Projection-operator methods for classical transport in magnetized plasmas. Part 2. Nonlinear response and the Burnett equations [Projection-operator methods for classical transport in magnetized plasmas. Part 1. Nonlinear response and the Burnett equations]

Krommes, John A.

doi:10.1017/s0022377818000892

Title: Projection-operator methods for classical transport in magnetized plasmas. Part 2. Nonlinear response and the Burnett equations [Projection-operator methods for classical transport in magnetized plasmas. Part 1. Nonlinear response and the Burnett equations]

Abstract

The time-independent projection-operator formalism for the derivation of Burnett equations is extended and considered in the context of multispecies and magnetized plasmas. The procedure provides specific formulas for transport coefficients in terms of two-time correlation functions involving both two and three phase-space points. It is shown how to calculate those correlation functions in the limit of weak coupling. The results are used to demonstrate, with the aid of a particular non-trivial example, that the Chapman–Enskog methodology employed by Catto & Simakov (CS) (Phys. Plasmas, vol. 11, 2004, pp. 90–102) to calculate the contributions to the parallel viscosity driven by temperature gradients is consistent with formulas previously derived from the two-time formalism by Brey (J. Chem. Phys., vol. 79, 1983, pp. 4585–4598). Here, the work serves to unify previous work on plasma kinetic theory with formalism usually applied to turbulence. Additional contributions include discussions of (i) Braginskii-order interspecies momentum exchange from the point of view of two-time correlations; and (ii) a simple stochastic model, unrelated to many-body theory, that exhibits Burnett effects. Insights from that model emphasize the role of non-Gaussian statistics in the evaluation of Burnett transport coefficients, including the effects calculated by CS that stem from the nonlinear collisionmore »« less

Authors:

^[1]

Princeton Univ., Princeton, NJ (United States). Plasma Physics Lab

Publication Date:: Fri Nov 09 00:00:00 EST 2018

Research Org.:: Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1558767

Grant/Contract Number:: AC02-09CH11466

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Plasma Physics

Additional Journal Information:: Journal Volume: 84; Journal Issue: 6; Journal ID: ISSN 0022-3778

Publisher:: Cambridge University Press

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; plasma nonlinear phenomena

Citation Formats


                    Krommes, John A. Projection-operator methods for classical transport in magnetized plasmas. Part 2. Nonlinear response and the Burnett equations [Projection-operator methods for classical transport in magnetized plasmas. Part 1. Nonlinear response and the Burnett equations].  United States: N. p., 2018. 
Web.  doi:10.1017/s0022377818000892.

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                    Krommes, John A. Projection-operator methods for classical transport in magnetized plasmas. Part 2. Nonlinear response and the Burnett equations [Projection-operator methods for classical transport in magnetized plasmas. Part 1. Nonlinear response and the Burnett equations].  United States.  https://doi.org/10.1017/s0022377818000892

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                    Krommes, John A. Fri .  
"Projection-operator methods for classical transport in magnetized plasmas. Part 2. Nonlinear response and the Burnett equations [Projection-operator methods for classical transport in magnetized plasmas. Part 1. Nonlinear response and the Burnett equations]".  United States.  https://doi.org/10.1017/s0022377818000892.  https://www.osti.gov/servlets/purl/1558767.

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@article{osti_1558767,

  title        = {Projection-operator methods for classical transport in magnetized plasmas. Part 2. Nonlinear response and the Burnett equations [Projection-operator methods for classical transport in magnetized plasmas. Part 1. Nonlinear response and the Burnett equations]},

  author       = {Krommes, John A.},

  abstractNote = {The time-independent projection-operator formalism for the derivation of Burnett equations is extended and considered in the context of multispecies and magnetized plasmas. The procedure provides specific formulas for transport coefficients in terms of two-time correlation functions involving both two and three phase-space points. It is shown how to calculate those correlation functions in the limit of weak coupling. The results are used to demonstrate, with the aid of a particular non-trivial example, that the Chapman–Enskog methodology employed by Catto & Simakov (CS) (Phys. Plasmas, vol. 11, 2004, pp. 90–102) to calculate the contributions to the parallel viscosity driven by temperature gradients is consistent with formulas previously derived from the two-time formalism by Brey (J. Chem. Phys., vol. 79, 1983, pp. 4585–4598). Here, the work serves to unify previous work on plasma kinetic theory with formalism usually applied to turbulence. Additional contributions include discussions of (i) Braginskii-order interspecies momentum exchange from the point of view of two-time correlations; and (ii) a simple stochastic model, unrelated to many-body theory, that exhibits Burnett effects. Insights from that model emphasize the role of non-Gaussian statistics in the evaluation of Burnett transport coefficients, including the effects calculated by CS that stem from the nonlinear collision operator. Together, Parts 1 and 2 of this series provide an introduction to projection-operator methods that should be broadly useful in theoretical plasma physics.},

  doi          = {10.1017/s0022377818000892},

  journal      = {Journal of Plasma Physics},

  number       = 6,

  volume       = 84,

  place        = {United States},

  year         = {Fri Nov 09 00:00:00 EST 2018},

  month        = {Fri Nov 09 00:00:00 EST 2018}

}

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Title: Projection-operator methods for classical transport in magnetized plasmas. Part 2. Nonlinear response and the Burnett equations [Projection-operator methods for classical transport in magnetized plasmas. Part 1. Nonlinear response and the Burnett equations]

Abstract

Citation Formats

A drift ordered short mean free path description for magnetized plasma allowing strong spatial anisotropy journal, January 2004

A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev’s Plasma Turbulence and the resonance-broadening theory of Dupree and Weinstock journal, September 2015

Failures of the Burnett and super-Burnett equations in steady state processes journal, April 2005

Decay of the Velocity Autocorrelation Function journal, January 1970

Long time behavior of the Burnett transport coefficients journal, November 1983

Plasma equilibrium in a magnetic field with stochastic regions journal, July 2009

Theory of Nonlinear Transport Processes: Nonlinear Shear Viscosity and Normal Stress Effects journal, October 1973

The Distribution of Molecular Velocities and the Mean Motion in a Non-Uniform Gas journal, January 1936

Statistical Dynamics of Classical Systems journal, July 1973

An introduction to the physics of the Coulomb logarithm, with emphasis on quantum-mechanical effects journal, January 2019

The invariant theory of isotropic turbulence journal, April 1940

Theory of the Dynamics of Simple Fluids for Large Spatial Gradients and Long Memory journal, November 1968

Transport equations and gradient instabilities in a high pressure collisional plasma journal, September 1971

Fundamental statistical descriptions of plasma turbulence in magnetic fields journal, April 2002

Regularization of Grad’s 13 moment equations: Derivation and linear analysis journal, August 2003

Anomalous transport due to long-lived fluctuations in plasma Part 1. A general formalism for two-time fluctuations journal, October 1976

Nonlinear transport equations in statistical mechanics journal, December 1981

Two new proofs of the test particle superposition principle of plasma kinetic theory journal, January 1976

Dynamics of Nonlinear Stochastic Systems journal, January 1961

Cross-field energy transport by plasma waves journal, January 1976

The Distribution of Velocities in a Slightly Non-Uniform Gas journal, January 1935

Convergent Classical Kinetic Equation for a Plasma journal, January 1963

Nonanalytic dispersion relations in classical fluids journal, September 1972

Transport Equations of Plasma in a Curvilinear Magnetic Field journal, January 1984

Theory of nonlinear transport in Burnett order journal, February 1978

Kinetic theory of nonlinear viscous flow in two and three dimensions journal, March 1978

Kolmogorov's Hypotheses and Eulerian Turbulence Theory journal, January 1964

Plasma Fluctuations and Convective Modes journal, January 1969

On the Theory of the Brownian Motion II journal, April 1945

Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems journal, June 1957

Test Particles in a Completely Ionized Plasma journal, January 1960

Projection-operator methods for classical transport in magnetized plasmas. Part 1. Linear response, the Braginskii equations and fluctuating hydrodynamics journal, July 2018

Renormalized kinetic theory of nonequilibrium many-particle classical systems journal, April 1979

Anomalous transport due to long-lived fluctuations in plasma Part 2. Hydrodynamic contributions to transport in two-dimensional, strongly magnetized systems journal, October 1976

Nonequilibrium gyrokinetic fluctuation theory and sampling noise in gyrokinetic particle-in-cell simulations journal, September 2007

Beyond the Navier–Stokes equations: Burnett hydrodynamics journal, August 2008

Derivations of Hierarchies for N ‐Particle Systems and Vlasov Systems by Means of the Functional Calculus journal, March 1967

Plasma Kinetic Theory journal, February 2010

Plasma Kinetic Theory journal, February 2012

Plasma Kinetic Theory journal, February 2008

An introduction to the physics of the Coulomb logarithm with emphasis on quantum-mechanical effects text, January 2018

A drift ordered short mean free path description for magnetized plasma allowing strong spatial anisotropy
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A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev’s Plasma Turbulence and the resonance-broadening theory of Dupree and Weinstock
journal, September 2015

Failures of the Burnett and super-Burnett equations in steady state processes
journal, April 2005

Decay of the Velocity Autocorrelation Function
journal, January 1970

Long time behavior of the Burnett transport coefficients
journal, November 1983

Plasma equilibrium in a magnetic field with stochastic regions
journal, July 2009

Theory of Nonlinear Transport Processes: Nonlinear Shear Viscosity and Normal Stress Effects
journal, October 1973

The Distribution of Molecular Velocities and the Mean Motion in a Non-Uniform Gas
journal, January 1936

Statistical Dynamics of Classical Systems
journal, July 1973

An introduction to the physics of the Coulomb logarithm, with emphasis on quantum-mechanical effects
journal, January 2019

The invariant theory of isotropic turbulence
journal, April 1940

Theory of the Dynamics of Simple Fluids for Large Spatial Gradients and Long Memory
journal, November 1968

Transport equations and gradient instabilities in a high pressure collisional plasma
journal, September 1971

Fundamental statistical descriptions of plasma turbulence in magnetic fields
journal, April 2002

Regularization of Grad’s 13 moment equations: Derivation and linear analysis
journal, August 2003

Anomalous transport due to long-lived fluctuations in plasma Part 1. A general formalism for two-time fluctuations
journal, October 1976

Nonlinear transport equations in statistical mechanics
journal, December 1981

Two new proofs of the test particle superposition principle of plasma kinetic theory
journal, January 1976

Dynamics of Nonlinear Stochastic Systems
journal, January 1961

Cross-field energy transport by plasma waves
journal, January 1976

The Distribution of Velocities in a Slightly Non-Uniform Gas
journal, January 1935

Convergent Classical Kinetic Equation for a Plasma
journal, January 1963

Nonanalytic dispersion relations in classical fluids
journal, September 1972

Transport Equations of Plasma in a Curvilinear Magnetic Field
journal, January 1984

Theory of nonlinear transport in Burnett order
journal, February 1978

Kinetic theory of nonlinear viscous flow in two and three dimensions
journal, March 1978

Kolmogorov's Hypotheses and Eulerian Turbulence Theory
journal, January 1964

Plasma Fluctuations and Convective Modes
journal, January 1969

On the Theory of the Brownian Motion II
journal, April 1945

Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems
journal, June 1957

Test Particles in a Completely Ionized Plasma
journal, January 1960

Projection-operator methods for classical transport in magnetized plasmas. Part 1. Linear response, the Braginskii equations and fluctuating hydrodynamics
journal, July 2018

Renormalized kinetic theory of nonequilibrium many-particle classical systems
journal, April 1979

Anomalous transport due to long-lived fluctuations in plasma Part 2. Hydrodynamic contributions to transport in two-dimensional, strongly magnetized systems
journal, October 1976

Nonequilibrium gyrokinetic fluctuation theory and sampling noise in gyrokinetic particle-in-cell simulations
journal, September 2007

Beyond the Navier–Stokes equations: Burnett hydrodynamics
journal, August 2008

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journal, March 1967

Plasma Kinetic Theory
journal, February 2010

Plasma Kinetic Theory
journal, February 2012

Plasma Kinetic Theory
journal, February 2008

An introduction to the physics of the Coulomb logarithm with emphasis on quantum-mechanical effects
text, January 2018