1. The Diffusion Region of Asymmetric Magnetic Reconnection Michael Shay – Univ. of Delaware Bartol Research Institute

2. Collaborators Paul Cassak Our Asymmetric reconnection publications (no guide field): –General Scaling theory and resistive MHD: Cassak and Shay, Physics of Plasmas, 14, 102114, 2007. –Hall MHD simulations Cassak and Shay, GRL, (In press)

3. Semantics Diffusion region –A non-MHD region where at least one species is not frozen-in –Not necessarily irreversible dissipation Example: Hall region of regular collisionless reconnection.

4. Review: Reconnection

5. Magnetic Reconnection V in CACA  Process breaking the frozen-in constraint determines the width of the dissipation region,  Y X Z

6. Magnetic Reconnection Simulation J z and Magnetic Field Lines Y X

7. d Reconnection drives convection in the Earth’s Magnetosphere. Kivelson et al., 1995

8. Reconnection in Solar Flares F. Shu, 1992 X-class flare:  100 sec. B ~ 100 G, n ~ 10 10 cm -3, L ~ 10 9 cm  A  L/c A ~ 10 sec.

9. Reconnection rate  V in Conservation of mass: Flow into and out of dissipation region: V in ~ (  /D) c A  determined by the process breaking the frozen-in constraint. => The spatial extent of the dissipation region is of key importance to determining the reconnection rate. Calculating Reconnection Rate V in cAcA  D Y X Z

10. Two Types of 2D Reconnection  Slow  ~ D V in ~ c A => Fast D D Out of Plane Current Y X Z

11. Kinetic Reconnection (cont.) dissipation region in hybrid model ( Shay, et al., 1999)  JeJe JiJi ViVi DiDi DeDe c  pi c  pe Effect of Hall Physics Ion dissipation region –Controls R. Rate V in ~ (c  pi  /D i ) c A (c  pi  /D i ) ~ 1/10 No system size Dependence! Electron dissipation region –No impact on R. Rate V ine ~ (c  pe  /D e ) c Ae Y X Z

12. Whistler signature Magnetic field from particle simulation (Pritchett, UCLA) Self generated out-of-plane field is whistler signature Confirmed with satellite and laboratory measurements.

13. Overview: Asymmetric Reconnection What is Asymmetric Reconnection? Diffusion region analysis Resistive MHD Simulations –No guide field Hall MHD Simulations –No guide field Conclusions

14. Asymmetric Reconnection Different B,n on either side of diffusion region. Dayside magnetosphere Solar reconnection? Heliopause reconnection

15. d Intense currents MHD not valid No frozen-in Kivelson et al., 1995 High n Low B Low n High B

16. Observation Asymmetric –Reconnecting B-field –Density –Temperature

17. Previous Work Shock structure –Petschek slow shocks => Intermediate wave+expansion fan (Levy et al., 1964) –Further work Petschek and Thorne, 1967; Sonnerup, 1974; Cowley, 1974; Semenov et al., 1983, MHD (Hoshino and Nishida, 1983; Scholer, 1989; Shi and Lee, 1990; Lin and Lee, 1993; La Belle-Hamer et al., 1995; Ku and Sibeck, 1997; Ugai, 2000; …), Kinetic - Hybrid: (Lin and Lee, 1993; Lin and Xie, 1997; Omidi et al, 1998; Krauss-Varban et al., 1999; Nakamura and Scholer, 2000; …), Particle: - Okuda, 1993. –Other relevant studies: Ding et al., 1992; Karimabadi et al., 1999; Siscoe et al., 2002; Swisdak et al., 2003; Linton, 2006; many dayside studies Scaling studies undertaken only recently –Diamagneticd Stabilization (Swisdak et al., 2003) –Orientation of X-line, outflow speed (Swisdak and Drake, 2007) –MHD studies: (Borovsky and Hesse, 2007, Birn et al., 2008) –Global MHD (Borovosky et al., 2008) –PIC: (Pritchett, 2008), Tanaka, 2008; Huang et al., 2008 –PIC-Satellite comparisons (Mozer, Pritchett et al., 2008)

18. Conservation Laws Write MHD in conservative form (  = mass density, v = flow velocity, B = magnetic field, P = pressure, E = electric field, –Integrate over closed surface.  = total energy)

19. More General Diffusion Region Steady state diffusion relation Integrate conservation relations B1B1 22 2L v1v1 v out 11 B2B2 v2v2 22  out Conservation of mass Conservation of momentum Conservation of Energy  B/  t = 0

20. More General Diffusion Region Steady state diffusion relation Integrate conservation relations B1B1 22 2L v1v1 v out 11 B2B2 v2v2 22  out Conservation of mass Conservation of momentum Conservation of Energy  B/  t = 0

21. Asymmetric Scaling Relations Solving gives Need  out Outflow speed Reconnection Rate

22. Outflow Density? Assume reconnected flux tubes mix and conserve total volume. –Each flux tube contains same amount of flux: B 1 A 1 ~ B 2 A 2 A2A2 A1A1 L L 11 22

23. Structure of the Dissipation Region Since v 1 B 1 ~ v 2 B 2, the stronger magnetic field flows in slower –So it makes sense that the X-line is displaced toward the strong field side of the dissipation region. But this is incorrect! Weak field B 1 Strong field B 2 Weak field B 1 Strong field B 2  X2  X1 X The X-line is actually shifted toward the weak field side! – Why? While the flow coming in the strong field side is slower, the flux of energy is larger.

24. Calculation of Location of X-line Evaluate conservation of energy for volume from edge to X-line B1B1  X2 2L v1v1 v out 11 B2B2 v2v2 22  out  X1 X Their ratio gives:

25. Location of the Stagnation Point Similar argument for mass flux Stagnation point offset toward side with smaller B/ . B2B2 B 1,  1 B 2,  2  S2  S1 v2v2 v1v1 S

26. X-line and Stagnation Point are not colocated! There is a flow across the X-line –Generic to asymmetric reconnection! –Previous magnetopause simulations (Siscoe, 2002; Dorelli et al., 2007, …) –Quantitative predictions of the location of X-line and stagnation point (Cassak and Shay, 2007) have been questioned (Birn et al., 2008)

27. Which plasma flows across the X-line? Inflow Alfven speeds control flow across X-line Since c Asp > c Ash  there is a flow of magnetosheath plasma in to magnetosphere. (Matches observations.) 

28. Results are General These relations give E and v out in terms of upstream parameters. –No specificaion of diffusion mechanism or Hall term. –General applicability Require diffusion (non-MHD) mechanism to determine absolute values: –Sets diffusion region widths      and L –Determines actual reconnection rate

29. Resistive MHD To find an absolute reconnection rate, we need to specify a dissipation mechanism. For asymmetric Sweet-Parker, Uniform resistivity Sweet-Parker reconnection

30. Fluid Simulations Double current sheet configuration x = outflow y = out-of-plane z = inflow B, T tanh functions n balances B 2

31. Resistive MHD Simulations V normalized to c A, Length normalized to L 0 Size: 409.6 X 204.8, 4096 X 2048 grids  0.05 (Lundquist number = 8,192-40,960)  min = 1 initially n 1 = n 2 [B 1,B 2 ] = [1,1], [2,1], [3,1], [4,1], [5,1], [4,2]

32. Resistive MHD Simulations [B 1,B 2 ] = [1,3] [n 1,n 2 ] = [1,1] x = outflow y = out-of-plane z = inflow

33. MHD Results Out-of-plane current density J Cut across X-line along inflow X S Decoupling of X-line and stagnation point borne out in MHD simulations.

34. MHD Results Color = out-of-plane current White = magnetic field lines Initial field asymmetry = 3, no density asymmetry Signatures –Typical “bulge” into low-field region –Particles flow across X-line

35. Energy and Mass Flux Check Determined geometry of diffusion region from simulations. –Non-trivial Energy and Mass Flux balances in each sub-region Flux in Flux out

36. Verification of Scaling Scaling laws for outflow speed v out and reconnection rate E in terms of geometry and upstream parameters tested Very good agreement Other studies find agreement: –Borovsky and Hesse, 2007 (anomalous resistivity MHD) –Birn et al., 2008 (Anomalous resistivity MHD) –Borovsky et al., 2008 (Global MHD) –Pritchett, 2008 (Kinetic PIC) v out EE

37. Hall MHD Simulations Two dimensional Hall-MHD simulations Anti-parallel magnetic fields Three sets of runs –Asymmetric fields [B 01,B 02 ] = [1,1], [2,1], [3,1], [0.5,1], Symmetric density –Asymmetric density [n 01,n 02 ] = [1,1], [2,1], [3,1], [0.5,1], Symmetric field –Asymmetric density and field [B 01 (n 01 ),B 02 (n 02 )] = [2(1),1(2)], [1(1),0.5(4)] Asymmetric initial temperature to balance pressure Box size = 204.8 x 102.4 c /  pi Grid scale = 0.05 c /  pi m e = m i / 25 (density asymmetry not included in electron inertia term)  min = 4 initially

38. Hall MHD Simulations [B 1,B 2 ] = [1,2] [n 1,n 2 ] = [2,1] x = outflow y = out-of-plane z = inflow

39. Hall-MHD Results Cuts across x-line along inflow Top - field lines (white) and out-of-plane magnetic field (color) Bottom - electron (black) and ion (white) flow lines and out-of-plane current (color) Initial field asymmetry = 3 Electron and ion stagnation points different!

40. Verification of Scaling Generalized Sweet-Parker like scaling is satisfied for both electrons and ions. v out (ions) v out (electrons) theory E

41. The Big Picture Magnetospheric Applications? Agreement of the scaling of E for Hall reconnection   / L ~ 0.1 is independent of the asymmetry in B and  Are the results applicable to dayside magnetopause reconnection? –Yes (Borovsky) In global MHD simulations, the reconnection rate at the nose of the magnetopause agreed with E based on local parameters rather than the solar wind electric field (Borovsky et al., 2008). –No (Dorelli) The analysis is manifestly two-dimensional, whereas 3D effects (such as flows) are important at the magnetopause. The orientation of the X-line between arbitrary fields not predicted. –Critical Question: Can significant portions of dayside reconnection be characterized as quasi-2D? Does a fluid element traversing the diffusion region see 3D effects?

42. Solar Wind-Magnetospheric Coupling Models Newell et al., 2007 –Best model to date, but it uses ad hoc fitting to achieve performance Borovsky (2008) used our scaling result to derive a coupling function from first principles –It performed as well as Newell’s Scaling of reconnection is a potential starting point for a quantitative understanding of solar wind-magnetospheric coupling

43. Conclusion We have derived the scaling of the reconnection rate and outflow speed with upstream parameters during asymmetric reconnection [Cassak and Shay, Phys. Plasmas 14, 102114 (2007)] –Numerical simulations agree with the theory for collisional and collisionless (Hall) reconnection Signatures of Asymmetric Reconnection –X-line and stagnation point not coincident for asymmetric B field –There is a bulk flow across the X-line Potential applications to the dayside magnetosphere (Borovsky, 2008; Turner et al., in prep), though future work is needed

44. Future Directions Much work to be done Effect of guide field –Diamagnetic stabilization (Swisdak et al., 2003) –Orientation of X-line (Swisdak et al, 2007) More realistic two-scale diffusion region –Requires Kinetic PIC –Pritchett, 2007 Separatrix structures –Mozer et al., 2007 Linking separatrix structures with diffusion region structure.