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A comparative study of the filamentation and Weibel instabilities and their cumulative effect. II. Weakly relativistic beams

Published online by Cambridge University Press:  01 August 2009

A. STOCKEM ,
M. LAZAR ,
P. K. SHUKLA  and
A. SMOLYAKOV
A. STOCKEM
Affiliation:
Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany (mlazar@tp4.rub.de)
M. LAZAR
Affiliation:
Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany (mlazar@tp4.rub.de) Center for Plasma Astrophysics, Celestijnenlaan 200B, 3001 Leuven, Belgium
P. K. SHUKLA
Affiliation:
Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany (mlazar@tp4.rub.de)
A. SMOLYAKOV
Affiliation:
Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, Saskatchewan S7N 5E2, Canada
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Abstract

Counterstreaming plasma systems with intrinsic temperature anisotropies are unstable against the excitation of Weibel-type instabilities, namely, filamentation and Weibel instabilities, and their cumulative effect. Here, the analysis is extended to counterstreaming plasmas with weakly relativistic bulk velocities, while the thermal velocities are still considered to be non-relativistic. Such plasma systems are relevant for fusion plasma experiments and the more violent astrophysical phenomena, such as jets in gamma-ray burst sources. Simple analytical forms of the dispersion relations are derived in the limit of a small transverse temperature or a large temperature anisotropy of the beams. The aperiodic growing solutions are plotted systematically for the representative cases chosen in Paper I (Lazar et al. 2009 J. Plasma Phys. 75, in press). In the limit of slow non-relativistic plasma flows, the numerical solutions fit well with those obtained in Paper I, but for weakly relativistic streams an important deviation is found.

Type
Papers
Information
Journal of Plasma Physics , Volume 75 , Issue 4 , August 2009 , pp. 529 - 543
Copyright
Copyright © Cambridge University Press 2008

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