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

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 Alfvén 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 an 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 Alfvén Mach number when the square of the Alfvén Mach number divided by the plasma beta is larger than about 20.