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

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.

8 pages, 11 figures

References in corpus (3)

• Instability of current sheets and formation of plasmoid chains
• Self-Feeding Turbulent Magnetic Reconnection on Macroscopic Scales
• Hamilton--Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity

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• Evolution, structure and topology of self-generated turbulent reconnection layers
• Formation of Plasmoid Chains in Fusion Relevant Plasmas
• Analytical model of plasma response to external magnetic perturbation in absence of no-slip condition
• Phase Diagrams of Forced Magnetic Reconnection in Taylor's Model
• Multi-region relaxed magnetohydrodynamics in plasmas with slowly changing boundaries --- resonant response of a plasma slab
• Magnetohydrodynamical equilibria with current singularities and continuous rotational transform
• Relaxation models for Single Helical Reversed Field Pinch plasmas
• Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium
• Onset of 2D magnetic reconnection in the solar photosphere, chromosphere and corona
• Rigidity of MHD equilibria to smooth incompressible ideal motion near resonant surfaces