Ideal MHD induced temperature flattening in spherical tokamaks

This paper extends the analysis first presented in Jardin et al. [Phys. Rev. Lett. 128, 245001 (2022)] to more thoroughly examine the stability of spherical torus equilibrium to ideal magnetohydrodynamic (MHD) infernal modes and their nonlinear consequences. We demonstrate that in a 3D resistive magnetohydrodynamic (MHD) simulation of a NSTX discharge, anomalous transport can occur due to these instabilities. We generate a family of equilibrium of differing beta and use this to show that these instabilities could explain the experimentally observed flattening of the electron temperature profile at modest beta. The modes studied in this paper are found to occur with poloidal mode number m and toroidal mode number n when the ratio m/n is in the range of 1.2-1.5, when the central safety factor is in this range or slightly lower, and when the central region has very low magnetic shear. Our analysis gives some insight as to why the unstable linear growth rates are oscillatory functions of the toroidal mode number n. We present a simulation of an initially stable configuration that passes through a stability boundary at a critical beta as it is heated. We also show that a particular NSTX discharge is unstable to these modes over a timescale of several hundred ms. We conclude that these modes must be taken into account when performing predictive modeling. An appendix shows that similar modes can be found in R / a = 4 tokamaks for certain q-profiles and beta values.