The Grad-Shafranov (GS) reconstruction tech- nique, a single-spacecraft based data analysis method for recovering approximately two-dimensional (2-D) magneto- hydrostatic plasma/field structures in space, is improved to become a multi-spacecraft technique that produces a single field map by ingesting data from all four Cluster spacecraft into the calculation. The plasma pressure, required for the technique, is measured in high time resolution by only two of the spacecraft, C1 and C3, but, with the help of spacecraft po- tential measurements available from all four spacecraft, the pressure can be estimated at the other spacecraft as well via a relationship, established from C1 and C3 data, between the pressure and the electron density deduced from the poten- tials. Consequently, four independent field maps, one for each spacecraft, can be reconstructed and then merged into a single map. The resulting map appears more accurate than the individual single-spacecraft based ones, in the sense that agreement between magnetic field variations predicted from the map to occur at each of the four spacecraft and those actually measured is significantly better. Such a composite map does not satisfy the GS equation any more, but is op- timal under the constraints that the structures are 2-D and time-independent. Based on the reconstruction results, we show that, even on a scale of a few thousand km, the magne- topause surface is usually not planar, but has significant cur- vature, often with intriguing meso-scale structures embedded in the current layer, and that the thickness of both the current layer and the boundary layer attached to its earthward side can occasionally be larger than 3000 km.
Hasegawa, H; Sonnerup, B U. Ö; Klecker, B; and Paschmann, G, "Optimal reconstruction of magnetopause structures from Cluster data" (2005). Open Dartmouth: Faculty Open Access Articles. 450.