Nonlinear Saturation of Toroidal Alfvén Eigenmodes via Ion Compton Scattering

The nonlinear interactions of high mode number toroidal Alfv\'en eigenmodes (TAE), mediated via Compton scattering off the bulk ions, are investigated. It is shown that nonlinear J_⊥×B_⊥ ponderomotive force produced by TAE's interaction drives sound-wave-like density fluctuation with low phase velocity which can resonantly interact with the bulk ion parallel motion. Consequently, fluctuation energy of TAE's is transferred to lower frequency and eventually absorbed by linearly stable TAE's near the lower shear Alfv\'en continuum, leading to nonlinear saturation. An explicit expression for the saturated magnetic fluctuation amplitude is derived.