Two-stream instability for a longitudinally compressing charged particle beam

The electrostatic two-stream instability for a cold, longitudinally compressing charged particle beam propagating through a background plasma has been investigated both analytically and numerically. Small-signal coupled equations describing the evolution of the perturbations are derived, and the asymptotic solutions are obtained. The results are confirmed by direct numerical solution of the linearized fluid equations. It is found that the longitudinal beam compression strongly modifies the space-time development of the instability. In particular, the dynamic compression leads to a significant reduction in the growth rate of the two-stream instability compared to the case without an initial velocity tilt.