Verification of a fully implicit particle-in-cell method for the v ?-formalism of electromagnetic gyrokinetics in the XGC code

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