Long-term evolution of electron acceleration in high Mach number shocks with MHD-PIC simulations

The questions of long-term evolution of shock waves in supernova remnants and the interplay between shocks and cosmic rays (CRs) remain under active investigation. We use a hybrid magnetohydrodynamic-particle-in-cell (MHD-PIC) approach to study electron acceleration in quasi-parallel shocks. The method treats CRs as particles, while the thermal electron-ion plasma is described as a fluid by MHD equations. We implement a novel injection prescription based on the self-consistent reflectivity of the shock, which we determine by tracing test particles through the MHD turbulence in the shock upstream. This approach allows us to study the long-term evolution of the particle acceleration and the upstream turbulence, particularly substantial in quasi-parallel shocks, on macroscopic scales, which are unachievable with the PIC method. We find that larger upstream turbulence confines accelerated particles closer to the shock, and leads to changes in the reflected particle fraction. As a result, the shock reaches a self-consistent particle injection level which is independent of the numerical parameters. Such self-regulation of injection is likely important in the strongly nonlinear turbulence of supernova remnant shocks.