magnetic turbulence in mrx (for discussions on a possible cross-cutting theme to relate turbulence,...

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)

2

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

3

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:

4

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:

5

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:

6

Magnetic Reconnection Experiment

7

Experimental Setup in MRX

8

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

9

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

10

Resistivity Enhancement Depends on Collisionality

Significant enhancement in

low collisionality plasmas

η* ≡Eθjθ

(Ji et al. PRL ‘98)

Eθ +VR ×BZ =ηjθ

11

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

12

Fluctuations Successfully Measured in Current Sheet Region

Both electrostatic and

magnetic fluctuations in

the lower hybrid

frequency range have

been detected.

13

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)

14

Magnetic Fluctuations Measured in Current Sheet Region

• Comparable amplitudes in all components

• Discrete peaks in the LH frequency range

15

Magnetic Fluctuations Peak Near the Current Sheet Center

16

Frequency Spectra of Magnetic Turbulence

Slope changes at fLH (based on edge B) from f-3 to f-12

17

“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)

18

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

19

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)

20

Short Coherence Lengths Indicate Strong Nonlinear Nature of Fluctuations

R=37.5cm

21

Fluctuation Amplitudes Strongly Depend on Collisionality

22

Fluctuation Amplitudes Correlate with Resistivity Enhancement

23

Evidence of non-classical electron heating

Ohmic heating can explain only ~20% of Te peaking

(Hsu et al. ‘00)

Localized ion heating (He plasma)

24

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?

……

25

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!

26

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

27

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

28

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)

29

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

30

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:

31

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

32

and Drift are Large in MRX

Ti=5Te

33

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

34

Magnetic Fluctuations Vary Substantially Along the Current () Direction

Correlations with local drift velocity ?

35

Sometime Onset Delays at Different Locations

~1s

€

"Vθ "~ 75km/s~3s

€

"VZ"~20km/s

€

(VA ~100km/s, Vd ~150km/s)

36

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