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

Published online by Cambridge University Press:  13 March 2009

Michael Mond  and
Georg Knorr
Michael Mond
Affiliation:
Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242
Georg Knorr
Affiliation:
Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242
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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.

Type
Research Article
Information
Journal of Plasma Physics , Volume 19 , Issue 1 , February 1978 , pp. 121 - 133
Copyright
Copyright © Cambridge University Press 1978

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References

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