On the existence of Weibel instability in a magnetized plasma. I. Parallel wave propagation

Abstract

In a uniform static magnetic field (B0) the nonresonant mechanism of Weibel instability is certainly affected, because the free energy stored in the temperature anisotropy (e.g., T⊥>T∥, where ⊥ and ∥ denote directions relative to the background magnetic field) can drive the parallel whistler instability due to the cyclotron resonance with plasma particles. However, it has already been shown that the nonresonant mechanism should exist and drive the whistler instability, at least, for anisotropic distribution functions with no parallel thermal velocity spread. Here the investigation is extended to a magnetized plasma with a bi-Maxwellian temperature anisotropy. New frequency limits are introduced and the necessary physical conditions are provided: The nonresonant whistler instabilities have in general small frequencies, smaller than the growth rate, ωr<ωi, and for a large temperature anisotropy, the nonresonant instabilities are limited to a β⊥=8πn0T⊥∕B02>1 regime. These criteria restricts in general the magnetic field to strengths less than a threshold value proportional to the square root of the temperature anisotropy. In the presence of an ambient magnetic field, the growth rate of the nonresonant instability is reduced and the large wavelengths are stabilized.