Plasmoid instability and secondary island evolution in three-dimensional complex magnetic configurations

Magnetic islands (or flux ropes) created by magnetic reconnection are believed to play a crucial role in magnetic topology variation and energy dissipation in various space and astro events, such as solar flares, magnetic storms, and coronal mass ejections, among others. However, the intricate magnetic configurations and corresponding geometric and dynamic characteristics of three-dimensional (3D) magnetic reconnection, such as those observed in solar coronal loops, interplanetary magnetic fields, and magnetospheres of Earth and other planets, still remain fundamental challenges. In this work, the formation and evolution of a 3D secondary magnetic island in a configuration designed for the planned SPERF–TREX experiment are investigated using 3D magnetohydrodynamics simulations, as a prediction subject to future experimental verification. It is shown that the reconnection process first forms an elongated thin current sheet. Due to continuous thinning, the current sheet is subsequently destabilized by a plasmoid instability, leading to the creation of a secondary island and a topological transformation of the initial X-line into a pair of 3D magnetic nulls connected by a separator. Concurrently, an O-line is generated for the 3D secondary island and connected with remnants of the initial X-line. The three-dimensionality of the 3D island is then analyzed. In particular, the topological features of the O–X line “connection” are investigated. Moreover, by comparing the temporal evolution of the 3D flux with the integral of the electric field along the separator, (Formula presented) (Formula presented), a measurement method is verified for the 3D reconnection rate calculation.