Spectral Study of Weibel Instability Evolution

Relativistic and sub-relativistic counter-propagating plasma beams are strongly unstable to the Weibel filamentation instability, which produces strong magnetic fields from scratch. High-energy density astrophysical systems, such as in collisionless shocks of GRBs and SN explosions, are the sites where this instability naturally occurs. There, it is responsible for shock formation, cosmic ray acceleration, energization of electrons and strong synchrotron emission and cooling. Here, we present the spectral analysis of the instability that is simulated with PIC TRISTAN-MP code in a collisionless, unmagnetized counter-streaming plasma. We show the time-dependent spectral analysis of electromagnetic plasma excitations in the $\omega-k$-space as the system evolves in time.