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

We introduce a new approach for predicting unstable nonresonant MHD modes, which are demonstrated to be destabilised preferentially to any other resonant instability with the same toroidal mode number for n>1, making these modes important for determining overall MHD stability properties in equilibria with weak magnetic shear.

We establish a clear connection between the spectrum of unstable modes and certain rational approximations of the safety factor at the magnetic axis, for equilibria that are consistent with pre-crash profiles in sawtoothing tokamak plasmas in the large aspect ratio limit. We consider how these observations may enable development of a procedure to reduce the uncertainty on q₀ obtained via measurement or through analysis and reconstruction of experimental results.

In equilibria with extended regions of weak magnetic shear, including some tokamak scenarios and stellarators, nonresonant MHD modes can be unattractive for confinement since these instabilities displace substantial volumes of plasma and potentially lead to more efficient pressure gradient flattening in the nonlinear regime.