Large-amplitude magnetic compression of a collision-free plasma. II. Development of a thermalized plasma

Abstract

Numerical calculations are made of a strong one-dimensional disturbance traveling perpendicular to a magnetic field in a fully ionized and collisionless plasma. When the Alfvén-Mach number Mk is greater than 2, orbit crossings of the ions occur, which rapidly leads to thermalization perpendicular to the magnetic field if the crossings are extensive (M h > 3). The thermalization approximates the behavior of a classical hydromagnetic shock, with a shock-front thickness roughly equal to the distance the shock front travels in one-half an ion gyration time. This length is somewhat greater than the ion gyration radius. The structure of the front is found to be strongly time dependent, and undergoes large fluctuations in an ion gyration period. It is argued that when the ion-electron mass is large, the magnetic forces tend to suppress electron orbit crossings. This results in relatively cold electrons in the shocked region, with the ions obtaining nearly all of the thermal energy. A relationship between the longitudinal electrostatic potential difference across the shock front and mass flow in the plane of the front is derived on the basis of a simplified model and is found to be in qualitative agreement with the numerical results. The range of applicability of the calculations to real plasmas is discussed.