Spectral studies of PIC simulations of multi-streaming plasmas

Interpenetrating plasma beams is unstable to electromagnetic instabilities such as the Weibel filamentation instability and others. Astrophysical systems with high energy density content, such as in collisionless shocks of gamma-ray bursts and supernova explosions, are the locations where the beam-plasma Weibel instability naturally occurs and affect plasma dynamics and observable electromagnetic radiation. Here we study the case of a collisionless, unmagnetized system with mildly relativistic counter-streaming beams of equal density with PIC simulations using TRISTAN-MP code. We developed the spectral analysis software used at the post-processing stage. Here we present the time-dependent spectral analysis in the omega-k space of the plasma modes present in the system as it evolves. We discuss various properties the excited plasma modes.