11

Multi-spacecraft, multi-scale Multi-spacecraft, multi-scale investigation of intermittency investigation of intermittency and multifractal structure of and multifractal structure of turbulence in the terrestrial turbulence in the terrestrial

magnetosheathmagnetosheath

M. Echim (1,2), H Lamy (1), T. Chang (3),M. Echim (1,2), H Lamy (1), T. Chang (3),D. Constantinescu (4)D. Constantinescu (4)

(1) Belgian Institute for Space Aeronomy, Brussels, Belgium (1) Belgian Institute for Space Aeronomy, Brussels, Belgium (2) Institute for Space Sciences, Bucharest, Romania (2) Institute for Space Sciences, Bucharest, Romania (3) Kavli Institute for Astrophysics and Space Research, M.I.T., Cambridge, MA, USA(3) Kavli Institute for Astrophysics and Space Research, M.I.T., Cambridge, MA, USA(4) TU Braunschweig, Germany(4) TU Braunschweig, Germany

22

OUTLINE OF THE TALKOUTLINE OF THE TALK Multi-spacecraft multi-scale configuration to study Multi-spacecraft multi-scale configuration to study

simultaneously the turbulence properties at the dawn and simultaneously the turbulence properties at the dawn and dusk flanks of the magnetosheathdusk flanks of the magnetosheath

Methodology: full toolbox of methods to investigate Methodology: full toolbox of methods to investigate intemittency and multifractal propertiesintemittency and multifractal properties

Physics: Multi-spacecraft results obtained downstream the Physics: Multi-spacecraft results obtained downstream the quasi-perpendicular(THEMIS) and the quasi-parallel shock quasi-perpendicular(THEMIS) and the quasi-parallel shock (Cluster); dawn/dusk assymetries from in-situ data(Cluster); dawn/dusk assymetries from in-situ data

Conclusions, future workConclusions, future work

33

Multiscale Solar wind - Multiscale Solar wind - magnetosphere interactionmagnetosphere interaction

• Energy transfer from large scales to kinetic scales ?

• Mass and momentum transfer between different magnetospheric regions

44

Multispacescraft investigation of the Multispacescraft investigation of the turbulence in the sheathturbulence in the sheath

• Cluster at dawn flank • THEMIS at dusk flank

55

Intermittent turbulence in space Intermittent turbulence in space plasmaplasma

ComplexityComplexity: the system as a whole behaves : the system as a whole behaves differently than ``the sum of its subsystems’’ (differently than ``the sum of its subsystems’’ (Chang, 2004Chang, 2004))

CriticalityCriticality: physical equivalence of all temporal and : physical equivalence of all temporal and spatial scales (spatial scales (Consolini and Chang, 2001Consolini and Chang, 2001))

IntermittencyIntermittency: coherent structures, sporadic and : coherent structures, sporadic and localized merging (localized merging (Chang, 2004Chang, 2004))

Self Organized CriticalitySelf Organized Criticality: ``spontaneous emergence : ``spontaneous emergence of criticality in complex dissipative systems’’ (of criticality in complex dissipative systems’’ (Bak et al., Bak et al.,

19871987); F/SOC magnetosphere driven by the solar wind ); F/SOC magnetosphere driven by the solar wind ((Chang, 1992Chang, 1992).).

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Intermittent turbulence in space Intermittent turbulence in space plasmaplasma

Chang, et al., 2004

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Methodology to investigate Methodology to investigate intermittency in the magnetosphereintermittency in the magnetosphere

Stationarity, Taylor hypothesis (cusp, Stationarity, Taylor hypothesis (cusp, magnetosheath)magnetosheath)

PDFs of magnetic fluctuations: histograms of time PDFs of magnetic fluctuations: histograms of time differences, at various scales; Bdifferences, at various scales; B22 as a critical as a critical parameterparameter

Structure functionsStructure functions

Wavelet analysis and LIMWavelet analysis and LIM

Multifractal analysis, Rank Ordered Multifractal Multifractal analysis, Rank Ordered Multifractal Analysis, PDFs rescalingAnalysis, PDFs rescaling

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A configuration to investigate simultaneously A configuration to investigate simultaneously turbulence properties at the dawn/dusk flanks of turbulence properties at the dawn/dusk flanks of

the magnetosheaththe magnetosheath

Cluster orbits , 19/05/2008

THEMIS orbits, 19/05/2008

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Cluster data overviewCluster data overview

1010

THEMIS data overviewTHEMIS data overview

THEMIS B 19/05/2008 THEMIS C 19/05/2008

1111

PDFs – Cluster 1PDFs – Cluster 1

Bx

B2

By

Bz

1212

PDFs – Cluster 2PDFs – Cluster 2

Bx

B2

By

Bz

1313

PDFs – Cluster 4PDFs – Cluster 4

Bx

B2

By

Bz

1414

Haar Wavelet analysis – Cluster Haar Wavelet analysis – Cluster

Cluster 1, B2 Cluster 4, B2

1515

ROMA – Cluster ROMA – Cluster

Cluster , B2

1616

ROMA – Cluster, high latitude ROMA – Cluster, high latitude magnetosheathmagnetosheath

Cluster , B2

1717

ROMA – Cluster, high latitude ROMA – Cluster, high latitude magnetosheath, rescaled PDFsmagnetosheath, rescaled PDFs

Cluster , B2

1818

PDFs – THEMIS BPDFs – THEMIS B

Bx

B2

By

Bz

1919

PDFs – THEMIS CPDFs – THEMIS C

Bx

B2

By

Bz

2020

Haar Wavelet analysis – THEMIS Haar Wavelet analysis – THEMIS

THEMIS-B, B2 THEMIS-C, B2

2121

ROMA – THEMIS ROMA – THEMIS

THEMIS, B2

2222

CONCLUSIONSCONCLUSIONS Intermittency has been evidenced in the magnetosheath by Intermittency has been evidenced in the magnetosheath by

statistical analysis of HR magnetic field fluctuations statistical analysis of HR magnetic field fluctuations measured by CLUSTER and THEMISmeasured by CLUSTER and THEMIS

Data at low latitude dawn flank suggest a turbulent process Data at low latitude dawn flank suggest a turbulent process with some similarities to SW turbulence (ROMA spectrum is with some similarities to SW turbulence (ROMA spectrum is rather flat), data at the dusk flank reveals a more dynamical rather flat), data at the dusk flank reveals a more dynamical spectrum, changing with distance from the quasi-spectrum, changing with distance from the quasi-perpendicular shockperpendicular shock

FUTURE: enhanced use of multi-spacecraft configuration, FUTURE: enhanced use of multi-spacecraft configuration, physical interpretation in the framework of plasma turbulence physical interpretation in the framework of plasma turbulence models, look for other advantageous Cluster-THEMIS models, look for other advantageous Cluster-THEMIS configurationsconfigurations

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CORRELATION CORRELATION COEFFICIENTSCOEFFICIENTS

= cross correlation coefficient between

Pi and Pj 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)

22

)()(

)()()(

dtPtPdtPtP

dtPtPPtPC

jjii

jjii

ij

2424

CORRELATION CORRELATION COEFFICIENTSCOEFFICIENTS

• Cluster 1 & 4

• Comp. Bz

• Complete data

Dynamic nature of the

turbulent eddies

2525

COMPARISON MACRO/MICRO-COMPARISON MACRO/MICRO-SCALESSCALES

CLUSTER 1 & 4

2626

LIM(2)/FLATNESSLIM(2)/FLATNESS

[4:30-6:00] UT

The flatness F is related to higher moments of the fluctuations :

F =<P(t,)4> / (<P(t,)2>)2

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CONCLUSIONSCONCLUSIONS

Intermittency has been evidenced in the cusp by Intermittency has been evidenced in the cusp by statistical analysis of HR magnetic field fluctuations statistical analysis of HR magnetic field fluctuations measured by CLUSTERmeasured by CLUSTER

Van Allen belts dynamics, substorm loading – Van Allen belts dynamics, substorm loading – unloading processes, BBFs, long term variations of the unloading processes, BBFs, long term variations of the geomagnetic indices contribute to a global view on the geomagnetic indices contribute to a global view on the multiscale (in time and space) dissipation of energy in multiscale (in time and space) dissipation of energy in SW/MSPHSW/MSPH

Scaling properties of fluctuations of global measures Scaling properties of fluctuations of global measures of activity and llocal measures of energy trnasfer of activity and llocal measures of energy trnasfer suggest that the MSPH is in a driven, close to suggest that the MSPH is in a driven, close to criticality state.criticality state.