Improved determination of the plasma potential and the sheath radius of positive cylindrical and spherical Langmuir-probes

Abstract

The probe current can be described by a formula from the orbital motion theory given by Langmuir. The probe current depends on the voltage difference between the probe and the plasma, the electron temperature, the probe radius and the sheath radius. On the other hand, an extension of Langmuirs formula for the space charge limited current is presented. In this extended formula the velocities of the electrons entering the sheath is accounted for. For several probe characteristics — with well-defined plasma potentials — the orbital motion formula together with the corrected space charge formula have been checked. A good agreement exists. On the other hand, in the case of a probe characteristic with a badly known plasma potential, the two formulas can be used together to determine the plasma potential and the sheath radius.