Structure and Detection ofRolled-up Kelvin-Helmholtz Vortices

in the Tail Flank of the Magnetosphere

H. Hasegawa, M. Fujimoto, T. K. M. Nakamura, K. Takagi (Tokyo Institute of Technology),

T.-D. Phan (SSL, UCB), Y. Saito, T. Mukai (ISAS/JAXA), M. W. Dunlop (Rutherford Appleton Lab.),

and H. Reme (CESR)

(Workshop in Romania, Sep. 6-10, 2005)

Introduction

Observations show: The magnetopause boundary layer gets THICK at low latitudes, and the plasma sheet becomes COLD and DENSE, during Northward interplanetary magnetic field (IMF) periods. (e.g., Mitchell et al., 1987; Terasawa et al., 1997)

These facts suggest significant transport of solar wind plasmas into the magnetosphere under northward IMF conditions.

What is the transport mechanism? □ Magnetic reconnection (e.g., Song & Russell, 1992)□ Transport through Kelvin-Helmholtz instability (KHI)(e.g., Fujimoto & Terasawa, 1994)□ Diffusion via wave-particle interactions, such as via Kinetic Alfven waves (e.g., Johnson & Cheng, 1997)

Introduction

Observations show: The magnetopause boundary layer gets THICK at low latitudes, and the plasma sheet becomes COLD and DENSE, during Northward interplanetary magnetic field (IMF) periods. (e.g., Mitchell et al., 1987; Terasawa et al., 1997)

These facts suggest significant transport of solar wind plasmas into the magnetosphere under northward IMF conditions.

What is the transport mechanism? □ Magnetic reconnection (e.g., Song & Russell, 1992)□ Kelvin-Helmholtz instability (KHI)(e.g., Fujimoto & Terasawa, 1994)□ Diffusion via wave-particle interactions, such as via Kinetic Alfven waves (e.g., Johnson & Cheng, 1997)

How can plasma transport be achieved in association with the KHI?

① Reconnection within a rolled-up KH vortex (e.g., Otto & Fairfield, 2000)

② Collapse of vortices mediated by electron inertia effects (Nakamura et al., 2004)

③ Rayleigh-Taylor instability in vortices (Matsumoto & Hoshino, 2004)

2-D simulations of KHI using Hall (2-fluid) MHD equations including finite electron inertia

Numerical simulation studies indicate that plasma transport can occur only when the KHI has grown to form “Rolled-up” vortices.

Can the growth of KHI at the magnetopause lead to the “rolled-up” vortices or just to ripples?

OR ?

Single-spacecraft measurements (e.g., Kivelson & Chen, 1995) could not answer this question. Multipoint measurements by the four Cluster spacecraft can answer.

Plasma transport can occur. Transport is unlikely to occur.

Cluster

Dusk MP

South of equator

Cluster detection of rolled-up KH vortices

・ Northward IMF・ Quasi-periodic plasma & magnetic field perturbations with a period of 2-4 min.

Key features: □ Higher density on the most magnetospheric side (at C1)□ Vortical flow pattern

M’sphere

Sheath

Spacecraft separation ~ 2000 km

Evidence of plasma transport across the magnetopause

Low energy ions of sheath origin detected throughout

Ion distribution in sheathIon distribution in BL

The observation is consistent with transport via KHI!

Ｘ

Ｙ

0 9D 15D

Flow speed higher than in sheath! Low density

Vx

Sheath Vx

N

1-SC detection of “Rolled-up” vortices possible?Difference between Rolled-up & Not rolled-up vortices

M’sphere Sheath M’sphere Sheath

Vx vs N seen in simulated data

High speed Low

density

Vx

N

Sheath Vx

Comparison with vortices observation

Low-density & High-speed flows are found in real data as well!

MHD simulationCluster observations of

rolled-up vortices

Applicable to single-spacecraft

observations!

Vx

N

Geotail E-T spectrogram

Application to Geotail dataFlank MP event on 1995-03-24(Fujimoto et al., 1998, Fairfield et al., 2000)

(X, Y, Z)~(-14, 20, 4) Re (GSM)

Signature of “Rolled-up” vortices found in 1-SC data

Signatures of KHI at the flank MP

Signatures seen ONLY WHEN a KH vortex is “Rolled-up”: □ Sheath plasma penetrating into the magnetosphere and sitting on the magnetospheric side of the low-density plasma. □ Low-density plasma flowing with an anti-sunward velocity higher than the magnetosheath plasma.

Other signatures seen also when a KH vortex is not rolled-up: □ Quasi-periodic plasma/field perturbations with an period of a few minutes. □ Vortical plasma flow pattern. □ Magnetic field perturbation pattern under 3D KHI effect.

Yellow: detectable only by multi-SC measurementsWhite: detectable even with single-SC measurements

When the SC separation of Cluster is small, ・ Detection of a parent rolled-up vortex can be made by either of the four spacecraft, by identifying Low-density & High-speed flows. Then, ・ Small-scale waves excited, or thin current sheet structures formed, in the vortex can be studied in detail with the help of multi-point measurements.

Connections between macro-scale KH vortices and micro-scale phenomena/structures can be studied.

Summary

□ Rolled-up KH vortices were detected from Cluster multi-point observations at the flank magnetopause during northward IMF. Furthermore, evidence for plasma transport was found in the rolled-up vortices. These suggest that the KHI plays a significant role in the plasma transport (formation of the flank boundary layer) under northward IMF.

□ “Rolled-up” vortices can be detected even with single-spacecraft measurements of the bulk plasma parameters. ⇒・ Coupling between large-scale vortices and small-scale phenomena/structures can now be studied with Cluster data. ・ Statistical survey of KH vortices is also possible with conventional 1-SC data.

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1

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211

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M

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rav

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How can the secondary velocity shear be produced?

Ｍ１

Ｍ２

v1

v2

r

At a certain radial distance from the vortex center, the centrifugal force exerting on the lighter and heavier fluids must be equal.

↓Then, the shear velocity depends on the mass ratio and on the curvature radius of the shear layer.

RATIOSECSEC NrV 11

rSEC = curvature radius of the 2nd velocity shear layer

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Hall (two-fluid) MHD equations including electron inertia effects

Continuity equation for mass

Momentum equation

Equation of state

Induction equation including finite electron inertia

z

V0(y)

B0

y

x

2D

A

B

B

2H C

M’sphere Magnetosheath

2220 Asf VCVM

Condition for the growth of KHI (Miura & Pritchett, 1982)・ V0 B⊥ 0 case

2sM2AM

・ V0 || B0 case

Simulation settings for 3-D KHI

Measurements for an earlier interval of the day

D-shaped ion distribution

Walen plot

The result suggests that reconnection occurred near Cluster. This reconnection might have been associated with the KHI growth.