Bayesian deconvolution for reconstructing the EEDF from Langmuir probe data

Obtaining the electron energy distribution function (EEDF) with intrusive diagnostics such as Langmuir probe (LP) is in general very challenging. Typically, this is done through double numerical differentiation of the probe current-voltage characteristic, which poses significant difficulties due to noise amplification. Traditional filtering and smoothing techniques often introduce arbitrary assumptions about the EEDF, which may unpredictably affect the results. This paper presents an innovative Bayesian deconvolution method that reconstructs the EEDF from LP data without requiring numerical or analog double differentiation. This approach allows for the estimation of plasma parameters while consistently accounting for the uncertainties in the inference. Additionally, it highlights correlations between model parameters which can, in turn, improve the quality of the experiments, by identifying quantities that require more accurate measurement. The methodology was validated with both synthetic data and real experimental measurements. In both cases, the method proved effective in reconstructing the EEDF, even in the presence of high noise levels in the probe characteristic. The probability distributions of the calculated plasma parameters were also consistent with the true values. Overall, the proposed Bayesian deconvolution method offers a fast and robust approach to reconstructing the EEDF from LP data. However, a more flexible parametrization of the unknown EEDFs is needed to capture all the features of the real distributions.