Turbulent processes in the Earth’s magnetotail: statistical and spectral analysis

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Space and Atmospheric Physics
1Kozak, L, 2Petrenko, B, 3Kronberg, E, 2Porokhorenkov, A, 4Grigorenko, E, 5Cheremnyh, O, 5Cheremnyh, S, 6Lui, A, 2Kozak, P, 2Kundelko, I
1Taras Shevchenko National University of Kyiv, Ukraine; Space Research Institute of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Kyiv, Ukraine
2Taras Shevchenko National University of Kyiv, Ukraine
3Max Planck Institute, Gettingen, Germany
4Institute for Space Research of the RAS, Moscow, Russia
5Space Research Institute of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Kyiv, Ukraine
6John Hopkins University, Baltimore, USA
Space Sci.&Technol. 2018, 24 ;(3):55-68
https://doi.org/10.15407/knit2018.03.055
Publication Language: Ukrainian
Abstract: 
Investigation of processes in the tail of Earth’s magnetosphere is substantially complicated by the presence of turbulence. Development of the instabilities results to a “catastrophic” reorganization of the flow and structure of the magnetic field. Complex turbulent processes observed in the Earth's magnetosphere cannot be described within the framework of analytical models of the MHD flows. To study the properties of the turbulence on large temporal and spatial scales one has to involve the methods of statistical physics and cascade models developed in hydrodynamic theories. At the same time, from an experiment it is possible to determine the statistical properties of the turbulence associated with the scale invariance. This approach allows us to obtain a comprehension about physical properties of plasma turbulence and to describe qualitatively and quantitatively the processes of transport in the turbulent regions.
     In the course of the work we analyzed the properties of the small-scale developed turbulence in the tail of Earth's magnetosphere by measurements of the flux-gate magnetometer on-board of the 3 spacecrafts of the “Cluster-2” mission with a sampling frequency of 22.5 Hz for October 17, 2005.
     To achieve this goal we used the fractal and multifractal research methods that we supplemented with spectral and wavelet analysis. In particular, we carried out the following methods: analysis of the wings of the PDF of the magnetic field fluctuations (fractal consideration); analysis of the expanded self-similarity (ESS-analysis, multifractal consideration); analysis of the power spectral density (spectral studies); amplitude analysis and wavelet power spectral analysis of the signal (wavelet analysis).
     As a result of the analysis we can conclude that the distribution of magnetic field fluctuations during the sub-storm indicates non-Gaussian statistics of the process as well as on the excess of large-scale perturbations generated by the source. When comparing the structure functions of the magnetic field fluctuations during the initiation of the sub-storm with the Kolmogorov, Kraichnan and three-dimensional isotropic log-Poisson model with the She and Leveque parameters we have found that these turbulent processes cannot be described by isotropic homogeneous models and, in addition, they are characterized by the presence of super-diffusion.
     There is a significant difference between the spectral indices for the moments before and during the initiation of the sub-storm: before the initiation of the sub-storm the spectral index is close to the Kolmogorov model, and during the initiation it is close to the electron-magneto-hydrodynamic turbulence. The wavelet analysis showed the presence of both direct and inverse cascade processes, as well as the presence of PC pulsations.
Keywords: Pc pulsations, substorm development models, tail of the Earth's magnetosphere, turbulence spectra in the tail of the earth's magnetosphere, turbulent processes
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References: 
1. Barenblatt G. I. Turbulent boundary layers at very high Reynolds numbers. Progress Math. Sci, 59 (1), 45—62 (2004), [In Russian].
2. Kozak L.V. Methods and approaches for determination of turbulent environment characteristics. Space Science and Technology, 22 (99), 60—77 (2016).
3. Kozak L.V., Pilipenko V. A., Chugunova O. M., Kozak P. N. Statistical analysis of the turbulence of a forshock region and earth’s magnetosheet. Cosmic Research, 49 (3), 202—212 (2011).
https://doi.org/10.1134/S0010952511030063
4. Kozak L. V., Savin S. P., Budaev V. P., Pilipenko V. A., Lezhen L. A Character of turbulence in the boundary regions of the Earth’s magnetosphere. Geomagnetism and Aeronomy, 52 (4), 445—455 (2012).
https://doi.org/10.1134/S0016793212040093
5. Kolmogorov A.N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. USSR Academy Report, 30 (4), 299—303 (1941).
6. Cosmic geoheliophysic / Eds L. M. Zelenyi, I. S. Veselovskiy. 624 p. (Physmatlit, Moscow, 2008). 1,
7. Nishida A. Geomagnetic diagnose of the magnetosphere. Mir (Moscow), 300 P. (1980).
8. Frick P. G. The turbulence: models and approaches. Perm’s State Tech. Univ. Part II, 139 P. (1999).
9. Frish U. The turbulence: the heritage of A.N. Kolmogorov. Phasic (Moscow), 343 P. (1998).
10. Biskamp D., Schwarz E., Drake J. F. two-dimensional electron magnetohydrodynamic turbulence. Phys. Rev. Lett. 76, 1264—1272 (1996).
https://doi.org/10.1103/PhysRevLett.76.1264
11. Benzi R., Ciliberto S., Tripiccione R., Baudet C., Massaioli F., Succi S. Extended self-similarity in turbulent flows. Phys. Rev. E. 48 (1), 29—32 (1993).
https://doi.org/10.1103/PhysRevE.48.R29
12. Chechkin A. V. Gonchar V. Y., Gorenflo R., Korabel N., Sokolov I. M. Generalized fractional diffusion equations for accelerating subdiffusion and truncated Levy flights. Phys. Rev. E. Stat. Nonlinear, Soft Matter Phys. 78 (2), 290—302 (2008).
13. Consolini G., Kretzschmar M., Lui A. T. Y., Zimbardo G., Macek W. M. On the magnetic field fluctuations during magnetospheric tail current disruption: A statistical approach. J. Geophys. Res. Sp. Phys. 110 (A7), 1—12 (2005).
https://doi.org/10.1029/2004JA010947
14. Dubrulle B. Intermittency in fully developed turbulence: Log-poisson statistics and generalized scale covariance. Phys. Rev. Lett. 73 (7), 959—962 (1994).
https://doi.org/10.1103/PhysRevLett.73.959
15. Farge M. Wavelet Transforms and their Applications to Turbulence. Annu. Rev. Fluid Mech. 24 (1), 395—458 (1992).
https://doi.org/10.1146/annurev.fl.24.010192.002143
16. Grinsted A. Moore J. C., Jevrejeva S. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Process. Geophys. 11 (5/6), 561—566 (2004).
https://doi.org/10.5194/npg-11-561-2004
17. Hadid L.Z. Sahraoui F., Kiyani K. H., Retinò A., Modolo R., Canu P., Masters A., Dougherty M. K. Nature of the MHD and Kinetic Scale Turbulence in the Magnetosheath of Saturn: Cassini Observations. Astrophys. J. 813 (2) 29 p. (2015).
18. Handbook of the Solar-Terrestrial Environment. Eds Kamide Y., Chian A. Berlin, Heidelberg: Springer Berlin Heidelberg. 539 P. (2007).
19. Jevrejeva S. Moore J. C., Grinsted A. Influence of the Arctic Oscillation and El Ni o-Southern Oscillation (ENSO) on ice conditions in the Baltic Sea: The wavelet approach. J. Geophys. Res. Atmos. 108 (D21), 4677—4708 (2003).
https://doi.org/10.1029/2003JD003417
20. Kiyani K. H. Chapman S. C., Khotyaintsev Y. V., Dunlop M. W., Sahraoui F. Global Scale-Invariant Dissipation in Collisionless Plasma Turbulence. Phys. Rev. Lett. 103 (7), 75006 (4 p.) (2009).
21. Kiyani K. H. Chapman S. C., Sahraoui F., Hnat B., Fauvarque O., Khotyaintsev Y. V. Enhanced magnetic compressibility and isotropic scale invariance at sub-ion Larmor scales in solar wind turbulence. Astrophys. J. 763 (1), 10 p. (2013).
22. Kozak L. V., Lui A. T. Y., Kronberg E. A., Prokhorenkov A.S. Turbulent processes in Earth’s magnetosheath by Cluster mission measurements. J. Atmos. Solar-Terrestrial Phys. 154, 115—126 (2017).
https://doi.org/10.1016/j.jastp.2016.12.016
23. Kozak L. V. Prokhorenkov A. S, Savin S. P. Statistical analysis of the magnetic fluctuations in boundary layers of Earth’s magnetosphere. Adv. Sp. Res. 56(10), 2091—2096 (2015).
https://doi.org/10.1016/j.asr.2015.08.009
24. Kraichnan R. H. The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497—543 (1959).
https://doi.org/10.1017/S0022112059000362
25. Kraichnan R. H. Convergents to turbulence functions. J. Fluid Mech. 41(1), 189—217 (1970).
https://doi.org/10.1017/S0022112070000587
26. Kronberg E .A., Ashour-Abdalla M., Dandouras I., Delcourt D. C., Grigorenko E. E., Kistler L. M., Kuzichev I. V., Liao J., Maggiolo R., Malova H. V., Orlova K. G., Peroomian V., Shklyar D. R., Shprits Y. Y., Welling D. T., Zelenyi L. M. Circulation of Heavy Ions and Their Dynamical Effects in the Magnetosphere: Recent Observations and Models. Space Sci. Rev. 184(1), 173—235 (2014).
https://doi.org/10.1007/s11214-014-0104-0
27. Lopez R. E. Magnetospheric substorms. Johns Hopkins APL Tech. Dig. 11, 264—271 (1990).
28. Lui A. T. Y. Multiscale phenomena in the near-Earth magnetosphere. J. Atmos. Solar-Terrestrial Phys. 64 (2), 125—143 (2002).
https://doi.org/10.1016/S1364-6826(01)00079-7
29. Lui A. T. Y. Potential plasma instabilities for substorm expansion onsets. Space Sci. Rev. 113 (1), 127—206 (2004).
https://doi.org/10.1023/B:SPAC.0000042942.00362.4e
30. Lui A. T. Y., Zheng Y., Zhang Y., Livi S., Rème H., Dunlop M. W., Gustafsson G., Mende S. B., Mouikis C., Kistler L. M. Cluster observation of plasma flow reversal in the magnetotail during a substorm. Ann. Geophys. 24 (7), 2005—2013 (2006).
https://doi.org/10.5194/angeo-24-2005-2006
31. Paschmann G., Daly P. W. Spectral Analysis, Reprinted from Analysis Methods for Multi-Spacecraft Data. ISSI Scientific Report SR-001 (Electronic edition 1.1). 491 p. (2000).
32. Prokhorenkov A., Kozak L. V., Lui A. T. Y., Gala I. Diffusion processes in the transition layer of the Earth’s magnetosphere. Adv. Astron. Sp. Phys. 5(2), 99—103 (2015).
https://doi.org/10.17721/2227-1481.5.99-103
33. Rae I. J., Mann I. R., Angelopoulos V., Murphy K. R., Milling D. K., Kale A., Frey H. U., Rostoker G., Russell C. T., Watt C. E. J., Engebretson M. J., Moldwin M. B., Mende S. B., Singer H. J., Donovan E. F. Near-Earth initiation of a terrestrial substorm. J. Geophys. Res. Sp. Phys. 114 (7), 2156—2202 (2009).
https://doi.org/10.1029/2008JA013771
34. Runov A., Angelopoulos V., Zhou X.-Z. Multipoint observations of dipolarization front formation by magnetotail reconnection. J. Geophys. Res. Sp. Phys. 117 (A5), 2156—2202 (2012).
https://doi.org/10.1029/2011JA017361
35. Savin S., Amata E., Zelenyi L., Lutsenko V., Safrankova J., Nemecek Z., Borodkova N., Buechner J., Daly P. W., Kronberg E. A., Blecki J., Budaev V., Kozak L., Skalsky A., Lezhen L. Super fast plasma streams as drivers of transient and anomalous magnetospheric dynamics. Ann. Geophys. 30 (1), 1—7 (2012).
https://doi.org/10.5194/angeo-30-1-2012
36. Savin S., Budaev V., Zelenyi L., Amata E., Sibeck D., Lutsenko V., Borodkova N., Zhang H., Angelopoulos V., Safrankova J., Nemecek Z., Blecki J., Buechner J., Kozak L., Romanov S., Skalsky A., Krasnoselsky V. Anomalous interaction of a plasma flow with the boundary layers of a geomagnetic trap. JETP Lett. 93 (12), 754—762 (2011).
https://doi.org/10.1134/S0021364011120137
37. She Z.-S., Leveque E. Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72 (3), 336—339 (1994).
https://doi.org/10.1103/PhysRevLett.72.336
38. THOR Exploring plasma energization in space turbulence. Assessment Study Report ESA/SRE. 109 p. (2017).
39. Torrence C., Compo G. P. A Practical Guide to Wavelet Analysis. Bull. Am. Meteorol. Soc. 79 (1), 61—78 (1998).
https://doi.org/10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2
40. Treumann R. A., Brostrom L., LaBelle J., Sckopke N. The plasma wave signature of a “magnetic hole” in the vicinity of the magnetopause. J. Geophys. Res. 95 (A11), 19099—19144 (1990).
https://doi.org/10.1029/JA095iA11p19099