Particle-in-cell simulations of particle energization from low Mach number fast mode shocks

TL;DR

This study uses particle-in-cell simulations to analyze particle acceleration mechanisms in low Mach number fast mode shocks, revealing shock drift acceleration and turbulence generation in astrophysical plasma conditions.

Contribution

It introduces a moving wall boundary method for simulating low Mach number shocks, providing better control and longer simulation times, and characterizes electron and ion energization processes.

Findings

Shock drift acceleration (SDA) accelerates electrons and ions.

A modified two-stream instability generates turbulence in the shock transition.

Simulation results match theoretical SDA electron distributions.

Abstract

Astrophysical shocks are often studied in the high Mach number limit but weakly compressive fast shocks can occur in magnetic reconnection outflows and are considered to be a site of particle energization in solar flares. Here we study the microphysics of such perpendicular, low Mach number collisionless shocks using two-dimensional particle-in-cell (PIC) simulations with a reduced ion/electron mass ratio and employ a moving wall boundary method for initial generation of the shock. This moving wall method allows for more control of the shock speed, smaller simulation box sizes, and longer simulation times than the commonly used fixed wall, reflection method of shock formation. Our results, which are independent of the shock formation method, reveal the prevalence shock drift acceleration (SDA) of both electron and ions in a purely perpendicular shock with Alfv\'en Mach number $M_A=6.8$ and ratio of thermal to magnetic pressure $\beta=8$. We determine the respective minimum energies required for electrons and ions to incur SDA. We derive a theoretical electron distribution via SDA that compares to the simulation results. We also show that a modified two-stream instability due to the incoming and reflecting ions in the shock transition region acts as the mechanism to generate collisionless plasma turbulence that sustains the shock.