Benchmarking-Charge-Conserving, Unconditionally Stable, Electromagnetic Finite-Element Particle-in-Cell Codes: Validating 3D nonlinear multiphysics simulations

To a large extent, particle-in-cell (PIC) methods have become the default means of understanding plasma physics. As a result, there are a spate of codes, public and otherwise, that are heavily used. Most of these codes fall under two categories: 1) they largely deal with electrostatic problems or 2) are 1D/2D. As a result, there is a paucity of benchmarking tests that can be used to validate codes and methods that are used to analyze 3D problems. This is especially true when designing methods that seek to break conventional analysis methods, like using unstructured meshes or implicit time-stepping schemes. This review seeks to address this need. We present a number of results that one can use to validate and benchmark 3D electromagnetic finite-element method PIC (EM-FEMPIC) codes for collisionless plasma and beam dynamics systems. Three test cases are presented in significant detail, including beam expansion due to static space-charge expansion, the acceleration of a relativistic bunch by an radio-frequency (RF)-accelerating structure, and benchmarks of accuracy and energy conservation of the particle push. The presented results are compared against either analytical data or those from other codes.