Electrostatic Waves and Electron Holes in Simulations of Low-Mach Quasi-Perpendicular Shocks

TL;DR

This study uses 2D PIC simulations to analyze electrostatic wave activity and electron hole formation in low Mach number quasi-perpendicular shocks, revealing how shock velocity influences wave characteristics and potentially explaining observational discrepancies.

Contribution

It provides the first detailed simulation-based analysis of electrostatic waves and electron holes in low Mach number shocks, linking wave properties to shock velocity and offering explanations for satellite measurement differences.

Findings

Electron acoustic waves are driven by counter-streaming electron beams in shock ramps.

Electrostatic solitary waves' wavelength and amplitude depend on shock velocity.

Predicted ESW characteristics at realistic velocities match some satellite observations.

Abstract

Collisionless low Mach number shocks are abundant in astrophysical and space plasma environments, exhibiting complex wave activity and wave-particle interactions. In this paper, we present 2D Particle-in-Cell (PIC) simulations of quasi-perpendicular nonrelativistic ($\vsh \approx (5500-22000)$ km/s) low Mach number shocks, with a specific focus on studying electrostatic waves in the shock ramp and the precursor regions. In these shocks, an ion-scale oblique whistler wave creates a configuration with two hot counter-streaming electron beams, which drive unstable electron acoustic waves (EAWs) that can turn into electrostatic solitary waves (ESWs) at the late stage of their evolution. By conducting simulations with periodic boundaries, we show that EAW properties agree with linear dispersion analysis. The characteristics of ESWs in shock simulations, including their wavelength and amplitude, depend on the shock velocity. When extrapolated to shocks with realistic velocities ($\vsh \approx 300$ km/s), the ESW wavelength is reduced to one tenth of the electron skin depth and the ESW amplitude is anticipated to surpass that of the quasi-static electric field by more than a factor of 100. These theoretical predictions may explain a discrepancy, between PIC and satellite measurements, in the relative amplitude of high- and low-frequency electric field fluctuations.