Effect of finite length on the current–voltage characteristic of a cylindrical Langmuir probe in a multidipole plasma chamber

Abstract

Cylindrical probes of finite length are shown to collect an electron current that increases more quickly with voltage than in the ideal orbital motion limited theory. For thin probes in a hot filament-generated plasma confined by a multipole arrangement of magnets, the strength of this effect varies inversely with the probe length and is significant even for probes in excess of 50 Debye lengths long. Modelling the excess current as being collected on the end by an ideal hemispherical probe (as has been done for ion collection) fails to accurately describe the experimental data. Instead a semi-empirical power law fitting first suggested by Sudit and Woods (1994 J. Appl. Phys. 76 4488) has been used. The exponent varies strongly with both the non-dimensional probe length and the probe radius. An approximate analytical expression for this exponent is presented.