Magnetic Turbulence in MRX (for discussions on a possible cross-cutting theme to relate turbulence, reconnection, and particle heating)

1
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
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
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

4
Sweet-Parker Model vs. Petschek Model
Classic Leading Theories
Petschek Model
Sweet-Parker Model

• 2D steady state
• Imcompressible
• Classical resistivity

• A much smaller diffusion region (LltltL)
• Shock structure to open up outflow channel

Problem not a solution for smooth resistivity
profiles
Problem predictions are too slow to be
consistent with observations
(Biskamp,1986 Uzdensky Kulsrud, 2000)
5
Turbulent and Laminar Reconnection Models
Modern Leading Theories
anomalous resistivity
Facilitated by Hall effects
ion current
e current
Drake et al. (1998)

• Resistivity enhancement due to (micro)
  instabilities
• Faster Sweet-Parker rates
• Help Petschek model by its localization

• Separation of ion and electron layers
• Mostly 2D and laminar

What do we see in experiment?
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 lt 1 kG, TeTi 5-20 eV,
  ne(0.02-1)?1020/m3 ?S lt 1000

Sweet-Parker like diffusion region
9
Agreement with a Generalized Sweet-Parker 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
10
Resistivity Enhancement Depends on Collisionality
(Ji et al. PRL 98)
Significant enhancement in low collisionality
plasmas
11
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
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
(Carter et al. 01)

• Localized in one side of the current sheet
• Disappear at later stage of reconnection
• Independent of collisionality

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
The wave vector is perpendicular to the plane
(the hodogram) defined by the consecutive ?B(t)
vectors (??B0)
well-defined hodogram and k vector
broad spread in direction of k vector
18
Waves Propagate with a Large Angle to Local B
While Remain Trapped within Current Sheet
Frequency (0-20MHz)
Anglek,B0
Anglek,r
R-wave
19
Measured Dispersion Relation Indicates Phase
Velocity in Electron Drifting Direction
Frequency (0-30MHz)
kz(m-1)
k?(m-1)
Vph (3.4?0.8)?105m/s comparable to
Vdrift(2.5?0.9)?105m/s
20
Short Coherence Lengths Indicate Strong Nonlinear
Nature of Fluctuations
R37.5cm
21
Fluctuation Amplitudes Strongly Depend on
Collisionality
22
Fluctuation Amplitudes Correlate with Resistivity
Enhancement
23
Evidence of non-classical electron heating
(Hsu et al. 00)
Localized ion heating (He plasma)
Ohmic heating can explain only 20 of Te peaking
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) B00
• Electrostatic, driven by relative drift, need Vd
  gt Ve ,th
• Ion acoustic instability B00
• Electrostatic, driven by relative drift, need Vd
  gt Vi ,th and Te gtgt Ti
• Electron-cyclotron-drift instability B0?0
• Electrostatic, driven by relative drift, k0,
  need Vd gt Vi ,th and Te gtgt Ti

• Lower hybrid drift instability B0?0
• Electrostatic with a B component along B0, driven
  by inhomogeniety, k0
• Stabilized by large ?
• Whistler anisotropy instability B0?0
• Electromagnetic, driven by Te? gt Te, k?0

• Modified two-stream instability B0?0
• Electrostatic and electromagnetic, driven by ?
  relative drift, kk?
• Low-? case need Vd gt Vi ,th, mainly
  electrostatic, similar to LHDI
• High-? case need Vd gt VA, mainly
  electromagnetic!

26
Wave Characteristics in fLH Range
No drift, Thermal electron response along B0
ES
Whistler waves
MTSI
LHDI
Ion acoustic waves
EM
90?
0?
Y. Ren
27
Propagation Characteristics with Drift
??LH
In an attempt to explain an experiment on
shock, later it was applied to the case of
collisionless shock in space
28
Linear Growth Rates by Local Kinetic Theory
Kinetic theory (Wu, Tsai, et al. 83,84)
Full ion response (Basu Coppi 92)

• Related experiments
• Parametric excitation (Porkolab et al. 1972)
• EMHD reconnection (Gekelman Stenzel 1984)

Collision effects (Choueiri, 1999, 2001) Global
2-fluid treatment (Yoon, 2002) Global kinetic
treatment (Daughton, 2003)
29
Qualitative Estimate of Resistivity Enhancement
Momentum carried by electromagnetic waves
the total wave energy density
Momentum transfer from electrons force on
electrons
linear growth rate due to inverse Landau
resonance
if coherence length (lt2cm) is used for
A simple model with relative drift based on a
2-fluid model is being developed to illustrate
the physical mechanism
30
Further Discussions
Reconnection
Ohmic, flow
accelerate
drive
Slow down?
Particle Heating
(Micro-)Turbulence
heat
Follow the energy

• 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)

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
Ti5Te
33
Linear Growth Rates by Local Kinetic Theory
Y. Ren
Follow-up theories Kinetic theory (Wu, Tsai,
1983, 1984) Full ion responses (Basu Coppi,
1992) Collision effects (Choueiri, 1999, 2001)

• Related experiments
• Parametric Inst. (Porkolab et al. 1972)
• EMHD reconnection (Gekelman Stenzel 1984)

34
Magnetic Fluctuations Vary Substantially Along
the Current (?) Direction
Correlations with local drift velocity ?
35
Sometime Onset Delays at Different Locations
1?s
3?s
36
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