A High-order piecewise field-aligned triangular finite element method for electromagnetic gyrokinetic particle simulations of tokamak plasmas with open field lines

Abstract

A high-order piecewise field-aligned triangular finite element method is developed and implemented for global electromagnetic gyrokinetic particle-in-cell simulations of tokamak plasmas with open field lines. The approach combines locally field-aligned finite element basis functions with unstructured $C^{1}$ triangular meshes in cylindrical coordinates, enabling whole-volume simulations with substantially reduced computational effort, while avoiding the grid distortion associated with globally field-aligned coordinates and the associated singularity at the separatrix of diverted plasmas. The formulation is compatible with both $\delta f$ and full-$f$ models and employs mixed-variable representations, along with a generalized pullback scheme, to control numerical cancellation in electromagnetic simulations. The method is implemented in the TRIMEG-C1 code and demonstrated using linear and nonlinear electromagnetic simulations of the TCV-X21 configuration. The results indicate that the approach accurately captures the key features of electromagnetic ion-temperature-gradient and kinetic ballooning mode physics, including the separatrix regions in the simulation, thereby providing a robust framework for whole-volume electromagnetic gyrokinetic simulations in realistic tokamak geometries.