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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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High-resolution particle-in-cell simulations of two-dimensional Bernstein–Greene–Kruskal modes
We present two-dimensional (2D) particle-in-cell (PIC) simulations of 2D Bernstein–Greene–Kruskal modes, which are exact nonlinear steady-state solutions of the Vlasov–Poisson equations, on a 2D plane perpendicular to a background magnetic field, with a cylindrically symmetric electric potential localized on the plane. PIC simulations are initialized using analytic electron distributions and electric potentials from the theory. We confirm the validity of such solutions using high-resolutions up to a 20482 grid. We show that the solutions are dynamically stable for a stronger background magnetic field, while keeping other parameters of the model fixed, but become unstable when the field strength is weaker than a certain value. When a mode becomes unstable, we observe that the instability begins with the excitation of azimuthal electrostatic waves that ends with a spiral pattern.
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- PAR ID:
- 10591989
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Physics of Plasmas
- Volume:
- 31
- Issue:
- 4
- ISSN:
- 1070-664X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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