Multi-region relaxed magnetohydrodynamics in plasmas with slowly changing boundaries --- resonant response of a plasma slab

TL;DR

This paper extends multi-region relaxed magnetohydrodynamics (MRxMHD) to plasmas with slowly changing boundaries, analyzing resonant responses and magnetic field behavior using a simplified slab model with boundary ripples.

Contribution

It introduces a formalism for MRxMHD in dynamic boundary conditions and demonstrates its application to a sheared magnetic field model with boundary ripples.

Findings

Resonant surface shielding currents oppose reconnection.

Low ripple amplitudes produce magnetic islands locking the rotational transform.

Beyond a critical ripple amplitude, islands vanish and the transform becomes discontinuous.

Abstract

The adiabatic limit of a recently proposed dynamical extension of Taylor relaxation, \emph{multi-region relaxed magnetohydrodynamics} (MRxMHD) is summarized, with special attention to the appropriate definition of relative magnetic helicity. The formalism is illustrated using a simple two-region, sheared-magnetic-field model similar to the Hahm--Kulsrud--Taylor (HKT) rippled-boundary slab model. In MRxMHD a linear Grad--Shafranov equation applies, even at finite ripple amplitude. The adiabatic switching on of boundary ripple excites a shielding current sheet opposing reconnection at a resonant surface. The perturbed magnetic field as a function of ripple amplitude is calculated by invoking conservation of magnetic helicity in the two regions separated by the current sheet. At low ripple amplitude "half islands" appear on each side of the current sheet, locking the rotational transform at the resonant value. Beyond a critical amplitude these islands disappear and the rotational transform develops a discontinuity across the current sheet.