Robust Extraction of Electron Energy Probability Function via Neural Network-Based Smoothing

Abstract

Accurate determination of the electron energy probability function (EEPF) is vital for understanding electron kinetics and energy distributions in plasmas. However, interpreting Langmuir probe current-voltage (I-V) characteristics is often hindered by nonlinear sheath dynamics, plasma instabilities, and diagnostic noise. These factors introduce fluctuations and distortions, making second derivative calculations highly sensitive and error-prone. Traditional smoothing methods, such as the Savitzky-Golay (SG) filter and AC modulation techniques, rely on local data correlations and struggle to differentiate between noise and meaningful plasma behavior. In this study, we present a neural network-based machine learning approach for robust EEPF extraction, specifically designed to address the challenges posed by non-Maxwellian electron energy distributions. A multi-layer perceptron combined with ensemble averaging captures the global structure of the I-V characteristics, enabling adaptive and consistent smoothing without compromising physical fidelity. Compared to conventional SG filtering, the proposed method achieves superior smoothing of the second derivative, resulting in more stable and accurate EEPF reconstruction across the entire electron energy range. This capability confers a strong diagnostic advantage in beam-driven, low-pressure, or other non-equilibrium plasma conditions, where accurate characterization of non-Maxwellian EEPFs is essential.