The Collisionless Diffusion Region: An Introduction

1. The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC

2. Overview: Diffusion region basics The (electron) diffusion region for anti-parallel reconnection The (electron) diffusion region for guide-field reconnection An avenue toward fast MHD reconnection without Hall terms Acknowledgements: J. Birn, M. Kuznetsova, K. Schindler, M. Hoshino, J. Drake

3. Magnetic Reconnection: Dissipation Mechanism (How does it work?) Conditions: IMPOSSIBLE (for species s) if

4. z x Electric Field Equations Electron eqn. of motion At reconnection site important? small, limited by me?

5. Results for anti-parallel reconnection: Brief review

6. Magnetic field and ion-electron flow velocities P. Pritchett M. Hoshino

7. Normal Magnetic Flux: evolution electron-mass independent! => Local electron physics adjusts to permit large scale evolution

8. Compare extremes along dashed lines - ion quantities - electron quantities

9. Large (ion) Scale Features -> Ion scale features approx invariant.

10. Small (electron) Scale Features

11. Pressure Tensor

13. 10.0<x< 11.0 -0.5<z< 0.5 log f 0.076 0.4 -0.739 0.2 -1.555 Sample Electron Distribution (Pxye) u 0.0 y -2.370 -0.2 -3.185 -0.4 -4.000 -0.4 -0.2 0.0 0.2 0.4 u x Thermal inertia (nongyrotropic pressure)-based dissipation seems key to anti-parallel reconnection

14. Can be explained by trapping scale: “bounce motion” [Horiuchi and Sato, 1996] [Biskamp and Schindler, 1971] => Estimate of reconnection electric field [Hesse et al., 1999] [Kuznetsova et al., 2000]

15. 3D – no LHD, kink, … Zeiler et al. realistic electron mass Ricci et al.

16. But, some questions remain… Kink, LHD, Ozaki et al. Ion sound mode… Sausage mode, Buechner et al.

17. …and other limitations, such as • Finite (small) system size • Finite (small) ion/electron mass ratio • Finite (small) speed of light • Periodicity …there is work to be done!

18. What changes in the presence of guide field? if guide field strong enough electrons are magnetized no bounce orbits no nongyrotropic pressures(?) bulk inertia dominant(?) Method: Theory and PIC simulations

19. Simulation Setup - 1-D “Harris” Equilibrium, Lx= 2Lz= 25.6 c/wpi - Flux function: A = -ln cosh(z/a) - normal magnetic field perturbation (X type, 2.5% of lobe field) - 0, 40, 80% guide field - Sheet Full-Width a= c/wpi - Ti/Te = 5 -mi/me=256 - 100x106 particles - 800x800 grid Results averaged over 60 plasma periods

21. Change of symmetry By P. Pritchett

22. Parallel electric fieldWit=16 …also analytic theory by Drake et al.

23. z x Electric Field Equations Electron eqn. of motion At reconnection site important? small, limited by me?

24. Magnitude of Bulk Acceleration Contribution Time derivative of (negative) electron velocity in y direction:

25. Pxye Pyze

26. -(vezBx-vexBz) -me(ve.grad vey)/e

27. vy vz vz vx vx vy Electron Distribution Functions F(vx,vy) F(vx,vz) F(vy,vz)

28. ..pressure tensor nearly(?) gyrotropic But: if Bx, Bz=0 -> nongyrotropy important. How to estimate?

29. Scaling the pressure tensor evolution equation Assume ignore heat flux…

30. Pressure tensor approximations Hesse, Kuznetsova, Hoshino, 2001

31. Electron Pressure Tensors approximation from simulation Pxye Pxye Pyze Pyze critical difference at reconnection site!

32. coll. skin depth

33. Qxyze Qxxye Pyza approximation

34. Heat Flux Tensor Time Evolution lots of work

35. Approximations for Qxyze x,y,x component: Assume near gyrotropy, By>>Bx, Bz Leading order, Pii>>Pjk

36. Approximations for Qxyze From simulation: Approximation: Ok in center, difference due to 4-tensor?

37. Scaling of diffusion region => 2 Scale lengths: Collisionless skin depth Electron Larmor radius in guide field

38. Physical Mechanism: Larmor orbit interacts with “anti-parallel” B components

39. 3D Modeling M. Scholer et al.: Formation of “2D” channel J. Drake et al.: Buneman modes, electron holes, anomalous resistivity

40. P. Pritchett: inertia important

41. …and other limitations, such as • Finite (small) system size • Finite (small) ion/electron mass ratio • Finite (small) speed of light • Periodicity …there is work to be done!

42. Results from GEM reconnection challenge: • Hall effect (dispersive waves) speeds up reconnection rate • Reconnection rate otherwise independent on model • MHD models with simple resistivity show only slow reconnection rates • Question: • Are Hall effects the only way to include fast reconnection in MHD • models?

43. Approach: • Hall effect result of ion-electron scale separation • Eliminate scale separation by • - Choosing equal ion and electron mass • - Choosing equal ion and electron temperatures • Simple and cheap…, includes ion and “electron” kinetic physics • “Small” GEM runs with and without guide field • “Large” runs, with and without guide field

44. GEM-size run, no By

45. GEM-size run, no By me=1/256 me=1

46. GEM-size run, By=0.8

47. GEM-size run, By=0.8 me=1/256 me=1

48. large run, By=0.

49. large run, By=0.8

50. large run, By=0. large run, By=0.8 Reconnection rates similar to GEM problem