1. Magnetic Reconnection and its Applications Zhi-Wei Ma Zhejiang University Institute of Plasma Physics Chengdu, 2007.8.8

2. Outline 1. Numerical Scheme 2. Steady-state reconnection A. Sweet-Parker model B. Petschek model 3. Time-dependent force reconnection A. Harris sheet B. Magnetotail C. Solar corona 4. Magnetic reconnection with Hall effects A. Harris sheet B. Magnetotail C. Solar corona current dynamics D. Coronal mass ejection 5. Summary

3. Numerical Scheme Consider the general first-order ordinary differential equation, • Euler's method y t

6. The standard fourth-order Runge-Kutta method takes the form:

7. for double precision for single precision

8. Global integration errors associated with Euler's method (solid curve) and a fourth-order Runge-Kutta method (dotted curve) plotted against the step-length. Double precision calculation.

9. The equation for the shock propagation:

10. * * n+1/2

12. Hall MHD Equations

16. Rouge-Kutta Scheme (4,4)

17. Dispersion Properties for Different Schemes

18. Fast rarefaction wave (FR), Slow compressional wave (SM), Contact discontinuity (CD) Slow shock (SS)

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

20. 1. Steady-state Reconnection • A. Sweet-Parker model (Y-type geometry) • Reconnection rate • Time scale

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

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

23. Substorm in the magnetotail

24. 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.

25. 2. Time-dependent force reconnection • A. Harris Sheet

26. Resistive MHD Equations

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

29. B. Substorms in the magnetotail

30. Observations (Ohtani et al. 1992)

31. Time evolution of the cross tail current density at the near-Earth region(Ma, Wang, & Bhattacharjee, 1995)

33. C. Flare dynamics in the solar corona

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

36. (Ma and Bhattacharjee, 1996)

37. 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.

38. 3. Magnetic reconnection with Hall effects Resistive term Inertia term ~ Hall term ~

39. 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). • For solar flare, • For magnetotail,

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

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

42. The GEM challenge results indicate that the saturated level from Hall MHD agrees with one obtained from hybrid and PIC simulation.

43. 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

45. 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.

47. The tail-ward propagation speed of the x-point or Disruption region ~ 50km/s

48. Zhang H., et al., GRL, 2007

49. Reconnection rate ~ 0.1