Electromagnetic PIC simulations using finite elements on unstructured grids

Abstract

There is an increasing demand to use kinetic plasma simulations to model real plasma devices such as e-beam diodes, plasma torches, opening switches, and so on. With this demands comes the realization that standard simulation tools based on rectangular structured meshes are often too inflexible to accommodate real device geometries. To gain geometric flexibility, one typically must abandon structured rectangular meshes. Some have had considerable success by distorting the grid to conform to boundary-fitted curvilinear coordinates. This gives substantial flexibility while retaining a logically rectangular data structure. However, to achieve the greatest flexibility, an unstructured mesh is necessary. For the last several years, we have been engaged in designing electromagnetic particle-in-cell (PIC) simulations that can be performed on unstructured grids of triangles. We feel this is a powerful strategy for matching kinetic plasma simulations to real problem geometries. Unstructured meshes not only accommodate complicated boundary shapes with ease, but also allow extreme local refinement without affecting resolution elsewhere. The basic challenges to overcome in formulating EM-PIC on these new meshes are: (1) grid generation; (2) particle interpolation and tracking, and (3) field solution. In this paper we briefly describe our techniques and give a simple example.