Problems in mhd reconnection
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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 uniformNonuniform

  • 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.


Problems in mhd reconnection

? 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)


Three source topologies

Three-Source Topologies


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


Reconnection heats loops ribbons

Reconnection heats loops/ribbons

[Forbes]


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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