Speed-dependent Threshold for Electron Injection into Diffusive Shock Acceleration

TL;DR

This paper uses kinetic simulations to determine the conditions under which electrons are injected into diffusive shock acceleration, revealing that electron speed relative to the shock is crucial for injection.

Contribution

It introduces a new speed-dependent criterion for electron injection into DSA based on first-principles kinetic simulations.

Findings

Electrons inject into DSA when their speed exceeds a certain threshold.

A minimal model reproduces observed nonthermal electron spectra.

The new criterion impacts understanding of shock-powered astrophysical emissions.

Abstract

Finding the injection threshold for diffusive shock acceleration (DSA) of electrons in collisionless shocks has been a longstanding unsolved problem. Using first-principles kinetic simulations, we identify the conditions for electron injection into DSA and quantify the evolution of the nonthermal tail in self-generated electromagnetic turbulence. By analyzing electron trajectories and their momentum gain during shock-recrossing cycles, we demonstrate that electrons start participating in DSA when their speed is large enough to overrun the shock. We develop a minimal model showing that speed-dependent injection reproduces nonthermal electron spectra observed in kinetic simulations. Our findings establish a new criterion for electron DSA, which has broad implications for the nonthermal emission of shock-powered space/astrophysical systems.