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

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.