Nonlinear Particle-in-Cell simulation of Toroidal Alfven Eigenmodes with gyrokinetic ions and drift-kinetic electrons

The GEM code is used to study the nonlinear evolution of reverse shear Alfven eigenmodes (RSAE) driven by energetic particles. Recent simulations with fluid electrons [Y.~Chen  et. al. Physics of Plasmas 25, 032304 (2018)] show that zonal structures are force generated, and reduce the saturation amplitude. The reduction is not caused by the zonal flow shearing of the RSAE, but by the force-generated n=0 component in the thermal ion distribution function and the electron density. These n=0 perturbations lead to nonlinear evolution of the RSAE mode structure and enhance damping. Here we continue to investigate this problem with kinetic electrons. Although the problem, in essence, involves a single-n RSAE excited by resonant beam particles, we find it necessary to include harmonics of the unstable RSAE in PIC simulations. The reason is, parallel electron current of high-n harmonics is nonlinearly generated and causes Joule heating and damping of RSAE, if the high-n EM fields are removed.  Low-n modes are difficult with kinetic electrons. To verify simulation results, we have implemented Mishchenko's mixed variable method with pull-back transformations, and will compare it with the split-weight scheme.