Reconnection in Large, High-Lundquist-Number Coronal Plasmas

A.Bhattacharjee and T. Forbes

University of New Hampshire

Monday, August 3, Salon D, 2-5 pm

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)

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 >> width

 Reconnection time scale

Δ

€

τ SP = τ Aτ R( )1/2

= S1/2τ A

Solar flares: ,10~ 12S

€

τA ~ 1s

sSP610~τ⇒ Too long to account for solar flares!

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)

€

δSP < di

€

δSP < ρ s

Neutral sheet Shape in MRXChanges from “Rectangular S-P” type to “Double edge X” shape as collisionality is reduced

Rectangular shape

Collisional regime: mfp < δSlow reconnection

No Quadrupolar field

Collisionless regime: mfp > δ Fast reconnection

Quadrupolar field present

X-type shape

<= Ma & Bhattacharjee 1996

M. Yamada

W. Daughton

W. Daughton

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,

€

B = B0 tanh(z /a ) ˆ x

€

ε =a / L ~ S−α

€

γL,max ~ S (3α −1) /2

€

κmax ~ SL(5α −1) /4

€

γL,max ~ S1/4

€

κmax ~ SL3/8

L. Ni, poster presentation

R. Fermo: Statistical model for island distribution

P. Cassak

L. Fletcher: Spatially extended reconnection?

‘Spatially extended’ could mean

(1)Extended along current sheet length (i.e. long, drawn out CS, like Sweet-Parker)

(1) Extended into 3rd dimension (e.g. an X-line)

(2) Both – i.e. the ‘monolithic current sheet’

Lin

ker

et a

l (2

003)

Vertically-extended current sheets?

Departed CME, plus several plasmoids

Extended post-CME current sheet?

Ciaravella & Raymond 2008

Fe XVII emission -> hot, turbulent, narrow, bright structure.

Closer to the Sun - HXR evidence for extended flare current sheet, but with multiple plasmoids – tearing instability?

Sui et al (2005)

Flare Ribbons

Particularly the flare late phase shows this ordered behaviour. Early impulsive phase ribbons tend to look more irregular.

Bastille Day 2000 flareRed = UV emission (C IV)Blue = EUV Fe IX/XGreen = EUV Fe XI/XIIImage made in flare late phase

1.8 ×105

km

Evidence for (2), (3)? Spatially extended ribbons in UV and Hα, and the arcade of loops joining them demonstrate coronal reconnection ‘orchestrated’ over scales of 105km.

Turbulent Reconnection in 2D: W. Mattaheus

Lazarian & Vishniac (1999)L/ reconnection simultaneous events

Reconnection of 3D weakly turbulent magnetic fields involves many simultaneous reconnection events

B dissipates on a small scale || determined by turbulence statistics.Key element:

Turbulent reconnection:

1. Outflow is determined by field wandering.

2. Reconnection is fast with Ohmic resistivity only.

Reconnection rate does not depend on anomalous resistivity

Flat dependence on anomalous resistivity

Reconnection does not require Hall MHD

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?