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Magnetic Turbulence in MRX (for discussions on a possible cross-cutting theme to relate
turbulence, reconnection, and particle heating)
PFC Planning Meeting for Magnetic Chaos and TransportChicago, September 8 - 10 2003
Hantao Ji
Princeton Plasma Physics Laboratory
In collaborations with MRX Team (R. Kulsrud, A. Kuritsyn, Y. Ren, S. Terry, M. Yamada)
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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
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Big Payoffs: Three Possible Cross-cutting Themes
• 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
We should focus on tasks only possible with the Center
Examples:
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Sweet-Parker Model vs. Petschek Model
• 2D & steady state• Imcompressible• Classical resistivity
Sweet-Parker Model Petschek Model
• A much smaller diffusion region (L’<<L)
• Shock structure to open up outflow channel
VRVA
= 1S
VRVA
≈ 1ln(S)
Problem: not a solution for smooth resistivity profiles
Problem: predictions are too slow to be consistent with observations
(Biskamp,1986; Uzdensky & Kulsrud, 2000)
Classic Leading Theories:
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Turbulent and Laminar Reconnection Models
• Resistivity enhancement due to (micro) instabilities
• Faster Sweet-Parker rates• Help Petschek model by its
localization
“anomalous” resistivity Facilitated by Hall effects
What do we see in experiment?
• Separation of ion and electron layers
• Mostly 2D and laminar
ion current
e current
Drake et al. (1998)
Modern Leading Theories:
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Magnetic Reconnection Experiment
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Experimental Setup in MRX
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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
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Agreement with a Generalized Sweet-Parker Model
• The model has to be modified to take into account of– Measured enhanced
resistivity
– Compressibility
– Higher pressure in downstream than upstream
(Ji et al. PoP ‘99)
model
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Resistivity Enhancement Depends on Collisionality
Significant enhancement in
low collisionality plasmas
η* ≡Eθjθ
(Ji et al. PRL ‘98)
Eθ +VR ×BZ =ηjθ
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Miniature Coils with Amplifiers Built in Probe Shaft to Measure High-frequency Fluctuations
Four amplifiers in a single board
Three-component, 1.25mm diameter coils
Combined frequency response up to 30MHz
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Fluctuations Successfully Measured in Current Sheet Region
Both electrostatic and
magnetic fluctuations in
the lower hybrid
frequency range have
been detected.
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Measured Electrostatic Fluctuations Do Not Correlate with Resistivity Enhancement
• Localized in one side of the current sheet
• Disappear at later stage of reconnection
• Independent of collisionality
(Carter et al. ‘01)
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Magnetic Fluctuations Measured in Current Sheet Region
• Comparable amplitudes in all components
• Discrete peaks in the LH frequency range
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Magnetic Fluctuations Peak Near the Current Sheet Center
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Frequency Spectra of Magnetic Turbulence
Slope changes at fLH (based on edge B) from f-3 to f-12
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“Hodogram” of Magnetic Fluctuations to Determines Direction of Wave Vector
well-defined hodogram and k vector broad spread in direction of k vector
The wave vector is perpendicular to the plane (the hodogram) defined by the consecutive B(t) vectors (B=0)
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Waves Propagate with a Large Angle to Local B While Remain Trapped within Current Sheet
Angle[k,B0]
Fre
qu
ency
(0-
20M
Hz)
Angle[k,r]R-wave
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Measured Dispersion Relation Indicates Phase Velocity in Electron Drifting Direction
k(m-1)
Fre
qu
ency
(0-
30M
Hz)
Vph [(3.40.8)105m/s] comparable to Vdrift[(2.50.9)105m/s]
kz(m-1)
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Short Coherence Lengths Indicate Strong Nonlinear Nature of Fluctuations
R=37.5cm
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Fluctuation Amplitudes Strongly Depend on Collisionality
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Fluctuation Amplitudes Correlate with Resistivity Enhancement
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Evidence of non-classical electron heating
Ohmic heating can explain only ~20% of Te peaking
(Hsu et al. ‘00)
Localized ion heating (He plasma)
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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?
……
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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: B00
– Electrostatic, driven by relative drift, k||~0, need Vd > Vi ,th and Te >> Ti
• Lower hybrid drift instability: B00
– Electrostatic with a B component along B0, driven by inhomogeniety, k||~0
– Stabilized by large • Whistler anisotropy instability: B00
– Electromagnetic, driven by Te > Te||, k~0
• Modified two-stream instability: B00
– 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!
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Wave Characteristics in fLH Range
90 0
No drift, Thermal electron response along B0
“MTSI”
“LHDI”
Whistler waves
Ion acoustic waves
Y. Ren
ES
EM
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Propagation Characteristics with Drift
In an attempt to explain an experiment on shock,later it was applied to the case of collisionless shock in space…
~LH
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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) EMHD reconnection (Gekelman & Stenzel 1984)
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Qualitative Estimate of Resistivity Enhancement
€ €
kεω
Momentum carried by electromagnetic waves:
€
enEθwave = 2kθ
˜ B 2
μ0
γ e
ω
Momentum transfer from electrons = force on electrons:
€
ε=2 ט B 2
2μ0
: the total wave energy density
€
e ~ ω : linear growth rate due to inverse Landau resonance
if coherence length (<2cm) is used for
€
Eθwave ~ Eθ
reconnection
€
kθ
A simple model with relative drift based on a 2-fluid model is being developed to illustrate the physical mechanism
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Further Discussions
• How does energy flow from magnetic field to (micro-)turbulence and/or particles?
• Relation with energy backflow from flow to magnetic field (dynamo) and self-organization (inverse cascade regulated by helicity conservation)
Reconnection
(Micro-)Turbulence Particle Heating
driveaccelerate
heat
Ohmic, flow
Slow down?
Follow the energy:
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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
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and Drift are Large in MRX
Ti=5Te
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Related experiments: Parametric Inst. (Porkolab et al. 1972) EMHD reconnection (Gekelman & Stenzel 1984)
Linear Growth Rates by Local Kinetic Theory
Follow-up theories: Kinetic theory (Wu, Tsai, 1983, 1984) Full ion responses (Basu & Coppi, 1992) Collision effects (Choueiri, 1999, 2001)
Y. Ren
€
ωpe /ωce =150,β e = 0.5,β i = 2.5,Vdrift /VA = 5
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Magnetic Fluctuations Vary Substantially Along the Current () Direction
Correlations with local drift velocity ?
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Sometime Onset Delays at Different Locations
~1s
€
"Vθ "~ 75km/s~3s
€
"VZ"~20km/s
€
(VA ~100km/s, Vd ~150km/s)
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Magnetic Fluctuations Measured in Current Sheet Region
Broadening of current sheet measured at 25 (16cm) away
Multiple peaks in the LH frequency range
Comparable amplitudes
for B and Bz