Macroscopic trends of linear tearing stability in cylindrical current profiles

The likelihood of realising tokamak power-plants will be greatly improved by the discovery of high-gain equilibria that resist the formation of small islands and hence avoid the disruptive neoclassical tearing mode. However the complexity and variety of tearing-onset physics has obscured the design decisions that may lead to such stability. Here we investigate the variation that current profiles can bring about in preventing tearing onset through the cylindrical linear tearing stability parameter ∆′. A database of 159148 realistic pilot-plant current profiles was generated with Monte Carlo sampling, and the distribution of ∆′ values was linked with interpretable profile characteristics. In agreement with prior theoretical and experimental studies, ∆′ was found to be strongly correlated with the existence and steepness of a local toroidal current well or hill, with the former destabilising and the latter stabilising. In the absence of these two cases, the remaining ∆′ values were linearly bounded by the toroidal current gradient at the rational surface.