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Problems in MHD Reconnection ??

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(Cambridge, Aug 3, 2004)

Eric Priest

St Andrews

1.Introduction

2.2DReconnection

3.3DReconnection

4. [Solar Flares]

5. Coronal Heating

- 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:

Reconnection -- at magnetopause (FTE’s)

& in tail (substorms) [Birn]

Reconnection key role in

Solar flares, CME’s [Forbes] +

Coronal heating

[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

- 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

- 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)

Simple current sheet - uniform inflow

- SP sheet small - bifurcates
Slow shocks- most of energy

- Reconnection speedve--
any rate up to maximum

- Depend on b.c.’s

Almost uniformNonuniform

- Petschek is one particular case -

can occur if enhanced in diff. region

- Theory agrees w numerical expts if bc’s same

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 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]

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

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

In 2D --

Separatrix curves

In 3D --

Separatrix surfaces

-- intersect inSeparator

transfers flux from one2Dregion to another.

In 3D, reconnection at separator

transfers flux from one 3D region to another.

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

E.g.

2 unbalanced sources

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

Skeleton:

null + spine + fan

(separatrix dome)

Sources, nulls, fans -> separator

Bifurcations from one state to another

Separate --

Touching --

Enclosed

Multiple separators

Coronal null points

See Longcope, Maclean

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]

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

(kinematic)

Impose continuous flow on top/bottom boundary across spine

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

3D pseudo-spectral code, 2563 modes.

Impose initial stagn-pt flow

v = vA/30

Rm = 5600

Isosurfaces of B2:

Colour shows locations of

strong Ep stronger Ep

Final twist

- Reconnection fragments

- Complex twisting/ braiding created

- Conservation of magnetic helicity:

Initial mutual helicity = final self helicity

- Higher Rm -> more reconnection locations/ more braiding

[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

- 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 !

Tubes

split

&

flip

Tubes split & flip -- but

don’t rejoin perfectly

- 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]

Magnetic tube twisted - erupts -

magnetic catastrophe/instability

drives reconnection

[Forbes]

Bright Pts,

Loops,

Holes

Recon-nection likely

(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

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

- Potential B
- Rotate one source about another

- Relative motion of 2 sources in solar surface
- Initially unconnected

Initial state of numerical expt. (Galsgaard & Parnell)

Magnetic field lines -- red and yellow

Strong current

Velocity isosurface

Parker’s Model

Initial B uniform / motions braiding

Current sheets grow --> turb. recon.

Heating localised in space --

Impulsive in time

? Effect on Coronal Heating of

“Magnetic Carpet”

- * (I) Magnetic sources in surface are
concentrated

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

- (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

- 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):

- (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

- 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

- 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

Demonstrate

sheet formation

Estimate heating

Preliminary numerical expt. (Galsgaard)

- 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

- 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

- ? 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

- Eruption
- Rising loops
- Overlying current sheet (30 MK) with downflowing plasma

- Eruption
- Inflow to reconnection site
- Rising loops that have cooled
(Yokoyama)