1. Reconnection rates in Hall MHD and Collisionless plasmas
Zhi-Wei Ma (马志为)& Jun Huang(黄俊)
IFTS, Zhejiang Univ. &
Institute of Plasma Physics, CAS
International Symposium on Fusion Energy Science & The 5th Workshop on Nonlinear Plasmas Sciences
Oct. 24, 2006, Hangzhou

2. Outline 1. Steady-state reconnection
2. Time-dependent force reconnection
3. Magnetic reconnection in Hall MHD
4. Magnetic reconnection in collisionless plasma
5. Summary

3. What is magnetic reconnection?
Another key requirement:
Time scale must be much
faster than diffusion time
scale.
Magnetic energy converts into kinetic or thermal energy and mass, momentum, and energy transfer between two sides of the central current sheet.

5. Where does magnetic reconnection take place and why is it important?
Solar flare

6. Earth’s and other planet’s magnetosphere

7. Tokamak

8. 1. Steady-state Reconnection
A. Sweet-Parker model (Y-type geometry) (1957&1958)
Reconnection rate
Time scale

9. B. Petschek model (X-type geometry) (1964)
Reconnection rate and time scale are
weakly dependent on resistivity.

10. Difficulties of the two models
For Sweet-Parker model
The time scale is too slow to explain the observations.
Solar flare

11. Substorm in the magnetotail

12. Sawtooth collapse in the Tokamak

13. For Petschek model
The time scale for this model is fast enough to explain the observation if it is valid. But the numerical simulations show that this model only works in the high resistive regime. For the low resistivity , the X-type configuration of magnetic reconnection is never obtained from simulations even if a simulation starts from the X-type geometry with a favorable boundary condition.
Basic problem in both models is due to the steady-state assumption. In reality, magnetic reconnection are time-dependent and externally forced.

14. 2. Time-dependent force reconnection
A. Harris Sheet

15. Resistive MHD Equations

16. New fast time scale in the nonlinear phase
(Wang, Ma, and Bhattacharjee, 1996)

18. B. Substorms in the magnetotail

19. Observations (Ohtani et al. 1992)

20. Time evolution of the cross tail current density at the near-Earth region (Ma et al. 1995)

22. C. Flare dynamics in the solar corona

24. Time evolution of maximum current density (Ma and Bhattacharjee, 1996)

25. (Ma and Bhattacharjee, 1996)

26. M=1 mode Sawtooth for Resistive Results

27. Brief summary for time-dependent force reconnection
1. New fast time scale is obtained for time-dependent force reconnection.
2. The new time scale is fast enough to explain the observed time scale in the space plasma.
3. The weakness of this model is sensitive to the external driving force which is imposed at the boundary.
4. The kinetic effects such as Hall effect are not included, which may become very important when the thickness of current sheet is thinner than the ion inertia length.

28. 3. Magnetic reconnection with Hall MHD
Resistive term
Inertia term ~
Hall term ~

29. Spatial scales If , the resistivity term is retained (resistive MHD).
If , both the resistivity and Hall terms have to be included (Hall MHD).
If , we need to keep the Hall and inertia terms and drop the resistive term (Collisionless MHD).

30. Hall MHD Equations

31. A. Harris Sheet X-type vs. Y-type Decoupling Separation Quadruple B_y
(Ma and Bhattacharjee,
1996 and 2001)
X-type vs. Y-type
Decoupling
Separation
Quadruple B_y
Time scale
Reconnection rate
No slow shock

32. Time evolution of the current density in the hall (dash line) and resistive MHD (solid line)

33. The GEM challenge
results indicate that the
saturated level from Hall
MHD agrees with one
obtained from hybrid and
PIC simulation
(Birn et al. 2001)

34. B. Hall MHD in the magnetotail (Ma and Bhattacharjee, 1998)
Impulsive growth
Quite fast disruption
Thin current sheet
Strong current density
Fast time scale
Fast reconnection rate

36. Explosive trigger of substorm onset
With increasing computer capability, we are able to further enhance our resolution of the simulation to reduce numerical diffusion. In the new simulation, explosive trigger of substorm onset is observed due to breaking up extreme thin current sheet.

38. The tail-ward propagation
speed of the x-point or
Disruption region ~ km/s

39. Reconnection rate ~ 0.1

40. C. Flare dynamics
Geometry
Electric field

41. Time evolution of current density and parallel electric field

42. Brief summary Hall MHD vs. Resistive MHD
Time scale and reconnection rate: Fast with very weak dependence of the resistivity vs. Fast with a suitable boundary conditions
Geometry: X-type vs. Y-type
Decoupling Motion of ions and electrons: yes vs. no
Spatial scale separation of electric field and current density: Yes vs. No
Magnitude and distribution of parallel electric field: strong and broad vs. weak and narrow
Quadruple distribution of B_y: yes vs. no
No slow shock for both cases, which is different from Petschek’s model

45. Reconnection rate with open system in Hall MHD (Huba and Rudakov PRL, 2004)

47. Revisit Huba and Rudakov

48. Dependence of system length

50. Rates for resistive MHD

51. Rates for closed or period boundary

53. Rates in Particle-in-Cell code

55. Brief summary
1. Reconnection rate ~0.1 is not universal. It is strong dependent on boundary and initial conditions.
2. In general, the rate is higher in a PIC simulation than in Hall MHD for open-system without external driving force, which may indicate that electron dynamics in the diffusion region are important.
3. But the reconnection rates for cases with the external driving force or with period conditions are in the same order for both PIC than Hall MHD simulation.

56. Thanks!!!

57. Thanks!!!