Abstract
Properties of the two-fluid plasma equations which lead to a partial theoretical model for the collisionless shock wave are investigated. First, a nonlinear symmetric-pulse solution to the two-fluid equations for a cold collisionless plasma is described. The propagation speed of the pulse is between the Alfvén speed and the fast-wave speed, and the pulse thickness is of the order of (mic2/4πe2N)½, except for geometries in which the wave normal makes an angle of the order of (me/mi)½ or less with the upstream magnetic field. An effective conductivity is then introduced in the equations of motion of the plasma and a shock thickness is estimated. The calculated dependence of shock thickness on Mach number is shown to agree with the available experimental data. Finally, the growth of a sinusoidal pinch instability of a current-carrying plasma is shown to have the average effect of a finite conductivity as was postulated.
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