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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

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problems in mhd reconnection
Problems in MHD Reconnection ??

(Cambridge, Aug 3, 2004)

Eric Priest

St Andrews

contents
CONTENTS

1.Introduction

2.2DReconnection

3.3DReconnection

4. [Solar Flares]

5. Coronal Heating

1 introduction
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:
magnetosphere
Magnetosphere

Reconnection -- at magnetopause (FTE’s)

& in tail (substorms) [Birn]

solar corona
Solar Corona

Reconnection key role in

Solar flares, CME’s [Forbes] +

Coronal heating

induction equation
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

current sheets how form
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
2 2d reconnection
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)
sweet parker 1958
Sweet-Parker (1958)

Simple current sheet - uniform inflow

petschek 1964
Petschek (1964)
  • SP sheet small - bifurcates

Slow shocks - most of energy

  • Reconnection speedve--

any rate up to maximum

newer generation of fast regimes
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
nature of inflow affects regime
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

2d questions
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]

3 3d reconnection
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

most generally near a null
Most generally, near a Null

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

ii topology of fields complex
(ii) Topology of Fields - Complex

In 2D --

Separatrix curves

In 3D --

Separatrix surfaces

-- intersect inSeparator

in 2d reconnection at x
In 2D, reconnection atX

transfers flux from one2Dregion to another.

In 3D, reconnection at separator

transfers flux from one 3D region to another.

slide18

? Reveal structure of complex field ? plot a few arbitrary B lines

E.g.

2 unbalanced sources

SKELETON -- set of nulls, separatrices -- from fans

2 unbalanced sources
2 Unbalanced Sources

Skeleton:

null + spine + fan

(separatrix dome)

simplest configuration w separator
Simplest configuration w. separator:

Sources, nulls, fans -> separator

looking down on structure
Looking Down on Structure

Bifurcations from one state to another

movie of bifurcations
Movie of Bifurcations

Separate --

Touching --

Enclosed

higher order behaviour
Higher-Order Behaviour

Multiple separators

Coronal null points

See Longcope, Maclean

iii 3d reconnection
(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]

spine reconnection
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

fan reconnection
Fan Reconnection

(kinematic)

Impose continuous flow on top/bottom boundary across spine

in absence of null
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

numerical exp t linton priest
Numerical Expt (Linton & Priest)

3D pseudo-spectral code, 2563 modes.

Impose initial stagn-pt flow

v = vA/30

Rm = 5600

Isosurfaces of B2:

b lines for 1 tube
B-Lines for 1 Tube

Colour shows locations of

strong Ep stronger Ep

Final twist

features
Features
  • Reconnection fragments
  • Complex twisting/ braiding created
  • Conservation of magnetic helicity:

Initial mutual helicity = final self helicity

  • Higher Rm -> more reconnection locations/ more braiding
iv nature of b line velocities w
(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
in 3d w does not exist for an isolated diffusion region d
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 !
locally 3d example
Locally 3D Example

Tubes

split

&

flip

fully 3d example
Fully 3D Example

Tubes split & flip -- but

don’t rejoin perfectly

3d questions
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]
4 flare overall picture
4. FLARE - OVERALL PICTURE

Magnetic tube twisted - erupts -

magnetic catastrophe/instability

drives reconnection

5 how is corona heated
5. HOW is CORONA HEATED ?

Bright Pts,

Loops,

Holes

Recon-nection likely

reconnection can heat corona
Reconnection can Heat Corona:

(i) Drive Simple Recon. at Null by photc. motions

--> X-ray bright point

(ii) Binary Reconnection -- motion of 2 sources

(iii) Separator Reconnection -- complex B

(iv) Braiding

(v) Coronal Tectonics

ii binary reconnection
(ii) Binary Reconnection

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
cartoon movie binary recon
Cartoon Movie (Binary Recon.)
  • Potential B
  • Rotate one source about another
iii separator reconnection longcope galsgaard
(iii) Separator Reconnection [Longcope, Galsgaard]
  • Relative motion of 2 sources in solar surface
  • Initially unconnected

Initial state of numerical expt. (Galsgaard & Parnell)

comput expt parnell galsgaard
Comput. Expt. (Parnell / Galsgaard

Magnetic field lines -- red and yellow

Strong current

Velocity isosurface

iv braiding
(iv) Braiding

Parker’s Model

Initial B uniform / motions braiding

numerical experiment galsgaard
Numerical Experiment (Galsgaard)

Current sheets grow --> turb. recon.

current fluctuations
Current Fluctuations

Heating localised in space --

Impulsive in time

v coronal tectonics
(v) CORONAL TECTONICS

? Effect on Coronal Heating of

“Magnetic Carpet”

  • * (I) Magnetic sources in surface are

concentrated

ii flux sources highly dynamic
* (II) Flux Sources Highly Dynamic

Magnetogram movie (white +ve , black -ve)

  • Sequence is repeated 4 times
  • Flux emerges ... cancels
  • Reprocessed very quickly (14 hrs !!!)

? Effect of structure/motion of carpet on Heating

life of magnetic flux in surface
Life of Magnetic Flux in Surface
  • (a) 90% flux in Quiet Sun emerges as ephemeral regions (1 per 8 hrs per supergran, 3 x 1019 Mx)
  • (b) Each pole migrates to boundary (4 hours), fragments --> 10 "network elements" (3x1018 Mx)
  • (c) -- move along boundary (0.1 km/s) -- cancel
from observed magnetograms construct coronal field lines
From observed magnetograms - construct coronal field lines

- statistical properties: most close low down

- each source connected to 8 others

Time for all field lines to reconnect

only 1.5 hours

(Close, Parnell, Priest):

coronal tectonics model
Coronal Tectonics Model
  • (Priest, Heyvaerts & Title)
  • Each "Loop" --> surface in many sources
  • Flux from each

source topology

distinct --

Separated by

separatrix surfaces

  • As sources move, coronal fields slip ("Tectonics")

--> J sheets on separatrices & separators --> Reconnect --> Heat

  • Corona filled w. myriads of separatrix/ separator J sheets, heating impulsively
fundamental flux units
Fundamental Flux Units
  • Intense tubes (B -- 1200 G, 100 km, 3 x 1017 Mx)

not Network Elements

  • Each network element -- 10 intense tubes
  • Single ephemeral

region (XBP) --

100 sources

800 seprs, 1600 sepces

  • Each TRACE
  • Loop --

10 finer loops

80 seprs, 160 sepces

theory
Theory
  • Parker -- uniform B -- 2 planes -- complex motions
  • Tectonics -- array tubes (sources) -- simple motions

(a) 2.5 D Model

  • Calculate equilibria --

Move sources -->

Find new f-f equilibria

  • --> Current sheets

and heating

3 d model
3 D Model

Demonstrate

sheet formation

Estimate heating

Preliminary numerical expt. (Galsgaard)

results
Results
  • Heating uniform along separatrix
  • Elementary (sub-telc) tube heated uniformly
  • But 95% photc. flux closes low down in carpet
  • -- remaining 5% forms large-scale connections
  • --> Carpet heated more than large-scale corona
  • So unresolved observations of coronal loops
  • --> Enhanced heat near feet in carpet
  • --> Upper parts large-scale loops heated uniformly & less strongly
6 conclusions
6. CONCLUSIONS
  • 2D recon - many fast regimes - depend on nature inflow
  • 3D - can occur with or without nulls

- several regimes (spine, fan, separator)

- sheet can fragment - role of twist/braiding

- concept of single field-line velyreplaced

- field lines continually change connections in D

- tubes split, flip, don’t rejoin perfectly

  • Reconnection on Sun crucial role -
  • * Solar flares
  • * Coronal heating
extra questions
?? Extra Questions ??
  • ? Threshold for onset of reconnection
  • ? Occur at nulls or without
  • ? Determines where it occurs
  • ? Rate and partition of energy
  • ? Role of microscopic processes
  • ? How does reconnection accelerate particles -

cf DC electric fields, stochastic accn, shocks

example from trace
Example from TRACE
  • Eruption
  • Rising loops
  • Overlying current sheet (30 MK) with downflowing plasma
ps example from soho eit 1 5 mk
PS-Example from SOHO (EIT - 1.5 MK)
  • Eruption
  • Inflow to reconnection site
  • Rising loops that have cooled

(Yokoyama)

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