Experimental Study of Magnetic Reconnection and Dynamics of Plasma Flare Arc in MRX

Masaaki Yamada

August 3 20092009 SHINE Meeting at Nova Scotia

Center for Magnetic Self-organization

PPPL, Princeton University

In collaboration with E. Oz, J. Xie, D. Lecoanet and H. Ji

Recent Progress

Experimental study of the reconnection layer on MRX=> Fast reconnection in collsionless regime is determined by

Hall effects except the e-diffusion regime

– Two-scale diffusion region

– Thickness of the electron diffusion layer > c/pe

• MRX scaling in transition from MHD to 2-fluid regime

• New results from our solar flare experiments

Experimental Setup and Formation of Current Sheet

Experimentally measured flux evolution

ne= 1-10 x1013 cm-3, Te~5-15 eV, B~100-500 G,

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

Rectangular shapeCollisional regime: mfp <Slow reconnection

No Q-P field

Collisionless regime: mfp > Fast reconnection

Q-P field present

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

X-type shape

<= Ma & Bhattacharjee ,’96

Fast Reconnection <=> Hall Effects

=>

• Hall Effects create a large E field (except at X point)

• e-i collisions ~ small

• A major question

=> What is a scaling law w.r.t. collisionality

MRX scaling shows a transition from the MHD to 2 fluid

regime based on (c/pi)/ sp

MRX Scaling: * vs (c/i)/ sp

Breslau

A linkage between space and lab on reconnection

Hall MHD

η* ≡Eθjθ

No

ma

lize

d b

y S

pitz

Yamada et al, PoP, 2006

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=4.5λmfpL

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1/ 2mimiH

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cωpi

1

SPδ

Anatomy of MRX Scaling

In the outside of the e-diffusion region, reconnecting field Ey is primarily determined by jHall xB:

€

E =η s j

EHall =jH × B

ne

η eff =jH × B

nej0

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⎠ ⎟

whereη S =mvene2λ mfp

η effη S

=BHBo

mime

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1/ 2λ mfpL

Collisional resistivity

MRX Scaling: eff linearly increases with mfp/L

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effη S

=BHBo

mime

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⎝ ⎜

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1/ 2λ mfpL

Hall effects:

Next Step=> Add guide field

Main Objectives(1) To determine stability conditions for a single flux

rope as a function of field line twist, q, curvature, and the “strapping”field,

(2) To evaluate the effects of line tying for flux rope plasma

(3) To measure the magnetic energy transfer to the plasma during magnetic self-organization (eruption)

Solar Flare Experiment on MRX

electrodes

D

flare

Magnetic probes

MRX vacuum vessel

Equilibrium Field

Equilibrium Field CoilsGuide Field

Coils

`

` Guide Field

D: 2R FLARE Diametera: Flare radius

a

Experimental Setup

Electrodes inside the MRX vacuum vessel

Flare photos taken with a commercial Canon Powershot 100 µs exposure

STABLE

UNSTABLE

Cathode

Anode

•Bt = 1.06 kG

q<1

q>1

Kink instability

•Bt = 0.36 kG

•Electrode angle ~90o

Stability Condition for a Partial Arc

1

180o

•=> line-tying effects?

•The data shows that the stability condition for a simple toroidal q value without line-tying effects describes the experimental data.

•R=20, a =7 cm

Magnetic Relaxation is observed

Taylor State: ~ constant

Magnetic relaxationRFP toroidal plasmas

Summary

• Hall effects facilitate fast reconnection in MRX• Transition from collisional MHD to two-fluid regime

=> changes the neutral sheet profile and the reconnection rate

• A new scaling found on reconnection rate

• A new experimental campaign has started to study the dynamics of solar flares (=> Oz, Poster)