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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≈ (5500–22000) km s−1) low-Mach-number shocks, with a specific focus on studying electrostatic waves in the shock ramp and precursor regions. In these shocks, an ion-scale oblique whistler wave creates a configuration with two hot counterstreaming 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 the 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≈ 300 km s−1), 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.
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This content will become publicly available on October 8, 2026
Magnitude of Short-wavelength Electric Field Fluctuations in Simulations of Collisionless Plasma Shocks
Large-amplitude electrostatic fluctuations are routinely observed by spacecraft upon traversal of collisionless shocks in the heliosphere. Kinetic simulations of shocks have struggled to reproduce the amplitude of such fluctuations, complicating efforts to un- derstand their influence on energy dissipation and shock structure. In this paper, 1D particle-in-cell simulations with realistic proton-to-electron mass ratio are used to show that in cases with upstream electron temperature Te exceeding the ion temperature Ti, the magnitude of the fluctuations increases with the electron plasma-to-cyclotron frequency ratio ωpe/Ωce, reaching realistic values at ωpe/Ωce ≳ 30. The large-amplitude fluctuations in the simulations are shown to be associated with electrostatic solitary structures, such as ion phase-space holes. In the cases where upstream temperature ratio is reversed, the magnitude of the fluctuations remains small.
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- PAR ID:
- 10642157
- Publisher / Repository:
- The American Astronomical Society.
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 992
- Issue:
- 1
- ISSN:
- 0004-637X
- Page Range / eLocation ID:
- 104
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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