Spectral analysis of PIC simulations of interpenetrating plasmas*

Plasma with interpenetrating beams is known to exhibit electromagnetic instabilities such as the filamentation (e.g., Weibel) instability. Extreme astrophysical environments, such as in collisionless shocks of cosmic explosions -- gamma-ray bursts and supernovae, are natural places where such beam-plasma instabilities naturally occur and affect plasma dynamics and observable light. 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.