Statistical Description of Merging Magnetic Islands

The physical picture of interacting magnetic islands provide a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, heliosheath and the Earth’s magnetosphere. The dynamics of magnetic islands has been treated with a statistical approach by previous works, where the evolution of the island distribution function in the phase space of islands characteristic properties is governed by an integrodifferential equation. In this work, we take a similar approach to study the inverse energy transfer through the coalescence of magnetic islands in 2D, enabled by magnetic reconnection. An island kinetic equation is derived with a special collisional integral to incorporate the physics of merging behavior. The numerical solution of our island kinetic equation provides the evolution of the island distribution functions. The time evolution of important quantities such as the magnetic energy, energy integral scale and number of islands agrees with our simplified analytical prediction. Properties of the distribution function and the magnetic energy spectrum are also studied.