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

Zhixin Lu; Guo Meng; Eric Sonnendruecker; Roman Hatzky; Giorgio Daneri; Gengxian Li; Peiyou Jiang; Klaus Reuter; Matthias Hoelzl

arXiv · 2602.03759

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

Zhixin Lu·Guo Meng·Eric Sonnendruecker·Roman Hatzky·Giorgio Daneri·Gengxian Li·Peiyou Jiang·Klaus Reuter·Matthias Hoelzl

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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.

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Zhixin Lu, Guo Meng, Eric Sonnendruecker, Roman Hatzky, Giorgio Daneri, Gengxian Li, Peiyou Jiang, Klaus Reuter, Matthias Hoelzl. 2026-02-03. A High-order piecewise field-aligned triangular finite element method for electromagnetic gyrokinetic particle simulations of tokamak plasmas with open field lines. https://arxiv.org/abs/2602.03759

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