Properties of energetic-particle continuum modes destabilized by energetic ions with beam-like velocity distributions

Properties of energetic-particle continuum modes (EPMs) destabilized by energetic ions in tokamak plasmas were investigated using a hybrid simulation code for magnetohydrodynamics and energetic particles. The energetic ions are assumed to have beam-like velocity distributions for the purpose of clarifying the dependence on energetic ion velocity. It was found that for beam velocities lower than the Alfv?n velocity, the unstable modes are EPMs while the toroidal Alfv?n eigenmodes are unstable for the beam velocities well above the Alfv?n velocity. The EPMs destabilized by the copassing energetic ions and those destabilized by the counterpassing energetic ions differ in primary poloidal harmonics and spatial locations. The frequencies of the EPMs are located close to the shear Alfv?n continuous spectrum when they are compared at the spatial peak locations of the primary poloidal harmonic or compared at the spatial tails if the primary poloidal harmonic is m=1. The frequencies of the EPMs were carefully compared with the energetic-ion orbital frequencies. It was found that the frequencies of the EPMs are in good agreement with the energetic-ion orbital frequencies with a correction for the toroidal circulation frequency. This demonstrates that the energetic-ion orbital frequency determines the EPM frequency

Linear and nonlinear particle-magnetohydrodynamic simulations of the toroidal Alfvén eigenmode

Linear and nonlinear particle-magnetohydrodynamic (MHD) simulation codes are developed to study interactions between energetic ions and MHD modes. Energetic alpha particles with the slowing-down distribution are considered and the behavior of n = 2 toroidal Alfv?n eigenmodes (TAE modes) is investigated with the parameters pertinent to the present large tokamaks. The linear simulation reveals the resonance condition between alpha particles and TAE mode. In the nonlinear simulation, two n = 2 TAE modes are destabilized and alpha particle losses induced thereby are observed. Counterpassing particles are lost when they cross the passing-trapped boundary. They are the major part of lost particles, but trapped particles are also lost appreciably