William Daughton Plasma Physics Group, X-1 Los Alamos National Laboratory Presented at:

1. The Onset of Magnetic Reconnection William Daughton Plasma Physics Group, X-1 Los Alamos National Laboratory Presented at: Second Workshop on Thin Current Sheets University of Maryland April 19, 2004

2. www-spof.gsfc.nasa.gov Motivation for this work Current sheet geometry is often employed to study the basic physics of collisionless magnetic reconnection www-spof.gsfc.nasa.gov Courtesy of Hantao Ji (PPPL) Kinetic Simulations are typically 2D with large initial perturbation: a. Does not allow instabilities in direction of current b. Avoids the question of onset completely Focus on the onset problem

3. Basic Approach Explicit PIC must resolve all relevant scales For a given problem with fixed box size 3D Simulations - Must choose very artificial parameters 2D Simulations - More realistic parameters are possible

4. Harris Current Sheet Background Distribution Main Distribution Anisotropy Thickness

5. Can collisionless tearing explain onset?

6. 2D Simulations of Tearing Consider 3 simulations - Only change the box length Single island saturation Two island saturation Four island saturation Equilibrium Parameters Reduced by 30% for

7. Single Island Tearing Saturation Mode Amplitude Linear Growth Rate PIC Simulation

8. Two Island Coalescence Linear Growth Rate Mode Amplitudes M=1 M=2

9. Four Island Coalescence Onset Stage • Central region of box • Linear tearing islands • Coalescence • Very slow process Fast Reconnection • Show entire box • Large scale reconnection • Saturation limited by box

10. How might this change in 3D? • LHDI is much faster than tearing • 2D simulations in oblique plane • Can the LHDI modify onset physics ? Reconnection Onset from Tearing • Single island tearing saturates at small amplitude • Onset requires coalescence of many islands • Finite Bz is stabilizing influence Laval & Pellat 1968 Biskamp, Sagdeev, Schindler, 1970 Pellat, 1991 Pritchett, 1994 Quest et al, 1996 Sitnov et al, 1998 -> can go unstable? Tearing is stable in magnetotail Scholer et al, PoP 2003 Horiuchi Shinohara & Fujimoto

11. Lower-hybrid Drift Instability (LHDI) • Driven by density gradient • Fastest growing modes • Real frequency • Growth rate • Stabilized by finite beta • Primarily electrostatic and localized on edge Example Eigenfunction Carter, Ji, Trintchouck, Yamada, Kulsrud, 2002 Experiment Davidson, Gladd, Wu & Huba, 1977 Huba, Drake and Gladd, 1980 Good Agreement Theory Bale, Mozer, Phan 2002 Observation

12. New results challenge this conclusion Direct penetration of longer wavelength linear modes Nonlinear development of short wavelength modes Established Viewpoint on LHDI Standard Arguments • Localized on edge of layer • Small anomalous resistivity • Wrong region to modify tearing • Not relevant to reconnection

13. Penetration of LHDI tWci=3 tWci=8 tWci=13 tWci=11 tWci=13

14. Nonlinear Development in a Thicker Sheet ?

15. 2D Simulation of Lower-Hybrid Equilibrium Parameters Thicker Sheet Colder Electrons Background More relevant to magnetospheric plasmas Simulation Parameters:

16. Electrostatic Fluctuations Two fastest Growing modes Lower-Hybrid Drift Mode Lower-Hybrid Drift Mode Fluctuations are confined to the edge of the sheet

17. Evolution of Current Density Initial Contours of Y-averaged

18. Evolution of Ion Density Initial Contours of Y-averaged

19. Evolution of Ion Velocity Initial Contours of Y-averaged

20. Evolution of Electron Velocity Initial Contours of Y-averaged

21. Evolution of Electron Anisotropy Contours of Y-averaged

22. Scale for Crossing Orbit Lower-hybrid fluctuations Crossing Noncrossing Example of scattering Crossing Resonant Scattering of Crossing Ions

23. Electrostatic Potential Net gain + + + + + + + + + Net loss - - - - - - - - - Net gain + + + + + + + + Contours of

24. Electron Acceleration Use Equilibrium Profiles Neglect

25. Inductive Heating of Electrons Evolution of current profile modifies magnetic field Changes on the ion time scale For electrons, magnetic field changes slowly Adiabatic Invariant Magnetic Moment Inductive Heating How to construct adiabatic invariant for these orbits?

26. Anisotropic Electron Heating Y-averaged Contours of Y-averaged

27. Physical Mass Plasma parameters are same but numerical requirements increase Results show same basic physics • Details are described in preprint • How big of a mass ratio is needed?

28. What about lower mass ratio?

29. New Model for Fast Onset of Reconnection Critical thickness for process to occur Potential structure accelerates electrons Enhances tearing mode Lower-hybrid drift instability Critical Scale Lower-hybrid drift instability 1. Current density 2. Anisotropy Tearing Growth Rate Forslund, 1968 J. Chen and Palmadesso, 1984 4. Rapid onset of reconnection

30. Test this idea at reduced mass ratio Tearing Growth Rate Factor of 17 increase in growth rate Fastest mode shifts to shorter wavelength Growth of small islands --> Coalescence Rapid onset of large scale reconnection Initialize previous 2-Mode case with

31. Electron Anisotropy Instabilities? Theory of Space Plasma Microinstabilities, S.P Gary 1. Whistler Anisotropy Instability 2. Electron Firehose Instability Should these occur in neutral sheet? Edge region is low beta Center has complicated orbits Does not appear in simulations?

32. Neutralization of Electrostatic Potential Growth of LHDI Time scale for electrons to flow in and neutralize

33. Future Work Working with collaborators to simulate in 3D However, many things left to examine in 2D: 1. Does predicted critical thickness hold? 2. Role of guide field and/or normal component 3. Influence of background (lobe) plasma More realistic boundary conditions Possible relevance to recent Cluster observations Runov et al, Cluster observation of a bifurcated current sheet, GRL, 2003