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.