Solar Wind Turbulence and the Role of Ion Instabilities

  • O. Alexandrova
  • C. H. K. Chen
  • L. Sorriso-Valvo
  • T. S. Horbury
  • S. D. Bale
Part of the Space Sciences Series of ISSI book series (SSSI, volume 47)


Solar wind is probably the best laboratory to study turbulence in astrophysical plasmas. In addition to the presence of magnetic field, the differences with neutral fluid isotropic turbulence are: (i) weakness of collisional dissipation and (ii) presence of several characteristic space and time scales. In this paper we discuss observational properties of solar wind turbulence in a large range from the MHD to the electron scales. At MHD scales, within the inertial range, turbulence cascade of magnetic fluctuations develops mostly in the plane perpendicular to the mean field, with the Kolmogorov scaling \(k_{\perp}^{-5/3}\) for the perpendicular cascade and \(k_{\|}^{-2}\) for the parallel one. Solar wind turbulence is compressible in nature: density fluctuations at MHD scales have the Kolmogorov spectrum. Velocity fluctuations do not follow magnetic field ones: their spectrum is a power-law with a −3/2 spectral index. Probability distribution functions of different plasma parameters are not Gaussian, indicating presence of intermittency. At the moment there is no global model taking into account all these observed properties of the inertial range. At ion scales, turbulent spectra have a break, compressibility increases and the density fluctuation spectrum has a local flattening. Around ion scales, magnetic spectra are variable and ion instabilities occur as a function of the local plasma parameters. Between ion and electron scales, a small scale turbulent cascade seems to be established. It is characterized by a well defined power-law spectrum in magnetic and density fluctuations with a spectral index close to −2.8. Approaching electron scales, the fluctuations are no more self-similar: an exponential cut-off is usually observed (for time intervals without quasi-parallel whistlers) indicating an onset of dissipation. The small scale inertial range between ion and electron scales and the electron dissipation range can be together described by \(\sim k_{\perp}^{-\alpha}\exp(-k_{\perp}\ell_{d})\), with α≃8/3 and the dissipation scale d close to the electron Larmor radius d ρ e . The nature of this small scale cascade and a possible dissipation mechanism are still under debate.


Plasma turbulence Solar wind Kinetic scales Ion instabilities 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. P. Abry, P. Gonçalves, P. Flandrin Wavelets, spectrum analysis and 1/f processes. Wavelets and statistics. Lecture Notes in Statistics (1995). doi: 10.1007/978-1-4612-2544-7_2
  2. P. Abry, P. Gonçalves, J. Lévy Véhel, Scaling, Fractals and Wavelets. Digital Signal and Image Processing Series (ISTE/Wiley, London, 2009) zbMATHGoogle Scholar
  3. O. Alexandrova, Solar wind vs magnetosheath turbulence and Alfvén vortices. Nonlinear Process. Geophys. 15, 95–108 (2008). doi: 10.5194/npg-15-95-2008 ADSGoogle Scholar
  4. O. Alexandrova, J. Saur, Alfvén vortices in Saturn’s magnetosheath: Cassini observations. Geophys. Res. Lett. 35, 15102 (2008). doi: 10.1029/2008GL034411 ADSGoogle Scholar
  5. O. Alexandrova, C. Lacombe, A. Mangeney, Spectra and anisotropy of magnetic fluctuations in the earth’s magnetosheath: cluster observations. Ann. Geophys. 26, 3585–3596 (2008). doi: 10.5194/angeo-26-3585-2008 ADSGoogle Scholar
  6. O. Alexandrova, A. Mangeney, M. Maksimovic, N. Cornilleau-Wehrlin, J.-M. Bosqued, M. André, Alfvén vortex filaments observed in magnetosheath downstream of a quasi-perpendicular bow shock. J. Geophys. Res. 111(A10), 12208 (2006). doi: 10.1029/2006JA011934 Google Scholar
  7. O. Alexandrova, V. Carbone, P. Veltri, L. Sorriso-Valvo, Solar wind cluster observations: turbulent spectrum and role of Hall effect. Planet. Space Sci. 55, 2224–2227 (2007). doi: 10.1016/j.pss.2007.05.022 ADSGoogle Scholar
  8. O. Alexandrova, V. Carbone, P. Veltri, L. Sorriso-Valvo, Small-scale energy cascade of the solar wind turbulence. Astrophys. J. 674, 1153–1157 (2008). doi: 10.1086/524056 ADSGoogle Scholar
  9. O. Alexandrova, J. Saur, C. Lacombe, A. Mangeney, J. Mitchell, S.J. Schwartz, P. Robert, Universality of solar-wind turbulent spectrum from MHD to electron scales. Phys. Rev. Lett. 103(16), 165003 (2009). doi: 10.1103/PhysRevLett.103.165003 ADSGoogle Scholar
  10. O. Alexandrova, J. Saur, C. Lacombe, A. Mangeney, S.J. Schwartz, J. Mitchell, R. Grappin, P. Robert, Solar wind turbulent spectrum from MHD to electron scales, in Twelfth International Solar Wind Conference, vol. 1216 (2010), pp. 144–147. doi: 10.1063/1.3395821 Google Scholar
  11. O. Alexandrova, C. Lacombe, A. Mangeney, R. Grappin Fluid-like dissipation of magnetic turbulence at electron scales in the solar wind. arXiv:1111.5649v1 (2011)
  12. O. Alexandrova, C. Lacombe, A. Mangeney, R. Grappin, M. Maksimovic, Solar wind turbulent spectrum at plasma kinetic scales. Astrophys. J. 760(2), 121 (2012). doi: 10.1088/0004-637X/760/2/121 ADSGoogle Scholar
  13. S.D. Bale, P.J. Kellogg, F.S. Mozer, T.S. Horbury, H. Reme, Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 94(21), 215002 (2005). doi: 10.1103/PhysRevLett.94.215002 ADSGoogle Scholar
  14. S.D. Bale, J.C. Kasper, G.G. Howes, E. Quataert, C. Salem, D. Sundkvist, Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind. Phys. Rev. Lett. 103, 211101 (2009). doi: 10.1103/PhysRevLett.103.211101 ADSGoogle Scholar
  15. A. Balogh, C.M. Carr, M.H. Acuña, M.W. Dunlop, T.J. Beek, P. Brown, K.-H. Fornaçon, E. Georgescu, K.-H. Glassmeier, J. Harris, G. Musmann, T. Oddy, K. Schwingenschuh, The cluster magnetic field investigation: overview of in-flight performance and initial results. Ann. Geophys. 19, 1207–1217 (2001). doi: 10.5194/angeo-19-1207-2001 ADSGoogle Scholar
  16. A. Bershadskii, K.R. Sreenivasan, Intermittency and the passive nature of the magnitude of the magnetic field. Phys. Rev. Lett. 93(6), 064501 (2004). doi: 10.1103/PhysRevLett.93.064501 ADSGoogle Scholar
  17. J.W. Bieber, W. Wanner, W.H. Matthaeus, Dominant two-dimensional solar wind turbulence with implications for cosmic ray transport. J. Geophys. Res. 101, 2511–2522 (1996). doi: 10.1029/95JA02588 ADSGoogle Scholar
  18. D. Biskamp, Nonlinear Magnetohydrodynamics (Cambridge University Press, Cambridge, 1993) Google Scholar
  19. D. Biskamp, E. Schwarz, J.F. Drake, Two-dimensional electron magnetohydrodynamic turbulence. Phys. Rev. Lett. 76, 1264–1267 (1996). doi: 10.1103/PhysRevLett.76.1264 ADSGoogle Scholar
  20. D. Biskamp, E. Schwarz, A. Zeiler, A. Celani, J.F. Drake, Electron magnetohydrodynamic turbulence. Phys. Plasmas 6, 751–758 (1999). doi: 10.1063/1.873312 ADSMathSciNetGoogle Scholar
  21. S. Boldyrev, Spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 96(11), 115002 (2006). doi: 10.1103/PhysRevLett.96.115002 ADSGoogle Scholar
  22. S. Boldyrev, J.C. Perez, Spectrum of weak magnetohydrodynamic turbulence. Phys. Rev. Lett. 103(22), 225001 (2009). doi: 10.1103/PhysRevLett.103.225001 ADSGoogle Scholar
  23. S. Boldyrev, J.C. Perez, Spectrum of kinetic-Alfvén turbulence. Astrophys. J. 758, 44 (2012). doi: 10.1088/2041-8205/758/2/L44 ADSGoogle Scholar
  24. S. Boldyrev, J.C. Perez, J.E. Borovsky, J.J. Podesta, Spectral scaling laws in magnetohydrodynamic turbulence simulations and in the solar wind. Astrophys. J. 741, 19 (2011). doi: 10.1088/2041-8205/741/1/L19 ADSGoogle Scholar
  25. S. Boldyrev, J.C. Perez, Y. Wang, Residual Energy in Weak and Strong MHD Turbulence, Numerical modeling of space plasma flows (astronum 2011), in Proceedings of a 6th internation conference, Velancia, Spain, 13–17 June, 2011, ed. by N.V. Pogorelov, J.A. Font, E. Audit, G.P. Zank, ASP Conference Series, vol. 459 (Astronomical Society of the Pacific, San Francisco, 2012), p. 3 Publication Date: 07/2012 Google Scholar
  26. J.E. Borovsky, Flux tube texture of the solar wind: strands of the magnetic carpet at 1 AU? J. Geophys. Res. 113(A12), 8110 (2008). doi: 10.1029/2007JA012684 Google Scholar
  27. J.E. Borovsky, Looking for evidence of mixing in the solar wind from 0.31 to 0.98 AU. J. Geophys. Res. 117(A16), 6107 (2012a). doi: 10.1029/2012JA017525 Google Scholar
  28. J.E. Borovsky, 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(A16), 5104 (2012b). doi: 10.1029/2011JA017499 Google Scholar
  29. S. Bourouaine, E. Marsch, F.M. Neubauer, Correlations between the proton temperature anisotropy and transverse high-frequency waves in the solar wind. Geophys. Res. Lett. 37, 14104 (2010). doi: 10.1029/2010GL043697 ADSGoogle Scholar
  30. S. Bourouaine, E. Marsch, F.M. Neubauer, Temperature anisotropy and differential streaming of solar wind ions. correlations with transverse fluctuations. Astron. Astrophys. 536, 39 (2011). doi: 10.1051/0004-6361/201117866 ADSGoogle Scholar
  31. S. Bourouaine, O. Alexandrova, E. Marsch, M. Maksimovic, 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 (2012). doi: 10.1088/0004-637X/749/2/102 ADSGoogle Scholar
  32. R. Bruno, V. Carbone, The solar wind as a turbulence laboratory. Living Rev. Sol. Phys. 2, 4 (2005). doi: 10.12942/lrsp-2005-4 ADSGoogle Scholar
  33. R. Bruno, V. Carbone, P. Veltri, E. Pietropaolo, B. Bavassano, Identifying intermittency events in the solar wind. Planet. Space Sci. 49(12), 1201–1210 (2001). Nonlinear Dynamics and Fractals in Space., doi: 10.1016/S0032-0633(01)00061-7. ADSGoogle Scholar
  34. R. Bruno, V. Carbone, L. Sorriso-Valvo, B. Bavassano, Radial evolution of solar wind intermittency in the inner heliosphere. J. Geophys. Res. 108, 1130 (2003). doi: 10.1029/2002JA009615 Google Scholar
  35. R. Bruno, V. Carbone, L. Primavera, F. Malara, L. Sorriso-Valvo, B. Bavassano, P. Veltri, On the probability distribution function of small-scale interplanetary magnetic field fluctuations. Ann. Geophys. 22, 3751–3769 (2004). doi: 10.5194/angeo-22-3751-2004 ADSGoogle Scholar
  36. R. Bruno, R. D’Amicis, B. Bavassano, V. Carbone, L. Sorriso-Valvo, Magnetically dominated structures as an important component of the solar wind turbulence. Ann. Geophys. 25, 1913–1927 (2007). doi: 10.5194/angeo-25-1913-2007 ADSGoogle Scholar
  37. L.F. Burlaga, Intermittent turbulence in the solar wind. J. Geophys. Res. 96, 5847–5851 (1991). doi: 10.1029/91JA00087 ADSGoogle Scholar
  38. L.F. Burlaga, Intermittent turbulence in large-scale velocity fluctuations at 1 AU near solar maximum. J. Geophys. Res. 98(A10), 17467–17473 (1993). doi: 10.1029/93JA01630. ADSGoogle Scholar
  39. V. Carbone, L. Sorriso-Valvo, R. Marino, On the turbulent energy cascade in anisotropic magnetohydrodynamic turbulence. Europhys. Lett. 88, 25001 (2009a). doi: 10.1209/0295-5075/88/25001 ADSGoogle Scholar
  40. V. Carbone, R. Marino, L. Sorriso-Valvo, A. Noullez, R. Bruno, Scaling laws of turbulence and heating of fast solar wind: the role of density fluctuations. Phys. Rev. Lett. 103(6), 061102 (2009b). doi: 10.1103/PhysRevLett.103.061102 ADSGoogle Scholar
  41. V. Carbone, P. Veltri, R. Bruno, Experimental evidence for differences in the extended self-similarity scaling laws between fluid and magnetohydrodynamic turbulent flows. Phys. Rev. Lett. 75, 3110–3113 (1995). doi: 10.1103/PhysRevLett.75.3110. ADSGoogle Scholar
  42. L.M. Celnikier, C.C. Harvey, R. Jegou, P. Moricet, M. Kemp, A determination of the electron density fluctuation spectrum in the solar wind, using the ISEE propagation experiment. Astron. Astrophys. 126, 293–298 (1983) ADSGoogle Scholar
  43. B.D.G. Chandran, E. Quataert, G.G. Howes, Q. Xia, P. Pongkitiwanichakul, Constraining low-frequency Alfvénic turbulence in the solar wind using density-fluctuation measurements. Astrophys. J. 707, 1668–1675 (2009). doi: 10.1088/0004-637X/707/2/1668 ADSGoogle Scholar
  44. C.H.K. Chen, T.S. Horbury, A.A. Schekochihin, R.T. Wicks, O. Alexandrova, J. Mitchell, Anisotropy of solar wind turbulence between ion and electron scales. Phys. Rev. Lett. 104, 255002 (2010a). doi: 10.1103/PhysRevLett.104.255002 ADSGoogle Scholar
  45. C.H.K. Chen, R.T. Wicks, T.S. Horbury, A.A. Schekochihin, Interpreting power anisotropy measurements in plasma turbulence. Astrophys. J. 711, 79–83 (2010b). doi: 10.1088/2041-8205/711/2/L79 ADSGoogle Scholar
  46. C.H.K. Chen, A. Mallet, T.A. Yousef, A.A. Schekochihin, T.S. Horbury, Anisotropy of Alfvénic turbulence in the solar wind and numerical simulations. Mon. Not. R. Astron. Soc. 415, 3219 (2011a). doi: 10.1111/j.1365-2966.2011.18933.x ADSGoogle Scholar
  47. C.H.K. Chen, S.D. Bale, C. Salem, F.S. Mozer, Frame dependence of the electric field spectrum of solar wind turbulence. Astrophys. J. 737, 41 (2011b). doi: 10.1088/2041-8205/737/2/L41 ADSGoogle Scholar
  48. C.H.K. Chen, C.S. Salem, J.W. Bonnell, F.S. Mozer, S.D. Bale, Density fluctuation spectrum of solar wind turbulence between ion and electron scales. Phys. Rev. Lett. 109(3), 035001 (2012a). doi: 10.1103/PhysRevLett.109.035001 ADSGoogle Scholar
  49. C.H.K. Chen, A. Mallet, A.A. Schekochihin, T.S. Horbury, R.T. Wicks, S.D. Bale, Three-dimensional structure of solar wind turbulence. Astrophys. J. 758, 120 (2012b). doi: 10.1088/0004-637X/758/2/120 ADSGoogle Scholar
  50. C.H.K. Chen, G.G. Howes, J.W. Bonnell, F.S. Mozer, K.G. Klein, S.D. Bale, Kinetic scale density fluctuations in the solar wind. Solar Wind 13 Proceedings 1539, 143–146 (2013a). arXiv:1210.0127 ADSGoogle Scholar
  51. C.H.K. Chen, S.D. Bale, C.S. Salem, B.A. Maruca, Residual energy spectrum of solar wind turbulence. Astrophys. J. 770, 125 (2013b). doi: 10.1088/0004-637X/770/2/125 ADSGoogle Scholar
  52. C.H.K. Chen, S. Boldyrev, Q. Xia, J.C. Perez, The nature of subproton scale turbulence in the solar wind. Phys. Rev. Lett. 110, 225002 (2013c). doi: 10.1103/PhysRevLett.110.225002 ADSGoogle Scholar
  53. S. Chen, G. Doolen, J.R. Herring, R.H. Kraichnan, S.A. Orszag, Z.S. She, Far-dissipation range of turbulence. Phys. Rev. Lett. 70, 3051–3054 (1993). doi: 10.1103/PhysRevLett.70.3051 ADSGoogle Scholar
  54. G.F. Chew, M.L. Goldberger, F.E. Low, The Boltzmann equation and the one-fluid hydromagnetic equations in the absence of particle collisions. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 236, 112–118 (1956). doi: 10.1098/rspa.1956.0116 ADSzbMATHMathSciNetGoogle Scholar
  55. J. Cho, A. Lazarian, The anisotropy of electron magnetohydrodynamic turbulence. Astrophys. J. 615, 41–44 (2004). doi: 10.1086/425215 ADSGoogle Scholar
  56. J. Cho, E.T. Vishniac, The anisotropy of magnetohydrodynamic Alfvénic turbulence. Astrophys. J. 539, 273–282 (2000). doi: 10.1086/309213 ADSGoogle Scholar
  57. J.T. Coburn, C.W. Smith, B.J. Vasquez, J.E. Stawarz, M.A. Forman, The turbulent cascade and proton heating in the solar wind during solar minimum. Astrophys. J. 754, 93 (2012). doi: 10.1088/0004-637X/754/2/93 ADSGoogle Scholar
  58. L. Danaila, F. Anselmet, T. Zhou, R.A. Antonia, Turbulent energy scale budget equations in a fully developed channel flow. J. Fluid Mech. 430, 87–109 (2001). doi: 10.1017/S0022112000002767. ADSzbMATHGoogle Scholar
  59. P.A. Davidson, Turbulence: an Introduction for Scientists and Engineers (Oxford University Press, Oxford, 2004) Google Scholar
  60. K.U. Denskat, H.J. Beinroth, F.M. Neubauer, Interplanetary magnetic field power spectra with frequencies from 2.4×10 to the −5th Hz to 470 Hz from HELIOS-observations during solar minimum conditions. J. Geophys. 54, 60–67 (1983) Google Scholar
  61. M. Dobrowolny, A. Mangeney, P. Veltri, Fully developed anisotropic hydromagnetic turbulence in interplanetary space. Phys. Rev. Lett. 45, 144–147 (1980). doi: 10.1103/PhysRevLett.45.144 ADSMathSciNetGoogle Scholar
  62. T. Dudok de Wit, O. Alexandrova, I. Furno, L. Sorriso-Valvo, G. Zimbardo, Methods for characterising microphysical processes in plasmas. Space Sci. Rev. (2013). doi: 10.1007/s11214-013-9974-9 Google Scholar
  63. U. Frisch, Turbulence (Cambridge University Press, Cambridge, 1995) zbMATHGoogle Scholar
  64. S. Galtier, Wave turbulence in incompressible Hall magnetohydrodynamics. J. Plasma Phys. 72, 721–769 (2006). doi: 10.1017/S0022377806004521 ADSGoogle Scholar
  65. S. Galtier, A. Pouquet, A. Mangeney, On spectral scaling laws for incompressible anisotropic magnetohydrodynamic turbulence. Phys. Plasmas 12(9), 092310 (2005). doi: 10.1063/1.2052507 ADSGoogle Scholar
  66. P.C. Gary, C.W. Smith, W.H. Matthaeus, N.F. Otani, Heating of the solar wind by pickup ion driven Alfvén ion cyclotron instability. Geophys. Res. Lett. 23, 113–116 (1996). doi: 10.1029/95GL03707 ADSGoogle Scholar
  67. S.P. Gary, Theory of Space Plasma Microinstabilities (Cambridge University Press, Cambridge, 1993) Google Scholar
  68. S.P. Gary, C.W. Smith, Short-wavelength turbulence in the solar wind: linear theory of whistler and kinetic Alfvén fluctuations. J. Geophys. Res. 114, 12105 (2009). doi: 10.1029/2009JA014525 Google Scholar
  69. S.P. Gary, M.D. Montgomery, W.C. Feldman, D.W. Forslund, Proton temperature anisotropy instabilities in the solar wind. J. Geophys. Res. 81, 1241–1246 (1976). doi: 10.1029/JA081i007p01241 ADSGoogle Scholar
  70. S.P. Gary, R.M. Skoug, J.T. Steinberg, C.W. Smith, Proton temperature anisotropy constraint in the solar wind: ACE observations. Geophys. Res. Lett. 28, 2759–2762 (2001). doi: 10.1029/2001GL013165 ADSGoogle Scholar
  71. S. Ghosh, E. Siregar, D.A. Roberts, M.L. Goldstein, Simulation of high-frequency solar wind power spectra using Hall magnetohydrodynamics. J. Geophys. Res. 101, 2493–2504 (1996). doi: 10.1029/95JA03201 ADSGoogle Scholar
  72. P. Goldreich, S. Sridhar, Toward a theory of interstellar turbulence. II. Strong Alfvénic turbulence. Astrophys. J. 438, 763–775 (1995). doi: 10.1086/175121 ADSGoogle Scholar
  73. P. Goldreich, S. Sridhar, Magnetohydrodynamic turbulence revisited. Astrophys. J. 485, 680 (1997). doi: 10.1086/304442 ADSGoogle Scholar
  74. M.L. Goldstein, D.A. Roberts, C.A. Fitch, Properties of the fluctuating magnetic helicity in the inertial and dissipation ranges of solar wind turbulence. J. Geophys. Res. 99, 11519–11538 (1994). doi: 10.1029/94JA00789 ADSGoogle Scholar
  75. H.L. Grant, R.W. Stewart, A. Moilliet, Turbulence spectra from a tidal channel. J. Fluid Mech. 12, 241–268 (1962). doi: 10.1017/S002211206200018X ADSzbMATHGoogle Scholar
  76. R. Grappin, J. Leorat, A. Pouquet, Dependence of MHD turbulence spectra on the velocity field-magnetic field correlation. Astron. Astrophys. 126, 51–58 (1983) ADSGoogle Scholar
  77. R. Grappin, A. Mangeney, E. Marsch, On the origin of solar wind MHD turbulence—HELIOS data revisited. J. Geophys. Res. 95, 8197–8209 (1990). doi: 10.1029/JA095iA06p08197 ADSGoogle Scholar
  78. R. Grappin, M. Velli, A. Mangeney, “Alfvénic” versus “standard” turbulence in the solar wind. Ann. Geophys. 9, 416–426 (1991) ADSGoogle Scholar
  79. A. Greco, W.H. Matthaeus, S. Servidio, P. Chuychai, P. Dmitruk, Statistical analysis of discontinuities in solar wind ACE data and comparison with intermittent MHD turbulence. Astrophys. J. 691, 111–114 (2009). doi: 10.1088/0004-637X/691/2/L111 ADSGoogle Scholar
  80. A. Greco, S. Servidio, W.H. Matthaeus, P. Dmitruk, Intermittent structures and magnetic discontinuities on small scales in MHD simulations and solar wind. Planet. Space Sci. 58, 1895–1899 (2010). doi: 10.1016/j.pss.2010.08.019 ADSGoogle Scholar
  81. A. Greco, W.H. Matthaeus, R. D’Amicis, S. Servidio, P. Dmitruk, Evidence for nonlinear development of magnetohydrodynamic scale intermittency in the inner heliosphere. Astrophys. J. 749, 105 (2012). doi: 10.1088/0004-637X/749/2/105 ADSGoogle Scholar
  82. K. Hamilton, C.W. Smith, B.J. Vasquez, R.J. Leamon, Anisotropies and helicities in the solar wind inertial and dissipation ranges at 1 AU. J. Geophys. Res. 113(A12), 1106 (2008). doi: 10.1029/2007JA012559 Google Scholar
  83. A. Hasegawa, Drift mirror instability of the magnetosphere. Phys. Fluids 12, 2642–2650 (1969). doi: 10.1063/1.1692407 ADSGoogle Scholar
  84. M. Haverkorn, S.R. Spangler, Plasma diagnostics of the interstellar medium with radio astronomy. Space Sci. Rev. (2013, submitted) Google Scholar
  85. J.-S. He, E. Marsch, C.-Y. Tu, Q.-G. Zong, S. Yao, H. Tian, Two-dimensional correlation functions for density and magnetic field fluctuations in magnetosheath turbulence measured by the cluster spacecraft. J. Geophys. Res. 116(A15), 06207 (2011a). doi: 10.1029/2010JA015974 Google Scholar
  86. J. He, E. Marsch, C. Tu, S. Yao, H. Tian, Possible evidence of Alfvén-cyclotron waves in the angle distribution of magnetic helicity of solar wind turbulence. Astrophys. J. 731, 85 (2011b). doi: 10.1088/0004-637X/731/2/85 ADSGoogle Scholar
  87. P. Hellinger, H. Matsumoto, New kinetic instability: oblique Alfvén fire hose. J. Geophys. Res. 105, 10519–10526 (2000). doi: 10.1029/1999JA000297 ADSGoogle Scholar
  88. P. Hellinger, H. Matsumoto, Nonlinear competition between the whistler and Alfvén fire hoses. J. Geophys. Res. 106, 13215–13218 (2001). doi: 10.1029/2001JA900026 ADSGoogle Scholar
  89. P. Hellinger, P. Trávníček, J.C. Kasper, A.J. Lazarus, Solar wind proton temperature anisotropy: linear theory and WIND/SWE observations. Geophys. Res. Lett. 33, 09101 (2006). doi: 10.1029/2006GL025925 ADSGoogle Scholar
  90. P. Hellinger, L. Matteini, Š. Štverák, P.M. Trávníček, E. Marsch, Heating and cooling of protons in the fast solar wind between 0.3 and 1 AU: Helios revisited. J. Geophys. Res. 116, 9105 (2011). doi: 10.1029/2011JA016674 Google Scholar
  91. P. Hellinger, P.M. Trávníček, Š. Štverák, L. Matteini, M. Velli, Proton thermal energetics in the solar wind: Helios reloaded. J. Geophys. Res. 118 (2013). doi: 10.1002/jgra.50107
  92. P. Henri, F. Califano, C. Briand, A. Mangeney, Low-energy Langmuir cavitons: asymptotic limit of weak turbulence. Europhys. Lett. 96, 55004 (2011). doi: 10.1209/0295-5075/96/55004 ADSGoogle Scholar
  93. J.C. Higdon, Density fluctuations in the interstellar medium: evidence for anisotropic magnetogasdynamic turbulence. I. Model and astrophysical sites. Astrophys. J. 285, 109–123 (1984). doi: 10.1086/162481 ADSGoogle Scholar
  94. B. Hnat, S.C. Chapman, G. Rowlands, 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 (2003). doi: 10.1103/PhysRevE.67.056404 ADSGoogle Scholar
  95. B. Hnat, S.C. Chapman, G. Rowlands, Compressibility in solar wind plasma turbulence. Phys. Rev. Lett. 94(20), 204502 (2005). doi: 10.1103/PhysRevLett.94.204502 ADSGoogle Scholar
  96. T.S. Horbury, M. Forman, S. Oughton, Anisotropic scaling of magnetohydrodynamic turbulence. Phys. Rev. Lett. 101(17), 175005 (2008). doi: 10.1103/PhysRevLett.101.175005 ADSGoogle Scholar
  97. T.S. Horbury, M.A. Forman, S. Oughton, Spacecraft observations of solar wind turbulence: an overview. Plasma Phys. Control. Fusion 47, 703–717 (2005). doi: 10.1088/0741-3335/47/12B/S52 Google Scholar
  98. G.G. Howes, E. Quataert, On the interpretation of magnetic helicity signatures in the dissipation range of solar wind turbulence. Astrophys. J. 709, 49–52 (2010). doi: 10.1088/2041-8205/709/1/L49 ADSGoogle Scholar
  99. G.G. Howes, S.C. Cowley, W. Dorland, G.W. Hammett, E. Quataert, A.A. Schekochihin, Astrophysical gyrokinetics: basic equations and linear theory. Astrophys. J. 651, 590–614 (2006). doi: 10.1086/506172 ADSGoogle Scholar
  100. G.G. Howes, S.C. Cowley, W. Dorland, G.W. Hammett, E. Quataert, A.A. Schekochihin, A model of turbulence in magnetized plasmas: implications for the dissipation range in the solar wind. J. Geophys. Res. 113(A12), 5103 (2008). doi: 10.1029/2007JA012665 Google Scholar
  101. G.G. Howes, J.M. TenBarge, W. Dorland, A weakened cascade model for turbulence in astrophysical plasmas. Phys. Plasmas 18(10), 102305 (2011a). doi: 10.1063/1.3646400 ADSGoogle Scholar
  102. G.G. Howes, J.M. TenBarge, W. Dorland, E. Quataert, A.A. Schekochihin, R. Numata, T. Tatsuno, Gyrokinetic simulations of solar wind turbulence from ion to electron scales. Phys. Rev. Lett. 107(3), 035004 (2011b). doi: 10.1103/PhysRevLett.107.035004 ADSGoogle Scholar
  103. G.G. Howes, S.D. Bale, K.G. Klein, C.H.K. Chen, C.S. Salem, J.M. TenBarge, The slow-mode nature of compressible wave power in solar wind turbulence. Astrophys. J. 753, 19 (2012a). doi: 10.1088/2041-8205/753/1/L19 ADSGoogle Scholar
  104. G.G. Howes, S.D. Bale, K.G. Klein, C.H.K. Chen, C.S. Salem, J.M. TenBarge, The slow-mode nature of compressible wave power in solar wind turbulence. Astrophys. J. 753, 19 (2012b). doi: 10.1088/2041-8205/753/1/L19 ADSGoogle Scholar
  105. P.S. Iroshnikov, Turbulence of a conducting fluid in a strong magnetic field. Astron. Zh. 40, 742 (1963) ADSGoogle Scholar
  106. P.A. Isenberg, M.A. Lee, J.V. Hollweg, The kinetic shell model of coronal heating and acceleration by ion cyclotron waves. 1. Outward propagating waves. J. Geophys. Res. 106, 5649–5660 (2001). doi: 10.1029/2000JA000099 ADSGoogle Scholar
  107. K. Issautier, A. Mangeney, O. Alexandrova, Spectrum of the electron density fluctuations: preliminary results from Ulysses observations. AIP Conf. Proc. 1216, 148–151 (2010). doi: 10.1063/1.3395822 ADSGoogle Scholar
  108. D. Jankovicova, Z. Voros, J. Simkanin, The influence of solar wind turbulence on geomagnetic activity. Nonlinear Process. Geophys. 15(1), 53–59 (2008). doi: 10.5194/npg-15-53-2008 ADSGoogle Scholar
  109. H. Karimabadi, V. Roytershteyn, M. Wan, W.H. Matthaeus, W. Daughton, P. Wu, M. Shay, B. Loring, J. Borovsky, E. Leonardis, S.C. Chapman, T.K.M. Nakamura, Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas. Phys. Plasmas 20(1), 012303 (2013). doi: 10.1063/1.4773205 ADSGoogle Scholar
  110. J.C. Kasper Solar wind plasma: kinetic properties and micro-instabilities. Ph.D. thesis, Massachusetts Institute Of Technology (2002) Google Scholar
  111. J.C. Kasper, A.J. Lazarus, S.P. Gary, Hot solar-wind helium: direct evidence for local heating by Alfvén-cyclotron dissipation. Phys. Rev. Lett. 101(26), 261103 (2008). doi: 10.1103/PhysRevLett.101.261103 ADSGoogle Scholar
  112. J.C. Kasper, B.A. Maruca, M.L. Stevens, A. Zaslavsky, Sensitive test for ion-cyclotron resonant heating in the solar wind. Phys. Rev. Lett. 110(9), 091102 (2013). doi: 10.1103/PhysRevLett.110.091102 ADSGoogle Scholar
  113. P.J. Kellogg, T.S. Horbury, Rapid density fluctuations in the solar wind. Ann. Geophys. 23, 3765–3773 (2005). doi: 10.5194/angeo-23-3765-2005 ADSGoogle Scholar
  114. K.H. Kiyani, S.C. Chapman, Y.V. Khotyaintsev, M.W. Dunlop, F. Sahraoui, Global scale-invariant dissipation in collisionless plasma turbulence. Phys. Rev. Lett. 103(7), 075006 (2009). doi: 10.1103/PhysRevLett.103.075006 ADSGoogle Scholar
  115. K.H. Kiyani, S.C. Chapman, F. Sahraoui, B. Hnat, O. Fauvarque, Y.V. Khotyaintsev, Enhanced magnetic compressibility and isotropic scale invariance at sub-ion Larmor scales in solar wind turbulence. Astrophys. J. 763, 10 (2013). doi: 10.1088/0004-637X/763/1/10 ADSGoogle Scholar
  116. K.G. Klein, G.G. Howes, J.M. TenBarge, S.D. Bale, C.H.K. Chen, C.S. Salem, Using synthetic spacecraft data to interpret compressible fluctuations in solar wind turbulence. Astrophys. J. 755, 159 (2012). doi: 10.1088/0004-637X/755/2/159 ADSGoogle Scholar
  117. A. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds’ numbers. Dokl. Akad. Nauk SSSR 30, 301–305 (1941a) ADSGoogle Scholar
  118. A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds’ numbers. Dokl. Akad. Nauk SSSR 30, 299–303 (1941b) ADSGoogle Scholar
  119. R.H. Kraichnan, Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8, 1385–1387 (1965) ADSMathSciNetGoogle Scholar
  120. R.J. Leamon, C.W. Smith, N.F. Ness, W.H. Matthaeus, H.K. Wong, Observational constraints on the dynamics of the interplanetary magnetic field dissipation range. J. Geophys. Res. 103, 4775 (1998). doi: 10.1029/97JA03394 ADSGoogle Scholar
  121. R.J. Leamon, C.W. Smith, N.F. Ness, H.K. Wong, Dissipation range dynamics: kinetic Alfvén waves and the importance of β e. J. Geophys. Res. 104, 22331–22344 (1999). doi: 10.1029/1999JA900158 ADSGoogle Scholar
  122. R.J. Leamon, W.H. Matthaeus, C.W. Smith, G.P. Zank, D.J. Mullan, S. Oughton, MHD-driven kinetic dissipation in the solar wind and corona. Astrophys. J. 537, 1054–1062 (2000). doi: 10.1086/309059 ADSGoogle Scholar
  123. R.P. Lepping, M.H. Acũna, L.F. Burlaga, W.M. Farrell, J.A. Slavin, K.H. Schatten, F. Mariani, N.F. Ness, F.M. Neubauer, Y.C. Whang, J.B. Byrnes, R.S. Kennon, P.V. Panetta, J. Scheifele, E.M. Worley, The wind magnetic field investigation. Space Sci. Rev. 71, 207–229 (1995). doi: 10.1007/BF00751330 ADSGoogle Scholar
  124. M.P. Leubner, Z. Voros, A nonextensive entropy approach to solar wind intermittency. Astrophys. J. 618(1), 547 (2005). doi: 10.1086/425893 ADSGoogle Scholar
  125. H. Li, S.P. Gary, O. Stawicki, On the dissipation of magnetic fluctuations in the solar wind. Geophys. Res. Lett. 28, 1347–1350 (2001). doi: 10.1029/2000GL012501 ADSGoogle Scholar
  126. Y. Lithwick, P. Goldreich, Compressible magnetohydrodynamic turbulence in interstellar plasmas. Astrophys. J. 562, 279–296 (2001). doi: 10.1086/323470 ADSGoogle Scholar
  127. Q.Y. Luo, D.J. Wu, Observations of anisotropic scaling of solar wind turbulence. Astrophys. J. 714, 138–141 (2010). doi: 10.1088/2041-8205/714/1/L138 ADSGoogle Scholar
  128. B.T. MacBride, M.A. Forman, C.W. Smith, Turbulence and third moment of fluctuations: Kolmogorov’s 4/5 law and its MHD analogues in the solar wind, in Solar Wind 11/SOHO 16, Connecting Sun and Heliosphere, ed. by B. Fleck, T.H. Zurbuchen, H. Lacoste, ESA Special Publication, vol. 592 (2005), p. 613 Google Scholar
  129. B.T. MacBride, C.W. Smith, M.A. Forman, The turbulent cascade at 1 AU: energy transfer and the third-order scaling for MHD. Astrophys. J. 679, 1644–1660 (2008). doi: 10.1086/529575 ADSGoogle Scholar
  130. B.T. MacBride, C.W. Smith, B.J. Vasquez, Inertial-range anisotropies in the solar wind from 0.3 to 1 AU: Helios 1 observations. J. Geophys. Res. 115(A14), 7105 (2010). doi: 10.1029/2009JA014939 Google Scholar
  131. F. Malara, L. Primavera, P. Veltri, Nonlinear evolution of parametric instability of a large-amplitude nonmonochromatic Alfvén wave. Phys. Plasmas 7, 2866–2877 (2000). doi: 10.1063/1.874136 ADSMathSciNetGoogle Scholar
  132. F. Malara, L. Primavera, P. Veltri, Nonlinear evolution of the parametric instability: numerical predictions versus observations in the heliosphere. Nonlinear Process. Geophys. 8, 159–166 (2001). doi: 10.5194/npg-8-159-2001 ADSGoogle Scholar
  133. A. Mangeney, Intermittency and regularity in the Alfvénic range of solar wind turbulence, in American Institute of Physics Conference Series, ed. by P.-L. Sulem, M. Mond, American Institute of Physics Conference Series, vol. 1439 (2012), pp. 26–41. doi: 10.1063/1.3701349 Google Scholar
  134. A. Mangeney, R. Grappin, M. Velli, Magnetohydrodynamic turbulence in the solar wind, in Advances in Solar System Magnetohydrodynamics, ed. by E.R. Priest, A.W. Hood (1991), p. 327 Google Scholar
  135. A. Mangeney, C. Salem, P.L. Veltri, B. Cecconi, Intermittency in the solar wind turbulence and the Haar wavelet transform, in Sheffield Space Plasma Meeting: Multipoint Measurements Versus Theory, ed. by B. Warmbein, ESA Special Pub., vol. 492 (2001), p. 53 Google Scholar
  136. A. Mangeney, C. Lacombe, M. Maksimovic, A.A. Samsonov, N. Cornilleau-Wehrlin, C.C. Harvey, J.-M. Bosqued, P. Trávníček, Cluster observations in the magnetosheath. Part 1. Anisotropies of the wave vector distribution of the turbulence at electron scales. Ann. Geophys. 24, 3507–3521 (2006). doi: 10.5194/angeo-24-3507-2006 ADSGoogle Scholar
  137. P.K. Manoharan, M. Kojima, H. Misawa, The spectrum of electron density fluctuations in the solar wind and its variations with solar wind speed. J. Geophys. Res. 99, 23411 (1994). doi: 10.1029/94JA01955 ADSGoogle Scholar
  138. R. Marino, L. Sorriso-Valvo, V. Carbone, A. Noullez, R. Bruno, B. Bavassano, Heating the solar wind by a magnetohydrodynamic turbulent energy cascade. Astrophys. J. 677, 71–74 (2008). doi: 10.1086/587957 ADSGoogle Scholar
  139. R. Marino, L. Sorriso-Valvo, V. Carbone, P. Veltri, A. Noullez, R. Bruno, The magnetohydrodynamic turbulent cascade in the ecliptic solar wind: study of Ulysses data. Planet. Space Sci. 59, 592–597 (2011). doi: 10.1016/j.pss.2010.06.005 ADSGoogle Scholar
  140. R. Marino, L. Sorriso-Valvo, R. D’Amicis, V. Carbone, R. Bruno, P. Veltri, On the occurrence of the third-order scaling in high latitude solar wind. Astrophys. J. 750, 41 (2012). doi: 10.1088/0004-637X/750/1/41 ADSGoogle Scholar
  141. S.A. Markovskii, B.J. Vasquez, C.W. Smith, Statistical analysis of the high-frequency spectral break of the solar wind turbulence at 1 AU. Astrophys. J. 675, 1576–1583 (2008). doi: 10.1086/527431 ADSGoogle Scholar
  142. J. Maron, P. Goldreich, Simulations of incompressible magnetohydrodynamic turbulence. Astrophys. J. 554, 1175–1196 (2001). doi: 10.1086/321413 ADSGoogle Scholar
  143. E. Marsch, Kinetic physics of the solar corona and solar wind. Living Rev. Sol. Phys. 3, 1 (2006). doi: 10.12942/lrsp-2006-1 ADSGoogle Scholar
  144. E. Marsch, S. Bourouaine, Velocity-space diffusion of solar wind protons in oblique waves and weak turbulence. Ann. Geophys. 29, 2089–2099 (2011). doi: 10.5194/angeo-29-2089-2011 ADSGoogle Scholar
  145. E. Marsch, A. Mangeney, Ideal MHD equations in terms of compressive Elsaesser variables. J. Geophys. Res. 92, 7363–7367 (1987). doi: 10.1029/JA092iA07p07363 ADSGoogle Scholar
  146. E. Marsch, C.-Y. Tu, Spectral and spatial evolution of compressible turbulence in the inner solar wind. J. Geophys. Res. 95, 11945–11956 (1990). doi: 10.1029/JA095iA08p11945 ADSGoogle Scholar
  147. E. Marsch, C.-Y. Tu, Evidence for pitch angle diffusion of solar wind protons in resonance with cyclotron waves. J. Geophys. Res. 106, 8357–8362 (2001). doi: 10.1029/2000JA000414 ADSGoogle Scholar
  148. E. Marsch, R. Schwenn, H. Rosenbauer, K.-H. Muehlhaeuser, W. Pilipp, F.M. Neubauer, Solar wind protons—three-dimensional velocity distributions and derived plasma parameters measured between 0.3 and 1 AU. J. Geophys. Res. 87, 52–72 (1982). doi: 10.1029/JA087iA01p00052 ADSGoogle Scholar
  149. L. Matteini, S. Landi, P. Hellinger, F. Pantellini, M. Maksimovic, M. Velli, B.E. Goldstein, E. Marsch, Evolution of the solar wind proton temperature anisotropy from 0.3 to 2.5 AU. Geophys. Res. Lett. 34, 20105 (2007). doi: 10.1029/2007GL030920 ADSGoogle Scholar
  150. L. Matteini, P. Hellinger, S. Landi, P.M. Trávníček, M. Velli Ion kinetics in the solar wind: coupling global expansion to local microphysics. Space Sci. Rev., 128 (2011). doi: 10.1007/s11214-011-9774-z
  151. W.H. Matthaeus, M.L. Goldstein, Low-frequency 1/f noise in the interplanetary magnetic field. Phys. Rev. Lett. 57, 495–498 (1986). doi: 10.1103/PhysRevLett.57.495 ADSGoogle Scholar
  152. W.H. Matthaeus, M. Velli, Who needs turbulence? A review of turbulence effects in the heliosphere and on the fundamental process of reconnection. Space Sci. Rev. 160, 145–168 (2011). doi: 10.1007/s11214-011-9793-9 ADSGoogle Scholar
  153. W.H. Matthaeus, M.L. Goldstein, C. Smith, Evaluation of magnetic helicity in homogeneous turbulence. Phys. Rev. Lett. 48, 1256–1259 (1982). doi: 10.1103/PhysRevLett.48.1256 ADSGoogle Scholar
  154. W.H. Matthaeus, M.L. Goldstein, D.A. Roberts, Evidence for the presence of quasi-two-dimensional nearly incompressible fluctuations in the solar wind. J. Geophys. Res. 95, 20673–20683 (1990). doi: 10.1029/JA095iA12p20673 ADSGoogle Scholar
  155. W.H. Matthaeus, S. Servidio, P. Dmitruk, Comment on “Kinetic simulations of magnetized turbulence in astrophysical plasmas”. Phys. Rev. Lett. 101(14), 149501 (2008). doi: 10.1103/PhysRevLett.101.149501 ADSGoogle Scholar
  156. W.H. Matthaeus, S. Servidio, P. Dmitruk, Dispersive effects of Hall electric field in turbulence. AIP Conf. Proc. 1216, 184–187 (2010). doi: 10.1063/1.3395832 ADSGoogle Scholar
  157. W.H. Matthaeus, S. Servidio, P. Dmitruk, V. Carbone, S. Oughton, M. Wan, K.T. Osman, Local anisotropy, higher order statistics, and turbulence spectra. Astrophys. J. 750, 103 (2012). doi: 10.1088/0004-637X/750/2/103 ADSGoogle Scholar
  158. N. Meyer-Vernet, Basics of the Solar Wind (Cambridge University Press, Cambridge, 2007) Google Scholar
  159. L.J. Milano, W.H. Matthaeus, P. Dmitruk, D.C. Montgomery, Local anisotropy in incompressible magnetohydrodynamic turbulence. Phys. Plasmas 8, 2673–2681 (2001). doi: 10.1063/1.1369658 ADSGoogle Scholar
  160. W.-C. Müller, R. Grappin, Spectral energy dynamics in magnetohydrodynamic turbulence. Phys. Rev. Lett. 95(11), 114502 (2005). doi: 10.1103/PhysRevLett.95.114502 ADSGoogle Scholar
  161. Y. Narita, S.P. Gary, S. Saito, K.-H. Glassmeier, U. Motschmann, Dispersion relation analysis of solar wind turbulence. Geophys. Res. Lett. 38, 5101 (2011). doi: 10.1029/2010GL046588 ADSGoogle Scholar
  162. K.T. Osman, W.H. Matthaeus, A. Greco, S. Servidio, Evidence for inhomogeneous heating in the solar wind. Astrophys. J. 727, 11 (2011). doi: 10.1088/2041-8205/727/1/L11 ADSGoogle Scholar
  163. K.T. Osman, W.H. Matthaeus, B. Hnat, S.C. Chapman, Kinetic signatures and intermittent turbulence in the solar wind plasma. Phys. Rev. Lett. 108(26), 261103 (2012). doi: 10.1103/PhysRevLett.108.261103 ADSGoogle Scholar
  164. M.J. Owens, R.T. Wicks, T.S. Horbury, Magnetic discontinuities in the near-earth solar wind: evidence of in-transit turbulence or remnants of coronal structure? Sol. Phys. 269(2), 411–420 (2011). doi: 10.1007/s11207-010-9695-0 ADSGoogle Scholar
  165. S. Perri, A. Balogh, Differences in solar wind cross-helicity and residual energy during the last two solar minima. Geophys. Res. Lett. 37, 17102 (2010). doi: 10.1029/2010GL044570 ADSGoogle Scholar
  166. S. Perri, V. Carbone, P. Veltri, Where does fluid-like turbulence break down in the solar wind? Astrophys. J. 725, 52–55 (2010). doi: 10.1088/2041-8205/725/1/L52 ADSGoogle Scholar
  167. S. Perri, M.L. Goldstein, J.C. Dorelli, F. Sahraoui, Detection of small-scale structures in the dissipation regime of solar-wind turbulence. Phys. Rev. Lett. 109(19), 191101 (2012). doi: 10.1103/PhysRevLett.109.191101 ADSGoogle Scholar
  168. D. Perrone, F. Valentini, S. Servidio, S. Dalena, P. Veltri, Vlasov simulations of multi-ion plasma turbulence in the solar wind. Astrophys. J. 762, 99 (2013). doi: 10.1088/0004-637X/762/2/99 ADSGoogle Scholar
  169. V.I. Petviashvili, O.A. Pokhotelov, Solitary Waves in Plasmas and in the Atmosphere (Gordon & Breach Science Pub, New York, 1992). ISBN2881247873 zbMATHGoogle Scholar
  170. J. Pietarila Graham, D.D. Holm, P. Mininni, A. Pouquet, Inertial range scaling, Kármán-Howarth theorem, and intermittency for forced and decaying Lagrangian averaged magnetohydrodynamic equations in two dimensions. Phys. Fluids 18(4), 045106 (2006). doi: 10.1063/1.2194966 ADSMathSciNetGoogle Scholar
  171. J.J. Podesta, Dependence of solar-wind power spectra on the direction of the local mean magnetic field. Astrophys. J. 698, 986–999 (2009). doi: 10.1088/0004-637X/698/2/986 ADSGoogle Scholar
  172. J.J. Podesta, On the energy cascade rate of solar wind turbulence in high cross helicity flows. J. Geophys. Res. 116(A15), 05101 (2011). doi: 10.1029/2010JA016306 Google Scholar
  173. J.J. Podesta, S.P. Gary, Magnetic helicity spectrum of solar wind fluctuations as a function of the angle with respect to the local mean magnetic field. Astrophys. J. 734, 15 (2011). doi: 10.1088/0004-637X/734/1/15 ADSGoogle Scholar
  174. J.J. Podesta, D.A. Roberts, M.L. Goldstein, Spectral exponents of kinetic and magnetic energy spectra in solar wind turbulence. Astrophys. J. 664, 543–548 (2007). doi: 10.1086/519211 ADSGoogle Scholar
  175. J.J. Podesta, M.A. Forman, C.W. Smith, D.C. Elton, Y. Malécot, Y. Gagne, Accurate estimation of third-order moments from turbulence measurements. Nonlinear Process. Geophys. 16, 99–110 (2009a). doi: 10.5194/npg-16-99-2009 ADSGoogle Scholar
  176. J.J. Podesta, B.D.G. Chandran, A. Bhattacharjee, D.A. Roberts, M.L. Goldstein, Scale-dependent angle of alignment between velocity and magnetic field fluctuations in solar wind turbulence. J. Geophys. Res. 114(A13), 1107 (2009b). doi: 10.1029/2008JA013504 Google Scholar
  177. H. Politano, A. Pouquet, Von Kármán-Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions. Phys. Rev. E 57, 21 (1998). doi: 10.1103/PhysRevE.57.R21 ADSGoogle Scholar
  178. L. Rezeau, A. Roux, C.T. Russell, Characterization of small-scale structures at the magnetopause from ISEE measurements. J. Geophys. Res. 98(17), 179–186 (1993). doi: 10.1029/92JA01668 ADSGoogle Scholar
  179. O.W. Roberts, X. Li, B. Li, Kinetic plasma turbulence in the fast solar wind measured by cluster. Astrophys. J. 769, 58 (2013). doi: 10.1088/0004-637X/769/1/58 ADSGoogle Scholar
  180. L. Rudakov, M. Mithaiwala, G. Ganguli, C. Crabtree, Linear and nonlinear landau resonance of kinetic Alfvén waves: consequences for electron distribution and wave spectrum in the solar wind. Phys. Plasmas 18(1), 012307 (2011). doi: 10.1063/1.3532819 ADSGoogle Scholar
  181. F. Sahraoui, M.L. Goldstein, G. Belmont, P. Canu, L. Rezeau, Three dimensional anisotropic k spectra of turbulence at subproton scales in the solar wind. Phys. Rev. Lett. 105, 131101 (2010). doi: 10.1103/PhysRevLett.105.131101 ADSGoogle Scholar
  182. F. Sahraoui, G. Belmont, M.L. Goldstein, New Insight into Short-wavelength Solar Wind Fluctuations from Vlasov Theory. Astrophys. J 748(2), 100 (2012) ADSGoogle Scholar
  183. C. Salem, Ondes, turbulence et phénoménes dissipatifs dans le vent solaire à partir des observations de la sonde wind. Ph.D. thesis, Univ. Paris VII (2000) Google Scholar
  184. C. Salem, A. Mangeney, S.D. Bale, P. Veltri, Solar wind magnetohydrodynamics turbulence: anomalous scaling and role of intermittency. Astrophys. J. 702, 537–553 (2009). doi: 10.1088/0004-637X/702/1/537 ADSGoogle Scholar
  185. C.S. Salem, G.G. Howes, D. Sundkvist, S.D. Bale, C.C. Chaston, C.H.K. Chen, F.S. Mozer, Identification of kinetic Alfvén wave turbulence in the solar wind. Astrophys. J. 745, 9 (2012). doi: 10.1088/2041-8205/745/1/L9 ADSGoogle Scholar
  186. A.A. Schekochihin, S.C. Cowley, W. Dorland, G.W. Hammett, G.G. Howes, E. Quataert, T. Tatsuno, Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophys. J. Suppl. Ser. 182, 310–377 (2009). doi: 10.1088/0067-0049/182/1/310 ADSGoogle Scholar
  187. S. Servidio, V. Carbone, L. Primavera, P. Veltri, K. Stasiewicz, Compressible turbulence in Hall magnetohydrodynamics. Planet. Space Sci. 55, 2239–2243 (2007). doi: 10.1016/j.pss.2007.05.023 ADSGoogle Scholar
  188. S. Servidio, P. Dmitruk, A. Greco, M. Wan, S. Donato, P.A. Cassak, M.A. Shay, V. Carbone, W.H. Matthaeus, Magnetic reconnection as an element of turbulence. Nonlinear Process. Geophys. 18, 675–695 (2011). doi: 10.5194/npg-18-675-2011 ADSGoogle Scholar
  189. S. Servidio, F. Valentini, F. Califano, P. Veltri, Local kinetic effects in two-dimensional plasma turbulence. Phys. Rev. Lett. 108(4), 045001 (2012). doi: 10.1103/PhysRevLett.108.045001 ADSGoogle Scholar
  190. J.V. Shebalin, W.H. Matthaeus, D. Montgomery, Anisotropy in MHD turbulence due to a mean magnetic field. J. Plasma Phys. 29, 525–547 (1983). doi: 10.1017/S0022377800000933 ADSGoogle Scholar
  191. C.W. Smith, J. L’Heureux, N.F. Ness, M.H. Acuña, L.F. Burlaga, J. Scheifele, The ACE magnetic fields experiment. Space Sci. Rev. 86, 613–632 (1998). doi: 10.1023/A:1005092216668 ADSGoogle Scholar
  192. C.W. Smith, K. Hamilton, B.J. Vasquez, R.J. Leamon, Dependence of the dissipation range spectrum of interplanetary magnetic fluctuations on the rate of energy cascade. Astrophys. J. 645, 85–88 (2006). doi: 10.1086/506151 ADSGoogle Scholar
  193. C.W. Smith, J.E. Stawarz, B.J. Vasquez, M.A. Forman, B.T. MacBride, Turbulent cascade at 1 AU in high cross-helicity flows. Phys. Rev. Lett. 103(20), 201101 (2009). doi: 10.1103/PhysRevLett.103.201101 ADSGoogle Scholar
  194. C.W. Smith, B.J. Vasquez, J.V. Hollweg, Observational constraints on the role of cyclotron damping and kinetic Alfvén waves in the solar wind. Astrophys. J. 745, 8 (2012). doi: 10.1088/0004-637X/745/1/8 ADSGoogle Scholar
  195. L. Sorriso-Valvo, E. Yordanova, V. Carbone, On the scaling properties of anisotropy of interplanetary magnetic turbulent fluctuations. Europhys. Lett. 90(5), 59001 (2010). doi: 10.1209/0295-5075/90/59001 ADSGoogle Scholar
  196. L. Sorriso-Valvo, V. Carbone, P. Veltri, G. Consolini, R. Bruno, Intermittency in the solar wind turbulence through probability distribution functions of fluctuations. Geophys. Res. Lett. 26, 1801–1804 (1999). doi: 10.1029/1999GL900270 ADSGoogle Scholar
  197. L. Sorriso-Valvo, V. Carbone, P. Giuliani, P. Veltri, R. Bruno, V. Antoni, E. Martines, Intermittency in plasma turbulence. Planet. Space Sci. 49, 1193–1200 (2001). ADSGoogle Scholar
  198. L. Sorriso-Valvo, V. Carbone, A. Noullez, H. Politano, A. Pouquet, P. Veltri, Analysis of cancellation in two-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 9, 89–95 (2002). doi: 10.1063/1.1420738 ADSMathSciNetGoogle Scholar
  199. L. Sorriso-Valvo, R. Marino, V. Carbone, A. Noullez, F. Lepreti, P. Veltri, R. Bruno, B. Bavassano, E. Pietropaolo, Observation of inertial energy cascade in interplanetary space plasma. Phys. Rev. Lett. 99(11), 115001 (2007). doi: 10.1103/PhysRevLett.99.115001 ADSGoogle Scholar
  200. S.R. Spangler, C.R. Gwinn, Evidence for an inner scale to the density turbulence in the interstellar medium. Astrophys. J. 353, 29–32 (1990). doi: 10.1086/185700 ADSGoogle Scholar
  201. J.E. Stawarz, C.W. Smith, B.J. Vasquez, M.A. Forman, B.T. MacBride, The turbulent cascade and proton heating in the solar wind at 1 AU. Astrophys. J. 697, 1119–1127 (2009). doi: 10.1088/0004-637X/697/2/1119 ADSGoogle Scholar
  202. J.E. Stawarz, C.W. Smith, B.J. Vasquez, M.A. Forman, B.T. MacBride, The turbulent cascade for high cross-helicity states at 1 AU. Astrophys. J. 713, 920–934 (2010). doi: 10.1088/0004-637X/713/2/920 ADSGoogle Scholar
  203. J.E. Stawarz, B.J. Vasquez, C.W. Smith, M.A. Forman, J. Klewicki, Third moments and the role of anisotropy from velocity shear in the solar wind. Astrophys. J. 736, 44 (2011). doi: 10.1088/0004-637X/736/1/44 ADSGoogle Scholar
  204. O. Stawicki, S.P. Gary, H. Li, Solar wind magnetic fluctuation spectra: dispersion versus damping. J. Geophys. Res. 106, 8273–8282 (2001). doi: 10.1029/2000JA000446 ADSGoogle Scholar
  205. G.I. Taylor, The spectrum of turbulence. Proc. R. Soc. A 164, 476–490 (1938) ADSGoogle Scholar
  206. J.M. TenBarge, J.J. Podesta, K.G. Klein, G.G. Howes, Interpreting magnetic variance anisotropy measurements in the solar wind. Astrophys. J. 753, 107 (2012). doi: 10.1088/0004-637X/753/2/107 ADSGoogle Scholar
  207. C.-Y. Tu, E. Marsch, MHD structures, waves and turbulence in the solar wind: observations and theories. Space Sci. Rev. 73, 1–2 (1995) ADSGoogle Scholar
  208. A.J. Turner, G. Gogoberidze, S.C. Chapman, B. Hnat, W.-C. Müller, Nonaxisymmetric anisotropy of solar wind turbulence. Phys. Rev. Lett. 107(9), 095002 (2011). doi: 10.1103/PhysRevLett.107.095002 ADSGoogle Scholar
  209. J. Šafránková, Z. Němeček, L. Přech, G.N. Zastenker, Ion kinetic scale in the solar wind observed. Phys. Rev. Lett. 110(2), 025004 (2013). doi: 10.1103/PhysRevLett.110.025004 Google Scholar
  210. B.J. Vasquez, V.I. Abramenko, D.K. Haggerty, C.W. Smith, Numerous small magnetic field discontinuities of Bartels rotation 2286 and the potential role of Alfvénic turbulence. J. Geophys. Res. 112(A11), 11102 (2007). doi: 10.1029/2007JA012504 Google Scholar
  211. P. Veltri, MHD turbulence in the solar wind: self-similarity, intermittency and coherent structures. Plasma Phys. Control. Fusion 41, 787–795 (1999). doi: 10.1088/0741-3335/41/3A/071 ADSGoogle Scholar
  212. P. Veltri, A. Mangeney, Scaling laws and intermittent structures in solar wind MHD turbulence, in Solar Wind Nine, ed. by S.R. Habbal, R. Esser, J.V. Hollweg, P.A. Isenberg. American Institute of Physics Conference Series, vol. 471 (1999), p. 543 Google Scholar
  213. P. Veltri, G. Nigro, F. Malara, V. Carbone, A. Mangeney, Intermittency in MHD turbulence and coronal nanoflares modelling. Nonlinear Process. Geophys. 12, 245–255 (2005). doi: 10.5194/npg-12-245-2005 ADSGoogle Scholar
  214. A. Verdini, R. Grappin, R. Pinto, M. Velli, On the origin of the 1/f spectrum in the solar wind magnetic field. Astrophys. J. 750, 33 (2012). doi: 10.1088/2041-8205/750/2/L33 ADSGoogle Scholar
  215. M. Wan, S. Servidio, S. Oughton, W.H. Matthaeus, The third-order law for increments in magnetohydrodynamic turbulence with constant shear. Phys. Plasmas 16 (2009). doi: 10.1063/1.3240333
  216. M. Wan, W.H. Matthaeus, H. Karimabadi, V. Roytershteyn, M. Shay, P. Wu, W. Daughton, B. Loring, S.C. Chapman, Intermittent dissipation at kinetic scales in collisionless plasma turbulence. Phys. Rev. Lett. 109(19), 195001 (2012). doi: 10.1103/PhysRevLett.109.195001 ADSGoogle Scholar
  217. R.T. Wicks, T.S. Horbury, C.H.K. Chen, A.A. Schekochihin, Power and spectral index anisotropy of the entire inertial range of turbulence in the fast solar wind. Mon. Not. R. Astron. Soc. 407, 31–35 (2010). doi: 10.1111/j.1745-3933.2010.00898.x ADSGoogle Scholar
  218. R.T. Wicks, T.S. Horbury, C.H.K. Chen, A.A. Schekochihin, Anisotropy of imbalanced Alfvénic turbulence in fast solar wind. Phys. Rev. Lett. 106, 045001 (2011). doi: 10.1103/PhysRevLett.106.045001 ADSGoogle Scholar
  219. R.T. Wicks, A. Mallet, T.S. Horbury, C.H.K. Chen, A.A. Schekochihin, J.J. Mitchell, Alignment and scaling of large-scale fluctuations in the solar wind. Phys. Rev. Lett. 110(2), 025003 (2013). doi: 10.1103/PhysRevLett.110.025003 ADSGoogle Scholar
  220. P. Wu, S. Perri, K. Osman, M. Wan, W.H. Matthaeus, M.A. Shay, M.L. Goldstein, H. Karimabadi, S. Chapman, Intermittent heating in solar wind and kinetic simulations. Astrophys. J. 763, 30 (2013). doi: 10.1088/2041-8205/763/2/L30 ADSGoogle Scholar
  221. A.M. Yaglom, O lokalnoi strukture polya temperatur v turbulentnom potoke. Dokl. Akad. Nauk SSSR 69, 743–746 (1949) zbMATHMathSciNetGoogle Scholar
  222. S. Yao, J.-S. He, E. Marsch, C.-Y. Tu, A. Pedersen, H. Rème, J.G. Trotignon, Multi-scale anti-correlation between electron density and magnetic field strength in the solar wind. Astrophys. J. 728, 146 (2011). doi: 10.1088/0004-637X/728/2/146 ADSGoogle Scholar
  223. V. Zhdankin, S. Boldyrev, J. Mason, J.C. Perez, Magnetic discontinuities in magnetohydrodynamic turbulence and in the solar wind. Phys. Rev. Lett. 108(17), 175004 (2012). doi: 10.1103/PhysRevLett.108.175004 ADSGoogle Scholar

Copyright information

© The Author(s) 2013

Authors and Affiliations

  • O. Alexandrova
    • 1
  • C. H. K. Chen
    • 2
  • L. Sorriso-Valvo
    • 2
    • 3
  • T. S. Horbury
    • 4
  • S. D. Bale
    • 2
  1. 1.LESIAObservatoire de ParisMeudonFrance
  2. 2.Space Sciences LaboratoryUniversity of CaliforniaBerkeleyUSA
  3. 3.IPCF/CNR, UOS di CosenzaRendeItaly
  4. 4.The Blackett LaboratoryImperial College LondonLondonUK

Personalised recommendations