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Transverse instability of Alfven wave :
Cluster observations and heuristic explication.
Olga Alexandrova
LESIA, Observatoire de Paris, France.
Summer school - Chalkidiki September 23-28 2003
B
Earth Bow Shock Temperature Anisotropywith respect to Bis a source of the waves.
Alfven waves (Alfven-Ion-Cyclotron waves, AIC) are
widely observed downstream of the quasi-perpendicular shock.
1 8/
)( 2 BnkT i
iFor :
n
B
31/03/2001; relative positions of C1, C2, C4 to C3 for the 1st
shock crossing : Shock plane
Observations (multi-satellite Cluster)
upstreamdownstream
temperature anisotropy
shock
(nT)
(nT)
time (s)
(I)(II)
Magnetic field waveforms around the shock crossing in NML-frame :
Time origin is the shock crossing time 18:02:17 UT
Dynamic spectrogram (Wavelet transforms of Bn) (II) : Field aligned current
tubes
(a) - 10 s observations(b) - 2 s observations(c) - z-aligned current tube
simulation
(I) : AIC waves (alpha, p)
Hz 0.6 Hz 0.3
2
1
ff
Be
// min
4 Cluster spacecraft : region (I)
f p 0.45Hz; f 0.9Hz
kp 2310 3 km 1;k 12 10 3 km 1
V VA 240km /s
In the plasma rest frame: km/s 80 t
R V14
14tube
km 620 R 14|| z
km 60 d
c
pi
30km
plane perpendicular to B
region (II)
2,3,4 j ,2π )r.k( Δ 1j1j1j n
Interpretation of the observations :
5.6 )/( shock|| pp TT
Anisotropy relaxation :
Collapse of the Alfvén wave and tubes generation as a result of
Filamentation Instability.
5.1 )/( tubes|| pp TT
5.2 )/( AIC|| pp TT
AIC generation
1.1 e p
pic / 15 cii ff 0.6 0 picd / 2
Filamentation Instability of Alfven wave, observed before in Hall-
MHD simulationsD. Laveder, T. Passot & PL Sulem, Phys. Plasmas, 9 , 293-304 and 9 , 305-314 (2002).
Local longitudinal fluctuations : 2 v , , xxb
AAx
Axx
xA BbbBV VV )
2 1(Vv
)(4v 0
000
0
0
Alfven wave phase velocity is a local Alfven velocity of the medium :
Initial wave front
0 2
²|| V bBA1 , 1V 00 BA
2 vV bxA
D. Laveder, these
Filamentation of finite amplitude Alfven waves : heuristic explication
x , 0 0k 0 2 ²|| v
Bb
x
)1(4
e
A
AB
t
iDynamic of the front
equilibrium instability
x , 0 0k 0 2
For
0
0 At
wave front distort
Initial wave front V A
V A
Conclusions
1) The finite amplitude Alfven wave and the resulting filaments are observed downstream of the bow shock; the possible interpretation is Filamentation Instability.
2) Filamentation instability seems to play a role in the final thermalization.
3) Thanks to the 4 satellites of Cluster, parameters and behaviour of the observed structures are obtained, that gives a possibility to compare the observations with the theory.