Shock Interaction with an Electromagnetic Field

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Abstract
The interaction between a traveling shock wave and a stationary magnetic field is analyzed for the simplest case of one-dimensional flow across a rectangular system of a magnetic and an electric field, while the flowing substance is a plasma of finite conductivity but associated with a sufficiently small magnetic Reynolds number to render the induced magnetic effects negligible. The acceleration of the shock wave produced by a constant electric field applied across the duct walls in the presence of a perpendicular magnetic field, as well as its attenuation due to a distributed system of outside resistances connecting a series of electrodes on the sidewalls of the duct, have been calculated by quadratures. The flow field behind the wave has been determined by means of a perturbation technique whose validity is restricted to cases of small Lorentz forces and moderate Joule heating effects. To gain more familiarity with the interaction process a hydraulic analog is proposed, based on the use of a piston driven, free surface, mercury channel. In this connection, a general solution is consequently obtained for the interaction of a hydraulic jump traveling in a conducting liquid with a vertical magnetic field in the presence of a horizontal electric field.