Magnetic Turbulence during Reconnection

General Meeting of CMSOMadison, August 4-6, 2004

Hantao Ji

Center for Magnetic Self-organization in Laboratory and Astrophysical PlasmasPrinceton Plasma Physics Laboratory, Princeton University

Contributors: Will FoxStefan GerhardtRussell KulsrudAleksey KuritsynYang RenMasaaki YamadaYansong Wang

2

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

3

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?

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,’86; Uzdensky & Kulsrud, ‘00)

Classic Leading Theories:

€

S =μ0LVA

ηLundquist #:

5

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?

6

Experimental Setup in MRX

Solid coils in vacuum

7

Realization of Stable Current Sheet and Quasi-steady Reconnection

• Measured by magnetic probe arrays, 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

8

Agreement with a Generalized Sweet-Parker Model

• The model modified to take into account of– Measured enhanced

resistivity

– Compressibility

– Higher pressure in downstream than upstream

(Ji et al. PoP ‘99)

model

9

Resistivity Enhancement Depends on Collisionality

Significant enhancement at

low collisionalities

η* ≡Eθjθ

Eθ +VR×BZ =ηjθ

(Ji et al. PRL ‘98)

At current sheet center:

10

Turbulent vs. Laminar Models

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

“anomalous” resistivity Facilitated by Hall effects

• Separation of ion and electron layers

• Mostly 2D and laminar

ion current

e current

(Drake et al. ‘98)

Modern Leading Theories for Fast Reconnection:

Expect: high-frequency turbulence

Expect: electron scale structure in B

What do we see in exp?

(Ugai & Tsuda, ‘77; Sato & Hayashi, ‘79; Scholer, ‘89….)

11

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

12

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

13

Magnetic Fluctuations Measured in Current Sheet Region

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

(Ji et al. PRL, ‘04)

14

Waves Propagate in the Electron Drift Direction with a Large Angle to Local B

Angle[k,B0]

Fre

qu

ency

(0-

20M

Hz)

R-wave

Vph ~ Vdrift

Local to certain angle and k

15

EM Wave Amplitude Correlates with Resistivity Enhancement

16

Similar Observation by Spacecraft at Earth’s Magnetopause

(Phan et al. ‘03)

ES

EM

(Bale et al. ‘04)

high

low

high

low

low

17

Physical Questions

• Q1:What is the underlying instability?

• Q2:How much resistivity does this instability produce?

• Q3:How much ions and electrons are heated?

18

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

In the context of collisionless shock…

• 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)

ESEM

19

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,

€

ωci << ω <<ωce

€

en0E0 = Ti∂n0

∂y

€

−en0 E0 −V0B0( ) = Te∂n0

∂y

€

E0 =σ

1+ σV0B0

€

σ =Ti

Te

n0

z

y

x E0

V0

B0 B0

(Ji et al. in preparation, ‘04)

20

Dispersion Relation

• Normal mode decomposition for wave quantities:

• “Dielectric tensor”:

• 1st and 2nd lines:

• 3rd line from electron force balance along z direction:

€

exp i(k ⋅x −ωt)[ ]

€

k × (k × E) = −iωμ0j

€

k = kx,0,kz( )

€

Dxx Dxy Dxz

Dyx Dyy Dyz

Dzx Dyz Dzz

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

E x

Ey

Ez

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟= 0

€

kz2E x − kxkz Ez = iωμ0 jx

€

k2Ey = iωμ0 jy

€

Ez + V0By = −ikzTe

e

n

n0

€

By =kz E x − kx Ez

ω

from continuity, ion, and electron equations

21

Dispersion Relation (Cont’d)

• Normalizations:

• Dispersion relation after re-arrangements:

• Fourth order in (K), with controlling parameters of V, , , σ.

€

=ωωci

,K = kc

ω pi,V =

V0

VA,β e =

n0Te

B02 /2μ0

,sinθ =kx

k,σ =

Ti

Te

€

K 2 cos2 θ +1−σ

1+ σ

KV sinθ

Ωi Ω − KV sinθ( ) −K 2 sinθ cosθ −

σ

1+ σ

KV cosθ

Ω

−i Ω −β e

2

K 2 sin2 θ

Ω

⎛

⎝ ⎜

⎞

⎠ ⎟ K 2 +1 i

βe

2

K 2 sinθ cosθ

Ω

KV cosθ −β e

2

K 2 sinθ cosθ

Ω0 Ω − KV sinθ −

β e

2

K 2 cos2 θ

Ω

= 0

22

Instability: Large Drifts Cause Coupling between Whistler and Sound Waves

Ang

le

K

sound waves(ion)

whistler waves(electron)

more ES

more EM

23

Unstable only at Certain Angles and K, Consistent with Observations

V=1 V=3 V=6

24

A Simple Physical Picture

• Cold electron limit; slow mode approximation

• Purely growing when unstable

€

−KV +V sin2 θ

KΩ2 −

K cos2 θ

VΩ2 = 0

ES (de)compression tension

electron density perturbation

z

y

B

n +e

n -e

n -e

E0

n0

B deforms in y direction

nE0 force

z

y

B

n +e

n -e

n -e

E0

n0

JB force in z direction

reinforce

25

Estimated Resistivity due to Observed Electromagnetic Waves

€

Total energy and momentum density of EM waves:

Resistivity:

€

εw = 2 ט B 2

2μ0

€

e ~ ω : since waves are highly nonlinear

€

ηw jθ ~ 100V /m ~ Eθreconnection

€

kθ ~2π

λcoherence€

ηw jθ =∂Pw

∂t=

2γ e

en

kθεw

ω=

2γ e

ω

kθ

en

˜ B 2

μ0€

Pw =k

ωεw

(Kulsrud et al. ‘03)

26

• 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?

Physical Questions on Reconnection

– 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

Answers or clues from MRX

27

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