Magnetic Turbulence during Reconnection

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Magnetic Turbulence during Reconnection
Hantao Ji
Center for Magnetic Self-organization in
Laboratory and Astrophysical Plasmas Princeton
Plasma Physics Laboratory, Princeton University
Contributors Will Fox Stefan
Gerhardt Russell Kulsrud Aleksey
Kuritsyn Yang Ren Masaaki Yamada Yansong
Wang
General Meeting of CMSO Madison, August 4-6, 2004
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Outline

• Introduction
• Magnetic Reconnection Experiment (MRX)
• Quantitative test of Sweet-Parker model
• High-frequency electromagnetic turbulence
  detected, in correlation with fast reconnection
• Similarities with space measurements
• Understanding EM turbulence
• An EM instability revealed by a simple 2-fluid
  theory
• Summary

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Physical Questions on Reconnection

• How does reconnection start? (The trigger
  problem)
• How local reconnection is controlled by global
  dynamic (constraints) and vice versa ?
• Why reconnection is fast compared to classical
  theory?
• How ions and electrons are heated or accelerated?
• Is reconnection inherently 3D or basically 2D?
• Is reconnection turbulent or laminar?

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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

Lundquist
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Magnetic Reconnection Experiment (MRX)
Other exps SSX,VTF, RSX etc in US TS-3/4
in Japan 1 in Russia 1 will start in China
What do we see in exp?
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Experimental Setup in MRX
Solid coils in vacuum
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Realization of Stable Current Sheet and
Quasi-steady Reconnection

• Measured by magnetic probe arrays, 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
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Agreement with a Generalized Sweet-Parker Model
(Ji et al. PoP 99)

• The model modified to take into account of
• Measured enhanced resistivity
• Compressibility
• Higher pressure in downstream than upstream

model
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Resistivity Enhancement Depends on Collisionality
(Ji et al. PRL 98)
At current sheet center
Significant enhancement at low collisionalities
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Turbulent vs. Laminar Models
Modern Leading Theories for Fast Reconnection
anomalous resistivity
Facilitated by Hall effects
ion current
e current
(Ugai Tsuda, 77 Sato Hayashi, 79 Scholer,
89.)
(Drake et al. 98)

• Enhanced due to (micro) instabilities
• Faster Sweet-Parker rates
• Re-establish Petschek model by localization

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

What do we see in exp?
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Miniature Coils with Amplifiers Built in Probe
Shaft to Measure High-frequency Fluctuations
Four amplifiers
Three-component, 1.25mm diameter coils
Combined frequency response up to 30MHz
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Fluctuations Successfully Measured in Current
Sheet Region
(Carter et al. PRL, 02)

• ES fluctuations, localized at low beta current
  sheet edge, did not correlate with resistivity
  enhancement

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Magnetic Fluctuations Measured in Current Sheet
Region
(Ji et al. PRL, 04)

• Comparable amplitudes in all components
• Often multiple peaks in the LH frequency range

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Waves Propagate in the Electron Drift Direction
with a Large Angle to Local B
Local to certain angle and k
Frequency (0-20MHz)
R-wave
Vph Vdrift
Anglek,B0
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EM Wave Amplitude Correlates with Resistivity
Enhancement
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Similar Observation by Spacecraft at Earths
Magnetopause
(Phan et al. 03)
(Bale et al. 04)
EM
ES
high b
low b
high b
low b
low b
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Physical Questions

• Q1
• What is the underlying instability?
• Q2
• How much resistivity does this instability
  produce?
• Q3
• How much ions and electrons are heated?

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Modified Two-Stream Instability at High-beta An
Electromagnetic Drift Instability

• First exploration local fluid theory (Ross,
  1970)
• Full electron kinetic treatment (Wu, Tsai, et
  al., 1983, 1984)
• Full ion kinetic treatment and quasi-linear
  theory (Basu Coppi, 1992 Yoon Lui, 1993)
• Collisional effects (Choueiri, 1999, 2001)
• Global treatment (Huba et al., 1980, Yoon et al.,
  2002, Daughton, 2003)

EM
ES
In the context of collisionless shock
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A Local 2-Fluid Theory

• Regime
• Assumptions
• Massless, isotropic, magnetized electrons
• Unmagnetized ions
• No e-i collisions
• Charge neutrality
• Constant ion and electron temperature
• Equilibrium
• Background magnetic field in z direction
• Density gradient in y direction
• Ions are at rest
• Electrons drift across B in x direction
• Thus,

(Ji et al. in preparation, 04)
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Dispersion Relation

• Normal mode decomposition for wave quantities
• Dielectric tensor
• 1st and 2nd lines
• 3rd line from electron force balance along z
  direction

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Dispersion Relation (Contd)

• Normalizations
• Dispersion relation after re-arrangements
• Fourth order in ?(K), with controlling parameters
  of V, ?, ?, ?.

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Instability Large Drifts Cause Coupling between
Whistler and Sound Waves
whistler waves (electron)
?
sound waves (ion)
?
more EM
Angle
more ES
K
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Unstable only at Certain Angles and K, Consistent
with Observations
V3
V6
V1
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A Simple Physical Picture

• Cold electron limit slow mode approximation
• Purely growing when unstable

ES
(de)compression
tension
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Estimated Resistivity due to Observed
Electromagnetic Waves
(Kulsrud et al. 03)
Total energy and momentum density of EM waves
Resistivity
since waves are highly nonlinear
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Physical Questions on Reconnection
Answers or clues from MRX

• Driven in MRX
• Boundary conditions important (large pdown)
• Due to an electromagnetic drift instability?
• Due to the same instability?
• Globally 2D but locally 3D
• Turbulent

• How does reconnection start? (The trigger
  problem)
• How local reconnection is controlled by global
  dynamic (constraints) and vice versa ?
• Why reconnection is fast compared to classical
  theory?
• How ions and electrons are accelerated?
• Is reconnection inherently 3D or basically 2D?
• Is reconnection turbulent or laminar?

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Summary

• Physics of fast reconnection is studied in MRX
• High frequency magnetic turbulence detected and
  identified as obliquely propagating whistler
  waves
• Correlate positively with resistivity enhancement
• Turbulence consistent with an EM drift
  instability
• Physics explored using a simple 2-fluid model
• Nonlinear effects (resistivity and particle
  heating) are being studied
• Need to be compared with simulations
• Connections to other plasmas
• Measurements planned for strong guide-field
  cases, such as in MST
• Commonalities with satellite in situ measurements
  in magnetosphere