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