Formation of current singularity in a topologically constrained plasma

Abstract

Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranov solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.

5 pages, 2 figures

References in corpus (5)

• Variational integration for ideal magnetohydrodynamics with built-in advection equations
• Lagrangian relaxation schemes for calculating force-free magnetic fields, and their limitations
• Current singularities in line-tied three-dimensional magnetic fields
• Do Potential Fields Develop Current Sheets Under Simple Compression or Expansion?
• Current Singularities at Quasi-Separatrix Layers and Three-Dimensional Magnetic Nulls

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