Verification Of A Fully Implicit Particle-In-Cell Method For The V(Parallel To)-Formalism Of Electromagnetic Gyrokinetics In The Xgc Code

A fully implicit particle-in-cell method for handling the v(parallel to)-formalism of electromagnetic gyrokinetics has been implemented in XGC. By choosing the v(parallel to)-formalism, we avoid introducing the nonphysical skin terms in Ampere's law, which are responsible for the well-known "cancellation problem" in the p(parallel to)-formalism. The v(parallel to)-formalism, however, is known to suffer from a numerical instability when explicit time integration schemes are used due to the appearance of a time derivative in the particle equations of motion from the inductive component of the electric field. Here, using the conventional delta f scheme, we demonstrate that our implicitly discretized algorithm can provide numerically stable simulation results with accurate dispersive properties. We verify the algorithm using a test case for shear Alfven wave propagation in addition to a case demonstrating the ion temperature gradient-kinetic ballooning mode (ITG-KBM) transition. The ITG-KBM transition case is compared to results obtained from other delta f gyrokinetic codes/schemes, whose verification has already been archived in the literature.