Comparison of a statistical model for magnetic islands in large current layers with Hall MHD simulations and Cluster FTE observations

Abstract

Magnetic islands have been observed in long current layers for various space plasmas, including the magnetopause and solar corona. In previous work exploring these magnetic islands, a statistical model was developed that described their formation, growth, convection, and coalescence in very large systems, for which simulations prove inadequate. An integro-differential equation was derived for the island distribution function, which characterized islands by the flux they contain ψ and the cross-sectional area they enclose A. The steady-state solution of the evolution equation predicted a distribution of islands. Here, we use a Hall MHD (magnetohydrodynamic) simulation of a very long current sheet with large numbers of magnetic islands to explore their dynamics, specifically their growth via two distinct mechanisms: quasi-steady reconnection and merging. We then use the simulation to validate the statistical model and benchmark its parameters. A database of 1,098 flux transfer events (FTEs) observed by Cluster between 2001 and 2003 is also compared with the model's predictions. In both simulations and observations, island merging plays a significant role. This suggests that the magnetopause is populated by many FTEs too small to be recognized by spacecraft instrumentation.