Bohm Criterion in the Presence of a Magnetic Field: A Descriptive Approach

Abstract

The present paper contains a complete description of the plasma column, including the diamagnetic effect due to the azimuthal electron currents. The principal result, however, is that the Bohm criterion is satisfied in this case. The quantity dn/d\(\phi\) approaches the Boltzmann value at the plasma boundary. Because the Boltzmann relation for electron density has not been assumed, this paper is very interesting. It should be remembered that Bohm developed the criterion using the Boltzmann equation for electron density. The principal point of interest in the present paper, however, was to verify that the Bohm criterion was still valid in the presence of a magnetic field in this case. It was not assumed that the electron density was given by the Boltzmann relation, an assumption originally made by Bohm in his derivation of the criterion for sheath formation. Some insight can be gained by considering the ion and electron densities plotted against potential, for both the plasma and the sheath regions. It would appear that the result is a general one applicable to other situations.