Kinetic modeling of cathode plasma formation and expansion in a pulsed high-voltage anode–cathode gap

A one-dimensional (1D), relativistic, particle-in-cell Monte Carlo collision (PIC–MCC) model is developed to study cathode plasma formation and expansion in pulsed, high-voltage diodes. The 1D PIC–MCC simulation model accounts for physical processes, such as Fowler–Nordheim field emission with field enhancement, Coulomb collisions, and electron–neutral collisions (e.g., electron-impact ionization), assuming a neutral gas layer of atomic hydrogen due to outgassing near the cathode surface. A Langevin approach is used to simulate Coulomb collisions for both electron–ion and electron–electron collisions in the presence of a drift velocity between electrons and ions. A pulsed DC voltage of 600 kV is applied to a 1 cm anode–cathode gap over 100 ns, which generates a quasineutral plasma density near the cathode that expands toward the anode, similar to a moving shock front. The extracted current agrees with the relativistic space charge limited theory. The cathode plasma expansion rate is found to be approximately 1.83 cm/μs, which is consistent with experimental observations. In the simulation, the impact of Coulomb collisions is also assessed, showing that the expansion rate is slower if Coulomb collisions are neglected due to the lack of thermalization processes that lead to lower plasma temperature. Additionally, stochastic bursts of current spikes are observed depending on the simulation conditions. Current spikes have been observed in experiments, and their associated mechanism is discussed.