Problems in MHD Reconnection ??

1. Problems in MHD Reconnection ?? (Cambridge, Aug 3, 2004) Eric Priest St Andrews

2. CONTENTS 1.Introduction 2.2DReconnection 3.3DReconnection 4. [Solar Flares] 5. Coronal Heating

3. 1. INTRODUCTION • Reconnection is a fundamental process in a plasma: • Changes the topology • Converts magnetic energy to heat/K.E • Accelerates fast particles • In solar system --> dynamic processes:

4. Magnetosphere Reconnection -- at magnetopause (FTE’s) & in tail (substorms) [Birn]

5. Solar Corona Reconnection key role in Solar flares, CME’s [Forbes] + Coronal heating

6. Induction Equation [Drake, Hesse, Pritchett] • B changes due to transport + diffusion • Rm>>1 in most of Universe --> B frozen to plasma -- keeps its energy Except SINGULARITIES -- & j & E large Heat, particle accelern

7. Current Sheets - how form ? • Driven by motions • At null points • Along separatrices • Occur spontaneously • By resistive instability in sheared field • By eruptive instability or nonequilibrium • In many cases shown in 2D but ?? in 3D

8. 2. 2D RECONNECTION • In 2D takes place only at an X-Point -- Current very large -- Strong dissipation allows field-lines to break • / change connectivity • In 2D theory well developed: • * (i) Slow Sweet-Parker Reconnection (1958) • * (ii) Fast Petschek Reconnection (1964) * (iii) Many other fast regimes -- depend on b.c.'s • Almost-Uniform (1986) • Nonuniform (1992)

9. Sweet-Parker (1958) Simple current sheet - uniform inflow

10. Petschek (1964) • SP sheet small - bifurcates Slow shocks - most of energy • Reconnection speedve-- any rate up to maximum

11. ?? Effect of Boundary Conditions on Steady Reconnection NB - lessons: Bc’s are crucial 2. Local behaviour is universal - Sweet-Parker layer Global ideal environment depends on bc’s 4. Reconnection rate - the rate at which you drive it 5. Maximum rate depends on bc’s

12. Newer Generation of Fast Regimes • Depend on b.c.’s Almost uniform Nonuniform • Petschek is one particular case - can occur if enhanced in diff. region • Theory agrees w numerical expts if bc’s same

13. Nature of inflow affects regime Converging Diverging -> Flux Pileup regime Same scale as SP, but different f, different inflow • Collless models w. Hall effect (GEM, Birn, Drake) -> fast reconnection - rate = 0.1 vA

14. 2D - Questions ? • 2D mostly understood • But -- ? effect of outflow bc’s - -- fast-mode MHD characteristic -- effect of environment • Is nonlinear development of tmi understood ?? • Linking variety of external regions to collisionless diffusion region ?? [Drake, Hesse, Pritchett, Bhattee]

15. 3. 3D RECONNECTION Many New Features (i) Structure of Null Point Simplest B = (x, y, -2z) 2 families of field lines through null point: Spine Field Line FanSurface

16. Most generally, near a Null (Neukirch…) Bx = x + (q-J) y/2, By = (q+J) x/2 + p y, Bz = j y - (p+1) z, in terms of parameters p, q, J (spine), j (fan) J --> twist in fan, j --> angle spine/fan

17. (ii) Topology of Fields - Complex In 2D -- Separatrix curves In 3D -- Separatrix surfaces -- intersect inSeparator

18. In 2D, reconnection atX transfers flux from one2Dregion to another. In 3D, reconnection at separator transfers flux from one 3D region to another.

19. ? Reveal structure of complex field ? plot a few arbitrary B lines E.g. 2 unbalanced sources SKELETON -- set of nulls, separatrices -- from fans

20. 2 Unbalanced Sources Skeleton: null + spine + fan (separatrix dome)

21. Three-Source Topologies

22. Simplest configuration w. separator: Sources, nulls, fans -> separator

23. Looking Down on Structure Bifurcations from one state to another

24. Movie of Bifurcations Separate -- Touching -- Enclosed

25. Higher-Order Behaviour Multiple separators Coronal null points [? more realistic models corona:Longcope, Maclean]

26. (iii) 3D Reconnection Can occur at a null point (antiparallel merging ??) or in absence of null (component merging ??) At Null -- 3 Types of Reconnection: Spine reconnection Fan reconnection [Pontin, Hornig] Separator reconnection [Longcope,Galsgaard]

27. Spine Reconnection Assume kinematic, steady, ideal. Impose B = (x, y, -2z) Solve E + v x B = 0 and curl E = 0 for v and E. --> E = grad F B.grad F = 0, v = ExB/B2 Impose continuous flow on lateral boundary across fan -> Singularity at Spine

28. Fan Reconnection (kinematic) Impose continuous flow on top/bottom boundary across spine [? Resolve singularities, ? Properties: Pontin, Hornig, Galsgaard]

29. Separator Reconnection(Longcope) Numerical: Galsgaard & Parnell

30. In Absence ofNull Qualitative model - generalise Sweet Parker. 2 Tubes inclined at : Reconnection Rate (local): Varies with - max when antiparl Numerical expts: (i) Sheet can fragment (ii) Role of magnetic helicity

31. Numerical Expt (Linton & Priest) 3D pseudo-spectral code, 2563 modes. Impose initial stagn-pt flow v = vA/30 Rm = 5600 Isosurfaces of B2:

32. B-Lines for 1 Tube Colour shows locations of strong Ep stronger Ep Final twist

33. Features • Reconnection fragments (cf Parnell & Galsgaard) • Complex twisting/ braiding created • Approx conservation of magnetic helicity: Initial mutual helicity = final self helicity • Higher Rm -> more reconnection locations & braiding ? keep as tubes / add twist:Linton

34. (iv) Nature of B-line velocities (w) [Hornig, Pontin] • Outside diffusion region (D), v = w In 2D • Inside D, w exists everywhere except at X-point. • B-lines change connections at X • Flux tubes rejoin perfectly

35. In 3D : w does not exist for an isolated diffusion region (D) • i.e., no solution for w to • fieldlines continually change their connections in D (1,2,3 different B-lines) • flux tubes split, flip and in general do not rejoin perfectly !

36. Locally 3D Example Tubes split & flip

37. Fully 3D Example Tubes split & flip -- but don’t rejoin perfectly

38. 3D - Questions ? • Topology - nature of complex coronal fields ? [Longcope, Maclean] • Spine, fan, separator reconnection - models ?? [Galsgaard, Hornig, Pontin] • Non-null reconnection - details ?? [Linton] • Basic features 3D reconnection such as nature w ? [Hornig, Pontin]

39. 4. FLARE - OVERALL PICTURE Magnetic tube twisted - erupts - magnetic catastrophe/instability drives reconnection

40. Reconnection heats loops/ribbons - rise / separate [Forbes]

41. 5. HOW is CORONA HEATED ? Bright Pts, Loops, Holes Recon-nection likely

42. Reconnection can Heat Corona: (i) Drive Simple Recon. at Null by photc. motions --> X-ray bright point (Parnell) (ii) Binary Reconnection -- motion of 2 sources (iii) Separator Reconnection -- complex B (iv) Braiding (v) Coronal Tectonics

43. (ii) Binary Reconnection (P and Longcope) Many magnetic sources in solar surface • Relative motion of 2 sources -- "binary" interaction • Suppose unbalanced and connected --> Skeleton • Move sources --> "Binary" Reconnection • Flux constant - - but individual B-lines reconnect

44. Cartoon Movie (Binary Recon.) • Potential B • Rotate one source about another

45. (iii) Separator Reconnection [Longcope, Galsgaard] • Relative motion of 2 sources in solar surface • Initially unconnected Initial state of numerical expt. (Galsgaard & Parnell)

46. Comput. Expt. (Parnell / Galsgaard Magnetic field lines -- red and yellow Strong current Velocity isosurface

47. (iv) Braiding Parker’s Model Initial B uniform / motions braiding

48. Numerical Experiment (Galsgaard) Current sheets grow --> turb. recon.

49. Current Fluctuations Heating localised in space -- Impulsive in time

50. (v) CORONAL TECTONICS ? Effect on Coronal Heating of “Magnetic Carpet” • * (I) Magnetic sources in surface are concentrated