Relaxation models of energy release in merging twisted solar coronal loops and spherical tokamaks
Asad Hussain
University of Manchester
P. K. Browning (University of Manchester), A. W. Hood (University of St. Andrews)
In 1974, Taylor proposed a relaxation model for Reverse Field Pinch experiments which determined the minimum energy state based on helicity conservation. This has subsequently been applied to various laboratory devices such as spheromaks and tokamaks, as well as to the solar coronal heating problem. Recent 3D MHD simulations show that kink instable twisted threads can cause disruption in nearby stable threads causing release of free magnetic energy. This was then applied to a much larger system of threads, suggesting that the corona can be heated through an avalanche of heating events. These calculations are, however, computationally intensive. We have applied the Taylor model to these MHD simulations, with results showing good agreement. Our approach has been to consider initially pairs of flux ropes with varied twist, involving various combinations of kink-unstable ropes and stable ropes. We then applied this model to 23 flux ropes with a single unstable flux rope resulting in a cascade of reconnection events. Finally, we explore the dependency of energy on the loop parameters such as magnitude and sign of twist. The computational ease of our model paves the ways towards modelling larger systems and a much wider parameter space. We will further comment on the use of our models for reconnection (merging compression) spherical tokamak startup.