Flapping Motion Configurations of Geomagnetotail Current Sheet

We explore the geometry of the flapping motion of geomagnetotail current sheet with the magnetic measurements of the Cluster (constellation) using a newly developed technique. The principal curvatures and directions of the surfaces of the flapping current sheet are successfully deduced by the normal field analysis (NFA). Results show that the directions with the minimum curvature of surfaces of flapping motion are approximately along the Sun-Earth line, while the ones with maximum curvature are mostly in the dawn-dusk plane. It is confirmed that the tail flapping motion is a wave arising in the Y-Z plane, but not bend along the Sun-Earth line. Furthermore, our calculations reveal that the maximum curvature radius of the flapping current sheet's surface along the X-axis is on the order of several dozen Earth radii. This implies that the flapping motion extends spatially over a range from several to a dozen Earth radii along the Sun-Earth direction.