Axisymmetric Alfvén modes induced by energetic particles in tokamak plasmas

Axisymmetric Alfvén modes in the presence of energetic ions are studied using the MHD-kinetic hybrid model for tokamak plasmas. The general dispersion relation of continuous spectra is derived for the coupled m=0,±2 poloidal harmonics. The dispersion relation is analyzed for the single pitch angle slowing down distribution of well circulating energetic particles. In addition to the conventional axisymmetric Alfvén modes existing in the pure MHD description, axisymmetric Alfvén modes are also induced by the energetic ions if the pressure ratio between the energetic ions and the magnetic energy density is larger than a critical value, and the transit frequency of the energetic ions is in resonance with the emerging Alfvén modes. The existence of global Alfvén eigenmodes is also discussed.