1 / 69

Problems in MHD Reconnection ??

Problems in MHD Reconnection ??. (Cambridge, Aug 3, 2004) Eric Priest St Andrews. CONTENTS. 1. Introduction 2. 2D Reconnection 3. 3D Reconnection 4. [Solar Flares] 5. Coronal Heating. 1. INTRODUCTION. Reconnection is a fundamental process in a plasma:. Changes the topology

chelsea-osborne
Télécharger la présentation

Problems in MHD Reconnection ??

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related