  Spontaneous nonlinear excitation of geodesic acoustic mode (GAM) by toroidal
Alfv\'en eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It
is found that, the nonlinear decay process depends on thermal ion \beta value.
Here, \beta is the plasma thermal to magnetic pressure ratio. In the low-\beta
limit, TAE decays into a GAM and a lower TAE sideband in the toroidicity
induced shear Alfv\'en wave continuous spectrum gap; while in the high-\beta
limit, TAE decays into a GAM and a propagating kinetic TAE in the continuum.
Both cases are investigated for the spontaneous decay conditions. The nonlinear
saturation levels of both GAM and daughter wave are derived. The corresponding
power balance and wave particle power transfer to thermal plasma are computed.
Implications on thermal plasma heating are also discussed.
