Structure and detection of Kelvin-Helmholtz vortices in the ... - GPSM

Structure and Detection of
Rolled-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
Reconnection within a rolled-up KH vortex (e.g., Otto &
Fairfield, 2000)
Collapse of vortices mediated by electron inertia effects
(Nakamura et al., 2004)
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
Plasma transport can occur.
Transport is unlikely to occur.
Single-spacecraft measurements (e.g., Kivelson & Chen, 1995)
could not answer this question.
Multipoint measurements by the four Cluster spacecraft
can answer.

Cluster detection of rolled-up KH vortices
Cluster
Dusk MP
South of
equator
・ Northward IMF
・ Quasi-periodic
plasma & magnetic
field perturbations
with a period of 2-4
min.

M’sphere
Sheath
Spacecraft separation ~ 2000 km
Key features:
□ Higher density on the
most magnetospheric side
(at C1)
□ Vortical flow pattern

Evidence of plasma transport across the magnetopause
Low energy ions of
sheath origin
detected throughout
Ion distribution
in BL
Ion distribution in sheath
The observation is consistent with transport via KHI!

1-SC detection of “Rolled-up” vortices possible
Difference between Rolled-up & Not rolled-up vortices
9
8
0 9D 15D
Vx
N
Sheath Vx
M’sphere Sheath M’sphere Sheath
Flow speed higher than in sheath! Low density

Vx vs N seen in simulated data
Vx
High
speed
Low
density
N
Sheath Vx

Comparison with vortices observation
MHD simulation
Cluster observations of
rolled-up vortices
Vx
Low-density & High-speed flows
are found in real data as well!
N
Applicable to
single-spacecraft
observations!

Application to Geotail data
Flank MP event on 1995-03-24
(Fujimoto et al., 1998, Fairfield et
al., 2000)
(X, Y, Z)~(-14, 20, 4) Re (GSM)
Geotail E-T
spectrogram
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 measurements
White: 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 microscale
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 singlespacecraft
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.

How can the secondary velocity shear be
produced
v
1
2
1
M
1v
r
⎧
⎪v1
=
⎪
⎨
⎪
⎪
v2
=
⎩
∴
− v
2
M
2v2
= = ≅
a r
M
M
2
1
a r
2
r
= a r
a
1
M
1
leads to,
1
−
M
2
r
=
M1
a r
M
1
v2
M2
v1
1−
M
M
1
2
⎛ ∆ VSEC
∝ rSEC
⎜1
− 1
⎝ N
RATIO
r SEC = curvature radius of the
2nd velocity shear layer
⎞
⎟
⎠
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.

Hall (two-fluid) MHD equations including electron inertia effects
∂n
+ ∇ ⋅( nV i
) = 0
∂t
Continuity equation for mass
dV
i
n = − ∇P
+ J × B
dt
Momentum equation
d
dt
∂
∂t
⎛
⎜
⎝
P
γ
n
⎞
⎟
⎠
⎛ 1
⎜1−
⎝ M
= 0
Equation of state
⎞ ⎡ ⎛ 1
∆⎟
B = ∇ × ⎢Ve
× ⎜1−
⎠ ⎣ ⎝ M
⎞ ⎤
∆⎟
B⎥
⎠ ⎦
λ
e
= 1
M =
Induction equation including finite electron inertia
Ve
= Vi
− J n
J = ∇ × B
m
e
m
i

Simulation settings for 3-D
KHI
z
2D
V0(y)
B
2H
x
M’sphere
A C
B
Magnetosheath
B0
y
Condition for the growth of
KHI (Miura & Pritchett, 1982)
・ V 0 ⊥B 0 case
M
f
・ V 0 || B 0 case
2 2
= V0 Cs
+ VA
<
2
M A
M s
> 2
< 2

Measurements for an earlier interval of the day
Walen plot
D-shaped ion
distribution
The result suggests that
reconnection occurred near Cluster.
This reconnection might have been
associated with the KHI growth.