Microphysics of Particle Reflection in Weibel-Mediated Shocks

Particle-in-cell (PIC) simulations have shown that relativistic collisionless shocks mediated by the Weibel instability accelerate about 1% of incoming particles, while the majority are transmitted through the shock and become thermalized. The microphysical processes that determine whether an incoming particle will be transmitted or reflected are poorly understood. We study the microphysics of particle reflection in Weibel-mediated shocks by tracking a shell of test particles in a PIC simulation of a shock in pair plasma. We find that electrons in positron-dominated filaments and positrons in electron-dominated filaments efficiently reflect off of strong magnetic structures at the shock. These reflected particles headed towards the upstream must then find filaments of the same sign of current as the current carried by the reflected particles in order to successfully move with the shock and participate in diffusive shock acceleration (DSA). The final injection efficiency on the order of about 1% thus results from the effectiveness of the initial reflection at the shock and the reflected particles' probability of survival in the upstream post-reflection. We develop a model that predicts the fraction of high-energy particles as a function of the properties of Weibel filamentation.