Advanced Algorithms for Particle-in-Cell Simulations of Low-Temperature Plasmas*

The particle-in-cell algorithm combined with Monte-Carlo collisions (PIC-MCC) is the de-facto technique for performing kinetic simulations of low-temperature plasmas. However, due to strict numerical resolution requirements, PIC simulations are currently too costly to perform fast and accurate prototyping of plasma devices. One approach to realizing this goal is to take advantage of modern heterogeneous computing architectures, including accelerator hardware such as GPUs. This has recently been realized for low-temperature plasma applications (Juhasz et. al. 2021) and we will show that these advantages extend to over 1,000 GPUs (Powis 2022). Despite advances, high computational cost still places full scale modeling of plasma devices tantalizingly out of reach. This motivates a return to the fundamentals of the PIC method, and exploration of algorithms to overcome the strict numerical requirements to significantly reduce simulation cost and realize accurate and rapid computational prototyping of plasma devices.

This presentation will focus on overcoming the restriction on cell size via the energy-conserving PIC algorithm, including the use of non-uniform grids (Lewis 1970). The Direct Implicit and fully implicit algorithms will be explored for overcoming restrictions on the simulation time step. A deeper analysis into the required number of particle-per-cell will also be explored, allowing us to define a more rigorous criterion for suitable resolution (Jubin et. al. 2024). These algorithms will be demonstrated on 1D (Powis & Kaganovich 2024) and 2D (Sun et. al. 2023) simulations of radio-frequency capacitively coupled plasma discharges relevant for silicon etching. Finally, a sub-cycled hyperbolic electromagnetic field solver will be explored as a faster and more scalable alternative to solving the elliptical Poisson equation. The advantages and disadvantages of each of these techniques will be discussed in depth and several other algorithms investigated by the low-temperature plasma community will be reviewed.

The author would like to thank Igor Kaganovich, Willca Villafana, Dmytro Sydorenko, Johan Carlsson, Stephane Ethier, Sierra Jubin, Alexander Khrabrov, Jian Chen, Haomin Sun, Alexander Khaneles, Grant Johnson and Maxwell Rosen for their contributions to this work.