Magnetic Reconnection:

Progress and Status of Lab Experiments

In collaboration with members of MRX group andNSF-DoE Center of Magnetic Self-organization

Masaaki Yamada

SLAC, April 28th 2011

Outline

• Basic physics issues on magnetic reconnection– Reconnection rate is faster than the classical MHD rate– Fast reconnection <=> Resistivity enhancement– But lower collisionality induces faster reconnection

• Two-fluid physics analysis in a local reconnection layer– X-shaped neutral sheet– Physics of Hall effects and experimental verification– Identification of e-diffusion region– Observation of fluctuations (EM-LHDW)

• A scaling in transition from MHD to 2-fluid regime• Global reconnection issues;

– Reconnection in fusion plasmas– High energy particles– Impulsive reconnection

M. Yamada, R. Kulsrud, H.Ji, Rev. Mod. Phys. v.82, 603 (2010) E. Zweibel & M. Yamada, Ann. Rev.AA, AA47-8, 291 (2009)

Magnetic Reconnection• Topological rearrangement of magnetic field lines• Magnetic energy => Kinetic energy• Key to stellar flares, coronal heating, particle acceleration, star

formation, self-organization of fusion plasmas

Before reconnection After reconnection

Solar flare

MagnetosphericAurora-substorm

Tokamak Sawtoothdisruption

Stellar flare

time(hour)

time(hour)

MagneticFieldstrength

time(sec)

X-rayintensity

X-rayintensity

Electrontemperature

Reconnection always occurs very fast (reconn << SP) after build-up phase of flux

Magnetic Reconnection in the Sun

• Flux freezing (Ideal MHD) makes storage (flux build up) of magnetic energy easy at the photo surface

• Magnetic reconnection occurs when flux freezing breaks

• Magnetic reconnection causes conversion of magnetic energy＝＞ radiation, particle acceleration, the kinetic energy of the solar wind.

A. Local Reconnection Physics

1. MHD analysis

2. Two-fluid analysis

The Sweet-Parker 2-D Model for Magnetic Reconnection

Assumptions:

• 2D

• Steady-state

• Incompressibility

• Classical Spitzer resistivity

€

∂B

∂t=∇ × (v × B) +

η

μ0

∇ 2B

€

VinB =η Spitz

μ0

B

δ

B is resistively annihilated

in the sheet

Mass conservation: δoutin VLV ≈

Pressure balance:

Aoutout VVB

V ≈⇒≈0

22

221

μρ

Vout

Vin

€

Vin

VA

=1

S

S =μ0LVA

η Spitz

reconn << SP ~ ６ ９ − months

S=Lundquist number

Dedicated Laboratory Experiments on Reconnection

Device Where When Who Geometry Issues

3D-CS Russia 1970 Syrovatskii, Frank Linear 3D, heating

LPD, LAPD UCLA 1980 Stenzel, Gekelman Linear Heating, waves

TS-3/4 Tokyo 1990 Katsurai, Ono Merging Rate, heating

MRX Princeton 1995 Yamada, Ji Toroidal, merging

Rate, heating, scaling

SSX Swarthmore 1996 Brown Merging Heating

VTF MIT 1998 Fasoli, Egedal Toroidal with guide B

Trigger

RSX Los Alamos 2002 Intrator Linear Boundary

RWX Wisconsin 2002 Forest Linear Boundary

MRX: Dedicated reconnection experimentGoal: Provide fundamental data on reconnection, by creating proto-typical reconnection phenomena, in a controlled setting

The primary issues;• Study non-MHD effects in the reconnection layer;

[two-fluid physics, turbulence]• How magnetic energy is converted to plasma flows

and thermal energy,• How local reconnection determine global

phenomena - Effects of external forcing and boundary

Local physics problemsaddressed in collaboration with numerical simulations

IPF

Pull Reconnection in MRX

Pull Reconnection in MRX

IPF

IPF

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,

Resistivity increases as collisionality is reduced in MRX

η* ≡Eθjθ

Effective resistivity

But the cause of enhanced was unknown

Local Reconnection Physics

1. MHD analysis

2. Two-fluid analysis

Extensive simulation work on two-fluid physics carried out in past 10 years

Out of plane magnetic field is generated during reconnection

P. L. Pritchett, J.G.R 2001

Sheath width ~ c/wpi ~ i

Ion diffusion region

The Hall Effect Facilitates Fast Reconnection

Vin

Vout~ VA Electron diffusion region

Ideal MHD region

0=×+ recinrec BVE

Hall term Electron inertia term

Electron pressure term

• The width of the ion diffusion region is c/pi

• The width of the electron diffusion region is c/pe ?

Normalized with

-jin

MRX with fine probe arrays

• Five fine structure probe arrays with resolution up to ∆x= 2.5 mm in radial direction are placed with separation of ∆z= 2-3 cm

Linear probe arrays

Evolution of magnetic field lines during reconnection in MRX

Measured region

Electrons pull field lines as they flow in the neutral sheet

e

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

X-type shape

Two-scale Diffusion Region measured in MRX

Ion Diffusion region measured: i > c/pi

Electron Diffusion region newly identified: 6-8 c/pe < e

Electron jetting measured in both z and y direction: ve > 3-6 VAi

Y. Ren et al, PRL 2008Presence of B fluctuations

First Detection of Electron Diffusion Layer Made in MRX: Comparison with 2D PIC Simulations

All ion-scale features reproduced; but electron-layer is 5 times thicker in MRX Þ importance of 3D effects

MRX:e = 8 c/pe

2D PIC Sim:e = 1.6 c/pe

Measured electron diffusion layer ismuch broader than 2-D simulation results

(Ji, et. al. Sub. GRL 2008)=> MMS program

23

Recent (2D) Simulations Find New Large S Phenomena

Daughton et al. (2009): PICBhattacharjee et al. (2009):MHD

Sweet-Parker layers break up to form plasmoids when S > ~104

Impulsive fast reconnection with multiple X points

In a large high S (>104) system, flux ropes can be generated

Daughton et al, Nature Phys.2011

=> Impulsive fast reconnection

Fast Reconnection <=> Two-fluid Physics

• Hall MHD Effects create a large E field (no dissipation)

• Electrostatic Turbulence

• Electromagnetic Fluctuations (EM-LHW)

• All Observed in space and laboratory plasmas

Mozer et al., PRL 2002

POLAR satellite

Magnetic Reconnection in the MagnetosphereA reconnection layer has been documented in the magnetopause

d ~ c/wpi

Similar Observations in Magnetopause and Lab Plasma

ES

EM

(Space:Bale et al. ‘04)

high

low

high blow b

low

(a) (b)

(c)

EM waves correlate with

MRX

EM waves

ES waves

MRX scaling shows a transition from the MHD to 2 fluid regime

based on (c/pi)/ sp

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

Breslau

(c/pi)/ sp

~ 5( mfp/L)1/2

A linkage between space and lab on reconnection

2 Fluid simulation

η* ≡Eθjθ

No

ma

lize

d b

y S

pitz

Yamada et al, PoP, 2006

System L (cm) B (G) di= c/wpi(cm) dsp (cm) di/ dsp

MRX 10 100-500 1-5 0.1-5 .2-100

RFP/Tokamak 30/100 103/ 104 10 0.1 100

Magnetosphere 109 10-3 107 104 1000

Solar flare 109 100 104 102 100

ISM 1018 10-6 107 1010 0.001

Proto-star di/ ds >> 1

Linkages between space and lab on reconnection

di/ dsp ~ 5( mfp/L)1/2

Global study of magnetic reconnection

How is reconnection rate determined by global boundary conditions?

1. Flux build up phase

2. Magnetic self-organization

External forcing: Vrec vs. f

Impulsiveness

Sawtooth relaxation; reconnection in a tokamak

H. Park et al (PRL-06) on Textor

2-D Te profiles obtained by measuring ECE (electron cyclotron emission) represent magnetic fluxes

Sawtooth crash (reconnection) occurs

after a long flux build up phase tH ~ 200 msectre ~ 0.2 msec

reconn << SP

Generation of high energy electron during reconnection

Suvrukhin, 2002

Ion Temperature increases during RFP sawtooth reconnection

Ti (eV)

Emag (kJ)

Summary

• Progress has been made in reconnection research both in laboratory and space astrophysical observations => collaboration started in study of magnetic reconnection/self-organization– Transition from collisional to collisionless regime documented– A scaling found on reconnection rate

• Notable progress made for identifying causes of fast reconnection– Two fluid MHD physics plays dominant role in the collisionless

regime. Hall effects have been verified through a quadrupole field– Electron diffusion identified – Impulsive reconnection coincides with disruption of formed current

sheet– Causal relationship between these processes for fast reconnection

is yet to be determined

• Guiding principles to be found for 3-D global reconnection phenomena– Magnetic self-organization– Global forcing– Impulsive reconnection after flux build-up

Physics Frontier Center for Magnetic Self-organization in Laboratory and Astrophysical plasmas [Sept.03-]

U. Wisconsin[PI], U. Chicago, Princeton U., SAIC, and Swarthmore

Global Plasma in Equilibrium State

Unstable PlasmaState

Self-organization Processes

-Magnetic reconnection -Dynamos -Magnetic chaos & waves -Angular momentum transport

Energy Source

• Reconnection research will build a new bridge between lab and astrophysical scientists

Assume Np=S/Sc

2 4 6 8 10

4

2

6

8

10

12

14

2D Reconnection “Phase Diagram” for MRX-U Study

Collisionless

Collisional MHD (Sweet-Parker)

Collisional MHDwith Plasmoids

€

log(λ )

€

λ ≡L /ρ S

€

S = λ2

€

S = Sc λ

€

Sc =103−4

Hybrid

Petschek model

€

VRec

=1

lnSV

A

Shock