An integral transform technique for kinetic systems with collisions

Heninger, J. M.; Morrison, P. J.

doi:10.1063/1.5046194

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:

Heninger, J. M. ^[1];

^[2]

Univ. of Texas, Austin, TX (United States). Dept. of Physics and Institute for Fusion Studies
Univ. of Texas, Austin, TX (United States). Dept. of Physics and Inst. for Fusion Studies

Publication Date:: Tue Aug 21 00:00:00 EDT 2018

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.

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                    Heninger, J. M., & Morrison, P. J. An integral transform technique for kinetic systems with collisions.  United States.  https://doi.org/10.1063/1.5046194

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                    Heninger, J. M., and Morrison, P. J. Tue .  
"An integral transform technique for kinetic systems with collisions".  United States.  https://doi.org/10.1063/1.5046194.  https://www.osti.gov/servlets/purl/1515033.

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@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         = {Tue Aug 21 00:00:00 EDT 2018},

  month        = {Tue Aug 21 00:00:00 EDT 2018}

}

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Works referenced in this record:

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Works referencing / citing this record:

Analytical solutions for nonlinear plasma waves with time-varying complex frequency
journal, November 2019

Woods, B. J. Q.
Plasma Research Express, Vol. 1, Issue 4
DOI: 10.1088/2516-1067/ab5052

Analytical solutions for nonlinear plasma waves with time-varying complex frequency
preprint, January 2019

Woods, Benjamin J. Q.
arXiv
DOI: 10.48550/arxiv.1905.03104

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Title: An integral transform technique for kinetic systems with collisions

Abstract

Citation Formats

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

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

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

Coulomb collision effects on linear Landau damping journal, May 2014

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

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

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

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

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

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

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

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

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

Observation of void formation patterns in SnAg films undergoing electromigration and simulation using random walk methods journal, April 2021

An Introduction to Plasma Physics journal, September 1963

Higher order Hamiltonian fluid reduction of Vlasov equation text, January 2014

Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence text, January 2015

GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods text, January 2016

Spatially Localized Particle Energization by Landau Damping in Current Sheets Produced by Strong Alfven Wave Collisions text, January 2017

Analytical solutions for nonlinear plasma waves with time-varying complex frequency journal, November 2019

Analytical solutions for nonlinear plasma waves with time-varying complex frequency preprint, January 2019

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

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

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

Coulomb collision effects on linear Landau damping
journal, May 2014

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

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

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

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

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

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

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

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

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

Observation of void formation patterns in SnAg films undergoing electromigration and simulation using random walk methods
journal, April 2021

An Introduction to Plasma Physics
journal, September 1963

Higher order Hamiltonian fluid reduction of Vlasov equation
text, January 2014

Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence
text, January 2015

GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
text, January 2016

Spatially Localized Particle Energization by Landau Damping in Current Sheets Produced by Strong Alfven Wave Collisions
text, January 2017

Analytical solutions for nonlinear plasma waves with time-varying complex frequency
journal, November 2019

Analytical solutions for nonlinear plasma waves with time-varying complex frequency
preprint, January 2019