Magnetic island merger as a mechanism for inverse magnetic energy transfer*

How large scale magnetic fields in the universe are formed is unclear. One possible mechanism is the transfer of magnetic energy from seed fields generated at kinetic scales to system scales. We investigate the mechanism of magnetic energy transfer to larger spatial scales in a system of parallel current filaments (corresponding to flux ropes or magnetic islands). We introduce a magnetic-reconnection-based model to describe the hierarchical coalescence of current filaments and analyze the self-similar properties and basic scalings of the system. A statistical model describing the coalescence in phase space is developed to confirm the local interaction approximation of the hierarchical model. Reduced MHD simulations confirm the existence of self-similar properties. Scaling exponents from simulation converge to the theoretical predictions as the resistivity is decreased, confirming that magnetic reconnection is the mechanism of inverse transfer of magnetic energy.