Reconnection in Large, HighLundquistNumber Coronal Plasmas

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Reconnection in Large, High-Lundquist-Number
Coronal Plasmas

• Bhattacharjee and T. Forbes
• University of New Hampshire
• Monday, August 3, Salon D, 2-5 pm

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Speakers

• Invited Lyndsay Fletcher, University of Glasgow
• William Daughton, LANL
• Contributions Masaaki Yamada (PPPL), Raymond
  Fermo (University of Maryland), Paul Cassak
  (WVU), Alex Lazarian (University of Wisconsin,
  Madison), William Matthaeus (University of
  Delaware), Amitava Bhattacharjee (UNH)

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Classical (2D) Steady-State Models of
Reconnection
Sweet-Parker Sweet 1958, Parker 1957
Geometry of reconnection layer Y-points
Syrovatskii 1971 Length of the reconnection
layer is of the order of the system size gtgt width
 Reconnection time scale
Solar flares
Too long to account for solar flares!
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Onset of fast reconnection in large,
high-Lundquist-number systems

• The scaling of reconnection in large systems is a
  problem of great interest where the dimensionless
  ratio of characteristic dissipation scale to
  system size is a very small number. What are the
  mechanisms for the onset of fast reconnection in
  such systems? Does the answer depend on the
  mechanism that breaks field lines?
• One criterion has emerged from Hall MHD (or
  two-fluid) models, and has been tested carefully
  in laboratory experiments (MRX at PPPL, VTF at
  MIT). The criterion is
• (Ma and Bhattacharjee 1996, Cassak et al.
  2005) or in the presence of a guide
  field (Aydemir 1992)

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M. Yamada

• Neutral sheet Shape in MRX
• Changes from Rectangular S-P type
• to Double edge X shape as
• collisionality is reduced

Rectangular shape Collisional regime ?mfp
lt?? Slow reconnection No Quadrupolar field
X-type shape
Collisionless regime ?mfp gt?? Fast
reconnection Quadrupolar field present
lt Ma Bhattacharjee 1996
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W. Daughton
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W. Daughton
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Super-Alfvenic secondary tearing instabilities
occur even in resistive MHD at high Lundquist
number

• Loureiro et al. (2007) and Bhattacharjee et al.
  (2009)
• Harris sheet
• Thin sheets of aspect ratio
• Fastest growing tearing instability
• Sweet-Parker sheets,

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L. Ni, poster presentation
R. Fermo Statistical model for island
distribution
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(No Transcript)
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P. Cassak
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L. Fletcher Spatially extended reconnection?

• Spatially extended could mean
• Extended along current sheet length (i.e. long,
  drawn out CS, like Sweet-Parker)
• Extended into 3rd dimension (e.g. an X-line)
• Both i.e. the monolithic current sheet

Linker et al (2003)
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Vertically-extended current sheets?
Fe XVII emission -gt hot, turbulent, narrow,
bright structure.
Extended post-CME current sheet?
Departed CME, plus several plasmoids
Ciaravella Raymond 2008
Closer to the Sun - HXR evidence for extended
flare current sheet, but with multiple plasmoids
tearing instability? Sui et al (2005)
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Flare Ribbons
Evidence for (2), (3)? Spatially extended ribbons
in UV and Ha, and the arcade of loops joining
them demonstrate coronal reconnection
orchestrated over scales of 105km.
Bastille Day 2000 flare Red UV emission (C
IV) Blue EUV Fe IX/X Green EUV Fe
XI/XII Image made in flare late phase
1.8 105 km
Particularly the flare late phase shows this
ordered behaviour. Early impulsive phase ribbons
tend to look more irregular.
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Turbulent Reconnection in 2D W. Mattaheus
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Reconnection of 3D weakly turbulent magnetic
fields involves many simultaneous reconnection
events
Turbulent reconnection
1. Outflow is determined by field wandering.
2. Reconnection is fast with Ohmic resistivity
only.

• B dissipates on a small scale ? determined by
  turbulence statistics.

Key element
L/l reconnection simultaneous events
Lazarian Vishniac (1999)
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Reconnection rate does not depend on anomalous
resistivity
Flat dependence on anomalous resistivity
Reconnection does not require Hall MHD
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Fast reconnection in large, high-Lundquist-number
systems

• Questions
• What controls the onset of fast
  reconnection in large coronal sheets? What is the
  role of secondary instabilities? Of collisionless
  mechanisms? What is the role of turbulence?
• How does reconnection scale with S,
  electron/ion skin depth, plasma beta, system
  size?
• What constraints do observations place on
  theories? How can observations be made to test
  theory?