Braided magnetic fields: equilibria, relaxation and heating

Abstract

We examine the dynamics of magnetic flux tubes containing non-trivial field line braiding (or linkage), using mathematical and computational modelling, in the context of testable predictions for the laboratory and their significance for solar coronal heating. We investigate the existence of braided force-free equilibria, and demonstrate that for a field anchored at perfectly-conducting plates, these equilibria exist and contain current sheets whose thickness scales inversely with the braid complexity - as measured for example by the topological entropy. By contrast, for a periodic domain braided exact equilibria typically do not exist, while approximate equilibria contain thin current sheets. In the presence of resistivity, reconnection is triggered at the current sheets and a turbulent relaxation ensues. We finish by discussing the properties of the turbulent relaxation and the existence of constraints that may mean that the final state is not the linear force-free field predicted by Taylor's hypothesis.

To appear in Plasma Physics and Controlled Fusion

References in corpus (9)

• Generalized Squashing Factors for Covariant Description of Magnetic Connectivity in the Solar Corona
• The Role of Turbulence in Coronal Heating and Solar Wind Expansion
• Evolution of field line helicity during magnetic reconnection
• Dynamic Topology and Flux Rope Evolution During Non-linear Tearing of 3D Null Point Current Sheets
• The structure of current layers and degree of field line braiding in coronal loops
• Topological Entropy of Braids on the Torus
• Lagrangian relaxation schemes for calculating force-free magnetic fields, and their limitations
• The coronal energy input from magnetic braiding
• Magnetic field relaxation and current sheets in an ideal plasma

Cited by in corpus (9)

• A solar coronal loop in a box: Energy generation and heating
• Evolution, structure and topology of self-generated turbulent reconnection layers
• Magnetohydrodynamic waves in braided magnetic fields
• Non-thermal line broadening due to braiding-induced turbulence in solar coronal loops
• Quantifying the Tangling of Trajectories Using the Topological Entropy
• Estimating the rate of field line braiding in the solar corona by photospheric flows
• Constructing current singularity in a 3D line-tied plasma
• Forward Modelling of MHD Waves in Braided Magnetic Fields
• Evolution of Field Line Helicity in Magnetic Relaxation