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.