Generation of geodesic acoustic mode by drift wave turbulence in tokamaks with toroidal rotation

Generation of geodesic acoustic mode by drift wave turbulence spectrum has been investigated in the toroidally rotating tokamak plasmas using the wave kinetic equation. Using the spectral function of the small scale turbulence, which is defined by the Wigner function, the form of the generalized wave action invariant of the drift wave turbulence in tokamaks with toroidal rotation is derived. Then from the wave kinetic equation, the nonlinear dispersion relation of the geodesic acoustic mode driven by the drift wave turbulence with toroidal rotation is given, which is applicable for any form of the wave action invariant. Finally, with the wave action function taken to be the Dirac function, the result of the wave kinetic approach is compared with that of the parametric approach, and it is shown that the form of the growth rate of the geodesic acoustic mode with toroidal rotation is similar to that obtained by the parametric approach.