Improved analysis techniques for cylindrical and spherical double probes

A versatile double Langmuir probe technique has been developed by incorporating analytical fits to Laframboise's numerical results for ion current collection by biased electrodes of various sizes relative to the local electron Debye length. Application of these fits to the double probe circuit has produced a set of coupled equations that express the potential of each electrode relative to the plasma potential as well as the resulting probe current as a function of applied probe voltage. These equations can be readily solved via standard numerical techniques in order to determine electron temperature and plasma density from probe current and voltage measurements. Because this method self-consistently accounts for the effects of sheath expansion, it can be readily applied to plasmas with a wide range of densities and low ion temperature (T(i)∕T(e) ? 1) without requiring probe dimensions to be asymptotically large or small with respect to the electron Debye length. The presented approach has been successfully applied to experimental measurements obtained in the plume of a low-power Hall thruster, which produced a quasineutral, flowing xenon plasma during operation at 200 W on xenon. The measured plasma densities and electron temperatures were in the range of 1 × 10(12)-1 × 10(17) m(-3) and 0.5-5.0 eV, respectively. The estimated measurement uncertainty is +6%∕-34% in density and +∕-30% in electron temperature.