A Framework for Charge Conserving Relativistic EM-FEMPIC

Recent advances in electromagnetic Finite Element Particle-in-Cell (EM-FEMPIC) simulations have made it possible to construct a simulation scheme that exactly satisfies Gauss’ Laws while using implicit time-marching schemes. In particular, one can now define a set of rules will allow any evolution scheme that obeys them to exactly conserve charge. However, these methods have thus far only been applied and studied for non-relativistic PIC schemes with rudimentary polynomial stencils for particle evolution. Here we seek to advance the state-of-the-art by constructing a relativistic PIC. To do so, we will exploit the advantages offered by our framework that decouples field evolution (via unconditionally stable time stepping methods) and equation of motion for particle evolution (or impressed current). Here we will exploit exponential predictor-corrector schemes to create a self-consistent update scheme, and examine both improved accuracy and conservation of physical quantities (charge and momentum).