Electromagnetic Acceleration of a Shock Wave in a Constant-Area Duct

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Abstract
When a rapid current discharge occurs in a gas between two electrodes, a current sheet forms which accelerates into the gas and produces a shock wave, much as a piston in conventional gas dynamics. Due to the high velocities which it reaches, the shock wave ionizes the gas, and a plasma is formed in the region between the current carrying contact front and the shock wave. Nonsteady electromagnetic acceleration of a one-dimensional shock wave has been studied for the case of an arbitrary but constant specific-heat ratio of the plasma. Approximate closed-form solutions for the velocity of the contact surface and shock wave have been obtained, illustrating both the weak dependence of the contact front velocity on γ, and the relation between the fluid mechanical and ``snowplow'' models of the shock acceleration. It has also been shown, for the case under consideration, that the contact surface and shock positions are initially parabolic, and finally hyperbolic functions of time, and that the pressure may be approximated by a linear function of the Lagrangian variable.

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