Formation and Evolution of Pair-Alfv\'en Shocks with PIC Simulations

Abstract

We consider the recently discovered \emph{pair-Alfv\'en shock wave} occurring in collisionless electron-positron plasmas. We perform a series of Particle-In-Cell studies in one and two dimensions in order to determine the stability conditions for such a shock and the mechanisms which sustain its growth. Building on our previous simulations, which established that these shocks are initially mediated by the Weibel instability before becoming Alfv\'enic, we demonstrate that the shock is sustained by self-generated Alfv\'en waves overtaking the shock in the upstream plasma. As a result growth is only possible when the guiding magnetic field strength, and hence Alfv\'en speed, is sufficiently small, $\omega_c \lesssim 0.4$ (in normalized units). Furthermore the production of the waves in the upstream is dependent on a resonance between the Alfv\'en wave mode and the thermal noise in the plasma, which is inhibited at high magnetization. This explains the conditional absence of this type of shock identified previously.