University of Maryland
A Statistical Model of Magnetic Islands in a Large Current Layer
We develop a statistical model describing the dynamics of magnetic islands in very large current layers, such as those found in the magnetopause, the magnetotail, and the solar corona. Two parameters characterize the island distribution: the flux contained in the island and the area A enclosed by it. We derive an integro-differential evolution equation for this distribution function, based on rules that govern the small-scale generation of secondary islands, the rates of island growth, and island merging. These rules have been verified by full particle-in-cell simulations. For instance, during the merging of two islands, the merged island has area A equal to the sum of the original two areas and flux equal to the larger of the two. The numerical solutions of the integro-differential equation produce island distributions relevant to the magnetosphere and corona. We also derive and analytically solve a differential equation for large islands that explicitly shows the role merging plays in large island growth. Progress in efforts to compare these predictions with observational data from THEMIS and other missions will also be presented.