Validating experimental and theoretical Langmuir probe analyses

Abstract

Analysis of Langmuir probe characteristics contains a paradox in that it is unknown a priori which theory is applicable before it is applied. Often theories are assumed to be correct when certain criteria are met although they may not validate the approach used. We have analysed the Langmuir probe data from cylindrical double and single probes acquired from a dc discharge plasma over a wide variety of conditions. This discharge contains a dual-temperature distribution and hence fitting a theoretically generated curve is impractical. To determine the densities, an examination of the current theories was necessary. For the conditions where the probe radius is the same order of magnitude as the Debye length, the gradient expected for orbital-motion limited (OML) is approximately the same as the radial-motion gradients. An analysis of the ‘gradients’ from the radial-motion theory was able to resolve the differences from the OML gradient value of two. The method was also able to determine whether radial or OML theories applied without knowledge of the electron temperature, or separation of the ion and electron contributions. Only the value of the space potential is necessary to determine the applicable theory.