Elementary derivation of the kinetic equation for the two-dimensional guiding centre plasma

Michael Mond; Georg Knorr

doi:10.1017/S0022377800023692

Elementary derivation of the kinetic equation for the two-dimensional guiding centre plasma

Michael Mond, Georg Knorr

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A kinetic equation for a two-dimensional inviscid hydrodynamic fluid is derived in two ways. First, the equations of motion for the modes of the fluid are interpreted as stochastic equations resembling the Langevin equation. To lowest order a Fokker-Planck equation can be derived which is the kinetic equation for one mode. Secondly, a suitable iteration scheme is applied to the Hopf equation which results in the same kinetic equation. A parameter describing the time scale is arbitrary and cannot be determined by the applied methods alone. It is shown that the kinetic equation satisfies the conservation requirements and relaxes to an equilibrium which is a rigorous solution of the Hopf equation.

Original language	English
Pages (from-to)	121-133
Number of pages	13
Journal	Journal of Plasma Physics
Volume	19
Issue number	1
DOIs	https://doi.org/10.1017/S0022377800023692
State	Published - 1 Jan 1978
Externally published	Yes

ASJC Scopus subject areas

Condensed Matter Physics

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10.1017/S0022377800023692

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title = "Elementary derivation of the kinetic equation for the two-dimensional guiding centre plasma",

abstract = "A kinetic equation for a two-dimensional inviscid hydrodynamic fluid is derived in two ways. First, the equations of motion for the modes of the fluid are interpreted as stochastic equations resembling the Langevin equation. To lowest order a Fokker-Planck equation can be derived which is the kinetic equation for one mode. Secondly, a suitable iteration scheme is applied to the Hopf equation which results in the same kinetic equation. A parameter describing the time scale is arbitrary and cannot be determined by the applied methods alone. It is shown that the kinetic equation satisfies the conservation requirements and relaxes to an equilibrium which is a rigorous solution of the Hopf equation.",

author = "Michael Mond and Georg Knorr",

note = "Funding Information: One of us (G.K.) is indebted to Dr P. Graeff who patiently pointed out to him the importance of the Hopf equation. The discussions with Dr Graeff and with Dr D. Pfirsch were made possible by the hospitality ofthe Max-Planck-Institute for Plasmaphysik, Garching, Germany, a senior fellowship of NATO and a grant of the Minna-James Heinemann Foundation. In Iowa this work was in part supported by ERDA grant No. EY-76-S-02-2059. We thank Dr D. Montgomery for critical remarks.",

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N2 - A kinetic equation for a two-dimensional inviscid hydrodynamic fluid is derived in two ways. First, the equations of motion for the modes of the fluid are interpreted as stochastic equations resembling the Langevin equation. To lowest order a Fokker-Planck equation can be derived which is the kinetic equation for one mode. Secondly, a suitable iteration scheme is applied to the Hopf equation which results in the same kinetic equation. A parameter describing the time scale is arbitrary and cannot be determined by the applied methods alone. It is shown that the kinetic equation satisfies the conservation requirements and relaxes to an equilibrium which is a rigorous solution of the Hopf equation.

AB - A kinetic equation for a two-dimensional inviscid hydrodynamic fluid is derived in two ways. First, the equations of motion for the modes of the fluid are interpreted as stochastic equations resembling the Langevin equation. To lowest order a Fokker-Planck equation can be derived which is the kinetic equation for one mode. Secondly, a suitable iteration scheme is applied to the Hopf equation which results in the same kinetic equation. A parameter describing the time scale is arbitrary and cannot be determined by the applied methods alone. It is shown that the kinetic equation satisfies the conservation requirements and relaxes to an equilibrium which is a rigorous solution of the Hopf equation.

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Elementary derivation of the kinetic equation for the two-dimensional guiding centre plasma

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