Two-stream instability for a scattered beam propagating in a coixisional plasma

We have made significant progress in the understanding of the collisional stabilization of the high-frequency two-stream instability in a relativistic electron beam through a rigorous Vlasov treatment. Substantially different scaling with parameters are obtained in comparison wi th previous, essentially phenomenological, models and we have gained insight into the mechanism of the stabilization process. Further investigation of the 2-D case remains to be done. The issue of stabilization of the two-stream instability in finite geometry is as yet unexplored as is that of nonlinear saturation, by trapping, of the instability in the presence of momentum spread on the beam and collisions on the plasma electrons. These are important in the application of relativistic electron beams to the heating of dense plasmas and possibly in the interpretation of neutral gas propagation experiments. Extension of our research into these areas will necessarily rely on the investigations outlined above.