear gyrokinetic equations play a fundamental role in our understanding of the long-time behavior of strongly magnetized plasmas. The foundations of modern nonlinear gyrokinetic theory are based on three pillars: (i) a gyrokinetic Vlasov equation written in terms of a gyrocenter Hamiltonian with quadratic low-frequency ponderomotivelike terms, (ii) a set of gyrokinetic Maxwell Poisson-Amp{\`{e}}re equations written in terms of the gyrocenter Vlasov distribution that contain low-frequency polarization Poisson and magnetization Amp{\`{e}}re terms, and (iii) an exact energy conservation law for the gyrokinetic Vlasov-Maxwell equations that includes all the relevant linear and nonlinear coupling terms. The foundations of nonlinear gyrokinetic theory are reviewed with an emphasis on rigorous application of Lagrangian and Hamiltonian Lie-transform perturbation methods in the variational derivation of nonlinear gyrokinetic Vlasov-Maxwell equations. The physical motivations and applications of the nonlinear gyrokinetic equations that describe the turbulent evolution of low-frequency electromagnetic fluctuations in a nonuniform magnetized plasmas with arbitrary magnetic geometry are discussed.},
author = {Brizard, a. J. and Hahm, T. S.},
doi = {10.1103/RevModPhys.79.421},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Brizard, Hahm - 2007 - Foundations of nonlinear gyrokinetic theory.pdf:pdf},
isbn = {0034-6861$\backslash$n1539-0756},
issn = {00346861},
journal = {Rev. Mod. Phys.},
number = {2},
pages = {421--468},
title = {{Foundations of nonlinear gyrokinetic theory}},
volume = {79},
year = {2007}
}
@article{Terry2015,
abstract = {{\textcopyright} 2015 IAEA, Vienna.Recent results on electromagnetic turbulence from gyrokinetic studies in different magnetic configurations are overviewed, detailing the physics of electromagnetic turbulence and transport, and the effect of equilibrium magnetic field scale lengths. Ion temperature gradient (ITG) turbulence is shown to produce magnetic stochasticity through nonlinear excitation of linearly stable tearing-parity modes. The excitation, which is catalyzed by the zonal flow, produces an electron heat flux proportional to $\beta$2 that deviates markedly from quasilinear theory. Above a critical beta known as the non-zonal transition (NZT), the magnetic fluctuations disable zonal flows by allowing electron streaming that shorts zonal potential between flux surfaces. This leads to a regime of very high transport levels. Kinetic ballooning mode (KBM) saturation is described. For tokamaks saturation involves twisted structures arising from magnetic shear; for helical plasmas oppositely inclined convection cells interact by mutual shearing. Microtearing modes are unstable in the magnetic geometry of tokamaks and the reversed field pinch (RFP). In NSTX instability requires finite collisionality, large beta, and is favored by increasing magnetic shear and decreasing safety factor. In the RFP, a new branch of microtearing with finite growth rate at vanishing collisionality is shown from analytic theory to require the electron grad-B/curvature drift resonance. However, gyrokinetic modeling of experimental MST RFP discharges at finite beta reveals turbulence that is electrostatic, has large zonal flows, and a large Dimits shift. Analysis shows that the shorter equilibrium magnetic field scale lengths increase the critical gradients associated with the instability of trapped electron modes, ITG and microtearing, while increasing beta thresholds for KBM instability and the NZT.},
author = {Terry, P. W. and Carmody, D. and Doerk, H. and Guttenfelder, W. and Hatch, D. R. and Hegna, C. C. and Ishizawa, A. and Jenko, F. and Nevins, W. M. and Predebon, I. and Pueschel, M. J. and Sarff, J. S. and Whelan, G. G.},
doi = {10.1088/0029-5515/55/10/104011},
issn = {17414326},
journal = {Nucl. Fusion},
title = {{Overview of gyrokinetic studies of finite-$\beta$ microturbulence}},
year = {2015}
}
@article{Wang2013,
abstract = {A mechanism for turbulent acceleration of parallel rotation is discovered using gyrokinetic theory. This new turbulent acceleration term cannot be written as a divergence of parallel Reynolds stress. Therefore, turbulent acceleration acts as a local source or sink of parallel rotation. The physics of turbulent acceleration is intrinsically different from the Reynolds stress. For symmetry breaking by positive intensity gradient, a positive turbulent acceleration, i.e., cocurrent rotation, is predicted. The turbulent acceleration is independent of mean rotation and mean rotation gradient, and so constitutes a new candidate for the origin of spontaneous rotation. A quasilinear estimate for ion temperature gradient turbulence shows that the turbulent acceleration of parallel rotation is explicitly linked to the ion temperature gradient scale length and temperature ratio T-i0/T-e0. Methods for testing the effects of turbulent parallel acceleration by gyrokinetic simulation and experiment are proposed},
author = {Wang, Lu and Diamond, P. H.},
doi = {10.1103/PhysRevLett.110.265006},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Wang, Diamond - 2013 - Gyrokinetic theory of turbulent acceleration of parallel rotation in Tokamak plasmas.pdf:pdf},
issn = {00319007},
journal = {Phys. Rev. Lett.},
number = {26},
title = {{Gyrokinetic theory of turbulent acceleration of parallel rotation in Tokamak plasmas}},
volume = {110},
year = {2013}
}
@article{SalarElahi2013,
author = {{Salar Elahi}, a. and Ghoranneviss, M.},
doi = {10.5923/j.jnpp.20120206.02},
issn = {2167-6895},
journal = {J. Nucl. Part. Phys.},
keywords = {4,also,analytical solution of the,be presented in section,between them also will,experimental results and comparative,grad-shafranov equation,grad-shafranov equation will be,poloidal flu x loop,presented in section 3,shafranov shift,tokamak},
month = {jan},
number = {6},
pages = {142--146},
title = {{Estimation of Plasma Horizontal Displacement using Flux Loops and Comparison with Analytical Solution in IR-T1 Tokamak}},
url = {http://article.sapub.org/10.5923.j.jnpp.20120206.02.html},
volume = {2},
year = {2013}
}
@article{Greenwald1988,
abstract = {While the results of early work on the density limit in tokamaks from the ORMAK and DITE groups have been useful over the years, results from recent experiments and the requirements for extrapolation to future experiments have prompted a new look at this subject. There are many physical processes which limit the attainable densities in tokamak plasmas. These processes include: (1) radiation from low Z impurities, convection, charge exchange and other losses at the plasma edge; (2) radiation from low or high Z impurities in the plasma core; (3) deterioration of particle confinement in the plasma core; and (4) inadequate fuelling, often exacerbated by strong pumping by walls, limiters or divertors. Depending upon the circumstances, any of these processes may dominate and determine a density limit. In general, these mechanisms do not show the same dependence on plasma parameters. The multiplicity of processes leading to density limits with a variety of scaling has led to some confusion when comparing density limits for different machines. The authors attempt to sort out the various limits and to extend the scaling law for one of them to include the important effects of plasma shaping, i.e. {\#}{\#}IMG{\#}{\#} [http://ej.iop.org/icons/Entities/barn.gif] {\{}bar n{\}} ; e = k {\#}{\#}IMG{\#}{\#} [http://ej.iop.org/icons/Entities/barJ.gif] {\{}bar J{\}} , where n e is the line average electron density (10 20 m −3 ), $\kappa$ is the plasma elongation and {\#}{\#}IMG{\#}{\#} [http://ej.iop.org/icons/Entities/barJ.gif] {\{}bar J{\}} (MA{\textperiodcentered}m −2 ) is the average plasma current density, defined as the total current divided by the plasma cross-sectional area. In a sense, this is the most important density limit since, together with the q-limit, it yields the maximum operating density for a tokamak plasma. It is shown that this limit may be caused by a dramatic deterioration in core particle confinement occurring as the density limit boundary is approached. This mechanism can help explain the disruptions and Marfes that are associated with the density limit.},
author = {Greenwald, Martin J. and Terry, J L and Wolfe, S M and Ejima, S and Bell, M G and Kaye, S M and Neilson, G H},
doi = {10.1088/0029-5515/28/12/009},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Greenwald et al. - 1988 - A new look at density limits in tokamaks.pdf:pdf},
isbn = {0029-5515},
issn = {0029-5515},
journal = {Nucl. Fusion},
number = {12},
pages = {2199},
title = {{A new look at density limits in tokamaks}},
url = {http://stacks.iop.org/0029-5515/28/i=12/a=009},
volume = {28},
year = {1988}
}
@article{Bateman1986,
author = {Bateman, Glenn and Storer, Robin G},
doi = {10.1016/0021-9991(86)90023-9},
issn = {00219991},
journal = {J. Comput. Phys.},
month = {may},
number = {1},
pages = {161--176},
title = {{Direct determination of axisymmetric magnetohydrodynamic equilibria in Hamada coordinates}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0021999186900239},
volume = {64},
year = {1986}
}
@article{Khater2006,
author = {Khater, a. H. and Moawad, S. M.},
doi = {10.1017/S1743921306002079},
isbn = {1743921306002},
issn = {1743-9213},
journal = {Proc. Int. Astron. Union},
keywords = {exact solutions,grad-shafranov equation,magnetostatic atmosphere},
month = {nov},
number = {S233},
pages = {307},
title = {{Exact solutions to the Grad-Shafranov equation for magnetically confined plasmas}},
url = {http://www.journals.cambridge.org/abstract{\_}S1743921306002079},
volume = {2},
year = {2006}
}
@article{Callaghan2009,
author = {Callaghan, J and Romanelli, M and Thyagaraja, A and Mcclements, K G and Ukaea, Euratom and Association, Fusion and Centre, Culham Science},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Callaghan et al. - 2009 - Test-particle simulations of impurity transport in tokamak plasmas.pdf:pdf},
journal = {36th EPS Conf. Plasma Phys. Sofia},
pages = {2--5},
title = {{Test-particle simulations of impurity transport in tokamak plasmas}},
volume = {33},
year = {2009}
}
@article{Cicogna2010,
author = {Cicogna, G. and Pegoraro, F. and Ceccherini, F.},
doi = {10.1063/1.3491426},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {10},
pages = {102506},
title = {{Symmetries, weak symmetries, and related solutions of the Grad–Shafranov equation}},
url = {http://link.aip.org/link/PHPAEN/v17/i10/p102506/s1{\&}Agg=doi},
volume = {17},
year = {2010}
}
@article{McKee2003,
author = {McKee, G. R. and Fonck, R. J. and Jakubowski, M. and Burrell, K. H. and Hallatschek, K. and Moyer, R. a. and Rudakov, D. L. and Nevins, W. and Porter, G. D. and Schoch, P. and Xu, X.},
doi = {10.1063/1.1559974},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {5},
pages = {1712},
title = {{Experimental characterization of coherent, radially-sheared zonal flows in the DIII-D tokamak}},
url = {http://link.aip.org/link/PHPAEN/v10/i5/p1712/s1{\&}Agg=doi},
volume = {10},
year = {2003}
}
@article{Reference3,
abstract = {Operating a laser diode in an extended cavity which provides frequency-selective feedback is a very effective method of reducing the laser's linewidth and improving its tunability. We have developed an extremely simple laser of this type, built from inexpensive commercial components with only a few minor modifications. A 780{\~{}}nm laser built to this design has an output power of 80{\~{}}mW, a linewidth of 350{\~{}}kHz, and it has been continuously locked to a Doppler-free rubidium transition for several days.},
author = {Arnold, A S and Wilson, J S and Boshier, M G},
journal = {Rev. Sci. Instrum.},
month = {mar},
number = {3},
pages = {1236--1239},
title = {{A Simple Extended-Cavity Diode Laser}},
url = {http://link.aip.org/link/?RSI/69/1236/1},
volume = {69},
year = {1998}
}
@article{Lovelace2002,
abstract = {The powerful narrow jets observed to emanate from many compact accreting objects may arise from the twisting of a magnetic field threading a differentially rotating accretion disk which acts to magnetically extract angular momentum and energy from the disk. Two main regimes have been discussed, it hydromagnetic outflows, which have a significant mass flux and have energy and angular momentum carried by both the matter and the electromagnetic field and, Poynting outflows, where the mass flux is negligible and energy and angular momentum are carried predominantly by the electromagnetic field. Here we consider a Keplerian disk initially threaded by a dipole-like magnetic field and we present solutions of the force-free Grad-Shafranov equation for the coronal plasma. We find solutions with Poynting jets where there is a continuous outflow of energy and toroidal magnetic flux from the disk into the external space. This behavior contradicts the commonly accepted ``theorem'' of Solar plasma physics that the motion of the footpoints of a magnetic loop structure leads to a stationary magnetic field configuration with zero power and flux outflows. In addition we discuss recent magnetohydrodynamic (MHD) simulations which establish that quasi-stationary collimated Poynting jets similar to our Grad-Shafranov solutions arise from the inner part of a disk threaded by a dipole-like magnetic field. At the same time we find that there is a steady uncollimated hydromagnetic outflow from the outer part of the disk. The Poynting jets represent a likely model for the jets from active galactic nuclei, microquasars, and gamma ray burst sources.},
archivePrefix = {arXiv},
arxivId = {astro-ph/0210571},
author = {Lovelace, R V E and Li, H and Koldoba, A V and Ustyugova, G V and Romanova, M M},
doi = {10.1086/340292},
eprint = {0210571},
journal = {Astrophys. J.},
pages = {7},
primaryClass = {astro-ph},
title = {{Poynting Jets from Accretion Disks}},
volume = {572},
year = {2002}
}
@book{LANDAU1989,
author = {LANDAU, L. D. and LIFSHITZ, E. M.},
isbn = {0080339336},
title = {{COURSE OF THEORETICAL PHYSICS Volume 6, Fluid mechanics}},
volume = {1},
year = {1989}
}
@article{Romeo2008,
abstract = {In the year 2003 a paper by G. Lapenta demonstrated that there is a new class of soliton-like solutions for the Grad-Shafranov Equations (GSE).The author determined an appropriate pair of transformations of the free fields p (fluid field of hydrodynamical pressure) and Bz (z- component of magnetic induction field) that leads from the Helmholtz Equation to the Non-Linear Schroedinger Equation (NLSE) with cubic non- linearity. In the following year (2004), the work of Lapenta was opposed by G.N. Throumoulopoulos et al.,who criticized his idea of the field transformations as a mathematically incoherent choice; contextually the authors suggested a new point of view for this one. In his response, in the same year, G. Lapenta carried out numerical simulations that showed the existence of solitonic structures in a Magnetohydrodynamical (MHD) plasma-context. In the present work I want to demonstrate a critical condition for a complex poloidal flux function psi in a plane framework (x;y) that leads to a class of pseudo-general NLSEs which establishes the validity of both G.Lapenta and G.N. Throumoulopoulos et al. choices for the field transformation functionals.},
archivePrefix = {arXiv},
arxivId = {0807.1629},
author = {Romeo, Michele},
eprint = {0807.1629},
journal = {Arxiv Prepr. arXiv08071629},
pages = {1--26},
title = {{From Grad-Shafranov equations set to a pseudo-general form of the non-linear Schroedinger equation}},
year = {2008}
}
@misc{Braginskii1965,
abstract = {Not Available},
author = {Braginskii, S. I.},
booktitle = {Rev. Plasma Phys.},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Braginskii - 1965 - Transport processes in a plasma.pdf:pdf},
pages = {205},
title = {{Transport processes in a plasma}},
volume = {1},
year = {1965}
}
@article{Snyder2011,
author = {Snyder, P.B. and Groebner, R.J. and Hughes, J.W. and Osborne, T.H. and Beurskens, M. and a.W. Leonard and Wilson, H.R. and Xu, X.Q.},
doi = {10.1088/0029-5515/51/10/103016},
issn = {0029-5515},
journal = {Nucl. Fusion},
month = {oct},
number = {10},
pages = {103016},
title = {{A first-principles predictive model of the pedestal height and width: development, testing and ITER optimization with the EPED model}},
url = {http://stacks.iop.org/0029-5515/51/i=10/a=103016?key=crossref.334289a0972991b200871ad1b82fa95c},
volume = {51},
year = {2011}
}
@article{Barnes2009,
abstract = {A new analytically and numerically manageable model collision operator is developed specifically for turbulence simulations. The like-particle collision operator includes both pitch-angle scattering and energy diffusion and satisfies the physical constraints required for collision operators: it conserves particles, momentum and energy, obeys Boltzmann's H-theorem (collisions cannot decrease entropy), vanishes on a Maxwellian, and efficiently dissipates small-scale structure in the velocity space. The process of transforming this collision operator into the gyroaveraged form for use in gyrokinetic simulations is detailed. The gyroaveraged model operator is shown to have more suitable behavior at small scales in phase space than previously suggested models. A model operator for electron-ion collisions is also presented.},
archivePrefix = {arXiv},
arxivId = {0808.1300},
author = {Barnes, M. and Abel, I. G. and Dorland, W. and Ernst, D. R. and Hammett, G. W. and Ricci, P. and Rogers, B. N. and Schekochihin, A. A. and Tatsuno, T.},
doi = {10.1063/1.3155085},
eprint = {0808.1300},
isbn = {1070-664X},
issn = {1070664X},
journal = {Phys. Plasmas},
number = {7},
pages = {1--13},
title = {{Linearized model fokker-planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests}},
volume = {16},
year = {2009}
}
@article{Cremaschini2008,
abstract = {The consistent theoretical description of gravitational Hall-MHD (G-Hall-MHD) equilibria is of fundamental importance for understanding the phenomenology of accretion disks (AD) around compact objects (black holes, neutron stars, etc.). The very existence of these equilibria is actually suggested by observations, which show evidence of quiescent, and essentially non-relativistic, AD plasmas close to compact stars, thus indicating that accretion disks may be characterized by slowly varying EM and fluid fields. These (EM) fields, in particular the electric field, may locally be extremely intense, so that AD plasmas are likely to be locally non-neutral and therefore characterized by the presence of Hall currents. This suggests therefore that such equilibria should be described in the framework of the Hall-MHD theory. Extending previous approaches, holding for non-rotating plasmas or based on specialized single-species model equilibria which ignore the effect of space-time curvature, the purpose of this work is the formulation of a generalized Grad-Shafranov (GGS) equation suitable for the investigation of G-Hall-MHD equilibria in AD's where non-relativistic plasmas are present. For this purpose the equilibria are assumed to be generated by a strong axisymmetric stellar magnetic field and by the gravitating plasma characterizing the AD.},
archivePrefix = {arXiv},
arxivId = {0806.4522},
author = {Cremaschini, C and Beklemishev, A and Miller, J and Tessarotto, M},
doi = {10.1063/1.3076440},
eprint = {0806.4522},
journal = {Rarefied Gas Dyn. Conf. Proc. Vol. 1084},
pages = {1067--1072},
title = {{Generalized Grad-Shafranov equation for gravitational Hall-MHD equilibria}},
volume = {1084},
year = {2008}
}
@article{Khater1988,
abstract = {In this paper, the problem of stationary MHD flow for a rotating toroidal plasma is investigated by assuming that the entropy is a surface quantity. Then, the system of ideal MHD equations is reduced to a single second-order elliptic partial differential equation known as the modified Grad-Shafranov (or Maschke-Perrin) equation. Under the assumption that both the function, P s and f 2 are quadratic polynomials of the flux function, a class of semi-analytical solutions is obtained for a plasma contained in a perfectly conducting toroidal boundary with a rectangular cross section. The flux function, poloidal current and the generalized pressure are obtained and discussed for relevant values of the parameters.},
author = {Khater, A H and Sheikh, M G and Callebaut, D K},
doi = {10.1007/BF00642104},
issn = {0004640X},
journal = {Astrophys. Space Sci.},
keywords = {physics astronomy},
pages = {277--286},
title = {{A class of semi-analytical solutions for a rotating toroidal plasma}},
volume = {145},
year = {1988}
}
@article{Hazeltine1973a,
abstract = {A drift kinetic equation is derived which contains higher order effects. The upper bound appropriate to the drift ordering is only imposed so that the result is quite general and can be reduced to previous drift equations. The differential geometry of the magnetic field enters only trivially and a single recursion suffices to obtain the desired result.},
author = {Hazeltine, R D},
doi = {10.1088/0032-1028/15/1/009},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Hazeltine - 1973 - Recursive derivation of drift-kinetic equation.pdf:pdf},
issn = {0032-1028},
journal = {Plasma Phys.},
number = {1},
pages = {77--80},
title = {{Recursive derivation of drift-kinetic equation}},
url = {http://stacks.iop.org/0032-1028/15/i=1/a=009?key=crossref.0e8ea9f4bfee5a31b84cb048242ab2fc},
volume = {15},
year = {1973}
}
@article{Sagdeev2003,
author = {Sagdeev, R Z and Meiss, J D},
title = {{Drift kinetic equation and neoclassical transport theory}},
year = {2003}
}
@article{Callen2008,
author = {Callen, J D},
file = {:home/adwiteey/Desktop/PhD/Mendeley{\_}Desktop/Callen - 2008 - Toroidal Rotation In Tokamak Plasmas Physics Key Poloidal And Toroidal Flow Processes.pdf:pdf},
journal = {October},
number = {October},
pages = {20--22},
title = {{Toroidal Rotation In Tokamak Plasmas Physics : Key Poloidal And Toroidal Flow Processes}},
year = {2008}
}