Swirl of a Conducting Gas due to the Hall Effect

Abstract

The Hall effect is shown to induce a swirling or transverse motion in the flow of an electrically conducting gas in a magnetic field and surrounded by an insulating medium. Both the two-dimmensional and the axi-symmetric floes are discussed. On the assumption that the magnetic Reynolds number and the magnetic interaction parameter are small, the transverse or helical velocity is shown to be independent of the Mach number to first order approximation. This velocity is explicitly determined for a slender symmetric flow with small Hall parameter in terms of the imposed magnetic field along the axis. A numerical example is given for a magnetic field of a single current loop.