1. 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

2. Magnetopause KH instability
Shocked solar wind
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.

3. 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?

4. 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)

5. Cluster event on 20 Nov 2001 C1 ion C1 electron density temperature
velocity
magnetic field
2.5 hours

6. Total-P perturbation in the vortex
streamline
Force balance

7. Wavelet spectrum of Total-P
Dominant-mode period ~200 s (Wavelength ~6 Re)
Power also at ~400 s: Beginning of vortex pairing?

8. Vortex structure from Grad-Shafranov-like (GS-like) reconstruction of streamlines (Sonnerup et al., 2006; Hasegawa et al., 2007) C3
The KHI seen by Cluster was fully in a nonlinear phase, characterized by coalescence/breakup (inverse-cascade/cascade) of the vortices.
Dominant-mode wavelength ~6 Re
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)?

9. 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.

10. THEMIS string-of-pearls observation of a dayside MP boundary layer (BL)@16 MLT
8 June 2007
closest to Earth
Y (dusk)
0600 UT
1000 UT
X (sunward)

11. 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 Re
closest to Earth
40 min
Eriksson et al., JGR, 2009

12. Bipolar BN (FTEs) on the surface wave
80 min
• Bipolar BN, at BL-to-sheath transitions, i.e., at the sunward-side edge of the surface wave.

13. Recovery of 2D MHD structure
streamline
sheath side
Plasma sheet
Recovery of 2D MHD structure
Eriksson et al., JGR, 2009
• Magnetic island & small vortex between two large-scale vortices
• Local reconnection
leading to the magnetic island formation
streamline N T
B-field

14. Interpretation of the THEMIS event
Nakamura et al., JGR, 2008
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?

15. 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.

17. GS-like reconstruction of streamlines
(Sonnerup et al., 2006; Hasegawa et al., 2007)
Assumptions: MHD, 2D, time-independent, & B along z axis
GS-like equation for the stream function y
As a spatial initial value problem,
V, n, & T recovered

18. Vortex structure from Grad-Shafranov-like reconstruction of streamlines (Sonnerup et al., 2006; Hasegawa et al., 2007) C1
Dominant-mode wavelength ~6 Re
Spatial initial value problem
Assumptions: MHD, d/dt =0, 2D, & B along invariant axis z. C3
Two vortices within one dominant-mode wavelength.
Breakup of a parent MHD-scale vortex (cascade)?

19. Fluctuation in the dayside boundary
Geotail
Cluster
Magnetic fluctuations had a period similar to that of the KH waves.
The KHI was excited by the mechanism that generated the magnetic fluctuations.