Computational modeling of hysteresis between Townsend and glow regimes

A one-dimensional (1D) particle-in-cell Monte Carlo collision (PIC-MCC) model is developed to investigate the mechanisms of hysteresis between the Townsend and glow regimes in a DC discharge. First, a ballast resistor is included in the PIC-MCC model to perform forward and backward voltage sweep (i.e., increase and decrease the applied voltage). When the applied voltage is larger than the breakdown voltage, transition from Townsend to glow discharges is observed. When decreasing the applied voltage from the glow regime, the discharge voltage between the anode-cathode gap can be smaller than the breakdown voltage, resulting in a hysteresis, which is consistent with experimental observations. Next, the PIC-MCC model is used to investigate the self-sustaining voltage in the presence of finite initial plasma densities between the anode-cathode gap. The self-sustaining voltage decreases with increased initial plasma density due to the space charge effects and saturates above a certain initial plasma density. The steady-state plasma profiles are discussed to understand how the plasma resistivity changes. Finally, it is demonstrated that the hysteresis is mitigated when field emission is dominant, which is also consistent with experimental observations.