Transcript Magnetic Turbulence During Reconnection

Magnetic Turbulence during Reconnection
Hantao Ji
Center for Magnetic Self-organization in Laboratory and Astrophysical Plasmas
Princeton Plasma Physics Laboratory, Princeton University
Contributors:
Will Fox
Stefan Gerhardt
Russell Kulsrud
Aleksey Kuritsyn
Yang Ren
Masaaki Yamada
Yansong Wang
General Meeting of CMSO
Madison, August 4-6, 2004
Outline
• Introduction
– Magnetic Reconnection Experiment (MRX)
– Quantitative test of Sweet-Parker model
• High-frequency electromagnetic turbulence detected, in
correlation with fast reconnection
– Similarities with space measurements
• Understanding EM turbulence
– An EM instability revealed by a simple 2-fluid theory
• Summary
2
Physical Questions on Reconnection
• How does reconnection start? (The trigger problem)
• How local reconnection is controlled by global dynamic
(constraints) and vice versa ?
• Why reconnection is fast compared to classical theory?
• How ions and electrons are heated or accelerated?
• Is reconnection inherently 3D or basically 2D?
• Is reconnection turbulent or laminar?
3
Classic Leading Theories:
Sweet-Parker Model vs. Petschek Model
Petschek Model
Sweet-Parker Model
•
•
•
2D & steady state
Imcompressible
Classical resistivity
VR
1

VA
S
 LV
Lundquist #: S  0 A

Problem: predictions are
too slow to be consistent
with observations 
•
•
A much smaller diffusion
region (L’<<L)
Shock structure to open up
outflow channel
VR
1

VA ln(S)
Problem: not a solution for
smooth resistivity profiles
4
(Biskamp,’86; Uzdensky & Kulsrud, ‘00)
Magnetic Reconnection Experiment (MRX)
Other exps:
SSX,VTF, RSX etc in US
TS-3/4 in Japan
1 in Russia
1 will start in China
5
What do we see in exp?
Experimental Setup in MRX
Solid coils in vacuum
6
Realization of Stable Current Sheet and
Quasi-steady Reconnection
• Measured by magnetic
probe arrays, triple
probes, optical probe,
…
• Parameters:
– B < 1 kG,
– Te~Ti = 5-20 eV
– ne=(0.02-1)1020/m3
S < 1000
Sweet-Parker like diffusion region
7
Agreement with a Generalized SweetParker Model
(Ji et al. PoP ‘99)
• The model modified to
take into account of
– Measured enhanced
resistivity
– Compressibility
– Higher pressure in
downstream than
upstream
model
8
Resistivity Enhancement Depends on
Collisionality
(Ji et al. PRL ‘98)
E  VR  BZ   j
At current sheet center:
E
 
j
*
Significant enhancement
at low collisionalities
9
Modern Leading Theories for Fast Reconnection:
Turbulent vs. Laminar Models
“anomalous” resistivity
Facilitated by Hall effects
ion current
e current
(Ugai & Tsuda, ‘77; Sato & Hayashi, ‘79;
Scholer, ‘89….)
•
•
•
Enhanced due to (micro) instabilities
Faster Sweet-Parker rates
Re-establish Petschek model by localization
(Drake et al. ‘98)
•
•
Separation of ion and electron
layers
Mostly 2D and laminar
Expect:
Expect:
high-frequency turbulence
electron scale structure in10B
What do we see in exp?
Miniature Coils with Amplifiers Built in Probe
Shaft to Measure High-frequency Fluctuations
Four amplifiers
Three-component,
1.25mm diameter coils
Combined frequency response up to 30MHz
11
Fluctuations Successfully Measured in
Current Sheet Region
(Carter et al. PRL, ‘02)
• ES fluctuations, localized at low beta current sheet
12
edge, did not correlate with resistivity enhancement
Magnetic Fluctuations Measured in
Current Sheet Region
(Ji et al. PRL, ‘04)
• Comparable amplitudes in all components
• Often multiple peaks in the LH frequency range
13
Waves Propagate in the Electron Drift Direction
with a Large Angle to Local B
Frequency (0-20MHz)
Local to certain
angle and k
R-wave
Vph ~ Vdrift
Angle[k,B0]
14
EM Wave Amplitude Correlates with
Resistivity Enhancement
15
Similar Observation by Spacecraft at
Earth’s Magnetopause
(Bale et al. ‘04)
(Phan et al. ‘03)
EM
ES
low high low
b
b
b
low
b
high
b
16
Physical Questions
• Q1:
What is the underlying instability?
• Q2:
How much resistivity does this instability produce?
• Q3:
How much ions and electrons are heated?
17
Modified Two-Stream Instability at High-beta:
An Electromagnetic Drift Instability
• First exploration: local fluid theory (Ross, 1970)
• Full electron kinetic treatment (Wu, Tsai, et al., 1983, 1984)
• Full ion kinetic treatment and quasi-linear theory (Basu & Coppi, 1992;
Yoon & Lui, 1993)
• Collisional effects (Choueiri, 1999, 2001)
• Global treatment (Huba et al., 1980, Yoon et al., 2002, Daughton, 2003)
EM
ES
In the context of collisionless shock…
18
A Local 2-Fluid Theory
•
•
Regime: ci
Assumptions

•
–
–
–
–
–
   ce
(Ji et al. in preparation, ‘04)
z
Massless, isotropic, magnetized electrons
Unmagnetized ions
No e-i collisions
Charge neutrality
Constant ion and electron temperature
B0
B0
n0
Equilibrium
– Background magnetic field in z direction
– Density gradient in y direction
– Ions are at rest
n 0
en 0 E 0  Ti
y
V0
y
– Electrons drift across B in x direction
n
en 0 E 0  V0 B0   Te 0
y

– Thus,

T
E0 
V0B0
 i
1 
Te
x
E0
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Dispersion Relation
•
Normal mode decomposition for wave quantities:
exp i(k  x  t)
•
“Dielectric tensor”:
D
 xx
Dyx
D
 zx

•
Dxy Dxz E x 
 
Dyy Dyz E y  0
 
Dyz Dzz 
E z 
1st and 2nd lines:
k  (k  E)  i0 j
•

k  k x ,0,kz 
kz2 E x  k x k z E z  i0 j x
k 2 E y  i0 jy

3rd line from electron force balance along z direction:
Te 
n
E z  V0 By  ik z
e n0
By 

kz E x  k x E z

from continuity,
ion, and electron
20
equations
Dispersion Relation (Cont’d)
•
Normalizations:

•


c
V
n T
k
T
,K  k
,V  0 , b e  2 0 e ,sin   x ,  i
 ci
 pi
VA
k
Te
B0 /20
Dispersion relation after re-arrangements:
 KV sin 
1 

2
2 
b e K sin 
K 2 cos 2   1

i 
2


 
b e K 2 sin  cos
KV cos 
2

•
 KV cos 
1 

2
b e K sin  cos 
i  KV sin   K 2 sin  cos 
K2 1
0
i
2
  KV sin  

0
b e K 2 cos 2 
2

Fourth order in (K), with controlling parameters of V, b, , .

21
Instability: Large Drifts Cause Coupling
between Whistler and Sound Waves
whistler waves
(electron)

sound waves
(ion)
Angle

more EM
more ES
K
22
Unstable only at Certain Angles and K,
Consistent with Observations
V=1
V=3
V=6
23
A Simple Physical Picture
• Cold electron limit; slow mode
approximation
• Purely growing when unstable
electron density
perturbation
reinforce
V sin 2  2 K cos2  2
KV 
 
 0
K
V
ES (de)compression

z
B
B
tension
ne n0
nE0 force
ne +
y
JB force in
z direction
B deforms in
y direction
E0
ne -
24
Estimated Resistivity due to
Observed Electromagnetic Waves
(Kulsrud et al. ‘03)
Total energy and momentum density of EM waves:
B˜ 2
k
Pw 
w 2
 w
20
Resistivity:


Pw 2 e k w 2 e k B˜ 2
w j   

t
en 
 en 0


 e ~  : since waves are highly nonlinear

k ~

2
coherence
w j ~ 100V /m ~ Ereconnection
25
Answers or clues from MRX
Physical Questions on Reconnection
• How does reconnection start? (The trigger problem)
– Driven in MRX
• How local reconnection is controlled by global dynamic
(constraints) and vice versa ?
– Boundary conditions important (large pdown)
• Why reconnection is fast compared to classical theory?
– Due to an electromagnetic drift instability?
• How ions and electrons are accelerated?
– Due to the same instability?
• Is reconnection inherently 3D or basically 2D?
– Globally 2D but locally 3D
• Is reconnection turbulent or laminar?
26
– Turbulent
Summary
• Physics of fast reconnection is studied in MRX
– High frequency magnetic turbulence detected and identified as
obliquely propagating whistler waves
– Correlate positively with resistivity enhancement
• Turbulence consistent with an EM drift instability
– Physics explored using a simple 2-fluid model
– Nonlinear effects (resistivity and particle heating) are being studied
– Need to be compared with simulations
• Connections to other plasmas
– Measurements planned for strong guide-field cases, such as in MST
– Commonalities with satellite in situ measurements in magnetosphere
27