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

TL;DR

This study uses two-dimensional full particle simulations to reveal how ion temperature perpendicular to magnetic fields in collisionless shocks depends on Mach number and plasma beta, supported by analytical insights.

Contribution

It demonstrates a proportional relationship between ion perpendicular temperature and the square of the Mach number divided by plasma beta, with analytical and numerical validation.

Findings

Ion temperature perpendicular to magnetic field scales with (Mach number)^2 / plasma beta.

Reflected ion fraction is largely independent of plasma beta and Mach number at high ratios.

Analytical model explains ion energy gain from upstream plasma flow.

Abstract

Ion temperature anisotropy is a common feature for (quasi-)perpendicular collisionless shocks. By using two-dimensional full particle simulations, it is shown, that the ion temperature component perpendicular to the shock magnetic field at the shock foot region is proportional to the square of the Alfven Mach number divided by the plasma beta. This result is also explained by a simple analytical argument, in which the reflected ions get energy from upstream plasma flow. By comparing our analytic and numerical results, it is also confirmed that the fraction of the reflected ions hardly depends on the plasma beta and the Alfven Mach number when the square of the Alfven Mach number divided by the plasma beta is larger than about 20.