Fundamentals of collisionless shocks for astrophysical application, 1. Non-relativistic shocks

Abstract

A comprehensive review is given of the theory and properties of nonrelativistic shocks in hot collisionless plasmas—in view of their possible application in astrophysics. Understanding non-relativistic collisionless shocks is an indispensable step towards a general account of collisionless astrophysical shocks of high Mach number and of their effects in dissipating flow-energy, in heating matter, in accelerating particles to high—presumably cosmic-ray—energies, and in generating detectable radiation from radio to X-rays. Non-relativistic shocks have Alfvénic Mach numbers ${{\fancyscript{M}}_A\ll \sqrt{m_i/m_e}(\omega_{pe}/\omega_{ce})}$, where m _i /m _e is the ion-to-electron mass ratio, and ω _pe , ω _ce are the electron plasma and cyclotron frequencies, respectively. Though high, the temperatures of such shocks are limited (in energy units) to T < m _e c ². This means that particle creation is inhibited, classical theory is applicable, and reaction of radiation on the dynamics of the shock can be neglected. The majority of such shocks are supercritical, meaning that non-relativistic shocks are unable to self-consistently produce sufficient dissipation and, thus, to sustain a stationary shock transition. As a consequence, supercritical shocks act as efficient particle reflectors. All these shocks are microscopically thin, with shock-transition width of the order of the ion inertial length λ _i = c/ω _pi (with ω _pi the ion plasma frequency). The full theory of such shocks is developed, and the different possible types of shocks are defined. Since all collisionless shocks are magnetised, the most important distinction is between quasi-perpendicular and quasi-parallel shocks. The former propagate about perpendicularly, the latter roughly parallel to the upstream magnetic field. Their manifestly different behaviours are described in detail. In particular, although both types of shocks are non-stationary, they have completely different reformation cycles. From numerical full-particle simulations it becomes evident that, on ion-inertial scales close to the shock transition, all quasi-parallel collisionless supercritical shocks are locally quasi-perpendicular. This property is of vital importance for the particle dynamics near the quasi-parallel shock front. Considerable interest focusses on particle acceleration and the generation of radiation. Radiation from non-relativistic shocks results mainly in wave–wave interactions among various plasma waves. Non-thermal charged particles can be further accelerated to high energies by a Fermi-like mechanism. The important question is whether the shock can pre-accelerate shock-reflected particles to sufficiently high energies in order to create the seed-population of the non-thermal particles required by the Fermi mechanism. Based on preliminary full-particle numerical simulations, this question is answered affirmatively. Such simulations provide ample evidence that collisionless shocks with high-Mach numbers—even when non-relativistic—could probably by themselves produce the energetic seed-particle population for the Fermi-process.