Transcript Experimental Study of Surface Waves on Liquid Gallium

Magnetic Turbulence in MRX
(for discussions on a possible cross-cutting theme to relate
turbulence, reconnection, and particle heating)
Hantao Ji
Princeton Plasma Physics Laboratory
In collaborations with MRX Team
(R. Kulsrud, A. Kuritsyn, Y. Ren, S. Terry, M. Yamada)
PFC Planning Meeting for Magnetic Chaos and Transport
Chicago, September 8 - 10 2003
Outline
• Introduction:
– Some thoughts on research themes in the Center
– Turbulence and leading theories for fast reconnection
• Measurements of magnetic turbulence
– Detailed characteristics studied
• Temporal and spatial dependence
• Frequency spectra and dispersion relation
• Polarization and propagation direction, etc.
– Correlate with resistivity enhancement and possibly
particle heating
• Discussions
2
Big Payoffs:
Three Possible Cross-cutting Themes
We should focus on tasks only possible with the Center
Examples:
• Dynamo-Reconnection-Helicity:
– Role of physics beyond MHD (i.e. Hall effect)
• Reconnection-Ion heating-Turbulence
– Energy transfer from B to ions and between scales
• Angular momentum-Dynamo-(Kinetic)
Helicity
– Flow dynamics due to magnetic field
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
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,1986; Uzdensky & Kulsrud, 2000)
Modern Leading Theories:
Turbulent and Laminar Reconnection Models
“anomalous” resistivity
Facilitated by Hall effects
ion current
e current
• Resistivity enhancement
due to (micro) instabilities
• Faster Sweet-Parker rates
• Help Petschek model by its
localization
Drake et al. (1998)
• Separation of ion and
electron layers
• Mostly 2D and laminar
What do we see in experiment?
5
Magnetic Reconnection Experiment
6
Experimental Setup in MRX
7
Realization of Stable Current Sheet and
Quasi-steady Reconnection
• Measured by extensive
sets of magnetic probe
arrays (3 components,
total 180 channels),
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
8
Agreement with a Generalized SweetParker Model
(Ji et al. PoP ‘99)
• The model has to be
modified to take into
account of
– Measured enhanced
resistivity
– Compressibility
– Higher pressure in
downstream than
upstream
model
9
Resistivity Enhancement Depends on
Collisionality
(Ji et al. PRL ‘98)
E  VR  BZ   j
E
 
j
*
Significant enhancement
in low collisionality
10
plasmas
Miniature Coils with Amplifiers Built in Probe
Shaft to Measure High-frequency Fluctuations
Three-component,
1.25mm diameter coils
Combined frequency
response up to 30MHz
Four amplifiers in a
single board
11
Fluctuations Successfully Measured in
Current Sheet Region
Both electrostatic and
magnetic fluctuations
in the lower hybrid
frequency range have
been detected.
12
Measured Electrostatic Fluctuations Do Not
Correlate with Resistivity Enhancement
(Carter et al. ‘01)
• Localized in one side of the
current sheet
• Disappear at later stage of
reconnection
13
• Independent of collisionality
Magnetic Fluctuations Measured in
Current Sheet Region
• Comparable amplitudes in all components
• Discrete peaks in the LH frequency range
14
Magnetic Fluctuations Peak Near the
Current Sheet Center
15
Frequency Spectra of Magnetic Turbulence
Slope changes at fLH (based on edge B) from f-3 to 16f-12
“Hodogram” of Magnetic Fluctuations to
Determines Direction of Wave Vector
The wave vector is perpendicular to the plane (the hodogram)
defined by the consecutive B(t) vectors (B=0)
well-defined hodogram and k vector
17
broad spread in direction of k vector
Frequency (0-20MHz)
Waves Propagate with a Large Angle to Local B
While Remain Trapped within Current Sheet
R-wave Angle[k,B0]
Angle[k,r]
18
Frequency (0-30MHz)
Measured Dispersion Relation Indicates Phase
Velocity in Electron Drifting Direction
kz(m-1)
k(m-1)
Vph
[(3.40.8)105m/s]
comparable to
19
Vdrift[(2.50.9)105m/s]
Short Coherence Lengths Indicate Strong
Nonlinear Nature of Fluctuations
R=37.5cm
20
Fluctuation Amplitudes Strongly Depend on
Collisionality
21
Fluctuation Amplitudes Correlate with
Resistivity Enhancement
22
Evidence of non-classical electron heating
(Hsu et al. ‘00)
Ohmic heating can explain
only ~20% of Te peaking
Localized ion heating
(He plasma)
23
Discussions: Physical Questions
• Q1:
What is the underlying instability?
• Q2:
How much resistivity does this instability produce?
• Q3:
How much ions and electrons are heated?
• Q4:
How universal is this instability?
• Q5:
Does it apply to space/astrophysical, other lab plasmas?
……
24
Candidate High-frequency Instabilities
• Buneman instability(two-stream instability): B0=0
– Electrostatic, driven by relative drift, need Vd > Ve ,th
• Ion acoustic instability: B0=0
– Electrostatic, driven by relative drift, need Vd > Vi ,th and Te >> Ti
• Electron-cyclotron-drift instability: B00
•
– Electrostatic, driven by relative drift, k||~0, need Vd > Vi ,th and Te >> Ti
Lower hybrid drift instability: B00
– Electrostatic with a B component along B0, driven by inhomogeniety, k||~0
– Stabilized by large 
• Whistler anisotropy instability: B00
– Electromagnetic, driven by Te > Te||, k~0
• Modified two-stream instability: B00
– Electrostatic and electromagnetic, driven by  relative drift, k||~k
• Low- case: need Vd > Vi ,th, mainly electrostatic, similar to LHDI
• High- case: need Vd > VA, mainly electromagnetic!
25
Wave Characteristics in fLH Range
No drift, Thermal electron response along B0
Whistler
waves
ES
“MTSI”
“LHDI”
Ion acoustic
waves
90
0
EM
26
Y. Ren
Propagation Characteristics with Drift
~LH
In an attempt to explain an experiment on shock,
27
later it was applied to the case of collisionless shock in space…
Linear Growth Rates by Local Kinetic Theory
Kinetic theory (Wu, Tsai, et al. ‘83,’84):
Full ion response (Basu & Coppi ‘92):
Collision effects (Choueiri, 1999, 2001)
Global 2-fluid treatment (Yoon, 2002)
Global kinetic treatment (Daughton, 2003)
Related experiments:
Parametric excitation (Porkolab et al. 1972)
28
EMHD reconnection (Gekelman & Stenzel 1984)


Qualitative Estimate of Resistivity Enhancement
Momentum carried by electromagnetic waves:
k
B˜ 2
2
: the total wave energy density
20



Momentum transfer from electrons = force on electrons:
2
˜
B
e
enE wave  2k


0 

 e ~  : linear growth rate due to inverse
Landau resonance
Ewave ~ Ereconnection if coherence length (<2cm) is used for k

A simple model with relative drift based on a 2-fluid model
is being developed to illustrate the physical mechanism
29
Further Discussions
Reconnection
accelerate
drive
Ohmic, flow
Slow down?
(Micro-)Turbulence heat
Follow the energy:
•
•
Particle Heating
How does energy flow from magnetic field to (micro-)turbulence and/or
particles?
Relation with energy backflow from flow to magnetic field (dynamo) and selforganization (inverse cascade regulated by helicity conservation)
30
Possible Tasks in the Center
• Experiment
– Measure correlation of magnetic turbulence with particle
heating during reconnection in MRX, SSX…
– Measure (high frequency) magnetic turbulence during
relaxation in MST, SSPX…
– Characterize more turbulence (e.g. multiple-point correlations)
in all experiments
• Theory
– Understand instability and its effects on dissipation, such as
resistivity enhancement and particle heating
– Relate it to MHD turbulence and self-organization
• Simulation
– Study nonlinear effects using 2-fluid or kinetic models
– Attempt to imbed non-MHD regions in a MHD simulation
31
 and Drift are Large in MRX
Ti=5Te
32
Linear Growth Rates by Local Kinetic Theory
 pe / ce  150,  e  0.5,  i  2.5,Vdrift /VA  5
Follow-up theories:
Kinetic theory (Wu, Tsai, 1983, 1984)
Full ion responses (Basu & Coppi, 1992)
Collision effects (Choueiri, 1999, 2001)
Y. Ren
Related experiments:
Parametric Inst. (Porkolab et al. 1972) 33
EMHD reconnection (Gekelman & Stenzel 1984)
Magnetic Fluctuations Vary Substantially
Along the Current () Direction
Correlations with local drift velocity ?
34
Sometime Onset Delays at Different Locations
~1s
"V "~ 75km/s
(VA ~ 100km/s, Vd ~150km/s)
~3s
"VZ "~ 20km/s
35
Magnetic Fluctuations Measured in
Current Sheet Region
Broadening of current
sheet measured at 25
(16cm) away
Comparable amplitudes
for B and Bz
Multiple peaks in the
LH frequency range
36