The effect of turbulence on the K-parallel-B relativistic beam instability

Abstract

We have considered the effect of magnetic turbulence, causing electron gyrophase diffusion, on the instability of an anisotropic, field-aligned relativistic electron beam. Formally, inclusion of gyrophase diffusion results in a change in the formula for the wave growth rate whereby the delta function describing the wave-particle resonance is replaced by a Lorentzian function. The width of the Lorentzian, delta, is directly proportional to the strength of the gyrophase diffusion coefficient. Depending on the properties of the beam and the background plamsa, the magnetic irregularities may either enhance or diminish the growth rate, or even produce a transition from wave growth to wave damping. Two of the more interesting results to emerge from our analysis are: (1) contrary to conventional opinion, some types of electron beams may exist without being isotropized by self-generated Alfven waves, (2) due to the frequency dependence of the broadening parameter delta, the actual growth rate spectrum might differ substantially from that calculated for a homogeneous plasma, even though the perturbations are still in the linear regime.