Journal of Plasma Physics

Table of Contents - 1979 - Volume 21, Issue 02  

Research Article

Nonlinear theory of the Weibel instability

Don S. Lemonsa1, D. Winskea1 and S. Peter Garya1

a1 Los Alamos Scientific Laboratory, University of California, Los Alamos, NM 87545

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 Txs22A5/Txs2016>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, Txs22A5/Txs2016 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 S0022377800021851_inline1 of the system's total energy. The results are in good agreement with computer simulations of the electron Weibel instability.

(Received March 20 1978)

(Revised September 30 1978)