Characteristics of RF Hollow Cathode Discharge at Moderate Pressure: Hybrid Plasma Simulation and Machine Learning Model Development

Radio-frequency (RF) hollow cathode discharges (HCD) at moderate pressures have gained significance for advanced plasma processes. HCDs form in cylindrical cavities in the cathode. An array of such cavities can be used to create large area HCDs. Under certain conditions plasma in hollow cavities becomes more intense. In this study, a single hollow cathode hole is simulated using a hybrid plasma model. The model includes continuity equations for charged and neutral species, drift-diffusion approximation for electron flux, momentum conservation equation for ions, and Poisson equation. A Monte Carlo model for secondary electrons is used to accurately compute production rates of species, which are coupled to the fluid plasma model. RF hollow cathode behavior is simulated for different design and operating conditions. The plasma penetration inside hollow cathode hole is enhanced depending on pressure and hole size. The plasma enhancement due to RF sheath heating with increase in frequency, and secondary electron emission have been explored synergistically. Hybrid plasma simulation being computationally expensive, a surrogate modeling framework is developed based on recurrent neural network, using LSTM (Long Short-Term Memory) based closure. Different methodologies have been explored to train and validate LSTM network. The prediction of trained network compares well with that of underlying physical model at different conditions, improving the applicability of plasma model for design and optimization purposes.