1. Observational signatures of ULF turbulence L. Rezeau CETP/IPSL/Université Pierre et Marie Curie F. Sahraoui, D. Attié CETP/IPSL/CNRS

2. Question : How ULF turbulence can influence energy and mass transfers at the magnetopause ? It can create the small scales where micro-physical processes occur  potential role for driving reconnection. ~10 4 km ~10 km

3. ULF turbulence is also observed in the nearby magnetosheath Is the ULF turbulence observed at the magnetopause generated locally or is it a product of the magnetoseath turbulence ? Local instability ? External source ? What do we know about its role for driving reconnection ?

4. Observational arguments in favor of an external source Analysis of the magnetosheath turbulence – Mode identification – Integrated k-spectra – Role of the Doppler shift Possible model Role of the multi-point measurements made by Cluster and Double Star Probe CLUSTER

5. Turbulence is very similar in the magnetosheath and at the magnetopause Cluster 1-STAFF/SC-2002/02/18- 04:58Cluster 1-STAFF/SC-2001/01/14- 15:05 magnetosheath magnetopause Power higher at the magnetopause Similar specral law Less steep slope at the magnetopause

6. The magnetic spectrum goes down with a similar slope to a frequency around low-hybrid frequency FGM Staff SC Staff SA Sensitivity of magnetic antenna

7. ULF fluctuations in the magnetopause are correlated to upstream activity DSP CLUSTER DSP : near the subsolar point CLUSTER : far from the subsolar point

8. Double Star Probe P msh (nT 2 ) Solar wind dynamic pressure(nPa) CLUSTER The ULF power is higher when the magnetosphere is compressed

9. Turbulence in magnetosheath can be an external source of the high wave activity at the magnetopause. P * msh P * max Wave power normalized to the local magnetic field amplification strong correlation Magnetopause Magnetosheath CLUSTER data

10. Each point is an observation by CLUSTER and DSP at the same time More power near the front of the magnetopause than on the flanks DSP CLUSTER

11. Interaction of ULF waves coming from the magnetosheath with the magnetopause Incident fast magnetosonic wave Trapping of an incident magnetosheath wave [Belmont&Rezeau, 2001] n y z MAGNETOPAUSE MAGNETOSPHEREMAGNETOGAINE kTkT 22 11 BoBo kiki kTkT nT 2  (deg) x ktkt Incident FMS Reflected Alfven magnetosheathmagnetosphereMP density gradient Evanescent waves Reflected FMS Incident FMS Reflected Alfvén The power in the boundary should be higher when the rotation angle is large Small scales created in the gradient

12.  (deg) Strong correlation between wave power and rotation of B at the magnetopause. Wave power Amplification into the boundary Amplification of the magnetosheath turbulence increasing with rotation of B P * max  (deg) Statistics

13. ULF large scale fluctuations observed in the magnetosheath could : Be the source of the turbulence observed at the magnetopause Cascade to small scale fluctuations when trapped in the magnetopause The model is not fully realistic and should be adapted to the observations made by Cluster

14. Observational arguments in favor of an external source Analysis of the magnetosheath turbulence – Mode identification – Integrated k-spectra – Role of the Doppler shift Possible model Role of the multi-point measurements made by Cluster and Double Star Probe CLUSTER

15. Analysis of the turbulence observed in the magnetosheath by CLUSTER Measurements provide temporal spectra B 2 ~  sc -7/3 Is it possible to obtain a wave-number spectrum from this frequency spectrum ?

16. Turbulence in the solar wind : Data from HEOS in the solar wind (Tu and Marsch, 1995) k -5/3 law How can you transform temporal signals in a wave number spectrum ?

17. In the solar wind : the Taylor’s hypothesis is valid Fast plasma velocity  strong Doppler effect  The calculation of a k spectrum is possible with one spacecraft But spectrum along one single direction

18. In the magnetosheath phase velocity of the modes  plasma velocity  One must understand better the structure of turbulence to de-Dopplerize the signal  The calculation of a k spectrum from an  spectrum is impossible Two methods : phase differencing, k-filtering Frequency (Hz)

19. Phase differencing method (2 spacecraft) Assuming the wave is mono-k for each  Each correlation of two components of the analyzed vector field at two spacecraft brings one information For B x1 and B x2 : No test of the mono-k hypothesis from this only correlation Different k obtained from different correlations No use of cross-correlations Gives the projection of k along the separation vector

20. K-filtering technique CLUSTER B1B1 B2B2 B3B3 B4B4 (Pinçon and Lefeuvre, 1991) Estimation of the energy distribution function of the waves in ( ,k) space P(,k)P(,k)  Use of the global correlation matrix  Allows to take into account theoretical constraints Only hypothesis: the analyzed fluctuations are «sufficiently» homogeneous and stationary → can be applied to magnetosheath not to magnetopause

21.  Works quite well with the 3 component B field (with constraint .(B)=0)  Is improved when including the two components of E (and the corresponding Faraday law as an extra-constraint). (Tjulin et al, 2005) Has been validated by numerical simulations (Pinçon et al, 1991) Applied for the first time to real data with CLUSTER (Sahraoui et al., 2003) Non linear method of the «maximum likelihood» type, based on filters depending on the data (but transparent for mono-k waves) More numerous the correlations are, more trustable is the estimate of the energy distribution in k space :

22. Identification of wave modes k z2 3.for each k z plane containing a significant maximum, the (k x,k y ) isocontours of P(  sc,k x,k y,k z ) and f(  sc,k x,k y,k z )=0 are then superimposed 1.the spatial energy distribution is calculated: P(  sc,k x,k y,k z ) 2.the theoretical linear dispersion relations are calculated and Doppler shifted: f(  sc,k x,k y,k z )=0 Ex: Alfvén mode:  sc -k z V A =k.v For each  sc :

23. Limits of validity of the k-filtering method Generic to all techniques intending to correlate fluctuations from a finite number of points. Two main points to be careful with: 1.Relative homogeneity /Stationarity 2.Spatial Aliasing effect ( > spacecraft separation) (Neubauer & Glassmeier, 1990) Two satellites cannot distinguish between k 1 and k 2 if :  k.r 12 = 2  n

24. Application to Cluster magnetic data Magnetosheath (FGM-18/02/2002)  Limit imposed by the Cluster minimum separation d~100 km:  max ~k max v  ~ 2  v  / min ~ 2  v  /d In the magnetosheath: v  ~200 km/s  f max ~ 2Hz !

25. k(  max )  instability (Sahraoui et al., Ann., 2004) Mirror mode identification  Mirror : f sat ~ 0.3f ci ; f plasma ~ 0 k o ~0.0039 rd/km; (k o,B o ) = 81° The energy of the spectrum is injected by a mirror instability well described by the linear kinetic theory k o  ~0.3~ k(  max ) Linear kinetic theory  instability if measurements: f 0 = 0.11Hz f ci= 0.33Hz

26. f ci ~0.33Hz Study of higher frequencies Observation of mirror structures over a wide range of frequencies in the satellite frame, but all are stationary in the plasma frame. Mirror: f 1 ~ f ci ; f plasma ~ 0 k 1 ~ 3k o ; (k 1,B o ) = 82° f 1 =0.37Hzf o =0.11Hz Mirror : f o = 0.11Hz ; f plasma ~ 0 k o  ~0.3~ k(  max ); (k o,B o ) = 81° Mirror: f 2 ~ 4 f ci ; f plasma ~ 0 k 2 ~ 10k o ; (k 2,B o ) = 86° f 2 = 1.32Hz

27. Role of Doppler shift All the observed mirror modes have different (low) frequencies in the spacecraft frame but they have a zero frequency in the plasma frame. A statistical study performed by Lacombe et al shows that the power at 11 Hz is correlated to the plasma velocity in the magnetosheath. It is an indication that the fluctuations observed at 11Hz are also Doppler-shifted waves. The limitation in the frequencies that can be studied by Cluster prevents from testing directly this result…. MMS

28. v n B0B0 C alculation of integrated k-spectra First direct determination of a fully 3-D k-spectra in space: it evidences an anistropic behaviour (v,n) ~ 104° (v,B o,) ~ 110° (n,B o ) ~ 81° Energy distribution of the identified mirror structures along : B0B0 nv

29. Integration over the spectra: Over frequencies : Over directions : L i ~1800kmL s ~150km We observe a cascade along v on the mirror mode : B 2 ~k v -8/3 Steeper slope than in all MHD theories (Sahraoui et al., submitted to PRL)

30. f sc -7/3 temporal signature in the satellite frame of k v -8/3 spatial cascade Comparison of temporal and spatial spectra

31. Linear mirror modes have been identified in the magnetosheath turbulence They are likely to cascade to smaller scales Doppler shift has a significant contribution in the resulting slope of the spectra Main results of the analysis of magnetosheath turbulence :

32.  The magnetosheath is likely to be the source of the magnetopause turbulence  First 3-D k-spectrum: evidence of strong anisotropies (Bo, v, n)  Evidence of a 1-D direct cascade of mirror structures from an injection scale (L v ~1800 km) up to 150 km with a new law k v -8/3 Conclusion : towards a model ? Main consequences:  A Turbulence theory is necessary to understand the non-linear cascade.  Necessity to explore much smaller scales to reach the reconnection scales  MMS (2010?) Open questions:  How are the magnetopause small scales generated ? Do they result of local cascade or are they coming from the magnetosheath  How can the new law be used in reconnection models ? open …

33. MagnetosheathMagnetopause ?