Analyses on the geometrical structure of magnetic field in the current sheet based on cluster measurements

[1] The geometrical structure of the magnetic field is a critical character in the magnetospheric dynamics. Using the magnetic field data measured by the Cluster constellation satellites, the geometrical structure including the curvature radius, directions of curvature, and normal of the osculating planes of the magnetic field lines within the current sheet/neutral sheet have been investigated. The results are ( 1) Inside of the tail neutral sheet (NS), the curvature of magnetic field lines points towards Earth, the normal of the osculating plane points duskward, and the characteristic half width ( or the minimum curvature radius) of the neutral sheet is generally less than 2 R-E, for many cases less than 1600 km. (2) Outside of the neutral sheet, the curvature of magnetic field lines pointed northward ( southward) at the north ( south) side of NS, the normal of the osculating plane points dawnward, and the curvature radius is about 5 R-E similar to 10 R-E. (3) Thin NS, where the magnetic field lines have the minimum of the curvature radius less than 0.25 R-E, may appear at all the local time between LT 20 hours and 4 hours, but thin NS occurs more frequently near to midnight than that at the dawnside and duskside. (4) The size of the NS is dependent on substorm phases. Generally, the NS is thin during the growth and expansion phases and grows thick during the recovery phase. (5) For the one-dimensional NS, the half thickness and flapping velocity of the NS could be quantitatively determined. Therefore the differential geometry analyses based on Cluster 4-point magnetic measurements open a window for visioning the three-dimensional static and dynamic magnetic field structure of geomagnetosphere.