  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.
