Plasma shaping effects on the geodesic acoustic mode in the large orbit drift width limit

Abstract

Plasma shaping effects on the geodesic acoustic mode (GAM) are revisited analytically in the large orbit drift width limit. Comparing with results from the small orbit drift width expansion method [Z. Gao et al., Phys. Plasmas 15, 074502 (2008)] the behavior of the real frequency is almost the same but the effect on the damping rate is different due to the change of dominant resonant mechanism, from low order harmonic transit resonance to high order harmonic resonance, or equivalently, to the magnetic drift resonance. As a result, although the GAM frequency decreases with an increasing elongation κ by dependence of [2/(κ2+1)]1/2, the damping is weakened mildly in the large orbit drift width limit, which is quite different from the result in the low small orbit drift limit, where the damping is enhanced exponentially with the decrease in frequency. Also, in the large orbit drift width limit, the dependence of the GAM damping rate on inverse aspect ratio ε is analytically obtained for the first time. As ε increases, the frequency behaves as a weakly decreasing parabola function of ε, and the damping rate increases parabolically, but more rapidly than the frequency decreases. The GAM with longer radial wavelength is more easily damped by the finite aspect ratio effect. It is also found that the Shafranov shift gradient has the similar effect as the inverse aspect ratio.