A neural-network-based model of radio-frequency hollow cathode discharge characterized using particle-in-cell/Monte Carlo collision simulation

An understanding of the plasma dynamics of radio-frequency (RF) hollow cathode discharges (HCDs) at low to moderate pressures is important due to their wide range of applications. A HCD consists of a hollow cylindrical cavity in the RF-powered cathode separated from a grounded electrode by a dielectric. In RF HCDs, RF sheath heating can play a significant role in plasma production in addition to secondary electrons. In this study, a single hollow cathode hole is modeled using the particle-in-cell/Monte Carlo collision (PIC-MCC) technique at low pressure, where kinetic effects are important. Characterization of a single hollow cathode using PIC-MCC simulation is, however, computationally expensive. For improved computational efficiency, a neural network modeling framework has been developed using the temporal variations of applied RF voltages as input and the electrode current as output. A space-filling design for computational experiments is used, where the variables include the RF voltage at the fundamental frequency, RF voltage at the second harmonic, and their phase difference. The predictions of the electrode current using the trained neural network model compare well with the results of the PIC/MCC simulations, but at a significantly lower computational cost. The neural network model predicts the current very well inside the training domain, and reasonably well even outside the training domain considered in this study.