Temporal Evolution Of Flux Rope/Tube Entanglement In 3-D Hall Mhd Simulations

At the Earth's magnetopause, flux tubes observed by the Magnetospheric Multiscale (MMS) spacecraft in "entangled" pairs have been interpreted as a precursory stage to the formation of a new pair of flux tubes by magnetic reconnection, of which one reconnected tube joins the magnetosphere. Understanding the connectivity of these tubes before and after the entanglement is essential to understanding the transport of particles and energy between the magnetosphere and the solar wind. In this study, we use a three-dimensional Hall Magnetohydrodynamics (MHD) model to simulate the interaction of two entangled flux tubes in the ambient plasma. Four types of interactions are simulated: Two types of magnetic field geometry (flux tube-flux tube and flux rope-flux rope) are tested separately, each under two different boundary conditions. With the boundary condition that drives the interaction with ambient flow, magnetic reconnection transforms the two tubes/ropes into new pairs. The process is performed under plasma conditions comparable to those of such events identified in recent MMS observations. The detailed three-dimensional evolution is shown at representative stages, with key parameters shown across the entanglement interface. The shape of the central current sheet and evolution of magnetic field curvature are also discussed. Our study supports the feasibility of reconnection between entangled flux tubes, recognizes the importance of ambient plasma conditions for the completion of such processes, and quantifies how such structures evolve to modify the solar wind-geomagnetic field interaction. In addition, this model is applicable to flux rope interactions in the solar corona.