Abstract
It is shown that the theory of the nonlinearly saturated ideal internal kink mode by Rosenbluth et al. [Phys Fluids 16(11), 1894 (1973)] can be used to find the fully nonlinear ideal plasma response to an externally applied resonant magnetic perturbation. It is also demonstrated that the solution leads to a jump in the rotational transform across the resonant surface caused by a zonal current sheet. Its amplitude scales linearly with the plasma perturbation despite the nonlinearity of the solution. This confirms a recent conjecture that three-dimensional MHD equilibria with nested magnetic surfaces generally contain discontinuities in the rotational transform [J. Loizu et al., Phys Plasmas 22(9), 090704 (2015)]. It also lends support to Parker's long-standing suggestion that “almost all” MHD equilibria possess current sheets.
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