Geodesic mode spectrum modified by the energetic particles in tokamak plasmas

• Effect of a minor concentration of the energetic particles on GAM spectrum on geodesic modes is analyzed.
• The effect is treated by kinetic theory using shifted Maxwell electron distribution.
• A novel method of Jacobi functions is applied to solve the drift kinetic equation for the energetic bounce particles.
• The instability occurs due to its cross term of the ion diamagnetic drift with the current as well with energetic ion drift.
• Modification of GAM dispersion by effective mass renormalization due to trapped particle dynamics is found.

Effect of a minor concentration of the energetic particles on GAM spectrum in a tokamak is analyzed by drift kinetic theory taking into the account the electron current and diamagnetic drift. A novel method of Jacobi functions is applied to solve the drift kinetic equation for the energetic bounce particles in the limit of high bounce frequency in comparison with the GAM frequency. Using the Q-asymptotic of Jacobi function, it is shown that the energetic minority ions can form the continuum minimum/maximum at the NB or ICR power deposition maximum where the geodesic eigenmode may be excited. In this case, the electron current modeled by shifted Maxwell distribution overcomes the ion Landau damping threshold thus resulting in the GAM instability.