The properties of resistive MHD modes and unstable spectra in advanced tokamak regimes

Abstract: Advanced tokamak regimes, featuring extended regions of low magnetic shear, are promising candidates for future fusion reactors but are also more prone to specific kinds of MHD instabilities. The proximity to a rational surface in a very low shear region weakens field line bending stabilisation and amplifies the effects of toroidal coupling between modes, leading to the emergence of long-wavelength resistive infernal modes. These modes can grow collectively as a discrete spectrum, leading to a cascade of different perturbations for single mode numbers $(m, n)$, with subdominant modes showing increasingly oscillatory radial structures. These spectra of fast-growing modes are significant for developing stable scenarios in future reactors, and for the understanding of global reconnection events like sawteeth, motivating a deeper investigation into their fundamental physics. Deriving new analytic solutions, including a generalisation of the ideal interchange dispersion relation to non monotonic $q$ profiles, and extending a modular linear resistive MHD solver, we investigate how resistivity, compressibility, toroidal effects, and shaping influence stability, especially in reversed shear $q$ profiles. It is also shown that common assumptions in numerical calculations prevent the observation of the full variety of modes present in these advanced scenarios.