Collisionless relaxation of downstream ion distributions in low-Mach number shocks

Abstract

Collisionlessly formed downstream distributions of ions in low-Mach number shocks are studied. General expressions for the asymptotic value of the ion density and pressure are derived for the directly transmitted ions. An analytical approximation for the overshoot strength is suggested for the low-β case. Spatial damping scale of the downstream magnetic oscillations is estimated.

Rankine‐Hugoniot Relations in Multispecies Plasma With Gyrotropic Anisotropic Downstream Ion Distributions

“…Kinematic relaxation does depend on the ion temperature. Taking into account low upstream β is straightforward (Gedalin et al, ) and would provide corrections to the derived expressions. High‐ β cases cannot be covered within the proposed approach, at this stage, since there may be a substantial population of ions that turn around within the ramp (Gedalin, ).…”

“…Yet low Mach number quasi‐perpendicular shocks are often one‐dimensional and stationary and have a ramp width of the order of the ion inertial length (Farris et al, ; Greenstadt et al, ; Russell et al, ). It has been shown (Balikhin et al, ; Gedalin, ; Gedalin et al, ; Ofman et al, ; Ofman & Gedalin, ) that in such shocks the downstream ion gyrotropization proceeds in a purely kinematic way due to gyrophase mixing of gyrating ions. This conclusion has been observationally supported by analyzing the correlation of the downstream magnetic oscillations with the oscillations of plasma velocity and temperature (Goncharov et al, ).…”

Transmitted, reflected, quasi‐reflected, and multiply reflected ions in low‐Mach number shocks

“…Ion transmission in such shocks for low β of incident ions has been extensively studied in the last several years. In particular, it has been shown that gyration and gradual gyrophase mixing of the downstream distribution of transmitted ions is responsible for the downstream coherent oscillations of the magnetic field strength [ Balikhin et al , ; Gedalin et al , ; Ofman et al , ; Gedalin et al , ; Gedalin , ]. Ion reflection at such shocks has not been devoted sufficient attention so far.…”

“…In low‐Mach number shocks the role of the small‐scale time‐dependent fields is secondary [ Oka et al , ], despite the upstream and downstream wave activity [ Russell et al , ; Kajdič et al , ]. Yet even in the time stationary one‐dimensional electric and magnetic fields, the equations of motion are not integrable and analytic approximations have been successful so far only for low upstream ratio of the ion kinetic pressure to the magnetic pressure [ Gedalin et al , ]. Here T iu is the upstream ion temperature and n u is the upstream number density.…”

Mach number and plasma beta dependence of the ion temperature perpendicular to the external magnetic field in the transition region of perpendicular collisionless shocks

“…15 In the downstream region, the ion distribution is no longer nongyropropic and its structures are smoothed out by collisionless gyrophase mixing, resulting in the downstream ion heating. [16][17][18][19][20][21] In order to understand such a multi-step dissipation process across the shock front, it is important to estimate the initial ion temperature component perpendicular to the shock magnetic field at the foot region. In the present study, using the two-dimensional full a) particle simulation of low-Mach-number, perpendicular, rippled and collisionless shocks, we study the ion perpendicular temperature at the shock foot region.…”