Final Report Summary - SOLWINDCAS (Cascade rates of magnetohydrodynamic turbulence in the solar wind) Yaglom’s equation, which for the hydrodynamic turbulence relates third order mixed moment with energy dissipation rate is equivalent to Kolmogorov’s -4/5 law, the most fundamental theoretical result on turbulence. If local isotropy and homogeneity is assumed, similar relation was shown to hold also in magnetohydrodynamic (MHD) turbulence. Using Ulysses spacecraft measurements, it has been shown that Yaglom’s equation is observed in fast solar wind, explicitly proving for the first time that energy cascade do exist in the solar wind and providing the method for derivation of energy dissipation rates in the solar wind. Existed Yaglom’s relation for MHD turbulence implied homogeneous turbulence. In fact the solar wind is expanding and can be hardly considered as homogeneous. Moreover, characteristic timescale of the expansion is comparable to the period of the low frequency Alfven waves presented in the solar wind. Consequently, expansion of the wind should have non trivial influence on the turbulence dynamics in general and on Yaglom’s relation in particular. Derivation of the generalized Yaglom’s relation for MHD turbulence taking into account the effect of expansion of the solar wind was the first objective of the project SOLWINDCAS. The second scientific objective of the project was to use derived extended Yaglom law to determine dissipation rates of counter-propagating Alfven waves in the solar wind and for making more precise predictions about the role of MHD turbulence in the local heating of the solar wind necessary for explanation of non adiabatic radial dependence of the wind temperature. The third scientific objective of the project was to use expansion-modified Yaglom’s relation to determine relation between the energies and energy dissipation rates for the fast and slow solar wind data and compare them to the predictions of the theoretical models. The forth objective of the presented project is to derive analogue of the pinning effect for MHD turbulence in case of kinetic dissipation and to apply it for the study of the solar wind data.Meeting main scientific objectives in the framework of the project SOLWINDCAS we studied the Yaglom law in a uniformly expanding solar wind by using the two-scale expansion model of MHD turbulence. Our theoretical analysis showed that due to the expansion of the solar wind, two new terms appear in the Yaglom law. The first term is related to the decay of the turbulent energy by nonlinear interactions, whereas the second term is related to the non-zero cross-correlation of the Elsasser fields. Using magnetic field and plasma data from WIND and Helios 2 spacecrafts, we showed that at lower frequencies in the inertial range of MHD turbulence the new terms become comparable to Yaglom’s third-order mixed moment, and therefore they cannot be neglected in the evaluation of the energy cascade rate in the solar wind. Therefore, incorporation of the new terms in the Yaglom law is very important for proper determination of the solar wind heating rate. Obtained results were published in the leading scientific journal in the field (G. Gogoberidze, V. Carbone & S. Perri, The Yaglom Law in the Expanding Solar Wind, Astrophyical. Journal, 769, 111 (2013).).Meeting the forth scientific objective of the project influence of the measurement uncertainties on the observed spectral characteristics of the solar wind turbulence has been studied as well. Namely, a general, instrument-independent method to estimate the uncertainty in velocity fluctuations obtained by in situ satellite observations in the solar wind has been proposed. It was shown that when the measurement uncertainties of the velocity fluctuations are taken into account the less energetic Elsasser spectrum obeys a unique power law scaling throughout the inertial range as prevailing theories of MHD turbulence predict. Moreover, in the solar wind interval analysed, the two Elsasser spectra are observed to have the same scaling exponent γ = −1.54 throughout the inertial range. These results has been published in the leading scientific journal in the field (G. Gogoberidze and S.C. Chapman, B. Hnat and M.W. Dunlop, Impact of observational uncertainties on universal scaling of MHD turbulence, MNRAS 426, 951 (2012).)In situ observations of the fluctuating solar wind flow show that the energy of magnetic field fluctuations always exceeds that of the kinetic energy, and therefore the difference between the kinetic and magnetic energies, known as the residual energy, is always negative. The same behaviour is found in numerical simulations of MHD turbulence. In the framework of the project the dynamics of the residual energy for strong, anisotropic, critically balanced MHD turbulence has been studied using the eddy damped quasi-normal Markovian approximation. Performed analysis showed that for stationary critically balanced MHD turbulence, negative residual energy will always be generated by nonlinear interacting Alfvén waves. This offered a general explanation for the observation of negative residual energy in solar wind turbulence and in the numerical simulations. These results has been published in the leading scientific journal in the field (G. Gogoberidze, S.C. Chapman & B. Hnat, Generation of residual energy in the turbulent solar wind, Phys. Plasmas, 19, 102310 (2012)).In the framework of the project the study of electrostatic plasma instabilities of Farley-Buneman (FB) type driven by quasi-stationary neutral gas flows in the solar chromosphere has been performed. The role of these instabilities in the chromosphere has been clarified. We found that the destabilizingion thermal effect is highly reduced by the Coulomb collisions and can be ignored for the chromospheric FB-type instabilities. On the contrary, the destabilizing electron thermal effect is important and causes a significant reduction of the neutral drag velocity triggering the instability. The resulting threshold velocity is found as function of chromospheric height. Our results indicate that the FB type instabilities are still less efficient in the global chromospheric heating than the Joule dissipation of the currents driving these instabilities. This conclusion does not exclude the possibility that the FB type instabilities develop in the places where the cross-field currents overcome the threshold value and contribute to the heating locally. Typical length-scales of plasma density fluctuations produced by these instabilities are determined by the wavelengths of unstable modes, which are in the range 10−102 cm in the lower chromosphere, and 102−103 cm in the upper chromosphere. These results suggest that the decimetric radio waves undergoing scattering (scintillations) by these plasma irregularities can serve as a tool for remote probing of the solar chromosphere at different heights. These results has been published in the leading scientific journal in the field (G. Gogoberidze, Y. Voitenko, S. Poedts, and J. De Keyser, Small scale electrostatic instabilities in the solar chromosphere, MNRAS 438, 3568 (2014).)
