Code Development of a 3D Finite Element Particle-In-Cell Code with Adaptive Meshing

Abstract

Summary form only given. Calabazas Creek Research, Inc., in association with U.C. Berkeley (UCB), is developing a fully relativistic, 3D, one-species, particle-in-cell simulation code with adaptive finite element meshing. This initial version will simulate particles in quasi-static fields, which are solved by the finite element methods. In quasi-static PIC analysis, all particles are synchronized in time, and the electric and magnetic fields are resolved at every time step. In later versions, the vector finite element with adaptive meshing technology will be used to solve the complete Maxwell's equations for the electromagnetic fields as they evolve in time in a fully explicit approximation. Currently, most PIC codes use finite difference techniques with fixed, orthogonal, structured elements. Finite element meshes, compared to finite difference meshes, allows more accurate modelling of non-orthogonal boundaries, eliminating the short wavelength noise introduced by orthogonal mesh stair step representations. Adaptive meshing, compared to fixed mesh models, may reduce the number of elements by 2-3 orders of magnitude while maintaining or improving accuracy, particularly when small features translate spatially. Similar improvements in PIC modelling could result in dramatic reduction in computation size and execution times, while allowing improved design and analysis. We will demonstrate uniform cold and warm plasma oscillations under influence of electric field and magnetic field. In addition, we will discuss quiet start methods for loading the (x, v) phase space for nonuniform warm plasmas for unstructured meshes including the inversion of the Maxwell-Boltzmann distribution using the Box-Muller method and the Maxwellian velocity distribution numerically to particle velocities, and the Markov chain Monte Carlo numerical integration scheme to load arbitrary particle densities