Current build-up as a result of the kink instability in a loop

The kink instability may be responsible for compact loop flares since the instability is triggered once the twist in a coronal loop exceeds a critical value. During the non-linear evolution of the instability a large current builds up, reconnection can occur and the magnetic energy released due to reconnection may explain the rapid heating of the flare. However, there has been some debate over the nature of the current concentration and, in particular, whether the current saturates or whether it is a current sheet, and what influences these possible states. In this paper we consider two similar equilibria having a twist function which rises to a peak and then falls off. One is steeper than the other allowing us to investigate whether the steepness of the peak has any effect on the nature of the current. For each profile, we run the code on five different grid resolutions and see how the maximum of the current scales with grid resolution. We also look for behavior in the x-component of the velocity which might be similar to the step-function behavior associated with singularities in the linear kink instability. For both profiles we find that the current scales almost linearly with resolution and that v(x) drops steeply at the position of the current concentration. This suggests that, for these particular profiles, there are indications of current sheet formation and that the steepness in the peak of the twist does not affect the nature of the current.