Reconstruction of Reconnection Configurations From Spacecraft Data

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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

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Magneto-hydrostatic GS Reconstruction

• and 2D, steady geometry
• GS equation

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

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• 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 gt2
  
• 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
  gt 0.17 mV/m for FTE 2 (reconnection rate gt 0.058)

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Structures with field-aligned flow Sonnerup et
al., JGR, September, 2006
Field-line invariants



Alfvén - Mach number
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Find derivatives from 7 linear equations

where
Note that
for
and for

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Benchmarking by use of exact solution

Black error in potential A (0.1 levels) Red
error in
(2 levels)
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Cluster Magnetopause Crossing
Crossing order C4 (blue) C1 (black) C2 (red)
C3 (green)
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HT Frame Quality
Walén Test
C1
C3
x component (GSE) ?
y component (GSE) ? z component (GSE)

(C1)
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Reconstruction from Cluster 1
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Reconstruction from Cluster 3
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Supersonic Field-Aligned Flow On Reconnected
Field Line
Distance along the field line
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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 gt 4
• 6. Guide field changes strength across the
  magnetopause

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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.
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MHD reconstruction from C3 of magnetopause
crossing at 0623 UT, July 5, 2001
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