Particle-in-Cell Simulations of Plasmas and Anomalous Transport on Advanced Research Computing Systems

Dense plasmas are commonly used in lighting sources, plasma arcs for welding and cutting, and for medicine applications. Low density and high-temperature plasmas, with combinations of electric and magnetic fields for confinement and particle acceleration, have applications in material deposition, space propulsion, and fusion reactors. Plasma dynamics is influenced by both electron and ion thermal motion and electromagnetic interactions. This leads to collective and complex behaviors which develop nonlinearly in time and include many kinetic phenomena like wave-particle trapping, and nonlinear turbulent wave structures. These turbulent structures tend to modify the plasma's electric conductivity and energy transport. Characterizing these turbulent behaviors and determining the transport properties remain active research areas. Electric conductivity, for example, exceeds classical values by many orders of magnitude. Simulations studying these plasmas require fully nonlinear kinetic techniques. This thesis explores the application of advanced research computing (ARC) simulations of plasmas relevant to plasma processing technologies and plasma propulsion using the kinetic Particle-In-Cell (PIC) method. The aim of the thesis is to both characterize the performance of specific numerical simulation tools such as Electrostatic Direct Implicit Particle-In-Cell (EDIPIC) plasma simulation code within the environment of ARC clusters such as those of the Digital Research Alliance of Canada (formerly Compute Canada) and investigate the characteristics of the highly turbulent and nonlinear plasma state expected in a particular type of $\boldsymbol{E} \times \boldsymbol{B}$ plasma devices. The thesis provides general discussion of fundamental plasma properties, the $\boldsymbol{E} \times \boldsymbol{B}$ Hall thruster device, and kinetic PIC simulation technique. We review the compute time and dataset scaling of parallel simulation codes, propose a method of selecting the optimal number of cores for a simulation run, and perform a full scaling analysis on EDIPIC. The optimal core calculation is shown to be valid using EDIPIC's scaling analysis results. Using EDIPIC, the electron cyclotron drift instability and associated anomalous electron transport in Hall thrusters has been investigated. We find that electron transport varies directly with the applied $\boldsymbol{E}$ demonstrating constant anomalous mobility. We also find that the dominant wavelength remains at the cyclotron resonance as $\boldsymbol{E}$ and $\boldsymbol{B}$ is varied confirming the cyclotron nature of the instability. The results of our EDIPIC simulations are described in a comparative study comparing several PIC and Vlasov codes, with the goal of clarifying the level and the role of numerical and statistical noise in kinetic plasma simulations. We demonstrate that the noise in the initial macroparticle distribution contributes significantly to the performance of PIC simulations. We find a reduction in initial noise improves accuracy, but, counter-intuitively, increases simulation noise. We also demonstrate that Vlasov codes maintained accuracy while having a noise performance magnitudes better than that of the PIC codes.

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