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

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

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.

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

Earth’s and other planet’s magnetosphere

Tokamak

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

B. Petschek model (X-type geometry) (1964) 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

Sawtooth collapse in the Tokamak

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)

M=1 mode Sawtooth for Resistive Results

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 MHD 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 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

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 (Birn et al. 2001)

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

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 ~ 50-100km/s

Reconnection rate ~ 0.1

C. Flare dynamics Geometry Electric field

Time evolution of current density and parallel electric field

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

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

Revisit Huba and Rudakov

Dependence of system length

Rates for resistive MHD

Rates for closed or period boundary

Rates in Particle-in-Cell code

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.

Thanks!!!

Thanks!!!