Electromagnetic instabilities for relativistic beam-plasma interaction in whole k space: nonrelativistic beam and plasma temperature effects.

For the system formed by a relativistic electron beam and its plasma return current, we investigate the effects of both transverse and parallel beam and plasma temperatures on the linear stability of collective electromagnetic modes. We focus on nonrelativistic temperatures and wave-vector orientations ranging from two-stream to filamentation instabilities. Water-bag distributions are used to model temperature effects and we discuss their relevance. Labeling Theta(k) the angle between the beam and the wave vector, one or two critical angles Theta(c,i) are determined exactly and separate the k space into two parts. Modes with Theta(k) < Theta(c) =min ( Theta(c,i)) are quasilongitudinal and poorly affected by any kind of temperature. Modes having Theta(k) > Theta(c) are very sensitive to transverse beam and plasma parallel temperatures. Also, parallel plasma temperature can trigger a transition between the beam-dependent filamentation instability (Theta(k) =pi/2) and the plasma-temperature-dependent Weibel instability so that two-stream, filamentation, and Weibel instabilities are eventually closely connected to each other. The maximum growth rate being reached for a mode with Theta(k) < Theta(c), no temperature of any kind can significantly reduce it in the nonrelativistic temperature regime.