PPPL-5373
Multi-region relaxed magnetohydrodynamics in plasmas with slowly
changing boundaries — resonant response of a plasma slab
Authors: S. Hudson and A. Bhattacharjee
Abstract: The adiabatic limit of a recently proposed
dynamical extension of Taylor relaxation, 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
nite 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.
Submitted to: Physics of Plasmas
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