A new method is described to analyze the dimensional character of observed structures using multipoint magnetic field measurements of four or more spacecraft. The technique can provide three directions along which the magnetic field has the minimum, intermediate, and maximum derivatives if the magnetic gradient tensor G = ∇ at every moment has been estimated by multipoint measurements. It follows that the structure's dimensionality and the variation direction can be directly determined. Both Cluster observations and simulations have shown that it is feasible to obtain the invariant axis orientation for two‐dimensional structures such as flux tubes, and to find the normal directions for one‐dimensional structures such as discontinuities. One advantage of this method is that these directions can be determined instantaneously, point by point in the time series, and so can be tracked through each observed structure. The analysis tool provides us a new perspective of the observed structures in the space.
[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 $ 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 onedimensional 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.
[1] A new method is described which calculates the velocity of observed, quasi-stationary structures at every moment in time from multi-point magnetic field measurements. Once the magnetic gradient tensor G = r B and the time variation of the magnetic field have been estimated at every moment, the velocity can then be determined, in principle, as a function of time. One striking property of this method is that we can calculate the velocity of structures for any dimensionality: for three-dimensional structures, all three components of the velocity vector can be calculated directly; for two-dimensional (or onedimensional) structures, we can calculate the velocity along two (or one) directions. The advantage of this method is that the velocity is determined instantaneously, point by point through any structure, and so we can see the time variation of the velocity as the spacecraft traverse the structure. In this paper, the feasibility of the method is tested by calculating the motion velocity of a three-dimensional, near cusp structure and a two-dimensional magnetotail current sheet. The results for one-dimensional structures in the magnetopause and cusp boundaries are compared to calculations for the standard techniques for analyzing discontinuities. Citation:
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