Magnetic Reconnection:
Progress and Status of Lab Experiments
Masaaki Yamada
SLAC, April 28th 2011
In collaboration with members of MRX group and
NSF-DoE Center of Magnetic Self-organization
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
Reconnection always occurs very fast (reconn << SP) after build-up
phase of flux
X-ray
intensity
Solar flare
time(hour)
Magnetospheric
Aurora-substorm
Magnetic
Field
strength
time(hour)
Stellar flare
Tokamak Sawtooth
disruption
X-ray
intensity
Electron
temperature
time(sec)
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
Vin
Vout
B is resistively annihilated
B
t
   (v  B) 

0
in the sheet
 B
2
V in B 
 Spitz B
0 
V in L  V out 
Mass conservation:
Pressure balance:
reconn << SP ~ ６−９ months
 1
2
 V out 
2
B
VA
S 
2
20
V in
 V out  V A

1
S
 0 LV A
 Spitz
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
Trigger
with guide B
RSX
Los Alamos
2002
Intrator
Linear
Boundary
RWX
Wisconsin
2002
Forest
Linear
Boundary
MRX: Dedicated reconnection experiment
Goal: Provide fundamental data on reconnection, by creating
proto-typical reconnection phenomena, in a controlled setting
Local physics problems
addressed in collaboration
with numerical simulations
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
Pull Reconnection in MRX
IPF
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
 
*
E
j
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
Sheath width ~ c/wpi ~ i
P. L. Pritchett, J.G.R 2001
Out of plane magnetic field is
generated during reconnection
The Hall Effect Facilitates Fast
Reconnection
Normalized with
E rec  V in  B rec  0
Hall term
Electron inertia
term
Electron
pressure term
Ideal MHD region
Vin
-jin
Vout~ VA
Ion diffusion region
Electron diffusion region
•
The width of the ion diffusion region is c/wpi
•
The width of the electron diffusion region is c/wpe ?
MRX with fine probe arrays
Linear 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
Evolution of magnetic field lines during reconnection in MRX
e
Measured region
Electrons pull field lines as they flow in the neutral sheet
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 <
Slow reconnection
No Q-P field
X-type shape
Collisionless regime: mfp >
Fast reconnection
Q-P field present
Two-scale Diffusion Region measured in MRX
Ion Diffusion region measured: i > c/wpi
Electron Diffusion region newly identified: 6-8 c/wpe < e
Electron jetting measured in both z and y direction
: ve > 3-6 VAi
Presence of B fluctuations
Y. Ren et al, PRL 2008
First Detection of Electron Diffusion Layer Made in MRX:
Comparison with 2D PIC Simulations
MRX:
e = 8 c/wpe
2D PIC Sim:
e = 1.6 c/wpe
All ion-scale features reproduced; but electron-layer is 5 times thicker in MRX
Þ importance of 3D effects
Measured electron diffusion layer is
much broader than 2-D simulation results
=> MMS program
(Ji, et. al. Sub. GRL 2008)
Recent (2D) Simulations Find New Large S Phenomena
Bhattacharjee et al. (2009):MHD
Daughton et al. (2009): PIC
Sweet-Parker layers break up to form
plasmoids when S > ~104
Impulsive fast reconnection with multiple X points
23
In a large high S (>104) system,
flux ropes can be generated
=> Impulsive fast reconnection
Daughton et al, Nature Phys.2011
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
Magnetic Reconnection in the Magnetosphere
A reconnection layer has been documented in the magnetopause
 ~ c/wpi
Mozer et al., PRL 2002
POLAR satellite
Similar Observations in Magnetopause and Lab Plasma
MRX
(a)
(Space:Bale et al. ‘04)
(b)
EM waves
EM
ES
(c)
ES waves
low 
low high


low

high 
EM waves correlate with 
MRX Scaling: * vs (c/wi)/ sp
Nomalized by Spitz
A linkage between space and lab on reconnection
Breslau2 Fluid
simulation
 
*
E
j
(c/wpi)/ sp
~ 5( mfp/L)1/2
Yamada et al, PoP, 2006
MRX scaling shows a transition from the MHD to 2 fluid regime
based on (c/wpi)/ sp
Linkages between space and lab on reconnection
System
L (cm)
B (G)
di= c/wpi(cm)
sp (cm)
di/ sp
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
104
102
100
107
1010
0.001
ISM
Proto-star
1018
100
10-6
di/ s >> 1
di/ sp ~ 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
H ~ 200 msec
re ~ 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
• Reconnection research will build a new bridge
between lab and astrophysical scientists
Global Plasma in
Equilibrium State
Self-organization Processes
Energy Source
-Magnetic reconnection
-Dynamos
-Magnetic chaos & waves
-Angular momentum transport
Unstable Plasma
State
Physics Frontier Center for Magnetic Self-organization
in Laboratory and Astrophysical plasmas [Sept.03-]
U. Wisconsin[PI], U. Chicago, Princeton U., SAIC, and Swarthmore
2D Reconnection “Phase Diagram” for MRX-U Study
14
12
S
10
2
Sc 
Assume Np=S/Sc
Hybrid
Collisionless
8
6
S
 MHD
Collisional
with Plasmoids

4
S c  10
2
Collisional MHD (Sweet-Parker)
2
4
log(  )
6
8

  L /S
10
3 4
Petschek model
Shock
V
Re c

1
ln S
V
A