Electrostatic two-stream instability for a scattered relativistic electron beam and collisional plasma

The Vlasov stability theory of the two-stream instability of a scattered relativistic electron beam in a collisional plasma is presented. New analytic results demonstrating the effect of a small but finite scatter (temperature) on the cold beam dispersion relation are given. These provide a basis for a discussion of the continuous transition, with increasing scatter, from the hydrodynamic to kinetic regime of instability. Numerical solutions of the dispersion relation are presented to illustrate some general features observed as well as trends in scaling with the beam parameters