A Statistical Model of Magnetic Islands in a Large Current Layer

TL;DR

This paper presents a new statistical model for magnetic island dynamics in large space plasma current layers, incorporating island growth, merging, and secondary island generation, with solutions relevant to magnetospheric and solar corona phenomena.

Contribution

It introduces an integro-differential equation for island distribution and provides analytical and numerical solutions highlighting merging effects.

Findings

Island distribution functions match observed space plasma data.

Merging significantly influences island growth dynamics.

Analytical solutions clarify the role of merging in large island evolution.

Abstract

We develop a statistical model describing the dynamics of magnetic islands in very large current layers that develop in space plasma. Two parameters characterize the island distribution: the flux contained in the island and the area it encloses. 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. Our numerical solutions of this 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 island growth.