Simulation Study of Magnetic Reconnection in the Magnetotail and Solar Corona Zhi-Wei Ma Zhejiang University & Institute of Plasma Physics Beijing,

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

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

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

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

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

 Substorm in the magnetotail

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.

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

Resistive MHD Equations

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

B. Substorms in the magnetotail

 Observations (Ohtani et al. 1992)

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

C. Flare dynamics in the solar corona

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

(Ma and Bhattacharjee, 1996)

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.

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

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).

Hall MHD Equations

A. Harris Sheet (Ma and Bhattacharjee, 1996 and 2001; GEM challenge: Birn et al. 2001) 1.X-type vs. Y-type 2.Decoupling 3.Separation 4.Quadruple B_y 5.Time scale 6.Reconnection rate 7.No slow shock In Situ Satellite Obsevations: Øieroset, et al., Nature, 2001 Deng, et al., Nature, 2001

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

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

B. Hall MHD in the magnetotail (Ma and Bhattacharjee, 1998) 1.Impulsive growth 2.Quite fast disruption 3.Thin current sheet 4.Strong current density 5.Fast time scale 6.Fast reconnection rate

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.

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

Reconnection rate ~ 0.1

Density depletion and heat plasma around the separatrices

C. Flare dynamics 1.Geometry 2.Electric field

Time evolution of current density and parallel electric field

D. Coronal mass ejection or flux rope eruption  Initial Geometry

Catastrophe Or loss equilibrium

Hall MHD Run MHD run

Flux rope region

Total energy Thermal energy Magnetic energy Kinetic energy

Brief summary Hall MHD vs. Resistive MHD 1.Time scale and reconnection rate: Fast with very weak dependence of the resistivity vs. Fast with a suitable boundary conditions 2.Geometry: X-type vs. Y-type 3.Decoupling Motion of ions and electrons: yes vs. no 4.Spatial scale separation of electric field and current density: Yes vs. No 5.Magnitude and distribution of parallel electric field: strong and broad vs. weak and narrow 6.Quadruple distribution of B_y: yes vs. no 7.No slow shock for both cases, which is different from Petschek’s model

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