1. Reconstruction of Reconnection Configurations From Spacecraft Data Bengt Sonnerup and Wai-Leong Teh Dartmouth College, Hanover, NH, USA Hiroshi Hasegawa ISAS/JAXA, Japan Magnetohydrostatic Grad-Shafranov (GS) Reconstruction of FTEs Seen by Cluster GS reconstruction with Field-Aligned flow: Onset of Reconnection Seen by Cluster Prospects for General MHD Reconstruction of 2D Time Independent Structures

5. Magneto-hydrostatic GS Reconstruction and 2D, steady geometry GS equation:

6. Get potential A on the x-axis (i.e., along the spacecraft trajectory): Can then determine. Step away from the x-axis :

10. 1.High correlation between GS map and actually measured B fields at the four SC indicates the GS model assumptions are well satisfied. 2. Consistent results for invariant axis indicates that it is well defined; it is tangent to the magnetopause and embedded in it: length >2 3. The FTEs studied are flux ropes with strong core (axial) fields. 4. They must have been produced by intermittent component reconnection at site sunward of Cluster. They convect tailward with the magnetosheath speed 5. When they reach Cluster, reconnection has ceased and the flux rope evolution is slow (relaxation toward minimum-energy state) 6. Pressure minimum in the FTE center may indicate a connection to the magnetosphere at one end (or possibly both ends) 7. Circumferential flux is generated in less than 5 minutes: reconnection electric field > 0.17 mV/m for FTE 2 (reconnection rate > 0.058)

11. Structures with field-aligned flow [Sonnerup et al., JGR, September, 2006] Field-line invariants: Alfvén - Mach number

12. Find derivatives from 7 linear equations: where Note that for and for

13. Benchmarking by use of exact solution Black = error in potential A (0.1% levels) Red = error in (2% levels)

14. Cluster Magnetopause Crossing Crossing order: C4 (blue); C1 (black); C2 (red); C3 (green)

15. + x component (GSE) □ y component (GSE) ○ z component (GSE) Walén Test HT Frame Quality (C1) C1 C3

16. Reconstruction from Cluster 1

17. Reconstruction from Cluster 3

18. Supersonic Field-Aligned Flow On Reconnected Field Line Distance along the field line

19. Onset of local reconnection : Results 1.Strong field-aligned flow seen in the HT frame. Its dynamic effects are included 2.Wedge of reconnected field lines is created in less than 30 s 3.Flux content in the wedge indicates 0.47 mV/m (reconnection rate 0.025) 4.Supersonic ( 2.1 – 2.4) field-aligned flow in the wedge 5.Axial extent > 4 6.Guide field changes strength across the magnetopause

21. Test case: Ideal radial flow with circumferential field Sub-Fast results Error contour line: 0.01% ([black, blue]), 0.1% ([red]). Comparison between exact solution and reconstruction. Solid lines are field lines; dashed lines are streamlines; color indicates normalized density. Solution has in lower left corner and in upper right corner.

22. MHD reconstruction from C3 of magnetopause crossing at 06:23 UT, July 5, 2001