AGU FALL MEETING 2008

(SM31A-1694)

Magnetic Reconnection Across A Dusty Harris-like Current Sheet S. A. Lazerson Geophysical Institute, University of Alaska, Fairbanks, Alaska, USA

Simulations of magnetic reconnection in a dusty plasma were conducted across a Harris-like current sheet. These simulations were conducted with the DENISIS 4-uid dusty magnetoplasma code. The simulations begin with a Harris-like current sheet which goes through a ballistic relaxation process. This allows the system to achieve suitable pressure proles. Multiple resistive models were employed. These included global resistivity, a locally enhanced resistivity, parameter dependent dynamic resistivity, and explicit use of collision frequencies in the induction equation. Magnetic topology, mass uxes, and magnetic uxes were examined throughout the simulations. These simulations indicate that while the assumptions of the Sweet- Parker and Petschek models of reconnection may be correct on small timescales, the overall process of reconnection across a current sheet can be highly dynamic. This includes reformation of current sheets on smaller scales after reconnection and multiple reconnection events across a dynamic sheet. Abstract.

applied perpendicular to the current sheet (in a pinching fashion, in the yˆ direction). The outow region is dened in horizontal extent by d and velocities ow along the current sheet perpendicular to the current (in the xˆ direction).

1. Introduction

Magnetic reconnection can be characterized by 3 distinct regimes dened by the current sheet prole, steady-state reconnection, and formation of a new current sheet after magnetic island ejection. The transition between current sheet and steady-state reconnection is necessarily a highly nonlinear and transient process. For many parameter regimes this transition period may constitute a signicant period of the overall reconnective event. This is particularly important for dusty astrophysical plasmas where the large dust inertia may prevent a steady-state from being achieved. Simulation of reconnection in a dusty plasma using the DENISIS 4-uid dusty plasma code (Schröer et al., 1998) may shed light on this transient period of reconnection. Classical steady-state models of reconnection (Sweet Parker and Petscheck) make certain assumptions regarding such a state. The rst of which is conservation of mass ux. The second of which is conservation of magnetic ux into and out of the reconnection region. Finally, assumptions are made regarding pressure gradients in the reconnection region being negligible. The reconnection rate (electric eld at the X-Line) should also approach a constant value. Mass ux and reconnection rate are tracked to determine the state of the reconnection process. Attention is paid to the evolution of the current sheet structure.

2. Method

The simulation begins with a Harris-like magnetic eld prole. Diculties in determining pressure proles for the system necessitate a ballistic relaxation technique. Once a relaxed current sheet is achieved the system is perturbed in a 'Sweet-Parker' like fashion through inows and outows. The simulation is allowed to evolve on timescales indicating a steady-state has been reached. The simulation is conducted using the DENISIS 4-uid dusty plasma code. The simulation box is of extent x ∈ [−10, 10], y ∈ [−2, 2], and z ∈ [0, 10], with a 49 × 49 × 15 grid (nonuniform in y ). A schematic representation of the system is given in gure 1. Collision frequencies which are representative of the protosolar nebula are chosen. A resistive form of the induction equation is chosen over a collisional form in order to better dene a diusive velocity. ~ ∂B ∇pi 2~ ~ = −∇ × + ∇ × v~i × B − η∇ B ∂t ni 

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       

       



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  

  

Harris sheet conguration. The magnetic eld has a hyper~ = B0 tanh (y/dsp) xˆ. The densties have a prole of bolic tangent prole B the form ρ = ρ0 + ρ0/ cosh2 (y/dsp). Pressures are initially chosen so as to produce an isothermal system. Three reconnective modes are examined. The rst ('Sweet-Parker') sets the outow velocity to the asymptotic Alfvén velocity. The inow velocity is then calculated via conservation of mass ux (in the Sweet-Parker fashion). The second ('Local Alfvén') attempts to avoid the locally superAlfvénic outow velocities by setting the outow velocity equal to the local Alfvén velocity. The third, mode assumes that the inow velocity is equal to the diusive velocity dened at vin = η/d. For these runs η = 0.0045. The outow velocity is then calculated via conservation of mass ux (in the Sweet-Parker fashion). Figure 1.

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3. Results

The current sheet is perturbed in a 'Sweet-Parker' like fashion. The reconnection region is dened by a length (l = 10.0) and a width (d = 1.0). Three models are examined for the velocity perturbations. In each case, the inow region is dened in horizontal extent by l and velocities are No copyright is claimed for this article.

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The mass uxes indicate that the transition from current sheet to reconnecting current sheet is marked by oscillations in the inow uxes. These oscillations are damped away on longer timescales. Once damped the ows conserve mass ux through the reconnection region. The outow mass uxes are fairly constant throughout the reconnection event. Figure 2 indicates that each perturbative mode results in a large spike in mass ux right after the perturbation is applied. In each case, the inow mass ux drops below the outow mass ux right after the compressive spike. These features are attributed to the compressive nature of the perturba-

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LAZERSON: MAGNETIC RECONNECTION

tion on the initial current sheet conguration. Once the current sheet has time to evolve, the ows enter a ow regime that is non-compressive. The electric eld at the X-Line (center grid point) serves as an analogue for the reconnection rate. Figure 3 shows the reconnection rate for each of the perturbative modes. The 'Sweet-Parker' and 'Local Alfvén' modes both show an initial enhancement of the reconnection rate. This is attributed to the compressive nature of the inow regions for those modes. The 'Diusive Equilibrium' mode does not show such a feature as the inow velocity is chosen to equal that of the diusive velocity of the magnetic eld. The 'Sweet-Parker' mode shows a gradual increase in the reconnection rate followed by a gradual decrease to the original value. The 'Local Alfvén' and 'Diusive Equilibrium' modes show multiple enhancements of the reconnection rate. This is indicative of multiple reconnection events taking place. In terms of the reconnection rate, the system does not appear to enter a steady state.

Dust Mass Fluxes. Here the dust mass uxes into (solid lines) and out of (dashed lines) the reconnection region are tracked. The current sheet structure is changing as the system evolves. Early on the current sheet experiences an enhancement of the current at the XLine (Figure 4). This then evolves into a forked structure later on in the simulation (Figure 5). This seems to indicate that the transition from current sheet to reconnecting current sheet involves and enhancement at the X-Line which transforms into a current sheet with shock-like structures. Clearly the current sheet is evolving. Figure 2.

must undergo a transitory state where the assumptions of analytic models of reconnection do not apply. The system will settle into a reconnective state which more closely matches the assumptions of analytic models. However, a constant reconnection rate is not universally achieved. It is also clear that the current sheet conguration for a 'steady-state' reconnective solution is far from that of a Harris-like current sheet. The current sheet evolves from an enhanced X-Line to that of a forked current sheet. Future work will focus on various aspects of the simulation. The inow perturbation clearly results in oscillations which may have an eect on the transition from current sheet to steady state reconnection. A more detailed non-compressive perturbation should be derived for the current sheet prole. A longer simulation box should be used so as to examine the propagation of the reconnective mode along the current sheet.

Figure 4.

Current Sheet Enhancement at t=9.0.

Figure 5.

Current Sheet Enhancement at t=21.0.

Acknowledgments. I'd like to thank Dr. Heinz Wiechen and Dr. Roger Smith for their continued commentary and nancial support of this work.

References S.A. Lazerson and H.M. Wiechen, Three-dimensional simulations of magnetic reconnection in a dusty plasma, Journal of Plas. Phys., 74, 4 (2008).

Reconnection Rate. The electric eld at the X-Line is used as a measure of the reconnection rate for the various perturbative methods. Figure 3.

A. Schröer G.T. Birk and A. Kopp, DENISIS - A three-dimensional partially ionized dusty magnetoplasma code, Computer Phys. Comm., 112, 7 (1998).

4. Discussion

Magnetic reconnection across a dusty Harris-like current sheet is examined. It is shown that despite choice of reconnective mode, a current sheet

S. A. Lazerson, Geophysical Institute, University of Alaska, Fairbanks 903 Koyuk Dr., Fairbanks, AK 99775, USA. ([email protected])