Stabilization of kinetic internal kink mode by ion diamagnetic effects

Ion diamagnetic effects on the m = 1 (poloidal mode number) and n = 1 (toroidal mode number) kinetic internal kink mode are studied numerically by the three-field gyro-reduced-MHD code in the cylindrical coordinates, GRM3F-CY. In the derivation of the gyro-reduced-MHD model including the ion diamagnetic effects, finite gyroradius effects of ions are added to the gyrokinetic Poisson equation (quasi-neutral condition) and the convection term of the conservation law of the ion density. It is found that the long wavelength approximation, ksub(perpendicular)ρti << 1, where ksub(perpendicular) is the wavenumber perpendicular to the magnetic field and ρti is the thermal ion gyroradius, fails to reproduce the correct dispersion relation; the formulation valid even for ksub(perpendicular)ρti >> 1 is necessary. The results of numerical calculation coincide with the theory for |ω*e| + |ω*i| < 2γ0, where the growth rate reduces as the density gradient increases. Here ω*e and ω*i are electron and ion diamagnetic angular frequencies estimated at the rational surface of q = 1 (q is a safety factor), respectively, and γ0 is the growth rate for the uniform density. Very weak instability, however, is observed for |ω*e| + |ω*i| > 2γ0, where the theory predicts the complete stabilization. This residual instability appears since the region with the density gradient is limited in the radial direction and the stabilization by the outgoing drift-wave like mode becomes incomplete. (author)