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Title: An integral transform technique for kinetic systems with collisions

Abstract

The linearized Vlasov-Poisson system can be exactly solved using the G-transform, an integral transform introduced in Morrison and Pfirsch [Phys. Fluids B 4, 3038–3057 (1992)] and Morrison [Phys. Plasmas 1, 1447 (1994); Transp. Theory Stat. Phys. 29, 397 (2000)] that removes the electric field term, leaving a simple advection equation. We investigate how this integral transform interacts with the Fokker-Planck collision operator. The commutator of this collision operator with the G-transform (the “shielding term”) is shown to be negligible. We exactly solve the advection-diffusion equation without the shielding term. This solution determines when collisions dominate and when advection (i.e., Landau damping) dominates. This integral transform can also be used to simplify gyro-/drift-kinetic equations. We present new gyrofluid equations formed by taking moments of the G-transformed equation. Since many gyro-/drift-kinetic codes use Hermite polynomials as base elements, we include an explicit calculation of their G-transform

Authors:
 [1]; ORCiD logo [2]
  1. Univ. of Texas, Austin, TX (United States). Dept. of Physics and Institute for Fusion Studies
  2. Univ. of Texas, Austin, TX (United States). Dept. of Physics and Inst. for Fusion Studies
Publication Date:
Research Org.:
Univ. of Texas, Austin, TX (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1515033
Alternate Identifier(s):
OSTI ID: 1465620
Grant/Contract Number:  
[FG05-80ET53088; FG05-80ET-53088]
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
[ Journal Volume: 25; Journal Issue: 8]; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Heninger, J. M., and Morrison, P. J. An integral transform technique for kinetic systems with collisions. United States: N. p., 2018. Web. doi:10.1063/1.5046194.
Heninger, J. M., & Morrison, P. J. An integral transform technique for kinetic systems with collisions. United States. doi:10.1063/1.5046194.
Heninger, J. M., and Morrison, P. J. Tue . "An integral transform technique for kinetic systems with collisions". United States. doi:10.1063/1.5046194. https://www.osti.gov/servlets/purl/1515033.
@article{osti_1515033,
title = {An integral transform technique for kinetic systems with collisions},
author = {Heninger, J. M. and Morrison, P. J.},
abstractNote = {The linearized Vlasov-Poisson system can be exactly solved using the G-transform, an integral transform introduced in Morrison and Pfirsch [Phys. Fluids B 4, 3038–3057 (1992)] and Morrison [Phys. Plasmas 1, 1447 (1994); Transp. Theory Stat. Phys. 29, 397 (2000)] that removes the electric field term, leaving a simple advection equation. We investigate how this integral transform interacts with the Fokker-Planck collision operator. The commutator of this collision operator with the G-transform (the “shielding term”) is shown to be negligible. We exactly solve the advection-diffusion equation without the shielding term. This solution determines when collisions dominate and when advection (i.e., Landau damping) dominates. This integral transform can also be used to simplify gyro-/drift-kinetic equations. We present new gyrofluid equations formed by taking moments of the G-transformed equation. Since many gyro-/drift-kinetic codes use Hermite polynomials as base elements, we include an explicit calculation of their G-transform},
doi = {10.1063/1.5046194},
journal = {Physics of Plasmas},
number = [8],
volume = [25],
place = {United States},
year = {2018},
month = {8}
}

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Works referenced in this record:

On the theory of stationary waves in plasmas
journal, January 1955


Transition between Saturation Regimes of Gyrokinetic Turbulence
journal, October 2013


GEMPIC: geometric electromagnetic particle-in-cell methods
journal, July 2017

  • Kraus, Michael; Kormann, Katharina; Morrison, Philip J.
  • Journal of Plasma Physics, Vol. 83, Issue 4
  • DOI: 10.1017/S002237781700040X

The Gyrokinetic Description of Microturbulence in Magnetized Plasmas
journal, January 2012


Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence
journal, April 2016

  • Schekochihin, A. A.; Parker, J. T.; Highcock, E. G.
  • Journal of Plasma Physics, Vol. 82, Issue 2
  • DOI: 10.1017/S0022377816000374

Coulomb collision effects on linear Landau damping
journal, May 2014


LIII. Dynamical problems in illustration of the theory of gases
journal, November 1891

  • Rayleigh, Lord
  • The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 32, Issue 198
  • DOI: 10.1080/14786449108620207

Spatially localized particle energization by Landau damping in current sheets produced by strong Alfvén wave collisions
journal, January 2018

  • Howes, Gregory G.; McCubbin, Andrew J.; Klein, Kristopher G.
  • Journal of Plasma Physics, Vol. 84, Issue 1
  • DOI: 10.1017/S0022377818000053

Foundations of nonlinear gyrokinetic theory
journal, April 2007


Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria
journal, January 1982


A discontinuous Galerkin method for the Vlasov–Poisson system
journal, February 2012

  • Heath, R. E.; Gamba, I. M.; Morrison, P. J.
  • Journal of Computational Physics, Vol. 231, Issue 4
  • DOI: 10.1016/j.jcp.2011.09.020

Collisional Relaxation of Fine Velocity Structures in Plasmas
journal, April 2016


The Fokker-Planck Asymptotics of the Boltzmann Collision Operator in the Coulomb case
journal, June 1992

  • Degond, P.; Lucquin-Desreux, B.
  • Mathematical Models and Methods in Applied Sciences, Vol. 02, Issue 02
  • DOI: 10.1142/s0218202592000119

Stochastic Problems in Physics and Astronomy
journal, January 1943


Phase space scales of free energy dissipation in gradient-driven gyrokinetic turbulence
journal, May 2014


Dielectric energy versus plasma energy, and Hamiltonian action‐angle variables for the Vlasov equation
journal, October 1992

  • Morrison, P. J.; Pfirsch, D.
  • Physics of Fluids B: Plasma Physics, Vol. 4, Issue 10
  • DOI: 10.1063/1.860415

The energy of perturbations for Vlasov plasmas* ,a)
journal, May 1994


Higher-order Hamiltonian fluid reduction of Vlasov equation
journal, September 2014


Direct determination of ion wave fields in a hot magnetized and weakly collisional plasma
journal, December 1996

  • Sarfaty, M.; De Souza‐Machado, S.; Skiff, F.
  • Physics of Plasmas, Vol. 3, Issue 12
  • DOI: 10.1063/1.871581

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


Coherent detection of the complete linear electrostatic plasma response of plasma ions using laser-induced fluorescence
journal, February 2002


Diagnosing collisionless energy transfer using field–particle correlations: Vlasov–Poisson plasmas
journal, January 2017

  • Howes, Gregory G.; Klein, Kristopher G.; Li, Tak Chu
  • Journal of Plasma Physics, Vol. 83, Issue 1
  • DOI: 10.1017/S0022377816001197

Hamiltonian description of Vlasov dynamics: Action-angle variables for the continuous spectrum
journal, April 2000


Plasma Oscillations with Diffusion in Velocity Space
journal, December 1958


Wave-particle interaction
journal, December 2000


Die mittlere Energie rotierender elektrischer Dipole im Strahlungsfeld
journal, January 1914


Analysis of the Hermite spectrum in plasma turbulence
journal, October 2017

  • White, R. L.; Hazeltine, R. D.
  • Physics of Plasmas, Vol. 24, Issue 10
  • DOI: 10.1063/1.5000518

Electrostatic degrees of freedom in non-Maxwellian plasma
journal, May 2002

  • Skiff, F.; Gunell, H.; Bhattacharjee, A.
  • Physics of Plasmas, Vol. 9, Issue 5
  • DOI: 10.1063/1.1462031