Electromagnetic full-$$f$$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods
Abstract
We present an energy-conserving discontinuous Galerkin scheme for the full- $$f$$ electromagnetic gyrokinetic system in the long-wavelength 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 open-field-line system as a rough model of the tokamak scrape-off 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:
-
[1];
[3]
- 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 Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1660956
- Alternate Identifier(s):
- OSTI ID: 1668767
- Grant/Contract Number:
- FG02-97ER25308; FC02-08ER54966; AC0209CH11466
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Plasma Physics
- Additional Journal Information:
- Journal Volume: 86; Journal Issue: 1; Journal ID: ISSN 0022-3778
- Publisher:
- Cambridge University Press
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
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. https://doi.org/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. https://doi.org/10.1017/s0022377820000070. https://www.osti.gov/servlets/purl/1660956.
@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 energy-conserving discontinuous Galerkin scheme for the full- $f$ electromagnetic gyrokinetic system in the long-wavelength 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 open-field-line system as a rough model of the tokamak scrape-off 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 = {Mon Mar 02 00:00:00 EST 2020},
month = {Mon Mar 02 00:00:00 EST 2020}
}
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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 1-3
Discontinuous Galerkin algorithms for fully kinetic plasmas
journal, January 2018
- Juno, J.; Hakim, A.; TenBarge, J.
- Journal of Computational Physics, Vol. 353
An Eulerian gyrokinetic-Maxwell solver
journal, April 2003
- Candy, J.; Waltz, R. E.
- Journal of Computational Physics, Vol. 186, Issue 2
Global 3D two-fluid 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 multi-fluid simulations of classical sheaths
journal, February 2017
- Cagas, P.; Hakim, A.; Juno, J.
- Physics of Plasmas, Vol. 24, Issue 2
Model Fokker-Planck 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 scrape-off 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
Numerical Methods for Fluid Dynamics
book, January 2010
- Durran, Dale R.
- Texts in Applied Mathematics
Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
journal, September 2001
- Cockburn, Bernardo; Shu, Chi-Wang
- Journal of Scientific Computing, Vol. 16, Issue 3, p. 173-261
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 2-3
Conventional δf-particle 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 open-field-line 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 gyro-kinetic 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 full-torus 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 low-to-high confinement mode bifurcation dynamics in the boundary-plasma 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
Finite-β 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 High-Order Discontinuous Galerkin Method for 2D Incompressible Flows
journal, May 2000
- Liu, Jian-Guo; Shu, Chi-Wang
- 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 drift-wave turbulence
journal, March 2000
- Jenko, Frank
- Computer Physics Communications, Vol. 125, Issue 1-3
TOKAM-3D: 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 multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm
journal, December 2015
- Chen, G.; Chacón, L.
- Computer Physics Communications, Vol. 197
Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma
journal, May 2017
- Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T.
- Journal of Plasma Physics, Vol. 83, Issue 3
Three-dimensional computation of drift Alfvén turbulence
journal, October 1997
- Scott, B.
- Plasma Physics and Controlled Fusion, Vol. 39, Issue 10
Nonlinear gyrokinetic theory for finite-beta 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 quasi-symmetric 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 full-f five-dimensional 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 open-field-line plasma
journal, January 2019
- Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, 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 hybrid-Lagrangian 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
Conservative discontinuous Galerkin scheme of a gyro-averaged Dougherty collision operator
journal, August 2020
- Francisquez, M.; Bernard, T. N.; Mandell, N. R.
- Nuclear Fusion, Vol. 60, Issue 9
The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V
journal, April 1998
- Cockburn, Bernardo; Shu, Chi-Wang
- 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 gyrokinetic-fluid 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
Full-f 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
The serendipity family of finite elements
text, January 2011
- Arnold, Douglas N.; Awanou, Gerard
- arXiv
A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell algorithm
text, January 2015
- Chen, Guangye; Chacon, Luis
- arXiv
Continuum Kinetic and Multi-Fluid Simulations of Classical Sheaths
text, January 2016
- Cagas, Petr; Hakim, Ammar; Juno, James
- arXiv
A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons
text, January 2017
- Bao, J.; Lin, Z.; Lu, Z. X.
- arXiv
Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma
text, January 2017
- Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T.
- arXiv
Discontinuous Galerkin algorithms for fully kinetic plasmas
text, January 2017
- Juno, J.; Hakim, A.; TenBarge, J.
- arXiv
Gyrokinetic continuum simulations of plasma turbulence in the Texas Helimak
text, January 2018
- Bernard, Tess N.; Shi, Eric L.; Gentle, Kenneth
- arXiv
Conservative gyrokinetic Vlasov simulation
journal, February 2008
- Idomura, Yasuhiro; Ida, Masato; Tokuda, Shinji
- Communications in Nonlinear Science and Numerical Simulation, Vol. 13, Issue 1
Gyrokinetic full-torus 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
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 3D two-fluid 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
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
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
Pullback transformation in gyrokinetic electromagnetic simulations
text, January 2014
- Mishchenko, Alexey; Könies, Axel; Kleiber, Ralf
- arXiv
Discontinuous Galerkin schemes for a class of Hamiltonian evolution equations with applications to plasma fluid and kinetic problems
preprint, January 2019
- Hakim, A.; Hammett, G.; Shi, E.
- arXiv
Works referencing / citing this record:
Conservative discontinuous Galerkin scheme of a gyro-averaged Dougherty collision operator
journal, August 2020
- Francisquez, M.; Bernard, T. N.; Mandell, N. R.
- Nuclear Fusion, Vol. 60, Issue 9
Discontinuous Galerkin schemes for a class of Hamiltonian evolution equations with applications to plasma fluid and kinetic problems
preprint, January 2019
- Hakim, A.; Hammett, G.; Shi, E.
- arXiv