Analytic solution for a joint Bohm sheath and pre-sheath potential profile

Abstract

An analytic solution is presented in this paper for the electric potential near a wall in a confined plasma. This is well fitted for both the sheath and pre-sheath regions. In the sheath region, the potential is well adapted to the differential equation proposed by Bohm. In the pre-sheath region, the potential is also well suited, decaying to zero electric field in the plasma, which is a physical condition. The potential is also valid for any value of the parameter K measuring the dimensionless Bohm velocity.