A New Langmuir Probe Analysis Algorithm Based on Wavelet Transforms to Obtain the Electron Energy Distribution Function of a Bi-Maxwellian Plasma

Abstract

A new algorithm to analyze digitized Langmuir probe (LP) data was developed with wavelet transforms to provide the electron energy distribution function (EEDF) for bi-Maxwellian plasmas. Because most algorithms to analyze probe data have been developed with the Druyvesteyn formula, which is based on the second derivative of the current with respect to the probe voltage, the accuracy of the analysis is very sensitive to the noise level during the acquisition of the data's derivative. Especially, the number of hot electrons in the bi-Maxwellian plasma is small enough to compare the noise level, and the noise-filtering method is the kernel in the development of the algorithm to analyze the bi-Maxwellian EEDF. Here, a bi-orthogonal wavelet and continuous wavelet transforms are chosen for the de-noising and the differentiation processes, respectively. This provides the filtered data with minimum loss of important information. Artificial LP data sets composed of electrons were generated with various bulk and hot temperatures, and the developed algorithm was evaluated for various white noise levels. For the case of noise levels 10 time,,; ion saturation current, the plasma parameters, such as the population of hot electrons and the temperatures of hot and bulk electrons, were accurately analyzed with only a few percent deviations from the input.