Mode spectrum characteristics and onset of the low-shear MHD stability regime

Equilibria with extended regions of weak magnetic shear, including some tokamak scenarios and stellarators, can be susceptible to pressure-driven internal MHD instabilities even though there is no mode rational surface in the plasma. Nonresonant modes, in particular, can have properties that are unattractive for confinement, including displacing substantial volumes of the plasma and leading to more efficient pressure gradient flattening in the nonlinear regime. The onset and linear properties of the low shear stability regime are examined using the initial-value, extended-MHD code M3D-C1. For monotonic q-profiles, we demonstrate a clear correlation between the convergents associated with the continued fraction representation of q0 and the spectrum of unstable modes. Nonresonant modes are observed to be destabilized preferentially to any other resonant instability with the same toroidal mode number when n > 1. Using the observed connection between the spectrum associated with q0 and the overall equilibrium stability properties, we suggest a technique for reducing the uncertainty on both q0 and magnetic shear in the core region, obtained either via measurement or through the analysis and reconstruction of experimental results.