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A comparative study of the filamentation and Weibel instabilities and their cumulative effect. I. Non-relativistic theory

Published online by Cambridge University Press:  01 February 2009

M. LAZAR ,
A. SMOLYAKOV ,
R. SCHLICKEISER  and
P. K. SHUKLA
M. LAZAR
Affiliation:
Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, Saskatchewan S7N 5E2, Canada Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany (ps@tp4.ruhr-uni-bochum.de)
A. SMOLYAKOV
Affiliation:
Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, Saskatchewan S7N 5E2, Canada
R. SCHLICKEISER
Affiliation:
Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany (ps@tp4.ruhr-uni-bochum.de)
P. K. SHUKLA
Affiliation:
Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany (ps@tp4.ruhr-uni-bochum.de)
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Abstract

A comparative study of the electromagnetic instabilities in anisotropic unmagnetized plasmas is undertaken. The instabilities considered are the filamentation and Weibel instability, and their cumulative effect. Dispersion relations are derived and the growth rates are plotted systematically for the representative cases of non-relativistic counterstreaming plasmas with isotropic or anisotropic velocity distributions functions of Maxwellian type. The pure filamentation mode is attenuated by including an isotropic Maxwellian distribution function. Moreover, it is observed that counterstreaming plasmas can be fully stabilized by including bi-Maxellian distributions with a negative thermal anisotropy. This effect is relevant for fusion plasma experiments. Otherwise, for plasma streams with a positive anisotropy the filamentation and Weibel instabilities cumulate leading to a growth rate by orders of magnitude larger than that of a simple filamentation mode. This is noticeable for the quasistatic magnetic field generated in astrophysical sources, and which is expected to saturate at higher values and explain the non-thermal emission observed.

Type
Papers
Information
Journal of Plasma Physics , Volume 75 , Issue 1 , February 2009 , pp. 19 - 33
Copyright
Copyright © Cambridge University Press 2008

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