Reconstruction of Reconnection Configurations From Spacecraft Data

1. Reconstruction of Reconnection Configurations From Spacecraft Data • 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 Bengt Sonnerup and Wai-Leong Teh Dartmouth College, Hanover, NH, USA Hiroshi Hasegawa ISAS/JAXA, Japan

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

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 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 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 fieldSub-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