Formation of current singularity in a topologically constrained plasma.

Area of Science:

• Plasma Physics
• Computational Magnetohydrodynamics
• Astrophysical Plasmas

Background:

• Ideal magnetohydrodynamics (MHD) describes plasma behavior.
• Current sheet formation is crucial in plasma dynamics.
• Variational integrators offer high fidelity for complex simulations.

Purpose of the Study:

• To apply a novel variational integrator to study current sheet formation.
• To analyze the Hahm-Kulsrud-Taylor problem in detail.
• To identify and characterize singular current sheets in magnetized plasmas.

Main Methods:

• Utilized a recently developed variational integrator for ideal MHD in Lagrangian coordinates.
• Applied the integrator to the Hahm-Kulsrud-Taylor problem with sinusoidal boundary forcing.
• Benchmarked results against a constrained Grad-Shafranov solver.

Main Results:

• Obtained an equilibrium solution preserving magnetic topology exactly.
• Identified a singular current sheet through non-differentiable fluid mapping.
• Demonstrated the presence of current singularity signatures in more complex topologies.

Conclusions:

• The variational integrator accurately captures essential plasma features like current singularities.
• Non-differentiable fluid mappings are key indicators of current sheet formation.
• The findings have implications for understanding magnetic reconnection and plasma dynamics in various astrophysical contexts.