M. Stepanova(1), E. E. Antonova(1, 2), J.M. Bosqued (3)

(1) University of Santiago de Chile (marina.stepanova@usach.cl)

(2) Skobeltsyn Institute of Nuclear Physics, MSU (antonova@orearm.msk.ru)

(3) CESR/CNRS, Toulouse, France (bosqued@cesr.fr)

Modelling of the turbulent Modelling of the turbulent plasma sheet during quiet and plasma sheet during quiet and

disturbed geomagnetic disturbed geomagnetic conditionsconditions

Ubatuba, Brazil, 4-11 October, 2009Ubatuba, Brazil, 4-11 October, 2009

Summary

• Importance of turbulence

• Statistical studies of turbulence in the plasma sheet

• Case study of the turbulent plasma sheet stability

If Re>>1 the turbulent wake is formed under the obstakle.

Magnetospheric tail can be considered as a turbulent wake under the obstacle formed under the conditions of very high values of Reynolds number (Reynolds numbers are larger than 1010 in accordance with Borovsky and Funsten, 2003). Such turbulent wake is formed even in case of laminar solar wind flow.

1

2

1

N

iV N

i

V i V V i k VA

V i V

kT

1

/N

iV V i N

autoexp /A

2

1

N

irms

V VV

N

2rms auto

2

VD

Borovsky, J.E. (1997, …)Antonova and Ovchinnikov (1997)Stepanova et al. (2008)

Velocity and magnetic field fluctuations are studied by Angelopoulos et al. (1992, 1993, 1996, 1999); Borovsky et al. (1997, 1998), Antonova et al. (2000, 2002); Ovchinnikov et al. (2002), Neagu et al. (2001, 2002); Troshichev et al. (2001, 2002); Petrukovich and Yermolaev (2002); Borovsky and Funsten (2003a,b); Voros et al. (2003); Volwerk et al. (2004); Goldstein (2005); Weygand et al. (2005); Stepanova et al. (2005, 2009) etc.

Interball/Tail probe results (Antonova et al., 2000, 2002)

ISEE-2 results (Angelopoulos et al., 1993)

CLUSTER results(Volwerk et al., 2004)

Statistical studies of eddy diffusion coefficients using the Interball/Tail satellite

3101.0 cm 0.3keV skm /100

Density Ion temperature Mean velocity

The interaction of large an medium-scale harmonics gives the possibility to explain the existence of the pressure balance across the plasma sheet/tail lobes supported by many measurements (Michalov et al. [1968], Stiles [1978], Spence et al. [1989], Tsyganenko [1990], Baumjohann et al. [1990], Kistler et al. [1993], Petrukovich [1999], Tsyganenko and Mukai [2003]) in spite of the observed turbulence.

0, , n D n p T const J V j B

Antonova and Ovchinnikpv [1996, 1999, 2003] model

IMF Bz>+4IMF Bz<-4 нТ

The regular plasma transport related to the regular dawn-dusk electric field acrossthe plasma sheet is compensated by the eddy diffusion turbulent transport.

It is possible to explain the bifurcation of plasma sheet when IMF Bz<0 and theta-aurora formation

Frank et al. [1986]

Huang et al. [1987]

Antonova and Ovchinnikpv [1999, 2003]

September 12, 2004 event: Cluster satellite mission

FGM – fluxgate magnetometer, three components of geomagnetic field

CIS - Cluster Ion Spectroscopy experiment, three components of bulk velocity, number density and temperature.

Main goal: Study of quiet time plasma sheet turbulence, in particular the variation of the eddy diffusion coefficients across the plasma sheet

September 12, 2004. Really quiet time event. OMNI 1 minute resolution.

Resume:

1. Dst>-20 nT

2. AL>-30 nT

3. Bz>0 nT

4. Vsw<280 km/s

Quiet time event, September 12, 2004

Doy 256

Thanks to IMAGE Extreme Ultra Violet (EUV) experiment - Bill Sandel (U/Arizona)

Cluster 4 measurements

Total width of the plasma sheet – 6 Re

Typical value of the Dzz 105 km2/s

Down Dusk potential drop - 40 kV

Conclusions

• Plasma sheet is turbulent even during quiet geomagnetic conditions.

• The level of turbulence depends on the position in the plasma sheet

• Observed Eddy diffusion coefficients are consistent with the observed thickness of the plasma sheet