Excitation and Multi-scale development of Kelvin-Helmholtz (KH) waves

at the Earth’s magnetopause

H. Hasegawa(1), A. Retinò(2), A. Vaivads(3), Y. Khotyaintsev(3), M. André(3), T. K. M.

Nakamura(1), S. Eriksson(4), W.-L. Teh(4), B. U. Ö. Sonnerup(5), S. J. Schwartz(6), & H. Rème(7)

(1) ISAS/JAXA, (2) Austrian Academy of Sci., (3) Swedish Inst. Space Phys., (4) LASP, Univ. of Colorado, (5) Dartmouth

Coll., (6) Imperial Coll. London, (7) CESR

Shocked solar wind

Magnetopause KH instability

Nakamura et al., 2004;Hasegawa et al., 2004

KH vortices may play a key role in transport of solar wind plasma into the Earth’s magnetosphere, namely, anomalous transport of collision-less plasma.

How does the KHI evolve?

• Worth to answer from the viewpoint of both “turbulence” and “anomalous transport of plasma”.

• How does KH wave energy cascade?

• How does the evolution of MHD-scale KH vortices set the condition for the onset of non-MHD (transport) processes?

Cluster event on 20 Nov 2001• Extended northward

IMF• Cluster @19 MLT

~3 Re behind terminator• Rolled-up KH vortices

identified(Hasegawa et al., 2004, 2006;

Chaston et al., 2007; Foullon et al., 2008)

C1 electron

C1 ion

density

temperature

velocity

magnetic field

2.5 hours

Cluster event on 20 Nov 2001

TotalPvv

)(

Total-P perturbation in the vortex

streamline

Force balance

Wavelet spectrum of Total-P

• Dominant-mode period ~200 s (Wavelength ~6 Re)• Power also at ~400 s: Beginning of vortex pairing?

C3

Vortex structurefrom Grad-Shafranov-like (GS-like) reconstruction of

streamlines (Sonnerup et al., 2006; Hasegawa et al., 2007)

• A GS-like eq. for “stream” function is solved, as a spatial initial value problem.

Assumptions: MHD, 2D, time-independent, & B || z.

• Two vortices within one dominant-mode wavelength.

Breakup of a parent MHD-scale vortex (cascade)?

Dominant-mode wavelength ~6 Re

TotalPvv

)(

The KHI seen by Cluster was fully in a nonlinear phase, characterized by coalescence/breakup (inverse-cascade/cascade) of the vortices.

A cascade process at flank magnetopause (Takagi et al., JGR, 2006)

• In the flanks, KHI can grow only near equator.

• A dominant KH mode grows and bends field lines.

• Magnetic tension of the bent field lines deforms the parent KH vortex, or create smaller vortices within.

closest to Earth0600 UT

1000 UT

X (sunward)

Y (dusk)

THEMIS string-of-pearls observation of a dayside MP boundary layer (BL)@16 MLT

8 June 2007

THEMIS obs. of a dayside BL

• Surface waves activity with 1-2 min period

• Simultaneous BL encounters by 2-4 SC, at several times.

• SC separation along MP normal ~0.5 Re.

↓BL width ~0.5 Re40 min

closest to Earth

Eriksson et al., JGR, 2009

• Bipolar BN, at BL-to-sheath transitions, i.e., at the sunward-side edge of the surface wave.

Bipolar BN (FTEs) on the surface wave

BN

80 min

streamline

B-field

streamline

Recovery of 2D MHD structureEriksson et al., JGR, 2009

• Magnetic island & small vortex between two large-scale vortices

• Local reconnectionleading to the magnetic island formation

sheath side

Plasma sheet

N

T

Nakamura et al., JGR, 2008

Interpretation of the THEMIS event

• Thin current sheet forms at the sunward-facing edge of KH waves, where the CS is compressed by vortex flow, and it may become subject to reconnection.

• KH-induced reconnection can form a magnetic island.• Open question: can it lead to large-scale or efficient

plasma transport?

Summary• Coalescence and breakup of KH vortices

(inverse-cascade & cascade) are beginning at ~19 MLT (just behind the terminator).

Evidence of nonlinear KHI development.

• Magnetic island formation preferentially at the sunward-facing edge of KH waves.

It most likely resulted from local reconnection at the current sheet thinned by vortex flow.

As a spatial initial value problem,V, n, & T recovered

Assumptions: MHD, 2D, time-independent, & B along z axis

GS-like equation for the stream function

GS-like reconstruction of streamlines(Sonnerup et al., 2006; Hasegawa et al., 2007)

TotalPvv

)(

• Spatial initial value problem• Assumptions: MHD, d/dt =0, 2D, & B along invariant axis z.

Dominant-mode wavelength ~6 Re

Vortex structurefrom Grad-Shafranov-like reconstruction of

streamlines (Sonnerup et al., 2006; Hasegawa et al., 2007)

C1

C3

• Two vortices within one dominant-mode wavelength.

Breakup of a parent MHD-scale vortex (cascade)?

Fluctuation in the dayside boundary

• Magnetic fluctuations had a period similar to that of the KH waves.

Geotail Cluster

The KHI was excited by the mechanism that generated the magnetic fluctuations.