Theory of an Electric‐Current‐Carrying Discontinuity Driven through Nonconducting Gas by a Lorentz Force

A physical model is presented for the structure of an electric‐current‐carrying discontinuity moving into nonconducting gas and leaving nonconducting gas behind. The model assumes a normal shock wave followed by a porous current sheet. A three‐fluid analysis (electrons, neutrals, and singly charged ions) is made for the case where the component of magnetic field normal to the plane of the discontinuity is zero. All the dependent variables can be computed as functions of displacement in the streamwise direction, as demonstrated in two specific examples. The model admits finite‐strength current sheets as solutions, with the electron and ion density diminishing to zero upstream and downstream of the sheet. As seen moving with the discontinuity, the impressed electric field and the induced electric field are additive on both sides of the discontinuity. This is in contrast to the case for magnetohydrodynamic shock waves, where these two fields cancel on both sides; and to gas‐ionizing shock waves, where the two fields cancel on the downstream side. In the frame of reference moving with the discontinuity, the discontinuity dissipates electrical energy and decelerates the gas. A new jump relation is found which may be described as a “sheet Ohm's law.” The fact that one and only one such relation exists, implies that a current‐carrying discontinuity moving through nonconducting gas is unstable and cannot be part of a unique flow solution unless the discontinuity moves supersonically with respect to the upstream gas and subsonically with respect to the downstream gas.