Full f and δ f gyrokinetic particle simulations of Alfvén waves and energetic particle physics

Abstract

In this work, we focus on the development of the particle-in-cell scheme and its application to the studies of Alfvén waves and energetic particle (EP) physics in tokamak plasmas. The δ f and full f schemes are formulated on the same footing adopting mixed variables and the pullback scheme for electromagnetic problems. The TRIMEG-GKX code (Lu et al 2021 J. Comput. Phys. 440 110384) has been upgraded using cubic spline finite elements and full f and δ f schemes. The toroidal Alfvén eigenmode (TAE) driven by EPs has been simulated for the International Tokamak Physics activity (ITPA)-TAE case featured by a small electron skin depth ∼ 1.18 × 10 − 3 m , which is a challenging parameter regime for electromagnetic simulations, especially for the full f model. The simulation results using the δ f scheme are in good agreement with previous work. Excellent performance of the mixed variable/pullback scheme has been observed for both full f and δ f schemes. Simulations with mixed full f EPs and δ f electrons and thermal ions demonstrate the good features of this novel scheme in mitigating the noise level. The full f scheme is a natural choice for EP physics studies, which allows for large variations of EP profiles and distributions in velocity space, providing a powerful tool for kinetic studies using realistic experimental distributions related to intermittent and transient plasma activities.