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

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.

20 pages, 19 figures. Accompanied by an eSupplement available as an ancillary file using the link on the right of this arXiv abstract page. Accepted for publication in Physics of Plasmas

References in corpus (6)

• Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics
• Formation of current singularity in a topologically constrained plasma
• Rapid Change of Field Line Connectivity and Reconnection in Stochastic Magnetic Fields
• Hamilton--Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity
• Spectrum of multi-region-relaxed magnetohydrodynamic modes in topologically toroidal geometry
• Exact axisymmetric Taylor states for shaped plasmas

Cited by in corpus (5)

• Numerical study of $\delta$-function current sheets arising from resonant magnetic perturbations
• Fast magnetic reconnection and the ideal evolution of a magnetic field
• Time-dependent relaxed magnetohydrodynamics -- inclusion of cross helicity constraint using phase-space action
• Rigidity of MHD equilibria to smooth incompressible ideal motion near resonant surfaces
• Relaxation of Compressible Euler Flow in a Toroidal Domain