1 Multi-spacecraft, multi-scale investigation of intermittency and multifractal structure of turbulence in the terrestrial magnetosheath M. Echim (1,2), H Lamy (1), T. Chang (3), D. Constantinescu (4) (1) Belgian Institute for Space Aeronomy, Brussels, Belgium (2) Institute for Space Sciences, Bucharest, Romania (3) Kavli Institute for Astrophysics and Space Research, M.I.T., Cambridge, MA, USA (4) TU Braunschweig, Germany

2 OUTLINE OF THE TALK  Multi-spacecraft multi-scale configuration to study simultaneously the turbulence properties at the dawn and dusk flanks of the magnetosheath  Methodology: full toolbox of methods to investigate intemittency and multifractal properties  Physics: Multi-spacecraft results obtained downstream the quasi-perpendicular(THEMIS) and the quasi-parallel shock (Cluster); dawn/dusk assymetries from in-situ data  Conclusions, future work

3 Multiscale Solar wind - magnetosphere interaction Energy transfer from large scales to kinetic scales ? Mass and momentum transfer between different magnetospheric regions

4 Multispacescraft investigation of the turbulence in the sheath Cluster at dawn flank THEMIS at dusk flank

5 Intermittent turbulence in space plasma  Complexity: the system as a whole behaves differently than ``the sum of its subsystems’’ ( Chang, 2004 )  Criticality: physical equivalence of all temporal and spatial scales ( Consolini and Chang, 2001 )  Intermittency: coherent structures, sporadic and localized merging ( Chang, 2004 )  Self Organized Criticality: ``spontaneous emergence of criticality in complex dissipative systems’’ ( Bak et al., 1987 ); F/SOC magnetosphere driven by the solar wind ( Chang, 1992 ).

6 Intermittent turbulence in space plasma Chang, et al., 2004

7 Methodology to investigate intermittency in the magnetosphere  Stationarity, Taylor hypothesis (cusp, magnetosheath)  PDFs of magnetic fluctuations: histograms of time differences, at various scales; B 2 as a critical parameter  Structure functions  Wavelet analysis and LIM  Multifractal analysis, Rank Ordered Multifractal Analysis, PDFs rescaling

8 A configuration to investigate simultaneously turbulence properties at the dawn/dusk flanks of the magnetosheath Cluster orbits, 19/05/2008 THEMIS orbits, 19/05/2008

9 Cluster data overview

10 THEMIS data overview THEMIS B 19/05/2008THEMIS C 19/05/2008

11 PDFs – Cluster 1 BxBx B2B2 ByBy BzBz

12 PDFs – Cluster 2 BxBx B2B2 ByBy BzBz

13 PDFs – Cluster 4 BxBx B2B2 ByBy BzBz

14 Haar Wavelet analysis – Cluster Cluster 1, B 2 Cluster 4, B 2

15 ROMA – Cluster Cluster, B 2

16 ROMA – Cluster, high latitude magnetosheath Cluster, B 2

17 ROMA – Cluster, high latitude magnetosheath, rescaled PDFs Cluster, B 2

18 PDFs – THEMIS B BxBx B2B2 ByBy BzBz

19 PDFs – THEMIS C BxBx B2B2 ByBy BzBz

20 Haar Wavelet analysis – THEMIS THEMIS-B, B 2 THEMIS-C, B 2

21 ROMA – THEMIS THEMIS, B 2

22 CONCLUSIONS  Intermittency has been evidenced in the magnetosheath by statistical analysis of HR magnetic field fluctuations measured by CLUSTER and THEMIS  Data at low latitude dawn flank suggest a turbulent process with some similarities to SW turbulence (ROMA spectrum is rather flat), data at the dusk flank reveals a more dynamical spectrum, changing with distance from the quasi-perpendicular shock  FUTURE: enhanced use of multi-spacecraft configuration, physical interpretation in the framework of plasma turbulence models, look for other advantageous Cluster-THEMIS configurations

23 CORRELATION COEFFICIENTS = cross correlation coefficient between P i and P j for the time-lag  Auto-correlation when i = j The Magnetic Field will be correlated with itself within a turbulent eddy and uncorrelated outside the eddy. The value of  for which the auto-correlation coefficient = 1/e gives the temporal scale size of the eddy. The length of the eddy can then be deduced from the flow speed of the plasma (Weygand et al. 2005)

24 CORRELATION COEFFICIENTS Cluster 1 & 4 Comp. B z Complete data Dynamic nature of the turbulent eddies

25 COMPARISON MACRO/MICRO- SCALES CLUSTER 1 & 4

26 LIM(2)/FLATNESS [4:30-6:00] UT The flatness F is related to higher moments of the fluctuations : F = / ( ) 2

27 CONCLUSIONS  Intermittency has been evidenced in the cusp by statistical analysis of HR magnetic field fluctuations measured by CLUSTER  Van Allen belts dynamics, substorm loading – unloading processes, BBFs, long term variations of the geomagnetic indices contribute to a global view on the multiscale (in time and space) dissipation of energy in SW/MSPH  Scaling properties of fluctuations of global measures of activity and llocal measures of energy trnasfer suggest that the MSPH is in a driven, close to criticality state.