Existence of ion temperature gradient driven shear Alfvén instabilities in tokamaks

The existence of unstable ion temperature gradient driven Alfvén eigenmodes (AITG) is demonstrated in tokamak plasmas, which are ideally stable with respect to magnetohydrodynamics (MHD). Conditions for the destabilization of such modes are quantitatively discussed on the basis of numerical solutions of a set of one-dimensional integral equations along the ballooning coordinate (quasi-neutrality and parallel Ampère’s law). Furthermore, theoretical analyses of the eigenmode dispersion relation, which is given in a compact analytical form in the small ion orbit width limit (compared to the radial wavelength), provide a basis for explaining the general properties of the modes. It is emphasized that instability requires both sufficiently strong thermal ion temperature gradients and that the plasma be not too far away from ideal MHD marginal stability.