Identifying and Visualizing Terrestrial Magnetospheric Topology using Geodesic Level Set Method

This study introduces a novel numerical method for identifying and visualizing the terrestrial magnetic field topology in a large-scale three-dimensional global MHD (Magneto-Hydro-Dynamic) simulation. The (un)stable two-dimensional manifolds are generated from critical points (CPs) located north and south of the magnetosphere using an improved geodesic level set method. A boundary value problem is solved numerically using a shooting method to forward a new geodesic level set from the previous set. These sets are generated starting from a small circle whose centre is a CP. The level sets are the sets of mesh points that form the magnetic manifold, which determines the magnetic field topology. In this study, a consistent method is proposed to determine the magnetospheric topology. Using this scheme, we successfully visualize a terrestrial magnetospheric field topology and identify its two neutral lines using the global MHD simulation. Our results present a terrestrial topology that agrees well with the recent magnetospheric physics and can help us understand various nonlinear magnetospheric dynamics and phenomena. Our visualization enables us to fill the gaps between current magnetospheric physics that can be observed via satellites and nonlinear dynamics, particularly, the bifurcation theory, in the future.