[1] We present a generalized multipoint analysis of physical quantities, such as magnetic field and plasma flow, based on spatial gradient properties, where the multipoint data may be taken by irregular (distorted) configurations of any number of spacecraft. The methodology is modified from a previous, fully 3-D gradient analysis technique, designed to apply strictly to 4-point measurements and to be stable for regular spacecraft configurations. Here, we adapt the method to be tolerant against distorted configurations and to return a partial result when fewer spacecraft measurements are available. We apply the method to a variety of important physical quantities, such as the electric current density and the vorticity of plasma flows based on Cluster and THEMIS multiple-point measurements. The method may also have valuable applications on the coming Swarm mission.

The Time History of Events and Macroscale Interactions during Substorms (THEMIS) observed several magnetopause crossings periodically at the duskside of magnetopause under southward interplanetary magnetic field (IMF), with significant sunward returning flows inside the magnetopause. The vortex features of the flows and the periodic enhancements in the calculated vorticity normal to the spacecraft plane could be found in the observation. The distortion of the magnetopause, the periodic features of vortex flows, the tailward propagation, and the evaluation of Kelvin-Helmholtz instability (KHI) condition support the evidence of the Kelvin-Helmholtz vortices produced by the velocity shear at the duskside of magnetopause. Based on three-point simultaneous observations of the flow, the vorticity was calculated to be about 0.15 s À1 , similar to previous results. The tailward propagation of the vortices along the flank magnetopause was estimated to be about 292 km/s. The circular-induced electric field of several mV/m was deduced perpendicular to the magnetic field when the magnetic field compression occurred at the edges of the vortices.

For the first time, the current density distribution in the inner equatorial magnetosphere ranging from 4 to 12 RE (RE is the Earth radius, 6371 km) has been obtained by using Time History of Events and Macroscale Interactions during Substorms (THEMIS) (P3, P4, and P5) three point magnetic measurements. This study mainly focuses on the storm events when the constellation of the three THEMIS spacecraft has relatively small separation distance. Two cases with different storm activities are first displayed to illustrate the effectiveness of the method. The inner magnetospheric equatorial current distribution ranging from 4 to 12 RE is shown through statistical analysis. The features of current density are separately analyzed for the storm main phase and the recovery phase. The statistical study reveals that with increasing radial distance the predominant ring current density reverses from Eastward (below r = 4.8 RE, where r is the geocentric radial distance) to Westward, but that the distribution behaves differently for the two phases of activity. During the main phase, both the westward and eastward current are enhanced by added signal and are more dynamic so that both radial profile and magnetic local time (MLT) structure is obscured. During the recovery phase, the radial profile of the westward current is smooth and peaks, then falls, between r = 5–7.5 RE showing some MLT dependence in this region. Beyond r = 7.5 RE, the current is lower and nearly constant and shows little MLT variation. The results also suggest that the change from eastward to westward current depends on the storm phase and hence storm activity.