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We have developed a hybrid code GMEC: Gyro-kinetic Magnetohydrodynamics (MHD) Energetic-particle Code that can numerically simulate energetic particle-driven Alfvén eigenmodes and energetic particle transport in tokamak plasmas. In order to resolve the Alfvén eigenmodes with high toroidal numbers effectively, the field-aligned coordinates and meshes are adopted. The extended MHD equations are solved with the five-point finite difference method and the fourth-order Runge–Kutta method. The gyrokinetic equations are solved by particle-in-cell method for the perturbed energetic particle pressures that are coupled into the MHD equations. Up to now, a simplified version of the hybrid code has been completed with several successful verifications, including linear simulations of toroidal Alfvén eigenmodes and reversed shear Alfvén eigenmodes.
Liu et al. (2024) studied this question.