Helicity-conserving relaxation in unstable and merging magnetic flux ropes

Twisted magnetic flux ropes are reservoirs of free magnetic energy. In a highly-conducting plasma such as the solar corona, energy release through multiple magnetic reconnections can be modelled as a helicity-conserving relaxation to a minimum energy state. One possible trigger for this relaxation is the ideal kink instability in a twisted flux rope. We show that this provides a good description for confined solar flares, and develop from idealised cylindrical models to realistic models of coronal loops. Using 3D magnetohydrodynamic simulations combined with test-particle simulations of non-thermal electrons and ions, we predict multiple observational signatures of such flares. We then show how interactions and mergers of flux ropes can release free magnetic energy, using relaxation theory to complement simulations of merging-compression formation in spherical tokamaks and heating avalanches in the solar corona.