The plasma–sheath boundary: its history and Langmuir's definition of the sheath edge

Abstract

The introduction of the terms sheath in 1923 and plasma in 1928 by Langmuir is described, followed by their use in the Tonks and Langmuir theory of the positive column at low pressures in 1929. Attention is drawn to the development of Langmuir's ideas during the period from 1923 to 1929. The well-known Bohm criterion for sheath formation, published in 1949, is shown to be closely related to the earlier work of Tonks and Langmuir. The much-used version of the Bohm criterion with the equality sign is obtained by employing the two-scale theory of the plasma and sheath, for the case where λD/L → 0.A generalized Bohm criterion is obtained by introducing the ion velocity distribution; the resulting expression can be understood by considering the propagation of ion-acoustic waves. The plasma–sheath boundary is found to be a sonic surface. Other generalizations of the Bohm criterion are given, including a mixture of positive ions, the presence of negative ions and a non-Maxwellian electron velocity distribution.