Particle in Cell solver with adaptive Cartesian Mesh: Simulations of Gas Breakdown and Streamer Formation

A new electrostatic Particle-in-Cell with Monte Carlo Collisions code with adaptive Cartesian mesh (ES-PIC-ACM) has been developed for simulation of low temperature plasmas. ESPIC-ACM has been validated for Capacitively Coupled Plasmas (CCPs) using the simplest firstorder accurate nearest grid point (NGP) technique and more accurate cloud-in-cell (CIC) methods. We have confirmed that the accuracy of our PIC-MCC strongly depends on the number of particles per cell (PPC). Only for PPC 2,000 do the calculated electron energy distributions (EEDs) and spatial distributions of plasma parameters converge for the CCP. To illustrate the adaptive mesh refinement (AMR) capabilities of ES-PIC-ACM, we performed simulations of gas breakdown between a point cathode and a planar anode with an interelectrode distance of 40 mm. This configuration was experimentally investigated in Ref. [1]. Simulations were first performed using the fluid plasma model described in Ref. [2], followed by a PIC model for the same conditions. Isosurfaces of electron density (at 10 m and 5×10 m levels), isolines (color) of electrostatic potential, and adapted mesh at 57 ns (left) and 33 (right) ns are shown in Fig. 1. For argon at 100 Torr, the number of super-particles were about 8M and 15M for applied voltages of 3.25 and 5 kV. At the higher applied voltage, breakdown occurs sooner (~35 ns vs. ~55 ns), higher electron densities are attained (as expected), and significant branching occurs. At the lower voltage, there is almost no branching. The results of the PIC and fluid simulations were quite different. The plasma channel predicted by the fluid model was narrower, the time when the ionization wave reached the anode surface (~90 ns) was larger, and there was no branching. The AMR capabilities of both PIC and fluid models were critical for efficient simulations of the breakdown dynamics. Although the results of the simulations are in qualitative agreement with the experimental observations, we were not able to simulate breakdown at the higher pressures used in the experiments, and could not simulate the experimentally observed return strike due to the very high computational cost of the PIC method under these conditions. A hybrid PIC-fluid model is being developed for streamer-spark-arc simulations.