A statistical model of magnetic islands in a current layer

This letter describes a statistical model of the dynamics of magnetic islands in very large current layers that develop in space plasma. Two parameters characterize the island distribution: the flux ψ contained in the island and the area A it encloses. The integrodifferential evolution equation for this distribution function is based on rules that govern the small-scale generation of secondary islands, the rates of island growth, and island merging. The numerical solutions of this equation produce island distributions relevant to the magnetosphere and solar corona. The solution of a differential equation for large islands explicitly shows the role merging plays in island growth.