Cosmic electric currents and the generalized Bennett relation

Abstract

A generalized form of the Bennett pinch is studied in both cylindrical geometry and plane-parallel geometry. In this kind of pinch electromagnetic forces, kinetic pressure gradient forces, centrifugal forces, and gravitational forces may act. For each of the two geometries considered a generalized Bennett relation is derived. By means of these relations it is possible to describe among other things the pure Bennett pinch, Jean's criterion in one and two dimensions, force-free magnetic fields, gravitationally balanced magnetic pressures, and continuous transitions between these states. The theory is applied to electric currents in the magnetosphere, in the solar atmosphere, and in the interstellar medium. It is pointed out that the currents in the solar atmosphere and in the interstellar medium may lead to pinches that are of vital importance to the phenomena of solar flares and star formation, respectively.