Nonlinear excitation of geodesic acoustic mode by collisionless trapped electron mode

Excitation of geodesic acoustic mode (GAM) by collisionless trapped electron mode (CTEM) is studied within the framework of nonlinear gyrokinetic theory. The dispersion relation describing GAM excitation by drift wave turbulence valid for arbitrary k perpendicular to rho(i) is derived. Here, k perpendicular to and rho(i) are, respectively, perpendicular wave vector and thermal ion Larmor radius. It is found that the parametric decay process of CTEM into a GAM and a CTEM sideband is unstable in both small and large k perpendicular to rho(i) regimes due to, respectively, ion and trapped electron nonlinearity. For moderate k perpendicular to rho(i), however, there exists a negligible-GAM-excitation state where ion and trapped electron nonlinearities cancel each other.