Formation of current singularity in a topologically constrained plasma

TL;DR

This paper uses a variational integrator to study current sheet formation in a 2D plasma, revealing a non-differentiable fluid mapping that indicates a singular current sheet, with results benchmarked against a Grad-Shafranov solver.

Contribution

It demonstrates the formation of a current singularity in a topologically constrained plasma using a novel variational integrator approach.

Findings

Identification of a non-differentiable fluid mapping indicating a current sheet.

Benchmarking results confirm the presence of current singularity.

Current singularity signature appears in complex magnetic topologies.

Abstract

Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranov solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.