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Variety of shapes of solar wind ion flux spectra: Spektr-R measurements

  • Maria Riazantseva (a1), V. Budaev (a1) (a2), L. Rakhmanova (a1), G. Zastenker (a1), Yu. Yermolaev (a1), I. Lodkina (a1), J. Šafránková (a3), Z. Němeček (a3) and L. Přech (a3)...


The paper is devoted to the shapes of the solar wind ion flux fluctuation spectrum at the transition between the inertial and the kinetic range using in situ high-resolution measurements of the Russian mission Spektr-R. We analyse the variability of the transition region and select five typical types of spectral shapes: (i) spectra with two slopes and one break, (ii) spectra characterized by a nonlinear steepening in the kinetic range, (iii) spectra with flattening in the vicinity of the break, (iv) spectra with a bump in the vicinity of the break and (v) spectra without any steepening in the kinetic range. The most popular is the well-known type (i) observed in approximately half of the cases. The second most popular type of spectra is type (iii) occurring in approximately one third of the cases. The other three types are observed less often: type (ii) – in approximately 6 %; type (iv) in 3 % and type (v) in 6 % of cases. An analysis of typical plasma conditions for different types of spectra revealed that the last two type of spectra (iv) and (v) are generally observed in a very slow solar wind with a low proton density, (i) and (iii) are observed in the solar wind with rather typical conditions and (ii) is usually observed in high-speed streams. The effect of nonlinear steepening of the spectra in the kinetic range increases with the solar wind speed. We present also the analysis of statistical properties of the observed events and compare them with the predictions of several statistical turbulence models. We show that intermittency is always observed in the solar wind flow despite the presence of one or another shape of spectra. The log-Poisson model with a dominant contribution of filament-like structures shows the best parameterization of the experimentally observed scaling.


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Alexandrova, O. 2008 Solar wind vs magnetosheath turbulence and Alfvén vortices. Nonlinear Process. Geophys. 15, 95108.
Alexandrova, O., Carbone, V., Veltri, P. & Sorriso-Valvo, L. 2008 Small-scale energy cascade of the solar wind turbulence. Astrophys. J. 674, 11531157.
Alexandrova, O., Chen, C. H. K., Sorisso-Valvo, L., Horbury, T. S. & Bale, S. D. 2013 Solar wind turbulence and the role of ion instabilities. Space Sci. Rev. 178 (2–4), 101139.
Alexandrova, O., Saur, J., Lacombe, C., Mangeney, A., Mitchell, J., Schartz, J. & Robert, P. 2009 Universality of solar-wind turbulent spectrum from MHD to electron scales. Phys. Rev. Lett. 103 (16), 165003.
Bartley, W. C., Bakata, R. P., McCracken, K. G. & Rao, U. R. 1966 Anisotropic cosmic radiation fluxes of solar origin. J. Geophys. Res. 71 (13), 32973304.
Benzi, R., Ciliberto, S., Baudet, C., Ruiz Chavarria, G. & Tripiccione, R. 1993 Extended selfsimilarity in turbulent flows. Phys. Rev. E 48, 2935.
Biskamp, D. 1994 Cascade models for magnetohydrodynamic turbulence. Phys. Rev. 50 (4), 27022711.
Biskamp, D. & Mueller, W. C. 2003 Statistical anisotropy of, magnetohydrodynamic turbulence. Phys. Rev. E 67, 066302.
Boldyrev, S. & Perez, J. C. 2012 Spectrum of kinetic-Alfvén turbulence. Astrophys. J. 758, L44.
Borovsky, J. 2008 Flux tube texture of the solar wind: strands of the magnetic carpet at 1AU? J. Geophys. Res. 113, A08110.
Borovsky, J. 2012 The velocity and magnetic field fluctuations of the solar wind at 1 AU: statistical analysis of Fourier spectra and correlations with plasma properties. J. Geophys. Res. 117, A05104.
Bourouaine, S., Alexandrova, O., Marsch, E. & Maksimovic, M. 2012 On spectral breaks in the power spectra of magnetic fluctuations in fast solar wind between 0.3 and 0.9 AU. Astrophys. J. 749 (102), 7.
Bruno, R. & Carbone, V. 2013 The solar wind as a turbulence laboratory. Liv. Rev. Sol. Phys. 10 (1), 2, 208 pp.
Bruno, R., Carbone, V., Sorriso-Valvo, L. & Bavassano, B. 2003 Radial evolution of solar wind Intermittency in the inner heliosphere. J. Geophys. Res. 108, 1130.
Bruno, R., Carbone, V., Veltri, P., Pietropaolo, E. & Bavassano, B. 2001 Identifying intermittency events in the solar wind. Planet. Space Sci. 49 (12), 12011210.
Bruno, R., Telloni, D., Primavera, L., Pietropaolo, E., D’Amicisi, R., Sorriso-Valvo, L., Carbone, V., Malara, F. & Veltri, P. 2014b Radial evolution of intermittency of density fluctuations in the fast solar wind. Astrophys. J. Lett. 786 (1), 53.
Bruno, R., Trenchi, L. & Telloni, D. 2014a Spectral slope variation at proton scales from fast to slow solar wind. Astrophys. J. Lett. 793 (1), L15.
Budaev, V. P. 2009 Scaling properties of intermittent edge plasma turbulence. Phys. Lett. A 373, 856861.
Budaev, V. P., Savin, S. P. & Zelenyi, L. M. 2011 Investigation of intermittency and generalized self-similarity of turbulent boundary layers in laboratory and magnetospheric plasmas: towards a quantitative definition of plasma transport features. Phys. Uspekhi 54 (9), 875918.
Budaev, V. P., Zelenyi, L. M. & Savin, S. P. 2015 Generalized self-similarity of intermittent plasma turbulence in space and laboratory plasmas. J. Plasma Phys. 81, 395810602.
Burlaga, L. F. 1991 Intermittent turbulence in the solar wind. J. Geophys. Res. 96 (A4), 58475851.
Carbone, V., Veltri, P. & Bruno, R. 1995 Experimental evidence for differences in the extended self-similarity scaling laws between fluid and magnetohydrodynamic turbulent flows. Phys. Rev. Lett. 75 (17), 31103113.
Celnikier, L. M., Harvey, C. C., Jegou, R., Moricet, P. & Kemp, M. 1983 A determination of the electron density fluctuation spectrum in the solar wind, using the ISEE propagation experiment. Astron. Astrophys. 126 (2), 293298.
Chandran, B. D. G., Quataert, E., Howes, G., Xia, Q. & Pongkitiwanichakul, P. 2009 Constraining low-frequency Alfvénic turbulence in the solar wind using density fluctuations measurement. Astrophys. J. 707, 1668.
Chen, C. H. K., Leung, L., Boldyrev, S., Maruca, B. A. & Bale, S. D 2014b Ion-scale spectral break of solar wind turbulence at high and low beta. Geophys. Res. Lett. 41, 80818088.
Chen, C. H. K., Salem, C. S., Bonnell, J. W., Mozer, F. S. & Bale, S. D. 2012 Density fluctuation spectrum on solar wind turbulence between ion and electron scales. Phys. Rev. Lett. 109, 035001.
Chen, C. H. K., Sorriso-Valvo, L., Šafránková, J. & Němeček, Z. 2014a Intermittency of solar wind density fluctuations from ion to electron scales. Astrophys. J. Lett. 789 (L8), 5.
Dubrulle, B. 1994 Intermittency in fully developed turbulence: log-Poisson statistics and generalized scale covariance. Phys. Rev. Lett. 73, 959.
Dudok de Wit, T., Alexandrova, O., Furno, I., Sorriso-Valvo, L. & Zimbardo, G. 2013 Methods for characterising microphysical processes in plasmas. Space Sci. Rev. 178 (2), 665693.
Frisch, U. 1995 Turbulence. Cambridge University Press.
Galtier, S. 2006 Wave turbulence in incompressible Hall magnetohydrodynamics. J. Plasma Phys. 72, 721769.
Gary, P. S. 2015 Short-Wavelength turbulence and temperature anisotropy instabilities: recent computational progress (review). Phil. Trans. R. Soc. A 373, 20140149.
Goldstein, M. L., Roberts, D. A. & Matthaeus, W. H. 1995 Magnetohydrodynamic turbulence in the solar wind. Annu. Rev. Astron. Astrophys. 33, 283325.
Goldreich, P. & Sridhar, S. 1995 Toward a theory of interstellar turbulence. II. Strong Alfvénic turbulence. Astrophys. J. 438 (2), 763775.
Grappin, R., Velli, M. & Mangeney, A. 1991 Alfvénic versus standard turbulence in the solar wind. Ann. Geophys. 9, 416426.
Greco, A., Matthaeus, W. H., D’Amicis, R., Servidio, S. & Dmitruk, P. 2012 Evidence for nonlinear development of magnetohydrodynamic scale intermittency in the inner heliosphere. Astrophys. J. 749, 105.
Hellinger, P. & Travnicek, P. M. 2013 Protons and alpha particles in the expanding solar wind: hybrid simulations. J. Geophys. Res. 118, 54215430.
Hnat, B., Chapman, S. C. & Rowlands, G. 2003 Intermittency, scaling, and the Fokker–Planck approach to fluctuations of the solar wind bulk plasma parameters as seen by the WIND spacecraft. Phys. Rev. E 67 (5), 056404.
Hnat, B., Chapman, S. C. & Rowlands, G. 2005 Compressibility in solar wind plasma turbulence. Phys. Rev. Lett. 94 (20), 204502.
Horbury, T. S., Forman, M. & Oughton, S. 2008 Anisotropic scaling of magnetohydrodynamic turbulence. Phys. Rev. Lett. 101, 175005.
Howes, G. G., Cowley, S. C., Dorland, V., Hammett, W., Quataert, E. & Schekochihin, A. A. 2008 A model of turbulence in magnetized plasmas: implications for the dissipation range in the solar wind. J. Geophys. Res. 113 (A12), 5103.
Kellogg, P. J. & Horbury, T. S. 2005 Rapid density fluctuations in the solar wind. Ann. Geophys. 23 (12), 37653773.
Kiyani, K. H., Chapman, S. C., Khotyaintsev, Y. V., Dunlop, M. W. & Sahraoui, F. 2009 Global scale-invariant dissipation in collisionless plasma turbulence. Phys. Rev. Let. 103 (7), 075006.
Klein, K. G., Howes, G. G. & TenBarge, J. M. 2014 The violation of the Taylor hypothesis in measurements of solar wind turbulence. Astrophys. J. Lett. 790 (2), L20.
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds’ numbers. Dokl. Akad. Nauk. SSSR 30 (4), 301305.
Leamon, R. J., Smith, C. W., Ness, N. F., Matthaeus, W. H. & Wong, H. K. 1998 Observational constraints on the dynamics of the interplanetary magnetic field dissipation range. J. Geophys. Res. 103, 47754787.
Lion, S., Alexandrova, O. & Zaslavsky, A. 2016 Coherent events and spectral shape at ion kinetic scales in the fast solar wind turbulence. Astrophys. J. 824 (1), 47, 13.
Markovskii, S. A., Vasquez, B. J. & Smith, C. W. 2008 Statistical analysis of the high-frequency spectral break of the solar wind turbulence at 1 AU. Astrophys. J. 675 (2), 15761583.
Marsch, E. & Tu, C.-Y. 1990 Spectral and spatial evolution of compressible turbulence in the inner solar wind. J. Geophys. Res. 95 (8), 1194511956.
Marsch, E. & Tu, C. Y. 1997 Intermittency, non-Gaussian statistics and fractal scaling of MHD fluctuations in the solar wind. Nonlinear Process. Geophys. 4 (2), 101124.
Matthaeus, W. H. & Velli, M. 2011 Who needs turbulence? Space Sci. Rev. 160, 145.
Matthaeus, W. H., Wan, M., Servidio, S., Greco, A., Osman, K. T., Oughton, S. & Dmitruk, P. 2015 Intermittency, nonlinear dynamics and dissipation in the solar wind and astrophysical plasmas. Phil. Trans. R. Soc. A 373, 20140154.
Neugebauer, M., Wu, C. S. & Huba, J. D. 1978 Plasma fluctuations in the solar wind. J. Geophys. Res. 83 (3), 10271034.
Novikov, E. A. & Stewart, R. 1964 Intermittency of turbulence and spectrum of fluctuations in energy-dissipation. Izv. Akad. Nauk. SSSR Ser. Geofiz. 3, 408412.
Perri, S., Carbone, V. & Veltri, P. 2010 Where does fluid-like turbulence break down in the solar wind. Astrophys. J. Lett. 725, L52L55.
Perri, S., Goldstein, M. L., Dorelli, J. C. & Sahraoui, F. 2012 Detection of small-scale structures in the dissipation regime of solar-wind turbulence. Phys. Rev. Lett. 109, 191101.
Pitňa, A., Šafránková, J., Němeček, Z., Goncharov, O., Němec, F., Přech, L., Chen, C. H. K. & Zastenker, G. N. 2016 Density fluctuations upstream and downstream of interplanetary shocks. Astrophys. J. 819 (1), 41, 9.
Podesta, J. J. 2013 Evidence of kinetic Alfvén waves in the solarwind at 1 AU. Solar Phys. 286, 529548.
Podesta, J. J., Roberts, D. A. & Goldstein, M. L. 2006 Power spectrum of small-scale turbulent velocity fluctuations in the solar wind. J. Geophys. Res. 111, A10109.
Rakhmanova, L., Riazantseva, M. & Zastenker, G. 2016 Plasma fluctuations at the flanks of the Earth’s magnetosheath at ion kinetic scales. Ann. Geophys. 34, 10111018.
Rakhmanova, L. S., Riazantseva, M. O., Zastenker, G. N. & Yermolaev, Yu. 2017 High frequency plasma fluctuations in the middle magnetosheath and near its boundaries: spectr-R observations. J. Plasma Phys. 83, 705830204.
Riazantseva, M. O., Budaev, V. P., Rakhmanova, L. S., Zastenker, G., Safrankova, J., Nemecek, Z. & Prech, L. 2016 Comparison of properties of small-scale ion flux fluctuations in the flank magnetosheath and in the solar wind. Adv. Space Res. 58 (2), 166174.
Riazantseva, M. O., Budaev, V. P., Zelenyi, L. M., Zastenker, G., Pavlos, G. P., Safrankova, J., Nemecek, Z., Prech, L. & Nemec, F. 2015 Dynamic properties of small scale solar wind plasma fluctuations. Phil. Trans. R. Soc. A 373, 20140146.
Riazantseva, M. O. & Zastenker, G. N. 2008 The intermittency of ion density fluctuations and it’s relation with sharp density changings. Cosmic Res. 46 (1), 39.
Riazantseva, M. O., Zastenker, G. N. & Karavaev, M. V. 2010 Intermittency of solar wind ion flux and magnetic field fluctuations in the wide frequency region from $10^{-5}$ up to 1 Hz and the influence of sudden changes of ion flux. In Solar Wind 12 Proceedings, AIP Conference Proceedings, vol. 1216, (1), pp. 132135. AIP.
Roberts, O. W., Li, X., Alexandrova, O. & Li, B. 2016 Observation of an MHD Alfvén vortex in the slow solar wind. J. Geophys. Res. 121 (5), 38703881.
Šafránková, J., Němeček, Z., Přech, L., Zastenker, G., Čermák, I., Chesalin, L., Komárek, A., Vaverka, J., Beránek, M., Pavlů, J. et al. 2013a Fast solar wind monitor (BMSW): description and first results. Space Sci. Rev. 175 (1–4), 165182.
Šafránková, J., Němeček, Z., Nemec, F., Pitna, A., Chen, C. H. K. & Zastenker, G. 2015 Solar wind density spectra around the ion spectral break. Astrophys. J. 803 (2), 107, 7.
Šafránková, J., Němeček, Z., Němec, F., Přech, L., Chen, C. H. K. & Zastenker, G. N. 2016 Power spectral density of fluctuations of bulk and thermal speeds in the solar wind. Astrophys. J. 825 (2), 121, 8.
Šafránková, J., Němeček, Z., Přech, L. & Zastenker, G. 2013b Ion kinetic scale in the solar wind observed. Phys. Rev. Lett. 110, 025004.
Sahraoui, F., Goldstein, M. L., Robert, P. & Khotyaintsev, Y. V. 2009 Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale. Phys. Rev. Lett. 102, 231102.
Salem, C., Mangeney, A., Bale, S. & Veltri, P. 2009 Solar wind magnetohydrodynamics turbulence: anomalous scaling and role of intermittency. Astrophys. J. 702 (1), 537553.
Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, W., Howes, G., Quataert, E. & Tatsuno, T. 2009 Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophys. J. Suppl. Ser. 182, 310377.
Servidio, S., Carbone, V., Primavera, L., Veltri, P. & Stasiewicz, K. 2007 Compressible turbulence in Hall magnetohydrodynamics. Planet. Space Sci. 55, 22392243.
Servidio, S., Valentini, F., Perrone, D., Greco, A., Califano, F., Matthaeus, W. H. & Veltri, P. 2015 A kinetic model of plasma turbulence. J. Plasma Phys. 81, 325810107.
She, Z. S. & Leveque, E. 1994 Universal scaling laws in fully developped turbulence. Phys. Rev. Lett. 72 (3), 336339.
Smith, C. W., Hamilton, K., Vasquez, B. J. & Leamon, R. J. 2006 Dependence of the dissipation range spectrum of interplanetary magnetic fluctuations on the rate of energy cascade. Astrophys. J. 645, 8588.
Sorriso-Valvo, L., Carbone, V., Veltri, P., Consolini, G. & Bruno, R. 1999 Intermittency in the solar wind turbulence through probability distribution functions of fluctuations. Geophys. Res. Lett. 26, 18011804.
Unti, T. W. J., Neugebauer, M. & Goldstein, B. E. 1973 Direct measurements of solar-wind fluctuations between 0.0048 and 13.3 Hz. Astrophys. J. 180, 591598.
Vaivads, A. et al. 2016 Turbulence Heating ObserveR – satellite mission proposal. J. Plasma Phys. 82, 905820501.
Valentini, F. et al. 2016 Differential kinetic dynamics and heating of ions in the turbulent solar wind. N. J. Phys. 18 (12), 125001.
Zastenker, G. N. et al. 2013 Fast measurements of solar wind parameters by BMSW instrument. Cosmic Res. 51 (2), 7889.
Zelenyi, L. M. & Milovanov, A. V. 2004 Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics. Phys.-Usp. 47 (8), 749.
Yermolaev, Y. I., Nikolaeva, N. S., Lodkina, I. G. & Yermolaev, M. Y. 2009 Catalog of large-scale solar wind phenomena during 1976–2000. Cosmic Res. 47 (2), 8194.
Yordanova, E., Balogh, A., Noullez, A. & von Steiger, R. 2009 Turbulence and intermittency in the heliospheric magnetic field in fast and slow solar wind. J. Geophys. Res. 114, A08101.
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Variety of shapes of solar wind ion flux spectra: Spektr-R measurements

  • Maria Riazantseva (a1), V. Budaev (a1) (a2), L. Rakhmanova (a1), G. Zastenker (a1), Yu. Yermolaev (a1), I. Lodkina (a1), J. Šafránková (a3), Z. Němeček (a3) and L. Přech (a3)...


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