Plasmoid solutions of the Hahm--Kulsrud--Taylor equilibrium model

TL;DR

This paper explores plasmoid solutions within the Hahm--Kulsrud equilibrium model, demonstrating how conformal mapping can generate a continuous spectrum of magnetic island configurations between fully shielded and fully reconnected states.

Contribution

It introduces a method to generate a continuum of plasmoid solutions in the HK model using conformal mapping, extending the understanding of magnetic reconnection states.

Findings

Plasmoid solutions form a continuous sequence between two HK solutions.

Conformal mapping transforms boundary conditions to generate new equilibrium states.

The approach links fully shielded and fully reconnected plasma configurations.

Abstract

The Hahm--Kulsrud (HK) [T. S. Hahm and R. M. Kulsrud, Phys. Fluids {\bf 28}, 2412 (1985)] solutions for a magnetically sheared plasma slab driven by a resonant periodic boundary perturbation illustrate fully shielded (current sheet) and fully reconnected (magnetic island) responses. On the global scale, reconnection involves solving a magnetohydrodynamic (MHD) equilibrium problem. In systems with a continuous symmetry such MHD equilibria are typically found by solving the Grad--Shafranov equation, and in slab geometry the elliptic operator in this equation is the 2-D Laplacian. Thus, assuming appropriate pressure and poloidal current profiles, a conformal mapping method can be used to transform one solution into another with different boundary conditions, giving a continuous sequence of solutions in the form of partially reconnected magnetic islands (plasmoids) separated by Syrovatsky current sheets. The two HK solutions appear as special cases.