Serendipity shape functions in NIMROD's delta-f PIC approach to energetic particle physics

Wave-particle resonances can have significant effects on plasma stability even in the case of small, resonant sub-populations. In tokamak plasmas, long-wavelength modes interact with the second-adiabatic moment of EPs produced by neutral beams, external RF sources, or fusion-produced alphas. This leads to uncertainty in plasma stability boundaries and enhanced EP particle transport. EP closures based on the PIC algorithm have long been used in extended MHD codes to capture this important physics. The extended MHD code NIMROD has both continuum and delta-f PIC [1] drift kinetic (DK) capability. Serendipity shape functions, up to sixth order, have been implemented in the delta-f PIC DK approach in an attempt to provide more accurate integration of particle trajectories. Such an approach may be vital for accurate integration near the separatrix of a diverted tokamak and for preserving the second-adiabatic invariant. Careful comparison of the performance of the serendipity shape functions against the bilinear, reduced set that is often used in NIMROD PIC simulations, and the full 2D Lagrange polynomials is presented. Improvements in accuracy, efficiency, and memory gain when using the serendipity set are also presented.