SIMULATIONS AND THEORY OF ION INJECTION AT NON-RELATIVISTIC COLLISIONLESS SHOCKS

Abstract

We use kinetic hybrid simulations (kinetic ions - fluid electrons) to\ncharacterize the fraction of ions that are accelerated to non-thermal energies\nat non-relativistic collisionless shocks. We investigate the properties of the\nshock discontinuity and show that shocks propagating almost along the\nbackground magnetic field (quasi-parallel shocks) reform quasi-periodically on\nion cyclotron scales. Ions that impinge on the shock when the discontinuity is\nthe steepest are specularly reflected. This is a necessary condition for being\ninjected, but it is not sufficient. Also by following the trajectories of\nreflected ions, we calculate the minimum energy needed for injection into\ndiffusive shock acceleration, as a function of the shock inclination. We\nconstruct a minimal model that accounts for the ion reflection from\nquasi-periodic shock barrier, for the fraction of injected ions, and for the\nion spectrum throughout the transition from thermal to non-thermal energies.\nThis model captures the physics relevant for ion injection at non-relativistic\nastrophysical shocks with arbitrary strengths and magnetic inclinations, and\nrepresents a crucial ingredient for understanding the diffusive shock\nacceleration of cosmic rays.\n