On the Bohm criterion in the presence of a magnetic field

Abstract

The present paper deals with a particular case involving a magnetic field, namely that of a positive column situated in an axial magnetic field, and it is shown that the Bohm criterion still holds for the normal component of the ion velocity at the plasma boundary. This result is of considerable interest because the Boltzmann relation for the electron density has not been assumed. It can be recalled that the criterion was originally derived by Bohm using the Boltzmann relation for the electron density. In the present case a Boltzm ann gradient conditionhas been found at the plasma boundary which leads to the usual Bohm velocity. 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.