MAGNETIC RECONNECTION

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MAGNETIC RECONNECTION
(Bozeman, July, 2004) Eric Priest
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CONTENTS

• Introduction
• 2. 2D Reconnection Theory
• EXAMPLES A, B
• 3. 3D Reconnection Theory
• 4. Conclusions

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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 --gt dynamic processes

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Magnetosphere
Reconnection at magnetopause in tail
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Solar Corona
Magnetic field comes thro' surface --gt Solar
flares, CMEs / heats Corona

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Induction Equation
A B

• B changes due to transport diffusion

• A gtgt B in most of Universe --gt

B frozen to plasma -- keeps its energy
Except SINGULARITIES -- j large
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Singularities form at NULL POINTS, B 0
- where magnetic field lines break reconnect
Large currents --gt ohmic heating
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2. 2D RECONNECTION

• Reconnection can
• Be driven by motions
• Occur spontaneously
• Occur when X-point collapses - Why ?

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X-Point Field
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Perturb - ? Grow
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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)

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Sweet-Parker (1958)
Simple current sheet - uniform inflow
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Petschek (1964)

• Sheet bifurcates -
• Slow shocks - most of energy
• Reconnection speed --
• any rate up to maximum

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New 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 bcs same

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EXAMPLE B
Effect of stagnation-point flow vx - Ux/a vy
Uy/a on magnetic field (
),
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(ii) Solve for B(x) if B(0)0. Sketch
it. (iii) Show this solution also satisfies
steady equations of continuity and motion if

i.e., Exact solution of nonlinear MHD equations !
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Solution B
Stagnation-point flow vx - Ux/a vy
Uy/a Mag. field (B(x) ) (i)
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Solve
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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
Fan Surface
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(ii) Global Topology of Complex Fields
In 2D -- Separatrix curves
In 3D -- Separatrix surfaces
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In 2D, reconnection at X
transfers flux from one 2D region to another.
In 3D, reconnection at separator transfers flux
from one 3D region to another.
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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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Looking Down on Structure
Bifurcations from one state to another
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Movie of Bifurcations
Separate -- Touching -- Enclosed
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Higher-Order Behaviour
Multiple separators
Coronal null points
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(iii) 3D Reconnection
Can occur at a null point or in absence of
null
At Null -- 3 Types of Reconnection
Spine reconnection
Fan reconnection
Separator reconnection
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Spine Reconnection
(kinematic) Solve curl E 0, E vxB 0
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Fan Reconnection
(kinematic)
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In Absence of Null
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
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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
Colour shows locations of strong Ep stronger Ep
Final twist
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Features

• Reconnection fragments

• Complex twisting/ braiding created

• Conservation of magnetic helicity

Initial mutual helicity final self
helicity

• Higher Rm -gt more reconnection locations/ more
  braiding

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(iv) Nature of B-line velocities (w)

• Outside diffusion region (D), w v

In 2D

• Inside D, w exists everywhere except at X-point.

• B-lines change connections at X

• Flux tubes rejoin perfectly

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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

• flux tubes split, flip and in general do not
  rejoin perfectly !

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Locally 3D Example
Tubes split flip
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4. CONCLUSIONS

• Reconnection fundamental process -
• - 2D theory well-developed
• - 3D new voyage of discovery
• topology
• reconnection regimes ( or - null)
• nature

• Coronal heating
• Solar flares

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