problems in mhd reconnection ?? (cambridge, aug 3, 2004) eric priest st andrews
TRANSCRIPT
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Problems in MHD Reconnection ?? (Cambridge, Aug 3, 2004)
Eric PriestSt Andrews
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CONTENTS
1. Introduction
2. 2D Reconnection
3. 3D Reconnection
4. [Solar Flares]
5. Coronal Heating
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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:
QuickTime™ and aYUV420 codec decompressor
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Magnetosphere
Reconnection -- at magnetopause (FTE’s)& in tail (substorms) [Birn]
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Solar Corona
Reconnection key role inSolar flares, CME’s [Forbes] +
Coronal heating
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Induction Equation∂B
∂ t= ∇ × (v × B) + η∇2B + ......
B changes due to transport + diffusion
[Drake, Hesse, Pritchett]
Rm>>1 in most of Universe -->
B frozen to plasma -- keeps its energy
Except SINGULARITIES -- & j & E large ∇B
Heat, particle accelern
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Current Sheets - how form ?
Driven by motions
At null points
Occur spontaneously
By resistive instability in sheared field
Along separatrices
By eruptive instability or nonequilibrium
In many cases shown in 2D but ?? in 3D
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2. 2D RECONNECTION
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)
In 2D takes place only at an X-Point-- Current very large-- Strong dissipation allows field-lines to break
/ change connectivity
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Sweet-Parker (1958)
Simple current sheet
- uniform inflow
€
Mass conservation: L v i = l vo
Advection / diffusion: v i = η / l
Accelerate along sheet: vo = vA
€
Rmi =L vA
η,
€
Recon. Rate M i =v i
vAi
=1
Rmi1/ 2
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Petschek (1964)
SP sheet small - bifurcates
Slow shocks- most of energy
€
M e =ve
vA
=π
8 log Rm e
≈ 0.1
Reconnection speed ve --
any rate up to maximum
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?? Effect of Boundary Conditions on Steady Reconnection
NB - lessons:
3. Global ideal environment depends on bc’s
5. Maximum rate depends on bc’s
1. Bc’s are crucial
2. Local behaviour is universal - Sweet-Parker layer
4. Reconnection rate - the rate at which you drive it
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Newer Generation of Fast Regimes Depend on b.c.’s
Almost uniform Nonuniform
Petschek is one particular case -
€
ηcan occur if enhanced in diff. region
Theory agrees w numerical expts if bc’s same
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Nature of inflow affects regime
Converging Diverging
€
Me =f
Rme1/ 2
-> 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
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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]
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3. 3D RECONNECTION
Simplest B = (x, y, -2z)
Spine Field LineFan Surface
(i) Structure of Null Point
Many New Features
2 families of field lines through null point:
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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
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(ii) Topology of Fields - Complex
In 2D -- Separatrix curves
In 3D -- Separatrix surfaces
-- intersect in Separator
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transfers flux from one 2D region to another.
In 3D, reconnection at separator
transfers flux from one 3D region to another.
In 2D, reconnection at X
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? Reveal structure of complex field ? plot a few arbitrary B lines
E.g.
2 unbalanced sources
SKELETON -- set of nulls, separatrices -- from fans
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2 Unbalanced Sources
Skeleton:
null + spine + fan
(separatrix dome)
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Three-Source Topologies
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Simplest configuration w. separator:
Sources, nulls, fans -> separator
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Looking Down on Structure
Bifurcations from one state to another
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Movie of Bifurcations
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Separate --
Touching --
Enclosed
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Higher-Order Behaviour
Multiple separators
Coronal null points
[? more realistic models corona: Longcope, Maclean]
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(iii) 3D Reconnection
At Null -- 3 Types of Reconnection:
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Can occur at a null point (antiparallel merging ??)
or in absence of null (component merging ??)
Spine reconnection Fan reconnection
[Pontin, Hornig]
Separator reconnection[Longcope, Galsgaard]
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Spine ReconnectionAssume kinematic, steady,
ideal. Impose B = (x, y, -2z)Solve E + v x B = 0 and curl E = 0 for v and E.
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--> E = grad FB.grad F = 0, v = ExB/B2
-> Singularity at Spine
Impose continuous flow on lateral boundary across fan
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Fan Reconnection
(kinematic)
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Impose continuous flow on top/bottom boundary
across spine
[? Resolve singularities,
? Properties:
Pontin, Hornig, Galsgaard]
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Separator Reconnection
(Longcope)
Numerical: Galsgaard & Parnell
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In Absence of NullQualitative model - generalise Sweet Parker.
2 Tubes inclined at :
€
ϑ
Reconnection Rate (local):
Varies with - max when antiparl
€
ϑ
Numerical expts: (i) Sheet can fragment
(ii) Role of magnetic helicity€
v i =vA
Rmi1/ 2 [2 sin 1
2ϑ ]1/ 2
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Numerical Expt (Linton & Priest)
3D pseudo-spectral code, 2563 modes.
Impose initial stagn-pt flow
v = vA/30
Rm = 5600
Isosurfaces of B2:
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B-Lines for 1 Tube
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are needed to see this picture.Colour shows
locations of strong Ep
stronger Ep
Final twist
€
π
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Features
Reconnection fragments (cf Parnell & Galsgaard)
€
F 2 = 2 ×Φ
2πF 2
€
∴Φ=π
Complex twisting/ braiding created
Initial mutual helicity = final self helicity
Higher Rm -> more reconnection locations & braiding
Approx conservation of magnetic helicity:
? keep as tubes / add twist: Linton
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(iv) Nature of B-line velocities (w)
QuickTime™ and aYUV420 codec decompressorare needed to see this picture.In 2D
Inside D, w exists everywhere except at X-point.
€
(E + w × B = 0)
Flux tubes rejoin perfectly
B-lines change connections at X
Outside diffusion region (D), v = w
[Hornig, Pontin]
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In 3D : w does not exist for an isolated diffusion region (D)
∃ i.e., no solution for w to
€
E + w × B = 0
fieldlines continually change their connections in D
(1,2,3 different B-lines)
flux tubes split, flip and in general do not rejoin
perfectly !
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Locally 3D Example
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Tubes
split
&
flip
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Fully 3D Example
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Tubes split & flip -- but
don’t rejoin perfectly
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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]
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4. FLARE - OVERALL PICTURE
Magnetic tube twisted - erupts -
€
Qmagnetic catastrophe/instabilitydrives reconnection
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Reconnection heats loops/ribbons
[Forbes]
- rise / separate
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5. HOW is CORONA HEATED ?
Bright Pts,
Loops,
Holes
Recon-nection likely
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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
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(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
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Cartoon Movie (Binary Recon.)
Potential B
Rotate one source about
another
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(iii) Separator Reconnection[Longcope, Galsgaard]
Relative motion of 2 sources in solar surface Initially unconnectedInitial state of numerical expt. (Galsgaard & Parnell)
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Comput. Expt. (Parnell / Galsgaard
Magnetic field lines -- red and yellow
Strong current
Velocity isosurface
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(iv) Braiding
Parker’s Model
Initial B uniform / motions braiding
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Numerical Experiment (Galsgaard)Current sheets grow --> turb. recon.
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Current Fluctuations
Heating localised in space --
Impulsive in time
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(v) CORONAL TECTONICS ? Effect on Coronal Heating of
“Magnetic Carpet”
* (I) Magnetic sources in surface are concentrated
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* (II) Flux Sources Highly Dynamic Magnetogram movie (white +ve , black -ve)
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Sequence is repeated 4 times Flux emerges ... cancels Reprocessed very quickly (14 hrs !!!)? Effect of structure/motion of carpet on Heating
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Life of Magnetic Flux in Surface
(a) 90% flux in Quiet Sun emerges as ephemeral regions
(b) Each pole migrates to boundary, fragments --> 10 "network elements" (3x1018 Mx)
(c) -- move along boundary -- cancel
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From observed magnetograms
- construct coronal field
lines - statistical properties: most close low down
Time for all field lines to reconnect
only 1.5 hours
(Close, Parnell, Priest):
- each source connected to 8 others
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Coronal Tectonics Model(Priest, Heyvaerts & Title)
Each "Loop" --> surface in many sources Flux from each source topology distinct -- Separated by separatrix surfaces
Corona filled w. myriads of separatrix/ separator J sheets, heating impulsively
As sources move, coronal fields slip ("Tectonics") --> J sheets on separatrices & separators
--> Reconnect --> Heat
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Fundamental Flux Units
Intense tubes (B -- 1200 G, 100 km, 3 x 1017 Mx)
100 sources
10 finer loops
not Network Elements
Each network element -- 10 intense tubes Single ephemeral region (XBP) --
Each TRACE Loop --
80 seprs, 160 sepces
800 seprs, 1600 sepces
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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
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3 D Model
Demonstrate sheet formation
Estimate heating
Preliminary numerical expt. (Galsgaard, Mellor …)
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Results Heating uniform along separatrixElementary (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
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6. CONCLUSIONS 2D recon - many fast regimes - depend on nature inflow
Reconnection on Sun crucial role - * Solar flares * Coronal heating
3D - can occur with or without nulls - several regimes (spine, fan, separator)- sheet can fragment - role of twist/braiding- concept of single field-line vely replaced- field lines continually change connections in D- tubes split, flip, don’t rejoin perfectly
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?? Extra Questions ??
? Threshold / conditions for onset of reconnection
? Occur equally easily at nulls or without
? Rate and partition of energy
? How does reconnection accelerate particles -
cf DC electric fields, stochastic accn, shocks
? Determines where non-null recon. occurs
? Role of microscopic processes
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PS-Example from SOHO (EIT - 1.5 MK)
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Eruption
Inflow to reconnection site
Rising loops that have cooled
(Yokoyama)
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Example from TRACE
QuickTime™ and a decompressor
are needed to see this picture.
Eruption
Rising loops
Overlying current sheet (30 MK) with downflowing plasma
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(Priest and Schrijver 1999)
Reconnection proceeds
New loopsform
Old loops cool
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PS-B-Lines for 1 Tube
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PS-Cause of Eruption
?Magnetic
Catastrophe
2.5 D Model
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Numerical Model
Suggestive of
Catastrophe
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PS- Reconn - Elegant Explanation for many Recent Space Observations
Yohkoh
Hottest loops are cusps or interacting loops X-ray jets - accelerated by reconnection
SOHO X-ray bright points (NIXT, EIT, TRACE)
Magnetic carpet (MDI) Explosive events (SUMER)
Nanoflares (EIT, TRACE, CDS)
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TRACE Loop
Reaches to surface in
many footpoints.
Separatrices & Separators form web in
corona
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Corona - Myriads Different LoopsEach flux element --> many neighbours
But in practice each source has 8 connections