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Electromagnetic full$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods
Abstract
We present an energyconserving discontinuous Galerkin scheme for the full $f$$ electromagnetic gyrokinetic system in the longwavelength limit. We use the symplectic formulation and solve directly for $$\unicode[STIX]{x2202}A_{\Vert }/\unicode[STIX]{x2202}t$ , the inductive component of the parallel electric field, using a generalized Ohm’s law derived directly from the gyrokinetic equation. Linear benchmarks are performed to verify the implementation and show that the scheme avoids the Ampère cancellation problem. We perform a nonlinear electromagnetic simulation in a helical openfieldline system as a rough model of the tokamak scrapeoff layer using parameters from the National Spherical Torus Experiment (NSTX). This is the first published nonlinear electromagnetic gyrokinetic simulation on open field lines. Comparisons are made to a corresponding electrostatic simulation.
 Authors:

 Princeton Univ., NJ (United States)
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Publication Date:
 Research Org.:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1660956
 Alternate Identifier(s):
 OSTI ID: 1668767
 Grant/Contract Number:
 FG0297ER25308; FC0208ER54966; AC0209CH11466
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Plasma Physics
 Additional Journal Information:
 Journal Volume: 86; Journal Issue: 1; Journal ID: ISSN 00223778
 Publisher:
 Cambridge University Press
 Country of Publication:
 United States
 Language:
 English
Citation Formats
Mandell, N. R., Hakim, A., Hammett, G. W., and Francisquez, M. Electromagnetic full$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods. United States: N. p., 2020.
Web. doi:10.1017/s0022377820000070.
Mandell, N. R., Hakim, A., Hammett, G. W., & Francisquez, M. Electromagnetic full$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods. United States. doi:10.1017/s0022377820000070.
Mandell, N. R., Hakim, A., Hammett, G. W., and Francisquez, M. Mon .
"Electromagnetic full$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods". United States. doi:10.1017/s0022377820000070.
@article{osti_1660956,
title = {Electromagnetic full$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods},
author = {Mandell, N. R. and Hakim, A. and Hammett, G. W. and Francisquez, M.},
abstractNote = {We present an energyconserving discontinuous Galerkin scheme for the full $f$ electromagnetic gyrokinetic system in the longwavelength limit. We use the symplectic formulation and solve directly for $\unicode[STIX]{x2202}A_{\Vert }/\unicode[STIX]{x2202}t$ , the inductive component of the parallel electric field, using a generalized Ohm’s law derived directly from the gyrokinetic equation. Linear benchmarks are performed to verify the implementation and show that the scheme avoids the Ampère cancellation problem. We perform a nonlinear electromagnetic simulation in a helical openfieldline system as a rough model of the tokamak scrapeoff layer using parameters from the National Spherical Torus Experiment (NSTX). This is the first published nonlinear electromagnetic gyrokinetic simulation on open field lines. Comparisons are made to a corresponding electrostatic simulation.},
doi = {10.1017/s0022377820000070},
journal = {Journal of Plasma Physics},
number = 1,
volume = 86,
place = {United States},
year = {2020},
month = {3}
}
Web of Science
Works referenced in this record:
Progress in Kinetic Simulation of Edge Plasmas
journal, March 2008
 Cohen, R. H.; Xu, X. Q.
 Contributions to Plasma Physics, Vol. 48, Issue 13
Discontinuous Galerkin algorithms for fully kinetic plasmas
journal, January 2018
 Juno, J.; Hakim, A.; TenBarge, J.
 Journal of Computational Physics, Vol. 353
An Eulerian gyrokineticMaxwell solver
journal, April 2003
 Candy, J.; Waltz, R. E.
 Journal of Computational Physics, Vol. 186, Issue 2
Global 3D twofluid simulations of the tokamak edge region: Turbulence, transport, profile evolution, and spontaneous E × B rotation
journal, May 2017
 Zhu, Ben; Francisquez, Manaure; Rogers, Barrett N.
 Physics of Plasmas, Vol. 24, Issue 5
Continuum kinetic and multifluid simulations of classical sheaths
journal, February 2017
 Cagas, P.; Hakim, A.; Juno, J.
 Physics of Plasmas, Vol. 24, Issue 2
Model FokkerPlanck Equation for a Plasma and Its Solution
journal, January 1964
 Dougherty, J. P.
 Physics of Fluids, Vol. 7, Issue 11
Global 3D Braginskii simulations of the tokamak edge region of IWL discharges
journal, August 2017
 Francisquez, M.; Zhu, B.; Rogers, B. N.
 Nuclear Fusion, Vol. 57, Issue 11
Gyrokinetic continuum simulations of plasma turbulence in the Texas Helimak
journal, April 2019
 Bernard, T. N.; Shi, E. L.; Gentle, K. W.
 Physics of Plasmas, Vol. 26, Issue 4
Global gyrokinetic simulation of ion temperature gradient driven turbulence in plasmas using a canonical Maxwellian distribution
journal, March 2003
 Idomura, Y.; Tokuda, S.; Kishimoto, Y.
 Nuclear Fusion, Vol. 43, Issue 4
Simulation of plasma turbulence in scrapeoff layer conditions: the GBS code, simulation results and code validation
journal, November 2012
 Ricci, P.; Halpern, F. D.; Jolliet, S.
 Plasma Physics and Controlled Fusion, Vol. 54, Issue 12
Electron Temperature Gradient Turbulence
journal, December 2000
 Dorland, W.; Jenko, F.; Kotschenreuther, M.
 Physical Review Letters, Vol. 85, Issue 26
Intermittent convective transport carried by propagating electromagnetic filamentary structures in nonuniformly magnetized plasma
journal, February 2010
 Xu, G. S.; Naulin, V.; Fundamenski, W.
 Physics of Plasmas, Vol. 17, Issue 2
Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities
journal, August 1995
 Kotschenreuther, Mike; Rewoldt, G.; Tang, W. M.
 Computer Physics Communications, Vol. 88, Issue 23
Conventional δfparticle simulations of electromagnetic perturbations with finite elements
journal, December 2004
 Mishchenko, Alexey; Hatzky, Roman; Könies, Axel
 Physics of Plasmas, Vol. 11, Issue 12
Full f version of GENE for turbulence in openfieldline systems
journal, June 2018
 Pan, Q.; Told, D.; Shi, E. L.
 Physics of Plasmas, Vol. 25, Issue 6
Comparisons and physics basis of tokamak transport models and turbulence simulations
journal, March 2000
 Dimits, A. M.; Bateman, G.; Beer, M. A.
 Physics of Plasmas, Vol. 7, Issue 3
A δf particle method for gyrokinetic simulations with kinetic electrons and electromagnetic perturbations
journal, August 2003
 Chen, Yang; Parker, Scott E.
 Journal of Computational Physics, Vol. 189, Issue 2
The nonlinear gyrokinetic flux tube code GKW
journal, December 2009
 Peeters, A. G.; Camenen, Y.; Casson, F. J.
 Computer Physics Communications, Vol. 180, Issue 12
Collisional effects on kinetic electromagnetic modes and associated quasilinear transport
journal, January 1987
 Rewoldt, G.; Tang, W. M.; Hastie, R. J.
 Physics of Fluids, Vol. 30, Issue 3
A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons
journal, February 2018
 Bao, J.; Lin, Z.; Lu, Z. X.
 Physics of Plasmas, Vol. 25, Issue 2
Gyrokinetic fulltorus simulations of ohmic tokamak plasmas in circular limiter configuration
journal, June 2016
 Korpilo, T.; Gurchenko, A. D.; Gusakov, E. Z.
 Computer Physics Communications, Vol. 203
Orb5: A global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry
journal, June 2020
 Lanti, E.; Ohana, N.; Tronko, N.
 Computer Physics Communications, Vol. 251
Nonlinear electromagnetic gyrokinetic simulations of tokamak plasmas
journal, November 2001
 Jenko, F.; Dorland, W.
 Plasma Physics and Controlled Fusion, Vol. 43, Issue 12A
A fast lowtohigh confinement mode bifurcation dynamics in the boundaryplasma gyrokinetic code XGC1
journal, May 2018
 Ku, S.; Chang, C. S.; Hager, R.
 Physics of Plasmas, Vol. 25, Issue 5
The dynamics of an isolated plasma filament at the edge of a toroidal device
journal, December 2006
 Ryutov, D. D.
 Physics of Plasmas, Vol. 13, Issue 12
Finiteβ simulation of microinstabilities
journal, February 2014
 Startsev, Edward A.; Lee, W. W.
 Physics of Plasmas, Vol. 21, Issue 2
Electromagnetic effect on the toroidal ion temperature gradient mode
journal, November 1993
 Kim, J. Y.; Horton, W.; Dong, J. Q.
 Physics of Fluids B: Plasma Physics, Vol. 5, Issue 11
Gyrokinetic turbulence simulations with kinetic electrons
journal, May 2001
 Chen, Yang; Parker, Scott
 Physics of Plasmas, Vol. 8, Issue 5
A HighOrder Discontinuous Galerkin Method for 2D Incompressible Flows
journal, May 2000
 Liu, JianGuo; Shu, ChiWang
 Journal of Computational Physics, Vol. 160, Issue 2
Field‐aligned coordinates for nonlinear simulations of tokamak turbulence
journal, August 1995
 Beer, M. A.; Cowley, S. C.; Hammett, G. W.
 Physics of Plasmas, Vol. 2, Issue 7
Massively parallel Vlasov simulation of electromagnetic driftwave turbulence
journal, March 2000
 Jenko, Frank
 Computer Physics Communications, Vol. 125, Issue 13
TOKAM3D: A 3D fluid code for transport and turbulence in the edge plasma of Tokamaks
journal, January 2010
 Tamain, P.; Ghendrih, Ph.; Tsitrone, E.
 Journal of Computational Physics, Vol. 229, Issue 2
A Suitable Boundary Condition for Bounded Plasma Simulation without Sheath Resolution
journal, January 1993
 Parker, S. E.; Procassini, R. J.; Birdsall, C. K.
 Journal of Computational Physics, Vol. 104, Issue 1
A multidimensional, energy and chargeconserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particleincell algorithm
journal, December 2015
 Chen, G.; Chacón, L.
 Computer Physics Communications, Vol. 197
Gyrokinetic continuum simulation of turbulence in a straight openfieldline plasma
journal, May 2017
 Shi, E. L.; Hammett, G. W.; StoltzfusDueck, T.
 Journal of Plasma Physics, Vol. 83, Issue 3
Threedimensional computation of drift Alfvén turbulence
journal, October 1997
 Scott, B.
 Plasma Physics and Controlled Fusion, Vol. 39, Issue 10
Nonlinear gyrokinetic theory for finitebeta plasmas
journal, January 1988
 Hahm, T. S.; Lee, W. W.; Brizard, A.
 Physics of Fluids, Vol. 31, Issue 7
Electromagnetic gyrokinetic PIC simulation with an adjustable control variates method
journal, July 2007
 Hatzky, R.; Könies, A.; Mishchenko, A.
 Journal of Computational Physics, Vol. 225, Issue 1
Global linear gyrokinetic simulations in quasisymmetric configurations
journal, July 2001
 Jost, G.; Tran, T. M.; Cooper, W. A.
 Physics of Plasmas, Vol. 8, Issue 7
Foundations of nonlinear gyrokinetic theory
journal, April 2007
 Brizard, A. J.; Hahm, T. S.
 Reviews of Modern Physics, Vol. 79, Issue 2
Conservative global gyrokinetic toroidal fullf fivedimensional Vlasov simulation
journal, September 2008
 Idomura, Yasuhiro; Ida, Masato; Kano, Takuma
 Computer Physics Communications, Vol. 179, Issue 6
Full f gyrokinetic simulation of turbulence in a helical openfieldline plasma
journal, January 2019
 Shi, E. L.; Hammett, G. W.; StoltzfusDueck, T.
 Physics of Plasmas, Vol. 26, Issue 1
A global collisionless PIC code in magnetic coordinates
journal, September 2007
 Jolliet, S.; Bottino, A.; Angelino, P.
 Computer Physics Communications, Vol. 177, Issue 5
A new hybridLagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
journal, June 2016
 Ku, S.; Hager, R.; Chang, C. S.
 Journal of Computational Physics, Vol. 315
The Serendipity Family of Finite Elements
journal, March 2011
 Arnold, Douglas N.; Awanou, Gerard
 Foundations of Computational Mathematics, Vol. 11, Issue 3
Gyrokinetic simulation of ion temperature gradient driven turbulence in 3D toroidal geometry
journal, September 1993
 Parker, S. E.; Lee, W. W.; Santoro, R. A.
 Physical Review Letters, Vol. 71, Issue 13
Velocity–space structures of distribution function in toroidal ion temperature gradient turbulence
journal, December 2005
 Watanabe, T. H; Sugama, H.
 Nuclear Fusion, Vol. 46, Issue 1
Gyrokinetic particle simulation model
journal, September 1987
 Lee, W. W.
 Journal of Computational Physics, Vol. 72, Issue 1
The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V
journal, April 1998
 Cockburn, Bernardo; Shu, ChiWang
 Journal of Computational Physics, Vol. 141, Issue 2
Plasma Oscillations with Diffusion in Velocity Space
journal, December 1958
 Lenard, A.; Bernstein, Ira B.
 Physical Review, Vol. 112, Issue 5
Verification of long wavelength electromagnetic modes with a gyrokineticfluid hybrid model in the XGC code
journal, May 2017
 Hager, Robert; Lang, Jianying; Chang, C. S.
 Physics of Plasmas, Vol. 24, Issue 5
Gyrokinetic simulations in general geometry and applications to collisional damping of zonal flows
journal, May 2000
 Lin, Z.; Hahm, T. S.; Lee, W. W.
 Physics of Plasmas, Vol. 7, Issue 5
Continuum kinetic modeling of the tokamak plasma edge
journal, May 2016
 Dorf, M. A.; Dorr, M. R.; Hittinger, J. A.
 Physics of Plasmas, Vol. 23, Issue 5
Fullf gyrokinetic particle simulation of centrally heated global ITG turbulence from magnetic axis to edge pedestal top in a realistic tokamak geometry
journal, September 2009
 Ku, S.; Chang, C. S.; Diamond, P. H.
 Nuclear Fusion, Vol. 49, Issue 11