Theory of non-linear non-resonant ideal MHD instabilities and application to the seeding of NTMs

A new theory is presented unifying the non-linear saturation of non-resonant n=m=1 internal kink modes with reverse shear and non-linearly saturated n=m=1 quasi interchange modes with an extended region of very low shear. The generalised set of new equations also describes non-linear external kink modes, and n=m>1 non-resonant infernal modes with arbitrary non-resonant q-profiles, including their evolution from linear growth to non-linear saturation. By explicitly evaluating the non-linear effect of these modes to, and on, the magnetic flux, it is possible to analytically quantify the effect of the 3D magnetic structures on the q-profile. A critically important extension of this work is the linear and non-linear seeding and saturation of NTMs by core pressure driven modes.