Continuum damping of low-n toroidicity-induced shear Alfvén eigenmodes

The effect of resonant continuum damping is investigated for the low-mode-number, toroidicity-induced, global shear Alfvén eigenmodes, which can be self-excited by energetic circulating alpha particles in an ignited tokamak plasma. Resonant interaction with the shear Alfvén continuum is possible for these eigenmodes, especially near the plasma periphery, leading to significant dissipation, which is typically larger than direct bulk plasma dissipation rates. Two perturbation methods are developed for obtaining the Alfvén resonance damping rate from the ideal fluid zeroth-order shear Alfvén eigenvalue and eigenfunction. In both methods the real part of the frequency is estimated to zeroth order, and the imaginary part, which includes the damping rate, is then obtained by perturbation theory. One method, which is applicable when the eigenfunction is nearly real, can readily be incorporated into general magnetohydrodynamic (MHD) codes. In the second method, the zeroth-order eigenfunctions may be complex; however, the application of this method to general MHD codes needs more detailed development. Also, an analytical estimate is found for the next-order real frequency shift of the fluid global Alfvén mode. Analytical and numerical studies of this continuum damping effect indicate that it can substantially reduce the alpha particle-induced growth rate. Thus, either it is possible to prevent instability or, if unstable, to use the Alfvén resonance damping to estimate the saturation amplitude level predicted from quasilinear theory.