Magnetic reconnection
in solar theory:
MHD vs Kinetics
Philippa Browning,
Jodrell Bank Centre for Astrophysics, Manchester
MHD and Kinetics Workshop February 2008
Some books
This talk is NOT a review of magnetic reconnection!
For overview of current state of play on reconnection
theory:
 “Magnetic reconnection” Priest and Forbes (2000)
 “Magnetic reconnection in plasmas” Biskamp (2005)
 “Reconnection of magnetic fields” Birn and Priest (2007)
MHD and Kinetics Workshop February 2008
Magnetic reconnection
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A restructuring of the magnetic field
topology due to localised
departures from frozen-in field
condition
Dissipation rates enhanced beyond
simple Ohmic dissipation (or
equivalent) due to interaction of
flow field with dissipation
Scale separation – global “ideal”
region with inner “dissipative”
region
Causes changes in field
connectivity and conversion of
magnetic energy to thermal energy
and kinetic energy (bulk flows and
nonthermal particles)
MHD and Kinetics Workshop February 2008
Where does reconnection occur?
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Solar flares – reconnection likely to
be primary energy release process
Solar and stellar coronal heating
Coronal mass ejections,
prominence eruptions; flux
emergence; magnetoconvection
and dynamo
MHD and Kinetics Workshop February 2008
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Magnetospheres
Flare stars, magnetars
Accretion discs and jets (AGNs, young
stars etc)
Protostar collapse, galactic and
intergalactic magnetic fields, pulsars…
Fusion plasmas e.g.
tokamak sawteeth,
spheromak formation
Laboratory
reconnection
experiments e.g. MRX
MHD and Kinetics Workshop February 2008
Modes of reconnection
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Spontaneous reconnection – a linear instability of resistive plasma
- tearing instability and variants
Forced reconnection – triggered by external disturbance – Hahm
and Kulsrud
Steady state reconnection – Sweet-Parker, Petschek and variant
models

General time dependent reconnection – numerical simulations
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Most models of reconnection are 2D - current sheets and X lines
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Some significant differences in 3D - separators and separatrices, nulls,
QSLs
3D reconnection usually 2D on local scale but global geometry is
different
MHD and Kinetics Workshop February 2008
Tearing instability
Furth et al, 1963
•Spontaneous linear instability in current sheet (field
reversal) or sheared field
•Outer ideal region matched to thin inner resistive
layer
•Maximum growth rate
 tear
S 1 2ta1
MHD and Kinetics Workshop February 2008
Steady state reconnection
Sweet Parker, Petschek and variants

trec
Steady inflow (vi) , fields
continually reconnect in
current sheet
t A ln S
Reconnection rate
vi
S 1 2
vA
(Sweet Parker)

tr
tAS1 2
t D S 1 2
vi  1

v A 8 ln S
(Petschek)
MHD and Kinetics Workshop February 2008
Forced reconnection
Hahm and Kulsrud, 1985

Current sheet forms at
Lz/2 where k.B0 = 0
Boundary disturbance δcosky
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Apply a transient
sinusoidal disturbance to
the boundary of a neutral
sheet field or sheared
field
A current sheet develops
which subsequently
reconnects, releasing
stored magnetic energy
Allows reconnection in an
initially stable field
MHD and Kinetics Workshop February 2008
Ohm’s Law
me j 1
E  v  B   2   j  B  pe 
 ne t ne
j
Ohmic
resistance
(collisions)
•Length scale of electron inertia –
electron skin depth
Electron
inertia
e 
c
 pe
 me 0 
 c 2 
 ne 
12
 m p 0 
i 
 c 2 
 pi
 ne 
c
•Length scale of Hall term – ion skin
depth
Hall
12
•In Hall MHD, plasma is frozen to
electron fluid – hence Hall term is not
dissipative but can strongly affect
reconnection dynamics – introduces two
fluid effects
MHD and Kinetics Workshop February 2008
Approaches to reconnection modelling
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MHD – numerous!
Hall e.g. Fitzpatrick, Arber and Haynes, Bhattarcharjee,
Huba
Hybrid – fluid electrons and particle ions
Gyrokinetic
Particle in Cell (PIC) e.g. Drake and co-workers
Compare for simple model problem – tearing instability
(GEM challenge – Birn et al, 2001) or forced
reconnection variant (Newton challenge – Birn et al,
2005)
MHD and Kinetics Workshop February 2008
Newton challenge (Birn et al, 2005)
MHD and Kinetics Workshop February 2008
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3D PIC simulation
of reconnection
(from Drake et al,
2006)
Doubly periodic
Harris current
sheets
Electron out of
plane current at
two successive
times and
temperature
MHD and Kinetics Workshop February 2008
Some numbers (solar corona)
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Typical length of coronal loop L = 107 - 108 m (widths of observed
loops ≈ 106 m ) – the global scale length
Take
n  1015 m3 , B  102 T , T  106 K
Lundquist number S =1014
Mean free path
coll  104 m
Current sheet width in classical MHD tearing theory or Sweet Parker
reconnection
l  S 1 2 L  10  100m
MHD valid for global scales but breaks down at local reconnection
scales
MHD and Kinetics Workshop February 2008
i  10 m
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Ion skin depth
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Ion gyroradius
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Typical MHD simulation grid cell ≈
105 - 106 m
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Typical kinetic simulation box size ≈
103 m
rLi ≈ 1 m
MHD and Kinetics Workshop February 2008
Questions: MHD vs kinetics
“Compare and contrast” or “link”
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What are similarities and differences between MHD and
various kinetic models (Hall MHD, PIC etc)?
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How does reconnection rate depend on dissipation
mechanism and on external conditions?
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Do net energy release and final state of reconnecting
field depend on local dissipation process?
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What is the most appropriate form of Ohm’s law for
modelling coronal plasmas?
MHD and Kinetics Workshop February 2008
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How can we develop models (numerical or other) to
incorporate wide range of length scales from kinetic to
MHD?
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How are charged particles accelerated in reconnecting
fields, and how do their properties depend on the
parameters of the reconnection?
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What is “anomalous resistivity”?
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What is role of micro turbulence in reconnecting fields?
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What about other kinetic effects (beyond Ohm’s law) in
reconnecting plasmas – heat transport, plasma waves
etc?
MHD and Kinetics Workshop February 2008
Possible tools for linking MHD and kinetics
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Test particle models
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Beyond test particles to self-consistent models – hybrid
codes?
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Comparison of simulations for “standard models”
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Coupled models
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Different models on different scales – local kinetic linked to
global MHD
Proper modelling of “ anomalous resistivity”
?
MHD and Kinetics Workshop February 2008
Links to other Workshop topics
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Strong electric fields in magnetic reconnection can be
efficient particle accelerators – studies of generation of
nonthermal particles in reconnecting fields requires
some kinetic modelling
Many reconnection models predict shocks (e.g. slow
shocks in Petchsek)
Reconnection is associated with turbulence on various
scales – within dissipation region and globally
Reconnection events may trigger waves and oscillations,
also reconnection may be modulated or triggered by
waves
Reconnection causes strong localised heating, so heat
transport needs to be properly modelled
MHD and Kinetics Workshop February 2008