Effects of the Second Harmonic and Plasma Shaping on the Geodesic Acoustic Mode

The effects of second harmonics of the density and temperature perturbations on the linear Geodesic Acoustic Mode (GAM) frequency and non-linear generation of the GAM are investigated, using a fluid model. We show that the second harmonics contribute to the frequency through the density gradient scale length and the wave number of the GAM. In addition, the linear frequency of the GAM is generally increased by coupling to the higher harmonic.