Stabilization of a magnetic island by localized heating in a tokamak with stiff temperature profile

In tokamaks plasmas, turbulent transport is triggered above a threshold in the temperature gradient and leads to stiff profiles. This particularity, neglected so far in the problem of magnetic island stabilization by a localized heat source, is investigated analytically in this paper. We show that the efficiency of the stabilization is deeply modified compared to the previous estimates due to the strong dependence of the turbulence level on the additional heat source amplitude inside the island.