The structure and formation mechanism of a total of five Flux Transfer Events (FTEs), encountered on the equatorward side of the northern cusp by the Cluster spacecraft, with separation of ~5000 km, are studied by applying the Grad-Shafranov (GS) reconstruction technique to the events. The technique generates a magnetic field/plasma map of the FTE cross section, using combined magnetic field and plasma data from all four spacecraft, under the assumption that the structure is two-dimensional (2-D) and time-independent. The reconstructed FTEs consist of one or more magnetic flux ropes embedded in the magnetopause, suggesting that multiple X-line reconnection was involved in generating the observed FTEs. The dimension of the flux ropes in the direction normal to the magnetopause ranges from about 2000 km to more than 1 R_E. The orientation of the flux rope axis can be determined through optimization of the GS map, the result being consistent with those from various single-spacecraft methods. Thanks to this, the unambiguous presence of a strong core field is confirmed, providing evidence for component merging. The amount of magnetic flux contained within each flux rope is calculated from the map and, by dividing it by the time interval between the preceding FTE and the one reconstructed, a lower limit of the reconnection electric field during the creation of the flux rope can be estimated; the estimated value ranges from ~0.11 to ~0.26 mV m^-1, with an average of 0.19 mV m^-1. This can be translated to the reconnection rate of 0.038 to 0.074, with an average of 0.056. Based on the success of the 2-D model in recovering the observed FTEs, the length of the X-lines is estimated to be at least a few R_E.

The Grad-Shafranov (GS) reconstruction technique, a single-spacecraft based data analysis method for recovering approximately two-dimensional (2-D) magnetohydrostatic 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 potential 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 potentials. 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 optimal 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 magnetopause surface is usually not planar, but has significant curvature, 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 3000km.

The paper discusses properties of the near-tail dawnside and boundary layer, as obtained from Cluster plasma and magnetic field measurements during a single skimming orbit on 4 and 5 July 2001 that included 24 well-defined crossings by all four spacecraft. As a result of variations of the interplanetary magnetic field, the magnetic shear across the local varied between ~0° and ~180°. Using an improved method, which takes into account acceleration and thickness variation, we have determined the orientation, speed, thickness and current for the 96 individual crossings. The orientations show clear evidence of surface waves. Magnetopause thicknesses range from ~100 to ~2500km, with an average of 753km. The speeds range from less than 10up to more than 300, with an average of 48. Both results are consistent with earlier ISEE and AMPTE results obtained for the dayside magnetopause. Importantly, scaling the thicknesses to the ion gyro radius or the ion inertial length did not reduce the large dynamic range. There is also no significant dependence of thickness on magnetic shear. Current densities range from ~0.01 up to ~0.3uA, with an average value of 0.05 . By including some extra crossings that did not involve all four spacecraft, we were able to apply the Walén test to a total of 60 by Cluster 1 and 3, and have classified 19 cases as rotational discontinuities (RDs), of which 12 and 7 were sunward and tailward of an X-line, respectively. Of these 60 crossings, 26 show no trace of a boundary layer. The only with substantial boundary layers are into the plasma mantle. Of the 26 without a boundary layer, 8 were identified as RDs. Since reconnection produces wedge-shaped boundary layers emanating from the X-line, RDs without may be considered close to the X-line, in which case the observed magnetic shear and Alfvén Mach number should be representative of the conditions at the X-line itself. It is therefore important that four of the eight cases had shear angles ≤100, i.e. the reconnecting fields were far from being anti-parallel, and that all eight cases had Alfvén Mach numbers M_A>1 in the adjoining magnetosheath. Another important conclusion can be drawn from the without a that were tangential discontinuities (TDs). To observe TDs with no at such large distances from the subsolar point appears to rule out diffusion over large portions of the as an effective means for plasma transport across the magnetopause.