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