Magnetic field rotation analysis and the applications

[1] An analysis technique, termed MRA ( magnetic rotation analysis), has been designed to probe three-dimensional magnetic field topology. It is based on estimating the gradient tensor of four-point measurements of the magnetic field which have been taken by the Cluster mission. The method first constructs the symmetrical magnetic rotation tensor and in general terms deduces the rotation rate of magnetic field along one arbitrary direction. In particular, the maximum, medium, and minimum magnetic rotation rates along corresponding characteristic directions of a magnetic structure can be obtained. The value of the curvature of a magnetic field line, for example, is given by the magnetic rotation rate along the magnetic unit vector and its corresponding radius of curvature is readily obtained. MRA has been applied here to analyze the geometrical structure of two distinct magnetospheric structures, i.e., the tail current sheet and the tail flux rope. The normal of the current sheet is the direction at which the magnetic field has the largest rotation rate. The half thickness of the one-dimensional neutral sheet can also be determined from the reciprocal of the maximum magnetic rotation rate. The advantage of the MRA method is that not only it can determine the orientation but also the internal geometrical configuration and spatial scale of the magnetic structures. A key feature of the MRA method is that it provides the detailed picture of the magnetic rotation point by point through any crossing of the current sheet. As a result, the thickness of the neutral sheet (NS) can be explicitly demonstrated to vary with time, as indicated in one case study, where the NS becomes thicker after the onset of a substorm. MRA has also been applied here to analyze the detailed features of magnetic field variations inside of a flux rope. The principal axis of the flux rope is the direction at which the magnetic field rotates at the least rate. The magnetic scale of the flux rope can also be determined ( about 1R(E) in the case chosen). It is also found that there are both frontside-backside and dawn-dusk asymmetries for the flux rope under study.