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Title: Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration

Abstract

Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for weakly-collisional high-temperature plasmas, high collisionality in colder regions render the equations numerically stiff due to disparate time scales. In this study, we propose an implicit–explicit algorithm for such cases, where the collisional term is integrated implicitly in time, while the advective term is integrated explicitly in time, thus allowing time step sizes that are comparable to the advective time scales. This partitioning results in a more efficient algorithm than those using explicit time integrators, where the time step sizes are constrained by the stiff collisional time scales. Finally, we implement semi-implicit additive Runge–Kutta methods in COGENT, a high-order finite-volume gyrokinetic code and test the accuracy, convergence, and computational cost of these semi-implicit methods for test cases with highly-collisional plasmas.

Authors:
ORCiD logo [1];  [2];  [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Physics Division
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1458696
Report Number(s):
LLNL-JRNL-735522
Journal ID: ISSN 0885-7474; 887762
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Scientific Computing
Additional Journal Information:
Journal Volume: 77; Journal ID: ISSN 0885-7474
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; IMEX time integration; plasma physics; gyrokinetic simulations; Vlasov–Fokker–Planck equations

Citation Formats

Ghosh, Debojyoti, Dorf, Mikhail A., Dorr, Milo R., and Hittinger, Jeffrey A. F.. Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration. United States: N. p., 2018. Web. https://doi.org/10.1007/s10915-018-0726-6.
Ghosh, Debojyoti, Dorf, Mikhail A., Dorr, Milo R., & Hittinger, Jeffrey A. F.. Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration. United States. https://doi.org/10.1007/s10915-018-0726-6
Ghosh, Debojyoti, Dorf, Mikhail A., Dorr, Milo R., and Hittinger, Jeffrey A. F.. Sat . "Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration". United States. https://doi.org/10.1007/s10915-018-0726-6. https://www.osti.gov/servlets/purl/1458696.
@article{osti_1458696,
title = {Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration},
author = {Ghosh, Debojyoti and Dorf, Mikhail A. and Dorr, Milo R. and Hittinger, Jeffrey A. F.},
abstractNote = {Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for weakly-collisional high-temperature plasmas, high collisionality in colder regions render the equations numerically stiff due to disparate time scales. In this study, we propose an implicit–explicit algorithm for such cases, where the collisional term is integrated implicitly in time, while the advective term is integrated explicitly in time, thus allowing time step sizes that are comparable to the advective time scales. This partitioning results in a more efficient algorithm than those using explicit time integrators, where the time step sizes are constrained by the stiff collisional time scales. Finally, we implement semi-implicit additive Runge–Kutta methods in COGENT, a high-order finite-volume gyrokinetic code and test the accuracy, convergence, and computational cost of these semi-implicit methods for test cases with highly-collisional plasmas.},
doi = {10.1007/s10915-018-0726-6},
journal = {Journal of Scientific Computing},
number = ,
volume = 77,
place = {United States},
year = {2018},
month = {5}
}

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Works referenced in this record:

Progress in Kinetic Simulation of Edge Plasmas
journal, March 2008


Conservative Numerical Schemes for the Vlasov Equation
journal, September 2001

  • Filbet, Francis; Sonnendrücker, Eric; Bertrand, Pierre
  • Journal of Computational Physics, Vol. 172, Issue 1
  • DOI: 10.1006/jcph.2001.6818

Tempest Simulations of Collisionless Damping of the Geodesic-Acoustic Mode in Edge-Plasma Pedestals
journal, May 2008


Detailed comparison of simulated and measured plasma profiles in the scrape-off layer and edge plasma of DIII-D
journal, September 2000

  • Porter, G. D.; Isler, R.; Boedo, J.
  • Physics of Plasmas, Vol. 7, Issue 9
  • DOI: 10.1063/1.1286509

Discretization methods for one-dimensional Fokker-Planck operators
journal, December 1985


Entropy Stable Numerical Schemes for Two-Fluid Plasma Equations
journal, November 2011


An IMEX-Scheme for Pricing Options under Stochastic Volatility Models with Jumps
journal, January 2014

  • Salmi, Santtu; Toivanen, Jari; von Sydow, Lina
  • SIAM Journal on Scientific Computing, Vol. 36, Issue 5
  • DOI: 10.1137/130924905

Gyrokinetic study of the edge shear layer
journal, April 2006


Conservative gyrokinetic Vlasov simulation
journal, February 2008

  • Idomura, Yasuhiro; Ida, Masato; Tokuda, Shinji
  • Communications in Nonlinear Science and Numerical Simulation, Vol. 13, Issue 1
  • DOI: 10.1016/j.cnsns.2007.05.015

A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov–Poisson equations
journal, July 2011


Progress with the COGENT Edge Kinetic Code: Collision Operator Options
journal, June 2012

  • Dorf, M. A.; Cohen, R. H.; Compton, J. C.
  • Contributions to Plasma Physics, Vol. 52, Issue 5-6
  • DOI: 10.1002/ctpp.201210042

Relaxation of a system of charged particles
journal, July 1985


TEMPEST simulations of the plasma transport in a single-null tokamak geometry
journal, May 2010


A drift-kinetic Semi-Lagrangian 4D code for ion turbulence simulation
journal, September 2006

  • Grandgirard, V.; Brunetti, M.; Bertrand, P.
  • Journal of Computational Physics, Vol. 217, Issue 2
  • DOI: 10.1016/j.jcp.2006.01.023

Fast implicit schemes for the Fokker–Planck–Landau equation
journal, May 2004


A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth–Fokker–Planck equation
journal, September 2015


Nonlinear gyrokinetic equations for turbulence in core transport barriers
journal, December 1996


Additive Runge–Kutta schemes for convection–diffusion–reaction equations
journal, January 2003


Jacobian-free Newton–Krylov methods: a survey of approaches and applications
journal, January 2004


Edge gyrokinetic theory and continuum simulations
journal, July 2007


NITSOL: A Newton Iterative Solver for Nonlinear Systems
journal, January 1998


Implicit–explicit time integration of a high-order particle-in-cell method with hyperbolic divergence cleaning
journal, October 2009


High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids
journal, May 2015

  • McCorquodale, P.; Dorr, M. R.; Hittinger, J. A. F.
  • Journal of Computational Physics, Vol. 288
  • DOI: 10.1016/j.jcp.2015.01.006

Fast Algorithms for Numerical, Conservative, and Entropy Approximations of the Fokker–Planck–Landau Equation
journal, May 1997

  • Buet, C.; Cordier, S.; Degond, P.
  • Journal of Computational Physics, Vol. 133, Issue 2
  • DOI: 10.1006/jcph.1997.5669

A forward semi-Lagrangian method for the numerical solution of the Vlasov equation
journal, October 2009

  • Crouseilles, Nicolas; Respaud, Thomas; Sonnendrücker, Eric
  • Computer Physics Communications, Vol. 180, Issue 10
  • DOI: 10.1016/j.cpc.2009.04.024

Fokker-Planck Equation for an Inverse-Square Force
journal, July 1957

  • Rosenbluth, Marshall N.; MacDonald, William M.; Judd, David L.
  • Physical Review, Vol. 107, Issue 1
  • DOI: 10.1103/PhysRev.107.1

New velocity-space discretization for continuum kinetic calculations and Fokker–Planck collisions
journal, June 2013


An implicit Vlasov–Fokker–Planck code to model non-local electron transport in 2-D with magnetic fields
journal, February 2004


Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation
journal, November 2005

  • Pareschi, Lorenzo; Russo, Giovanni
  • Journal of Scientific Computing, Vol. 25, Issue 1-2
  • DOI: 10.1007/BF02728986

Kinetic simulation of a plasma collision experiment
journal, August 1993

  • Larroche, Olivier
  • Physics of Fluids B: Plasma Physics, Vol. 5, Issue 8
  • DOI: 10.1063/1.860670

GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
journal, July 1986

  • Saad, Youcef; Schultz, Martin H.
  • SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3
  • DOI: 10.1137/0907058

Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov–Poisson system
journal, September 2011


Anomalous Transport Scaling in the DIII-D Tokamak Matched by Supercomputer Simulation
journal, July 2003


Implicit–explicit Runge–Kutta methods applied to atmospheric chemistry-transport modelling
journal, September 2000


An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov–Darwin particle-in-cell algorithm
journal, October 2014


Particle Simulation of the Neoclassical Plasmas
journal, November 2001

  • Heikkinen, J. A.; Kiviniemi, T. P.; Kurki-Suonio, T.
  • Journal of Computational Physics, Vol. 173, Issue 2
  • DOI: 10.1006/jcph.2001.6891

Conservative finite-difference schemes for the Fokker-Planck equation not violating the law of an increasing entropy
journal, March 1987


Simulation of neoclassical transport with the continuum gyrokinetic code COGENT
journal, January 2013

  • Dorf, M. A.; Cohen, R. H.; Dorr, M.
  • Physics of Plasmas, Vol. 20, Issue 1
  • DOI: 10.1063/1.4776712

Fully Implicit Kinetic Solution of Collisional Plasmas
journal, September 1997

  • Mousseau, V. A.; Knoll, D. A.
  • Journal of Computational Physics, Vol. 136, Issue 2
  • DOI: 10.1006/jcph.1997.5736

Spontaneous rotation sources in a quiescent tokamak edge plasma
journal, June 2008


Full linearized Fokker–Planck collisions in neoclassical transport simulations
journal, December 2011


Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator
journal, September 2011


Kinetic simulation of a collisional shock wave in a plasma
journal, October 1991


Conservative and Entropy Decaying Numerical Scheme for the Isotropic Fokker–Planck–Landau Equation
journal, September 1998


Semi-Implicit Formulations of the Navier–Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling
journal, January 2010

  • Giraldo, F. X.; Restelli, M.; Läuter, M.
  • SIAM Journal on Scientific Computing, Vol. 32, Issue 6
  • DOI: 10.1137/090775889

An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes
journal, August 2016


An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm
journal, August 2011


Kinetic simulations of fuel ion transport in ICF target implosions
journal, November 2003

  • Larroche, O.
  • The European Physical Journal D - Atomic, Molecular and Optical Physics, Vol. 27, Issue 2
  • DOI: 10.1140/epjd/e2003-00251-1

FPPAC: A two-dimensional multispecies nonlinear Fokker-Planck package
journal, September 1981


The solution of poisson's equation for isolated source distributions
journal, October 1977


hypre: A Library of High Performance Preconditioners
book, April 2002

  • Falgout, Robert D.; Yang, Ulrike Meier; Goos, Gerhard
  • Computational Science — ICCS 2002: International Conference Amsterdam, The Netherlands, April 21–24, 2002 Proceedings, Part III
  • DOI: 10.1007/3-540-47789-6_66

Implicit and Conservative Difference Scheme for the Fokker-Planck Equation
journal, June 1994


Gyrokinetic Simulation of Particle and Heat Transport in the Presence of Wide Orbits and Strong Profile Variations in the Edge Plasma
journal, September 2006

  • Heikkinen, J. A.; Henriksson, S.; Janhunen, S.
  • Contributions to Plasma Physics, Vol. 46, Issue 7-9
  • DOI: 10.1002/ctpp.200610035

Gyrokinetic approach in particle simulation
journal, January 1983


A hybrid method of semi-Lagrangian and additive semi-implicit Runge–Kutta schemes for gyrokinetic Vlasov simulations
journal, September 2012

  • Maeyama, S.; Ishizawa, A.; Watanabe, T. -H.
  • Computer Physics Communications, Vol. 183, Issue 9
  • DOI: 10.1016/j.cpc.2012.04.028

Implicit–Explicit Multistep Methods for Fast-Wave–Slow-Wave Problems
journal, April 2012


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

An Implicit Energy-Conservative 2D Fokker–Planck Algorithm
journal, January 2000

  • Chacón, L.; Barnes, D. C.; Knoll, D. A.
  • Journal of Computational Physics, Vol. 157, Issue 2
  • DOI: 10.1006/jcph.1999.6395

Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA)
journal, January 2013

  • Giraldo, F. X.; Kelly, J. F.; Constantinescu, E. M.
  • SIAM Journal on Scientific Computing, Vol. 35, Issue 5
  • DOI: 10.1137/120876034

Two-Dimensional Nonlocal Electron Transport in Laser-Produced Plasmas
journal, November 1988


Vlasov simulations of electron-ion collision effects on damping of electron plasma waves
journal, March 2016

  • Banks, J. W.; Brunner, S.; Berger, R. L.
  • Physics of Plasmas, Vol. 23, Issue 3
  • DOI: 10.1063/1.4943194

A second order self-consistent IMEX method for radiation hydrodynamics
journal, November 2010

  • Kadioglu, Samet Y.; Knoll, Dana A.; Lowrie, Robert B.
  • Journal of Computational Physics, Vol. 229, Issue 22
  • DOI: 10.1016/j.jcp.2010.07.019

Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
journal, November 1997


A review of Vlasov–Fokker–Planck numerical modeling of inertial confinement fusion plasma
journal, February 2012

  • Thomas, A. G. R.; Tzoufras, M.; Robinson, A. P. L.
  • Journal of Computational Physics, Vol. 231, Issue 3
  • DOI: 10.1016/j.jcp.2011.09.028

Implicit Schemes for the Fokker--Planck--Landau Equation
journal, January 2005

  • Lemou, Mohammed; Mieussens, Luc
  • SIAM Journal on Scientific Computing, Vol. 27, Issue 3
  • DOI: 10.1137/040609422

Rapid self-magnetization of laser speckles in plasmas by nonlinear anisotropic instability
journal, March 2009


Semi-implicit Time Integration of Atmospheric Flows with Characteristic-Based Flux Partitioning
journal, January 2016

  • Ghosh, Debojyoti; Constantinescu, Emil M.
  • SIAM Journal on Scientific Computing, Vol. 38, Issue 3
  • DOI: 10.1137/15M1044369

The integration of the vlasov equation in configuration space
journal, November 1976


Multipole expansions for the Fokker-Planck-Landau operator
journal, February 1998


A Numerical Method for the Accurate Solution of the Fokker–Planck–Landau Equation in the Nonhomogeneous Case
journal, June 2002

  • Filbet, Francis; Pareschi, Lorenzo
  • Journal of Computational Physics, Vol. 179, Issue 1
  • DOI: 10.1006/jcph.2002.7010

High-order, finite-volume methods in mapped coordinates
journal, April 2011

  • Colella, P.; Dorr, M. R.; Hittinger, J. A. F.
  • Journal of Computational Physics, Vol. 230, Issue 8
  • DOI: 10.1016/j.jcp.2010.12.044

A conservative high order semi-Lagrangian WENO method for the Vlasov equation
journal, February 2010


A practical difference scheme for Fokker-Planck equations
journal, August 1970


An Implicit Energy-Conservative 2D Fokker–Planck Algorithm
journal, January 2000

  • Chacón, L.; Barnes, D. C.; Knoll, D. A.
  • Journal of Computational Physics, Vol. 157, Issue 2
  • DOI: 10.1006/jcph.1999.6394