The evolution of twisted coronal loops

The evolution of coronal loops in response to slow photospheric twisting motions is investigated using a variety of methods. Firstly, by solving the time-dependent equations it is shown that the field essentially evolves through a sequence of 2D equilibria with no evidence of rapid dynamic evolution. Secondly, a sequence of 1D equilibria are shown to provide a remarkably good approximation to the 2D time-dependent results using a fraction of the computer time. Thus, a substantial investigation of parameter space is now possible. Finally, simple bounds on the 3D stability of coronal loops are obtained. Exact stability bounds can be found by using these bounds to reduce the region of parameter space requiring further investigation. Twisting the loop too much shows that a 3D instability must be triggered.