Non-linear saturation of non-resonant ideal long wavelength instabilities and application to sustained hybrid operational regimes

A new theory is presented unifying the non-linear saturation of non-resonant n=m=1 internal kink modes with reverse shear [1], and non-linearly saturated n=m=1 quasi interchange modes with an extended region of very low shear [2].  The generalised set of new equations also describes n=m>1 modes [3] with arbitrary non-resonant q-profiles. 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.  Over the initial phase of the resistively diffusing plasma scenario, the associated growing 3D magnetic perturbations are assumed to cause strong cross-field transport.  Under these conditions the plasma will cease to resistively diffuse, and the modes cease to grow, so that the hybrid regime can in principle be sustained, possibly in line with previous ideas concerning a magnetic flux pump [4].  The picture remains robust to potential kinetic corrections of core instabilities in the weakly collisional regimes of future tokamak reactors.

[1] K. Avinash Phys. Fluids B 2 2373 (1990)

[2] F. L. Waelbroeck, Phys. Fluids B 1 499 (1989)

[3] J. P. Graves, M. Coste-Sarguet and C. Wahlberg, Plasma Phys. Control. Fusion 64 014001 (2022)

[4] I Krebs, S.C. Jardin, S. Günter, et al., Physics of Plasmas 24, 102511 (2017)