Simulations and theory of ion injection at non-relativistic collisionless shocks

Damiano Caprioli, Ana-Roxana Pop, Anatoly Spitkovsky

Abstract:

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