Two-stream instability analysis for propagating charged particle beams with a velocity tilt

The linear growth of the two-stream instability for a charged-particle beam that is longitudinally compressing as it propagates through a background plasma (due to an applied velocity tilt) is examined. Detailed, 1D particle-in-cell (PIC) simulations are carried out to examine the growth of the wave packet produced by a small amplitude density perturbation in the background plasma. Recent analytic and numerical work by Startsev and Davidson [Phys. Plasmas 13, 062108 (2006)] predicted reduced linear growth rates, which are indeed observed in the PIC simulations. Here, small-signal asymptotic gain factors are determined in a semianalytic analysis and compared with the simulation results in the appropriate limits. Nonlinear effects in the PIC simulations, including wave breaking and particle trapping, are found to limit the linear growth phase of the instability for both compressing and noncompressing beams.