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

Abstract

Ion temperature anisotropy is a common feature for (quasi-)perpendicular collisionless shocks. By using twodimensional 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 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.In various kinds of solar-terrestrial, astrophysical and laboratory plasmas, ubiquitous is the collisionless shock, at which the upstream kinetic energy of the supersonic plasma flow dissipates into downstream energy of thermal ions and electrons, waves (turbulence), and nonthermal particles. 1,2 Despite various kinds of studies, detailed processes of the shock dissipation remain to be clarified. For example, we do not fully understand how energies are partitioned between downstream thermal electrons and ions, although the total pressure of them can be simply predicted by the fluid Rankine-Hugoniot relation.For supercritical (quasi-)perpendicular shocks, a fraction of incoming ions can be specularly reflected toward the upstream region but gyrates back to the shock front. 3-10 Such reflected-gyrating ions can gain energy from the motional electric field of the upstream plasma flow and contribute to the increase of the ion temperature component perpendicular to the local magnetic field. Consequently, a large temperature anisotropy arises at the shock foot, exciting waves through the ion temperature anisotropy instability, which is responsible for the shock ripples. 11,12 Electron preheating at the foot also takes place under some conditions. 3,13,14 The ripple further dissipates ions, increasing ion parallel temperature, and even electron acceleration occurs. 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. We show, for the first time, that it is proportional to the square of the Alfvén Mach number divided by the plasma beta, or the square of the sonic Mach number, which is consistent with the analytical scaling relation. 5 We perform two-dimensional (2D) simulations of perpendicular (θ Bn = 90 • ) collisionle...

High-power laser experiment forming a supercritical collisionless shock in a magnetized uniform plasma at rest

“…When the upstream low-entropy flow comes into the shock, the kinetic energy is converted into various forms like high-temperature ions and electrons, magnetic turbulence, and nonthermal particles. However, despite state-of-the-art observations [3,4], particle-in-cell (PIC) simulations [5][6][7][8][9][10][11], and analytical arguments [12], detailed mechanism of the energy dissi-pation is not fully understood. In many cases, the upstream plasma is magnetized, and the pre-existing and/or self-generated magnetic fields around the shock work as "catalyst" in the process of kinetic energy dissipation.…”