Simulations and Theory of Ion Injection at Non-relativistic Collisionless Shocks

TL;DR

This paper uses hybrid simulations and theoretical modeling to analyze ion injection processes at non-relativistic collisionless shocks, providing insights into the conditions necessary for ions to enter diffusive shock acceleration.

Contribution

It introduces a minimal model that describes ion reflection, injection fraction, and energy spectrum transition at non-relativistic shocks with various magnetic inclinations.

Findings

Quasi-parallel shocks reform periodically on ion cyclotron scales.

Reflected ions at the steepest shock phase are key for injection.

The model accurately predicts ion injection and spectrum transition.

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.