The fluid-kinetic hybrid electron model for global electromagnetic gyrokinetic particle simulations has been formulated in toroidal geometry using magnetic coordinates, providing the capabilities to describe low frequency processes in electromagnetic turbulence with electron dynamics. In the limit of long wavelength and no parallel electric field our equations reduce to the ideal magnetohydrodynamic equations. The formulation has been generalized to include equilibrium flows. The equations for zonal components of electrostatic and vector potentials have been derived, demonstrating the electron screening of the zonal vector potential.
The beta-induced Alfvén eigenmode ͑BAE͒ in toroidal plasmas is studied using global gyrokinetic particle simulations. The BAE real frequency and damping rate measured in the initial perturbation simulation and in the antenna excitation simulation agree well with each other. The real frequency is slightly higher than the ideal magnetohydrodynamic ͑MHD͒ accumulation point frequency due to the kinetic effects of thermal ions. Simulations with energetic particle density gradient show exponential growth of BAE with a growth rate sensitive to the energetic particle temperature and density. The nonperturbative contributions by energetic particles modify the mode structure and reduce the frequency relative to the MHD theory. The finite Larmor radius effects of energetic particles reduce the BAE growth rate. Benchmarks between gyrokinetic particle simulation and hybrid MHD-gyrokinetic simulation show good agreement in BAE real frequency and mode structure.
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