Energy dissipation and helicity in coronal loops of variable cross-section

A model is developed to describe a coronal loop, which may originate from a photospheric source of smaller size than the coronal radius of the loop. The energy and relative helicity of the loop are evaluated, as are two alternative estimates of the energy available for coronal heating. Both of these estimates are strongly dependent on the size of the photospheric footprint of the loop. A coronal heating rate is then deduced, based on a nanoflare-type scenario, where slowly accumulated energy is rapidly released as heat. An explicit calculation is carried out for one particular choice of loop length and coronal radius, with dissipation timescale and photospheric radius as parameters. Two main conclusions are reached. Firstly, the proposed mechanism can make a significant contribution to coronal heating. Secondly, the mechanism is more effective for a more concentrated photospheric flux source.