Verification of the MOOSE-based finite-element kinetic plasma simulation capability in FENIX

As magnetic confinement fusion (MCF) matures there is a need to accurately model plasma material interactions between the fusion plasma edge and plasma-facing components. The plasma edge can be modeled with a kinetic representation. To address this, a particle-in-cell (PIC) functionality is being developed within the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) as a part of the Fusion Energy Integrated Multiphys-X (FENIX) framework. This PIC capability serves as a general-purpose low temperature plasma modeling platform. This will enable massively parallel PIC simulations on unstructured meshes using the finite-element method. PIC simulations require several new capabilities: particle initialization, particle movement (updating positions and velocities) on an unstructured mesh, charge/current density mapping to the mesh, solution of field variables (based on particle locations), and mapping of field variables to particles. Moreover, to meet the high software quality assurance requirements of MOOSE, a suite of verification problems is being developed, including convergence studies that demonstrate particle initialization following the expected convergence rate of O(N^-½) to a known solution with increasing particle count, N. Single particle motion follows second-order accuracy in time, as expected for the Boris algorithm, and the electrostatic potential solves with second-order accuracy, as expected for the finite-element basis functions being used.