The structure of current layers and degree of field line braiding in coronal loops

TL;DR

This study investigates how magnetic field complexity in coronal loops influences the formation of current layers and the energy available for solar coronal heating, revealing scaling laws and an upper bound on braid complexity.

Contribution

It demonstrates that force-free equilibria of braided magnetic fields contain finite-thickness current layers governed by field line mapping scales, providing bounds on braid complexity and energy for coronal heating.

Findings

Current layers have finite thickness determined by field line mapping scales.

Scaling laws relate current layer properties to braid complexity.

Upper bound on braid complexity implies sufficient energy for nanoflares.

Abstract

One proposed resolution to the long-standing problem of solar coronal heating involves the buildup of magnetic energy in the corona due to turbulent motions at the photosphere that braid the coronal field, and the subsequent release of this energy via magnetic reconnection. In this paper the ideal relaxation of braided magnetic fields modelling solar coronal loops is followed. A sequence of loops with increasing braid complexity is considered, with the aim of understanding how this complexity influences the development of small scales in the magnetic field, and thus the energy available for heating. It is demonstrated that the ideally accessible force-free equilibrium for these braided fields contains current layers of finite thickness. It is further shown that for any such braided field, if a force-free equilibrium exists then it should contain current layers whose thickness is determined by length scales in the field line mapping. The thickness and intensity of the current layers follow scaling laws, and this allows us to extrapolate beyond the numerically accessible parameter regime and to place an upper bound on the braid complexity possible at coronal plasma parameters. At this threshold level the braided loop contains $10^{26}$--$10^{28}{\rm ergs}$ of available free magnetic energy, more than sufficient for a large nanoflare.