Visualization and criticality of magnetotail field topology in a three-dimensional particle simulation

We present the temporal evolution of magnetic field topology in the magneto tail with a southward IMF in order to identify the magnetic reconnection. T he magnetic field topology is uniquely determined by the eigenvalues of the critical points, if they are not degenerated. This is because the critical points, their number, and the rules between them characterize the whole ma gnetic field pattern. At the critical points, the magnetics become zero. Th e magnetic vector field curves and surfaces are both integrated out along t he principal directions of certain classes of critical points including the Earth's dipole magnetic field. The skeleton that includes the critical poi nts, characteristic curves, and surfaces provides the three-dimensional top ological structure of the reconnection. The change of the skeleton, i.e. th e change of the topology, has revealed the occurrence of magnetic reconnect ion. Namely, three-dimensional "X-points" or the more-than-two critical poi nts that are saddle and connected each other are unstable and can move, van ish, and generated.