Weibel instability in a plasma with nonzero external magnetic field

O A Pokhotelov,M A Balikhin

doi:10.5194/angeo-30-1051-2012

Abstract

Abstract. The theory of the Weibel instability is generalized for the case of a plasma immersed in a nonzero external magnetic field. It is shown that the presence of this external field modifies the dispersion relation for this mode which now possesses a nonzero frequency. The explicit expression for the real and imaginary parts of the frequency is then calculated. It turns out that the linear growth rate remains unchanged, whereas the frequency becomes nonzero due to the finite value of the electron cyclotron frequency. The frequency of the Weibel mode is found to be proportional to the electron temperature anisotropy. The formal similarity of the Weibel and drift-mirror instabilities is outlined.

Highlights

The Weibel instability (Weibel, 1959) is one of the most wellknown plasma instabilities
Under conditions of marginal stability, which were assumed in the derivation presented here, the Weibel mode remains low frequency even in the presence of nonzero external magnetic field
In the present study we have investigated the effect of a nonzero external magnetic field in relation to the Weibel instability

Summary

Introduction

The Weibel instability (Weibel, 1959) is one of the most wellknown plasma instabilities. A simplified version of this instability has been considered by Fried (1959) who pointed out that it can be found in a plasma with the superposition of counter-streaming beams In this respect it becomes similar to the ordinary two-stream instability (Schlickeiser and Shukla, 2003). Treumann and Baumjohann (2012) recently discussed the problem of the Weibel infrared catastrophe which arises due to the fact that magnetic field fluctuations are strongly dependent on their wave numbers ( δB2 k ∝ k−3). These authors confirmed that thermal fluctuations can support a weak, spontaneous magnetic fluctuation background level in plasma and recalculated the thermal level for Weibel instability.

Basic equations

Weibel dispersion relation

Discussion and conclusions