Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium

Abstract Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic (MHD) equilibria with a continuum of nested flux and continuous rotational transition. These have two components: surface current (Dirac δ -function labeling) that prevents the formation magnetic islands, an algebraically divergent Pfirsch–Schlüter density when pressure gradient is present across surface. On adjacent to surface, traditional treatment gives scaling as J ∼ 1 / Δ ι , where $\Delta\iota$?> difference transform relative If distance s between proportional relation $J\sim1/\Delta\iota\sim1/s$?> s will lead paradox not integrable. In this work, we investigate issue by considering pressure-gradient-driven singular Hahm–Kulsrud–Taylor problem, which prototype for arising from resonant perturbations. We show only but also diamagnetic are ${\sim}1/\Delta\iota$?> . However, due Dirac sheet at neighboring strongly packed $s\sim(\Delta\iota)^{2}$?> ( stretchy="false">) 2 Consequently, $J\sim1/\sqrt{s}$?> making total finite, thus resolving paradox. Furthermore, strong packing causes steepening near $\nabla p \sim \mathrm {d}p/\mathrm {d}s 1/\sqrt{s}$?> mathvariant="normal">∇ p mathvariant="normal">d general MHD equilibrium, contrary Grad’s conjecture profile flat around densely distributed surfaces, our result suggests steepens them.