Between two stream and filamentation instabilities: Temperature and collisions effects

We will consider relativistic electron beam interacting with plasma and study the electromagnetic instabilities obtained for arbitrarily oriented wave vectors ranging from two-stream to filamentation instabilities. For these unstable modes, we will study every temperature effects, namely beam and plasma normal, and parallel temperatures. Temperatures are supposed to be non-relativistic and modeled through water bag distributions. It is found that only normal beam temperature and parallel plasma temperature have a significative influence over the growth rates for wave vector making an angle with the beam larger than a critical angle θ_c which is determined exactly. The largest growth rate being reached for a wave vector making an angle with the beam smaller than θ_c, it is not damped by any kind of temperatures. We finally explore collisions effects and show they can reduce the largest growth rate.