3D PIC-DSMC Simulation of Arc Initiation: A Cautionary Tale of Strongly Coupled Plasmas*

As HPC computational resources increase, 3D simulations of vacuum arc initiation via the Particle-In-Cell (PIC) Direct Simulation Monte Carlo (DSMC) method are becoming more and more feasible. Using Sandia’s PIC-DSMC code EMPIRE, we have performed simulations of cathode spot plasma initiation and encountered a variety of numerical challenges. Prior models of electrode vaporization have found that the typical electrode-gas density is nearly solid density close (~100 nm) to the electrode [1] and is nearly completely ionized as the neutral gas expands from the near-electrode region. The ion densities (>10²⁶ m^-3) and temperatures (~2000K) result in a strongly coupled plasma (Γ_i > 10) and a sub-nm mesh size is required to avoid numerical grid heating. However, this results in less than one physical particle per element resulting in “late” time (~100ω_p^‑1) numerical heating. If we use particle weights less than one or accept numerical heating at late times by increasing the mesh size, then we will not capture the physical disorder induced heating (DIH) that should occur [2]. Furthermore, at these densities DSMC’s assumption of a dilute gas is extremely questionable and even if that model-form error is small, the nonlinear relationship between ionization rate and the background E/n will lead to wrong ionization rates due to unphysical spikes in the density. The present work will discuss these limitations and challenges in more depth as well as the role that DIH and charge exchange play in the evolution and expansion velocity of the cathode spot plasma. Similar concerns and challenges exist for initiation of atmospheric pressure arcs and the present work will focus on Artificial Correlation Heating in the streamer causing an instability where the plasma density runs away if one naively just refines the mesh without corresponding reduction in the particle weights [2].

 

[1] Koitermaa et al., “Simulating vacuum arc initiation by coupling emission, heating, and plasma processes”, Vacuum 224 113176 (2024).

[2] Acciarri et al., “When should PIC simulations be applied to atmospheric pressure plasmas? Impact of correlation heating”, PSST 33 035009 (2024).