Ideal MHD stability properties of pressure driven modes in low shear tokamaks

The role of shear in determining the ideal MHD stability properties of tokamaks is discussed. In particular, the effects of low shear within the plasma upon pressure driven modes are assessed. The standard ballooning theory is shown to break down as the shear is reduced, and the growth rate is shown to be an oscillatory function of n, the toroidal mode number, treated as a continuous parameter. The oscillations are shown to depend on both the pressure profile and the safety factor profile. When the shear is sufficiently weak, the oscillations can result in bands of unstable n-values, which are present even when the standard ballooning theory predicts complete stability. These instabilities are named 'infernal modes'. The occurrence of these instabilities at integer n is shown to be a sensitive function of the q-axis, raising the possibility of a sharp onset as the plasma parameters evolve.