skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on March 2, 2021

Title: 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:
ORCiD logo [1];  [2];  [2]; ORCiD logo [3]
  1. Princeton Univ., NJ (United States)
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  3. 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:  
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

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 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 = {2020},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on March 2, 2021
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Progress in Kinetic Simulation of Edge Plasmas
journal, March 2008


Discontinuous Galerkin algorithms for fully kinetic plasmas
journal, January 2018


An Eulerian gyrokinetic-Maxwell solver
journal, April 2003


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
  • DOI: 10.1063/1.4978885

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
  • DOI: 10.1063/1.4976544

Model Fokker-Planck Equation for a Plasma and Its Solution
journal, January 1964


Global 3D Braginskii simulations of the tokamak edge region of IWL discharges
journal, August 2017


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
  • DOI: 10.1063/1.5085457

Simulation of plasma turbulence in scrape-off layer conditions: the GBS code, simulation results and code validation
journal, November 2012


Electron Temperature Gradient Turbulence
journal, December 2000


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
  • DOI: 10.1063/1.3302535

Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities
journal, August 1995


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
  • DOI: 10.1063/1.1812275

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
  • DOI: 10.1063/1.5008895

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
  • DOI: 10.1063/1.873896

A δf particle method for gyrokinetic simulations with kinetic electrons and electromagnetic perturbations
journal, August 2003


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
  • DOI: 10.1016/j.cpc.2009.07.001

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
  • DOI: 10.1063/1.866332

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
  • DOI: 10.1063/1.5016432

Gyrokinetic full-torus simulations of ohmic tokamak plasmas in circular limiter configuration
journal, June 2016


Orb5: A global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry
journal, June 2020


Nonlinear electromagnetic gyrokinetic simulations of tokamak plasmas
journal, November 2001


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
  • DOI: 10.1063/1.5020792

The dynamics of an isolated plasma filament at the edge of a toroidal device
journal, December 2006


Finite-β simulation of microinstabilities
journal, February 2014

  • Startsev, Edward A.; Lee, W. W.
  • Physics of Plasmas, Vol. 21, Issue 2
  • DOI: 10.1063/1.4863847

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
  • DOI: 10.1063/1.860623

Gyrokinetic turbulence simulations with kinetic electrons
journal, May 2001

  • Chen, Yang; Parker, Scott
  • Physics of Plasmas, Vol. 8, Issue 5
  • DOI: 10.1063/1.1351828

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
  • DOI: 10.1006/jcph.2000.6475

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
  • DOI: 10.1063/1.871232

Massively parallel Vlasov simulation of electromagnetic drift-wave turbulence
journal, March 2000


TOKAM-3D: A 3D fluid code for transport and turbulence in the edge plasma of Tokamaks
journal, January 2010


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
  • DOI: 10.1006/jcph.1993.1005

Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma
journal, May 2017


Three-dimensional computation of drift Alfvén turbulence
journal, October 1997


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
  • DOI: 10.1063/1.866641

Electromagnetic gyrokinetic PIC simulation with an adjustable control variates method
journal, July 2007


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
  • DOI: 10.1063/1.1374585

Foundations of nonlinear gyrokinetic theory
journal, April 2007


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
  • DOI: 10.1016/j.cpc.2008.04.005

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
  • DOI: 10.1063/1.5074179

A global collisionless PIC code in magnetic coordinates
journal, September 2007


A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
journal, June 2016


The Serendipity Family of Finite Elements
journal, March 2011

  • Arnold, Douglas N.; Awanou, Gerard
  • Foundations of Computational Mathematics, Vol. 11, Issue 3
  • DOI: 10.1007/s10208-011-9087-3

Gyrokinetic simulation of ion temperature gradient driven turbulence in 3D toroidal geometry
journal, September 1993


Velocity–space structures of distribution function in toroidal ion temperature gradient turbulence
journal, December 2005


Gyrokinetic particle simulation model
journal, September 1987


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
  • DOI: 10.1006/jcph.1998.5892

Plasma Oscillations with Diffusion in Velocity Space
journal, December 1958


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
  • DOI: 10.1063/1.4983320

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
  • DOI: 10.1063/1.874008

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
  • DOI: 10.1063/1.4943106