Thickness of a resistivity-controlled hydromagnetic shock wave

Abstract

Studies the structure of a hydromagnetic shock wave when resistivity is the only source of entropy. The equations used are classical one-fluid equations and the generalized Ohm's law which describes the relative diffusion of matter and magnetic field due to resistivity. In Section 1 the law of diffusion of the plasma in the magnetic field is given and the equations are integrated for the stationary case. It is shown that the profiles obtained may be characterized by a finite thickness along which variations are appreciable. This thickness is given as a function of the strength of the shock wave. It is shown that it is dependent on resistivity only through the length L2= eta (T2)/2 mu 0v1 while eta (T2) represents resistivity in the downstream plasma. The domain of validity of the actual computation is, as is well known, limited to shock waves for which the fluid velocity in the downstream plasma is exactly equal to the sound velocity. In Section 2, the influence of the power radiated by the plasma is studied phenomenologically when it constitutes a measurable part of the incident energy. Then T2 is entirely limited by radiation, but the thickness varies with resistivity as L2, as in the prededing case.