1. K. Galsgaard1, A.L. Haynes2, C.E. Parnell2
How complicated can the reconnection process be in a simple MHD flux interaction problem?
K. Galsgaard1, A.L. Haynes2, C.E. Parnell2
1 Niels Bohr Institute
2 University of St Andrews
Workshop on Magnetic Reconnection and Plasma turbulence
Uppsala 29th May 2007

2. Solar “Magnetic field” TRACE - SOHO
Complicated structures
Potential B-model
Magnetic field lines!?
Localised sources

3. Numerical Experiment – + Negative Source Positive Source
Simple magnetic setup with two sources and overlying field
Lower boundary:
Negative Source –
Overlying Field
Overlying Field +
Positive Source
Upper boundary: Closed
Side boundaries: Periodic
Galsgaard et al (2000)

4. Equations and Numerical Code
∂(𝜌𝑢 ∂𝑡 =−∇.(𝜌𝐮𝐮+𝜏 −∇ 𝑝+𝐽×𝐵
𝐸=−𝑢×𝐵+𝜂𝐽
∂𝑒 ∂𝑡 =−∇.(𝑒𝑢 − 𝜌(𝑇− 𝑇 0 𝑡 𝑐𝑜𝑜𝑙 + 𝑄 𝑣𝑖𝑠𝑐 + 𝑄 𝑗𝑜𝑢𝑙𝑒
𝐽=∇×𝐵
∂𝐵 ∂𝑡 =−∇×𝐸
𝑒= 𝑝 𝛾−1
∂𝜌 ∂𝑡 =−∇.(𝜌𝑢
𝑝=𝜌𝑇
Finite difference resistive MHD code of size (1, 1, ¼) with (128, 128, 66) grid points.
Third order predictor-corrector method.
Sixth order spacial derivatives.
Fifth order spacial interpolation.
Hyper viscosity and magnetic diffusion.
Combined 2ed and 4th order + Shock diffusion.

5. Magnetic Field Structure of Magnetic Field: 4 Sources (P1, P∞, N1, N∞)
4 Source Pairs:
N∞ to P∞ (overlying)
N1 to P∞ (negative open)
N∞ to P1 (positive open)
N1 to P1 (closed)
2 Null points (on base)
Evolution of source flux:
Open → Closed → Reopened.

6. Evolution of 3D Magnetic Skeleton
Positive
Separatrix
Surface
Negative
Separatrix
Surface
Separators
Haynes et al (2007)

7. Phases of Skeleton (cuts at y=0.5)
D=3
Phase 2
D=5
Phase 3
D=4
Phase 4
D=8
Phase 5
D=6
Separatrix Surfaces:
Negative
Positive
Separators:
The skeleton evolves due to reconnection
What is the nature of the reconnection?
Haynes et al (2007)

8. Separator Labels XC XR XL

9. Movement of particles Trace fieldline to plane y=0.5
Plot point on y=0.5
Particle moving with plasma flow
XC XL XR
Distance of fieldline to nearest separator
determines colour of point on y=0.5.

10. Particles near Separators (Phase 5)
Particle fieldlines
near XL
near XC
near XR
XC XL XR

11. Recursive Reconnection
Particles fieldlines about to change
connectivity are all coloured
 separator reconnection
XC XL XR
Closing
Reopens
Reopens

12. Particles near Separators (Phase 5)

13. Flux in Domains tR Examine reconnection at highest rate of change.
Flux in (original) open tails off
due to recursive reconnection tR

14. But we want to understand more…
Current Sheet (t = tR)
Twisted Current Sheet
But we want to understand more…

15. Central Separator (XC): Where Does Reconnection Occur?
Use time slices of E|| along the separator XC.
Reconnection occurs at 0.5 of the normalised separator length
Time (tR) of fastest reconnection rate

16. Planes of Properties (t = tR)
Plane – fixed at 0.5 of
separator XC's length.
Set plane perpendicular
to separator
Dots – connectivity
(closed, -ve open, +ve open, overlying)
normal
Thin current sheet visible on XC.

17. XC: Radial velocity from separator (t=tR)
Reconnection is closing magnetic field
Strong subalfvénic outflow jets

18. What drives reconnection?
Possible Mechanisms:
Plasma Pressure/Magnetic Pressure.
Magnetic Tension.

19. Plasma Pressure Little/no change of pressure at XC.
Significant pressure gradient at XL and XR. XC XL XR

20. Magnetic Pressure Generally opposite to plasma pressure.
Still little pressure change at XC, high at XL and XR. XC XL XR

21. Total Pressure Central reconnection is not pressure driven.
Side separators are pressure driven. XC XL XR

22. Magnetic Tension
Only reconnection at central separator driven by magnetic tension. XC XL XR

23. Conclusions Separator reconnection.
Closing of field driven by magnetic tension force.
Reopening driven by total pressure force.
Reconnection is complex.
Multiple separator reconnection.
Isolated region(s) of diffusion along each separator.
Fronts in outflow jets.
Unlikely to be shocks.
Possible contact discontinuity.
Recursive reconnection.
Flux is closed ↔ reopened multiple times.

24. Introduction to Magnetic Skeletons
2D magnetic skeleton
Sources and sinks.
Null points (B = 0).
Separatrix curves.
3D magnetic skeleton
Separatrix surfaces
Separators (intersection of separatrix surfaces). 3D

25. Evolution of 3D Magnetic Skeleton
Negative
Separatrix
Surface
Positive
Separatrix
Surface
Separators
Many separators implies
many reconnection sites.
Haynes et al (2007)

26. XC: Current
Thin current sheet visible on XC.

27. Plasma Flows Expect reconnection to occur at stagnation-like point.
Direction of plasma flow shows direction of reconnection.

28. XC: Magnetic tension (t = tR)
Closing Driven by Magnetic Tension

29. Conclusions Shown reconnection is separator reconnection.
Multiple separators imply:
Multiple heating sites.
Recursive reconnection:
Flux is repeatedly closed ↔ reopen.
Each separator has an isolated diffusion region.
Central separator (XC):
Closing magnetic field.
Tension driven reconnection.
Subalfvénic jets.