Abstract
Aims: Our aim is to investigate the resistive relaxation of a magnetic loop that contains braided magnetic flux but no net current or helicity. The loop is subject to line-tied boundary conditions. We investigate the dynamical processes that occur during this relaxation, in particular the magnetic reconnection that occurs, and discuss the nature of the final equilibrium. Methods: The three-dimensional evolution of a braided magnetic field is followed in a series of resistive MHD simulations. Results: It is found that, following an instability within the loop, a myriad of thin current layers forms, via a cascade-like process. This cascade becomes more developed and continues for a longer period of time for higher magnetic Reynolds number. During the cascade, magnetic flux is reconnected multiple times, with the level of this `multiple reconnection' positively correlated with the magnetic Reynolds number. Eventually the system evolves into a state with no more small-scale current layers. This final state is found to approximate a non-linear force-free field consisting of two flux tubes of oppositely-signed twist embedded in a uniform background field.
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