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Magnetosphere of the Earth is formed in the process of turbulent solar wind flow under the obstacle - the magnetic field of the Earth. Amplitudes of turbulent fluctuations of particle flux and magnetic field is considerably increased in the Earth's magnetosheath. We present the lust results of the studies of solar wind and magnetosheath turbulence using data of Russian spacecraft SPECTR-R and THEMIS mission. Data obtained with extremely high resolution of BMSW device operating on SPECTR-R satellite are used for the study of solar wind ion flux fluctuations on 0.03-100 s scales. Change of solar wind ion flux value and its direction are studied with the extreme time resolution (up to 30 ms). Spectra of solar wind ion flux fluctuations on scales less than 1 sec is presented for the first time. The existence of the break frequency in spectra of solar wind plasma parameters fluctuations is demonstrated. Variations of spectra slopes before and after break, and of the frequency of break are analyzed. The difference in spectral properties of ion flux value and it’s direction is discussed. We obtain the probability distribution function (PDF) of ion flux vector fluctuations and demonstrate the existence of great level of intermittency on scales less than 10 s. We analyze the evolution of small- and middle-scale solar wind structures (with duration from tens of seconds to tens of minutes) in the process of their motion from the solar wind to magnetosheath using data two closely spaced THEMIS satellites. The creation of structures after bow shock crossing and structure spreading in the magnetosheath are analyzed.