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A set of electromagnetic formulations with gyrokinetic ions and drift kineticelectrons for global gyrokinetic simulations has been formulated and verifiedin the framework of Gyrokinetic Toroidal Code (GTC), which is particularlysuitable for the low-frequency electromagnetic modes including drift waves,Alv\'{e}n Eigenmodes and MHD modes. This gyrokinetic simulation model canreduce to the ideal MHD model in the long wavelength limit, and recover thewell-known MHD dispersion relation. Especially, the magnetic compressionperturbation and the equilibrium current are carefully treated in this model.Furthermore, the detailed implementation of the equations in Boozer coordinatesystem is provided. The internal kink mode simulations in DIII-D and ITERtokamaks using this model have been successfully bench-marked with otherkinetic and MHD codes. The physical model has also been used to generate adatabase to train the machine learning surrogate model of GTC.

Formulations and verification of gyrokinetic simulation of kinetic-MHD processes in toroidal plasmas