PIC simulations and spectral analysis of plasma with interpenetrating beams*

Plasma with interpenetrating beams is known to exhibit instabilities such as the filamentation and two-stream instabilities. Beam-plasma systems are ubiquitous in high-energy-density environments, e.g., in laser-produced plasmas and astrophysical sources, such as in collisionless shocks of cosmic explosions -- gamma-ray bursts and supernovae. Here we investigate the case of a collisionless, unmagnetized system with relativistic counter-streaming beams with PIC simulations.  We present the spectral analysis of the system as it evolves. We discuss the spectrum, temporal and angular distribution of the generated plasma modes.