{'fraction_non_alphanumeric': 0.028460543337645538, 'fraction_numerical': 0.0, 'mean_word_length': 5.696969696969697, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Electron Acceleration by Moderate-Mach-number Low-β Shocks: Particle-in-Cell Simulations

Particle acceleration is ubiquitous at shock waves, occurring on scales ranging from supernova remnants in the universe to coronal-mass-ejection-driven shocks and planetary bow shocks in the heliosphere. The most promising mechanism responsible for the almost universally observed power-law spectra is diffusive shock acceleration (DSA). However, how electrons are preaccelerated by different shocks to the energy required by the DSA theory is still unclear. In this paper, we perform two-dimensional particle-in-cell plasma simulations to investigate how the magnetic field orientations, with respect to simulation planes, affect electron preacceleration in moderate-Mach-number low- β shocks. Simulation results show that instabilities can be different as the simulation planes capture different trajectories of particles. For magnetic fields perpendicular to the simulation plane, electron cyclotron drift instability dominates in the foot. Electrons can be trapped by the electrostatic wave and undergo shock-surfing acceleration. For magnetic fields lying in the simulation plane, whistler waves produced by modified two-stream instability dominate in the foot and scatter the electrons. In both cases, electrons undergo multistage acceleration in the foot, shock surface, and immediate downstream, during which process shock-surfing acceleration takes place as part of the preacceleration mechanism in moderate-Mach-number quasi-perpendicular shocks.