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Nonlinear theory of the Weibel instability

Published online by Cambridge University Press:  13 March 2009

Don S. Lemons ,
D. Winske  and
S. Peter Gary
Don S. Lemons
Affiliation:
Los Alamos Scientific Laboratory, University of California, Los Alamos, NM 87545
D. Winske
Affiliation:
Los Alamos Scientific Laboratory, University of California, Los Alamos, NM 87545
S. Peter Gary
Affiliation:
Los Alamos Scientific Laboratory, University of California, Los Alamos, NM 87545
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Abstract

A canonical distribution function is proposed to describe the instantaneous state of a single nonlinear wave–plasma system as it evolves quasi-statically in time. This function is based on two single particle constants of motion for a charged particle in a zero-frequency transverse magnetic wave and determines a wavenumber condition and two system energy constants. In the case of a onecomponent bi-Maxwellian plasma with T⊥/T‖>1, these relations are particularly simple and yield expressions for the energy in the magnetic wave field, the wavenumber, the temperatures, and the entropy of the system in terms of one unknown parameter, chosen to be the instantaneous temperature ratio, T⊥/T‖ The maximum value of the field energy is expressed in terms of only the initial temperature anisotropy, and is shown to be always less than of the system's total energy. The results are in good agreement with computer simulations of the electron Weibel instability.

Type
Research Article
Information
Journal of Plasma Physics , Volume 21 , Issue 2 , April 1979 , pp. 287 - 300
Copyright
Copyright © Cambridge University Press 1979

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References

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