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

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
Section: Space and Atmospheric Physics
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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