Magnetohydrodynamical equilibria with current singularities and continuous rotational transform *

Publication Year
2019
Keywords
Abstract

We revisit the Hahm-Kulsrud-Taylor (HKT) problem, a classic prototype problem for studying resonant magnetic perturbations and 3D magnetohydrodynamical equilibria. We employ the boundary-layer techniques developed by Rosenbluth, Dagazian, and Rutherford (RDR) for the internal m=1 kink instability, while addressing the subtle difference in the matching procedure for the HKT problem. Pedagogically, the essence of RDR's approach becomes more transparent in the simplified slab geometry of the HKT problem. We then compare the boundary-layer solution, which yields a "DC" current singularity at the resonant surface, to the numerical solution obtained using a flux-preserving Grad-Shafranov solver. The remarkable agreement between the solutions demonstrates the validity and universality of RDR's approach. In addition, we show that RDR's approach consistently preserves the rotational transform, which hence stays continuous, contrary to a recent claim that RDR's solution contains a discontinuity in the rotational transform.

Journal
Physics of Plasmas
Volume
26
Issue
2
Date Published
02/2019
ISSN Number
1089-7674
Other Numbers
https://arxiv.org/abs/1810.08268