Space Science Reviews

, Volume 178, Issue 2–4, pp 665–693 | Cite as

Methods for Characterising Microphysical Processes in Plasmas

  • T. Dudok de WitEmail author
  • O. Alexandrova
  • I. Furno
  • L. Sorriso-Valvo
  • G. Zimbardo


Advanced spectral and statistical data analysis techniques have greatly contributed to shaping our understanding of microphysical processes in plasmas. We review some of the main techniques that allow for characterising fluctuation phenomena in geospace and in laboratory plasma observations. Special emphasis is given to the commonalities between different disciplines, which have witnessed the development of similar tools, often with differing terminologies. The review is phrased in terms of few important concepts: self-similarity, deviation from self-similarity (i.e. intermittency and coherent structures), wave-turbulence, and anomalous transport.


Plasma turbulence Plasma fluctuations Data analysis methods 



We all thank the International Space Science Institute (ISSI, Bern) for hospitality. In preparing this review we made extensive use of NASA’s Astrophysics Data System.


  1. P. Abry, P. Goncalves, P. Flandrin, Wavelets, spectrum analysis and 1/f processes, in Wavelets in Statistics, ed. by A. Antoniadis, G. Oppenheim. Lecture Notes in Statistics, vol. 103 (Springer, Berlin, 1995), pp. 15–30 Google Scholar
  2. M. Agostini, P. Scarin, R. Cavazzana, F. Sattin, G. Serianni, M. Spolaore, N. Vianello, Edge turbulence characterization in RFX-mod with optical diagnostics. Plasma Phys. Control. Fusion 51(10), 105003 (2009). doi: 10.1088/0741-3335/51/10/105003 ADSGoogle Scholar
  3. A.I. Akhiezer, I.A. Akhiezer, R.V. Polovin, A.G. Sitenko, K.N. Stepanov, Plasma Electrodynamics. Volume 1—Linear Theory. Oxford Pergamon Press International Series on Natural Philosophy, vol. 1 (1975) Google Scholar
  4. A.I. Akhiezer, I.A. Akhiezer, R.V. Polovin, A.G. Sitenko, K.N. Stepanov, Plasma Electrodynamics. Volume 2—Non-Linear Theory and Fluctuations. Oxford Pergamon Press International Series on Natural Philosophy, vol. 1 (1975) Google Scholar
  5. O. Alexandrova, Solar wind vs magnetosheath turbulence and Alfvén vortices. Nonlinear Process. Geophys. 15, 95–108 (2008) ADSGoogle Scholar
  6. O. Alexandrova, J. Saur, Alfvén vortices in Saturn’s magnetosheath: cassini observations. Geophys. Res. Lett. 35, 15102 (2008). doi: 10.1029/2008GL034411 ADSGoogle Scholar
  7. 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
  8. 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. (Space Phys.) 111(A10), 12208 (2006). doi: 10.1029/2006JA011934 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. P. Amblard, S. Moussaoui, T. Dudok de Wit, J. Aboudarham, M. Kretzschmar, J. Lilensten, F. Auchère, The EUV Sun as the superposition of elementary Suns. Astron. Astrophys. 487, 13–16 (2008). doi: 10.1051/0004-6361:200809588 ADSGoogle Scholar
  11. G.Y. Antar, On the origin of “intermittency” in the scrape-off layer of linear magnetic confinement devices. Phys. Plasmas 10, 3629–3634 (2003). doi: 10.1063/1.1599855 ADSGoogle Scholar
  12. G.Y. Antar, P. Devynck, X. Garbet, S.C. Luckhardt, Turbulence intermittency and burst properties in tokamak scrape-off layer. Phys. Plasmas 8, 1612–1624 (2001). doi: 10.1063/1.1363663 ADSGoogle Scholar
  13. M. Anton, H. Weisen, M.J. Dutch, W. von der Linden, F. Buhlmann, R. Chavan, B. Marlétaz, P. Marmillod, P. Paris, X-ray tomography on the TCV tokamak. Plasma Phys. Control. Fusion 38, 1849–1878 (1996). doi: 10.1088/0741-3335/38/11/001 ADSGoogle Scholar
  14. M.J. Aschwanden, Solar image processing techniques with automated feature recognition. Sol. Phys. 262(2), 235–275 (2010). doi: 10.1007/s11207-009-9474-y ADSGoogle Scholar
  15. M.J. Aschwanden, Solar stereoscopy and tomography. Living Rev. Sol. Phys. 8(5) (2011).
  16. R. Badii, A. Politi, Complexity. Cambridge Nonlinear Science Series, vol. 6 (Cambridge Univeristy Press, Cambridge, 1999) zbMATHGoogle Scholar
  17. D.N. Baker, Statistical analyses in the study of solar wind/magnetosphere coupling, in Astrophysics and Space Science Library, ed. by Y. Kamide, J.A. Slavin. Astrophysics and Space Science Library, vol. 126 (1986), pp. 17–38 Google Scholar
  18. S.D. Bale, P.J. Kellogg, F.S. Mozer, T.S. Horbury, H. Rème, Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 94(21), 215002 (2005). doi: 10.1103/PhysRevLett.94.215002 ADSGoogle Scholar
  19. J.M. Beall, Y.C. Kim, E.J. Powers, Estimation of wavenumber and frequency spectra using fixed probe pairs. J. Appl. Phys. 53, 3933–3940 (1982). doi: 10.1063/1.331279 ADSGoogle Scholar
  20. N. Ben Ayed, A. Kirk, B. Dudson, S. Tallents, R.G.L. Vann, H.R. Wilson, M. Team, Inter-ELM filaments and turbulent transport in the mega-amp spherical tokamak. Plasma Phys. Control. Fusion 51(3), 035016 (2009). doi: 10.1088/0741-3335/51/3/035016 ADSGoogle Scholar
  21. S. Benkadda, P. Gabbai, G.M. Zaslavsky, Passive particle dynamics in a flow exhibiting transition to turbulence. Phys. Plasmas 4, 2864–2870 (1997). doi: 10.1063/1.872577 MathSciNetADSGoogle Scholar
  22. S. Benkadda, T. Dudok de Wit, A. Verga, A. Sen, X. Garbet, Characterization of coherent structures in tokamak edge turbulence. Phys. Rev. Lett. 73, 3403–3406 (1994). doi: 10.1103/PhysRevLett.73.3403 ADSGoogle Scholar
  23. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, S. Succi, Extended self-similarity in turbulent flows. Phys. Rev. E 48, 29 (1993). doi: 10.1103/PhysRevE.48.R29 ADSGoogle Scholar
  24. D. Biskamp, Magnetohydrodynamic Turbulence (Cambridge University Press, Cambridge, 2003) zbMATHGoogle Scholar
  25. T. Bohr, M.H. Jensen, G. Paladin, A. Vulpiani, Dynamical Systems Approach to Turbulence. Cambridge Nonlinear Science Series, vol. 8 (Cambridge Univeristy Press, Cambridge, 2005) zbMATHGoogle Scholar
  26. J.E. Borovsky, M.H. Denton, Solar wind turbulence and shear: a superposed-epoch analysis of corotating interaction regions at 1 AU. J. Geophys. Res. (Space Phys.) 115, 10101 (2010). doi: 10.1029/2009JA014966 ADSGoogle Scholar
  27. R. Bruno, V. Carbone, The solar wind as a turbulence laboratory. Living Rev. Sol. Phys. 2, 4 (2005) ADSGoogle Scholar
  28. G.S. Bust, C.N. Mitchell, History, current state, and future directions of ionospheric imaging. Rev. Geophys. 46, 1003 (2008). doi: 10.1029/2006RG000212 ADSGoogle Scholar
  29. M.D. Butala, R.J. Hewett, R.A. Frazin, F. Kamalabadi, Dynamic three-dimensional tomography of the solar corona. Sol. Phys. 262, 495–509 (2010). doi: 10.1007/s11207-010-9536-1 ADSGoogle Scholar
  30. V. Carbone, Scaling exponents of the velocity structure functions in the interplanetary medium. Ann. Geophys. 12(7), 585–590 (1994). doi: 10.1007/s00585-994-0585-3 ADSGoogle Scholar
  31. V. Carbone, R. Bruno, P. Veltri, Evidences for extended self-similarity in hydromagnetic turbulence. Geophys. Res. Lett. 23, 121–124 (1996). doi: 10.1029/95GL03777 ADSGoogle Scholar
  32. V. Carbone, L. Sorriso-Valvo, E. Martines, V. Antoni, P. Veltri, Intermittency and turbulence in a magnetically confined fusion plasma. Phys. Rev. E 62, 49–56 (2000) ADSGoogle Scholar
  33. V. Carbone, F. Lepreti, L. Sorriso-Valvo, P. Veltri, V. Antoni, R. Bruno, Scaling laws in plasma turbulence. Nuovo Cimento Riv. Ser. 27(8), 1–108 (2004). doi: 10.1393/ncr/i2005-10003-1 Google Scholar
  34. B.A. Carreras, V.E. Lynch, G.M. Zaslavsky, Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model. Phys. Plasmas 8, 5096–5103 (2001). doi: 10.1063/1.1416180 ADSGoogle Scholar
  35. B.A. Carreras, B.P. van Milligen, M.A. Pedrosa, R. Balbín, C. Hidalgo, D.E. Newman, E. Sánchez, M. Frances, I. García-Cortés, J. Bleuel, M. Endler, C. Riccardi, S. Davies, G.F. Matthews, E. Martines, V. Antoni, A. Latten, T. Klinger, Self-similarity of the plasma edge fluctuations. Phys. Plasmas 5, 3632–3643 (1998). doi: 10.1063/1.873081 ADSGoogle Scholar
  36. S.C. Chapman, R.M. Nicol, Generalized similarity in finite range solar wind magnetohydrodynamic turbulence. Phys. Rev. Lett. 103(24), 241101 (2009). doi: 10.1103/PhysRevLett.103.241101 ADSGoogle Scholar
  37. A.C.-L. Chian, R.A. Miranda, Cluster and ACE observations of phase synchronization in intermittent magnetic field turbulence: a comparative study of shocked and unshocked solar wind. Ann. Geophys. 27, 1789–1801 (2009). doi: 10.5194/angeo-27-1789-2009 ADSGoogle Scholar
  38. N. Christlieb, L. Wisotzki, G. Graßhoff, Statistical methods of automatic spectral classification and their application to the Hamburg/ESO survey. Astron. Astrophys. 391, 397–406 (2002). doi: 10.1051/0004-6361:20020830 ADSGoogle Scholar
  39. A. Clauset, C. Rohilla Shalizi, M.E.J. Newman, Power-law distributions in empirical data. SIAM Rev. 51, 661–703 (2009). doi: 10.1137/070710111 MathSciNetADSzbMATHGoogle Scholar
  40. A. Diallo, A. Fasoli, I. Furno, B. Labit, M. Podestà, C. Theiler, Dynamics of plasma blobs in a shear flow. Phys. Rev. Lett. 101(11), 115005 (2008). doi: 10.1103/PhysRevLett.101.115005 ADSGoogle Scholar
  41. A. Dinklage, C. Wilke, G. Bonhomme, A. Atipo, Internally driven spatiotemporal irregularity in a dc glow discharge. Phys. Rev. E 62, 7219–7226 (2000). doi: 10.1103/PhysRevE.62.7219 ADSGoogle Scholar
  42. D.A. D’Ippolito, J.R. Myra, S.J. Zweben, Convective transport by intermittent blob-filaments: comparison of theory and experiment. Phys. Plasmas 18(6), 060501 (2011). doi: 10.1063/1.3594609 Google Scholar
  43. T. Dudok de Wit, Spectral and statistical analysis of plasma turbulence: beyond linear techniques, in Space Plasma Simulation, ed. by J. Büchner, C. Dum, M. Scholer. Lecture Notes in Physics, vol. 615 (Springer, Berlin, 2003), pp. 315–343 Google Scholar
  44. T. Dudok de Wit, Can high-order moments be meaningfully estimated from experimental turbulence measurements? Phys. Rev. E 70(5), 055302 (2004). doi: 10.1103/PhysRevE.70.055302 ADSGoogle Scholar
  45. T. Dudok de Wit, Extracting individual contributions from their mixture: a blind source separation approach. Contrib. Plasma Phys. 51(2–3), 143–151 (2011). doi: 10.1002/ctpp.201000052 ADSGoogle Scholar
  46. T. Dudok de Wit, A. Pecquet, J. Vallet, R. Lima, The biorthogonal decomposition as a tool for investigating fluctuations in plasmas. Phys. Plasmas 1, 3288–3300 (1994). doi: 10.1063/1.870481 ADSGoogle Scholar
  47. T. Dudok de Wit, V.V. Krasnosel’skikh, S.D. Bale, M.W. Dunlop, H. Lühr, S.J. Schwartz, L.J.C. Woolliscroft, Determination of dispersion relations in quasi-stationary plasma turbulence using dual satellite data. Geophys. Res. Lett. 22, 2653–2656 (1995). doi: 10.1029/95GL02543 ADSGoogle Scholar
  48. T. Dudok de Wit, V.V. Krasnosel’skikh, M. Dunlop, H. Lühr, Identifying nonlinear wave interactions in plasmas using two-point measurements: a case study of short large amplitude magnetic structures (SLAMS). J. Geophys. Res. 104, 17079–17090 (1999). doi: 10.1029/1999JA900134 ADSGoogle Scholar
  49. B.D. Dudson, R.O. Dendy, A. Kirk, H. Meyer, G.F. Counsell, Comparison of L- and H-mode plasma edge fluctuations in MAST. Plasma Phys. Control. Fusion 47, 885–901 (2005). doi: 10.1088/0741-3335/47/6/010 ADSGoogle Scholar
  50. M.W. Dunlop, R. Bingham, S. Chapman, P. Escoubet, Q. Zhang, C. Shen, J. Shi, R. Trines, R. Wicks, Z. Pu, J. de-Keyser, S. Schwartz, Z. Liu, Use of multi-point analysis and modelling to address cross-scale coupling in space plasmas: lessons from cluster. Planet. Space Sci. 59, 630–638 (2011). doi: 10.1016/j.pss.2010.06.014 ADSGoogle Scholar
  51. A.I. Eriksson, Spectral analysis, in Analysis Methods for Multi-Spacecraft Data, ed. by G. Paschmann, P.W. Daly. ISSI Scientific Report SR-01, vol. 1, Amsterdam (1998), pp. 5–42 Google Scholar
  52. M. Farge, Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24, 395–457 (1992). doi: 10.1146/annurev.fl.24.010192.002143 MathSciNetADSGoogle Scholar
  53. M. Farge, G. Pellegrino, K. Schneider, Coherent vortex extraction in 3D turbulent flows using orthogonal wavelets. Phys. Rev. Lett. 87(5), 054501 (2001). doi: 10.1103/PhysRevLett.87.054501 ADSGoogle Scholar
  54. M. Farge, K. Schneider, P. Devynck, Extraction of coherent bursts from turbulent edge plasma in magnetic fusion devices using orthogonal wavelets. Phys. Plasmas 13(4), 042304 (2006). doi: 10.1063/1.2172350 ADSGoogle Scholar
  55. M. Farge, N.K.-R. Kevlahan, V. Perrier, K. Schneider, Turbulence analysis, modelling and computing using wavelets, in Wavelets in Physics, ed. by J.C. van den Berg (Cambridge University Press, Cambridge, 2004), p. 117. Chap. 4 Google Scholar
  56. A. Fasoli, A. Burckel, L. Federspiel, I. Furno, K. Gustafson, D. Iraji, B. Labit, J. Loizu, G. Plyushchev, P. Ricci, C. Theiler, A. Diallo, S.H. Mueller, M. Podesta, F. Poli, Electrostatic instabilities, turbulence and fast ion interactions in the TORPEX device. Plasma Phys. Control. Fusion 52(12, Part 2), 124020 (2010). doi: 10.1088/0741-3335/52/12/124020 ADSGoogle Scholar
  57. L. Fattorini, Å. Fredriksen, H.L. Pécseli, C. Riccardi, J.K. Trulsen, Turbulent transport in a toroidal magnetized plasma. Plasma Phys. Control. Fusion 54(8), 085017 (2012). doi: 10.1088/0741-3335/54/8/085017 ADSGoogle Scholar
  58. U. Frisch, Turbulence, the Legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, 1995) zbMATHGoogle Scholar
  59. A. Fujisawa, A review—observations of turbulence and structure in magnetized plasmas. J. Plasma Fusion Res. 5, 46 (2010). doi: 10.1585/pfr.5.046 ADSGoogle Scholar
  60. I. Furno, B. Labit, M. Podestà, A. Fasoli, S.H. Müller, F.M. Poli, P. Ricci, C. Theiler, S. Brunner, A. Diallo, J. Graves, Experimental observation of the blob-generation mechanism from interchange waves in a plasma. Phys. Rev. Lett. 100(5), 055004 (2008). doi: 10.1103/PhysRevLett.100.055004 ADSGoogle Scholar
  61. M.K. Georgoulis, Turbulence in the solar atmosphere: manifestations and diagnostics via solar image processing. Sol. Phys. 228, 5–27 (2005). doi: 10.1007/s11207-005-2513-4 ADSGoogle Scholar
  62. J. Giacalone, Large-scale hybrid simulations of particle acceleration at a parallel shock. Astrophys. J. 609, 452–458 (2004). doi: 10.1086/421043 ADSGoogle Scholar
  63. J. Giacalone, Cosmic-ray transport and interaction with shocks. Space Sci. Rev., 117 (2011). doi: 10.1007/s11214-011-9763-2
  64. M. Gilmore, C.X. Yu, T.L. Rhodes, W.A. Peebles, Investigation of rescaled range analysis, the Hurst exponent, and long-time correlations in plasma turbulence. Phys. Plasmas 9, 1312–1317 (2002). doi: 10.1063/1.1459707 ADSGoogle Scholar
  65. T. Goodman, S. Ahmed, S. Alberti, Y. Andrebe, C. Angioni, K. Appert, G. Arnoux, R. Belm, P. Blanchard, P. Bosshard, Y. Camenen, R. Chavan, S. Coda, I. Condrea, A. Degeling, B. Duval, P. Etienne, D. Fasel, A. Fasoli, J. Favez, I. Furno, M. Henderson, F. Hofmann, J. Hogge, J. Horacek, P. Isoz, B. Joye, A. Karpushov, I. Klimanov, P. Lavanchy, J. Lister, X. Llobet, J. Magnin, A. Manini, B. Marletaz, P. Marmillod, Y. Martin, A. Martynov, J. Mayor, J. Mlynar, J. Moret, E. Nelson-Melby, P. Nikkola, P. Paris, A. Perez, Y. Peysson, R. Pitts, A. Pochelon, L. Porte, D. Raju, H. Reimerdes, O. Sauter, A. Scarabosio, E. Scavino, S. Seo, U. Siravo, A. Sushkov, G. Tonetti, M. Tran, H. Weisen, M. Wischmeier, A. Zabolotsky, G. Zhuang, An overview of results from the TCV tokamak. Nucl. Fusion 43(12), 1619–1631 (2003). doi: 10.1088/0029-5515/43/12/008 ADSGoogle Scholar
  66. A. Greco, P. Chuychai, W.H. Matthaeus, S. Servidio, P. Dmitruk, Intermittent MHD structures and classical discontinuities. Geophys. Res. Lett. 35, 19111 (2008). doi: 10.1029/2008GL035454 ADSGoogle Scholar
  67. 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. Lett. 691, 111–114 (2009a). doi: 10.1088/0004-637X/691/2/L111 ADSGoogle Scholar
  68. A. Greco, W.H. Matthaeus, S. Servidio, P. Dmitruk, Waiting-time distributions of magnetic discontinuities: clustering or Poisson process? Phys. Rev. E 80(4), 046401 (2009b). doi: 10.1103/PhysRevE.80.046401 ADSGoogle Scholar
  69. 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
  70. O. Grulke, J. Terry, B. LaBombard, S. Zweben, Radially propagating fluctuation structures in the scrape-off layer of Alcator C-Mod. Phys. Plasmas 13(1), 012306 (2006). doi: 10.1063/1.2164991 ADSGoogle Scholar
  71. K. Gustafson, P. Ricci, I. Furno, A. Fasoli, Nondiffusive suprathermal ion transport in simple magnetized toroidal plasmas. Phys. Rev. Lett. 108(3), 035006 (2012). doi: 10.1103/PhysRevLett.108.035006 ADSGoogle Scholar
  72. S. Haaland, B.U.Ö. Sonnerup, M.W. Dunlop, E. Georgescu, G. Paschmann, B. Klecker, A. Vaivads, Orientation and motion of a discontinuity from cluster curlometer capability: minimum variance of current density. Geophys. Res. Lett. 31, 10804 (2004). doi: 10.1029/2004GL020001 ADSGoogle Scholar
  73. T. Hada, D. Koga, E. Yamamoto, Phase coherence of MHD waves in the solar wind. Space Sci. Rev. 107, 463–466 (2003). doi: 10.1023/A:1025506124402 ADSGoogle Scholar
  74. K. Hayashi, M. Kojima, M. Tokumaru, K. Fujiki, MHD tomography using interplanetary scintillation measurement. J. Geophys. Res. (Space Phys.) 108, 1102 (2003). doi: 10.1029/2002JA009567 ADSGoogle Scholar
  75. 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
  76. B. Hnat, B.D. Dudson, R.O. Dendy, G.F. Counsell, A. Kirk, MAST Team, Characterization of edge turbulence in relation to edge magnetic field configuration in ohmic L-mode plasmas in the mega amp spherical tokamak. Nucl. Fusion 48(8), 085009 (2008). doi: 10.1088/0029-5515/48/8/085009 ADSGoogle Scholar
  77. M. Hoppe, C.T. Russell, Whistler mode wave packets in the Earth’s foreshock region. Nature 287, 417–420 (1980). doi: 10.1038/287417a0 ADSGoogle Scholar
  78. T. Horbury, R. Wicks, C. Chen, Anisotropy in space plasma turbulence: solar wind observations. Space Sci. Rev. 172, 325–342 (2012). doi: 10.1007/s11214-011-9821-9 Google Scholar
  79. T. Huld, A.H. Nielsen, H.L. Pécseli, J.J. Rasmussen, Coherent structures in two-dimensional plasma turbulence. Phys. Fluids B 3, 1609–1625 (1991). doi: 10.1063/1.859680 ADSGoogle Scholar
  80. K.-J. Hwang, M.L. Goldstein, M.M. Kuznetsova, Y. Wang, A.F. Viñas, D.G. Sibeck, The first in situ observation of Kelvin-Helmholtz waves at high-latitude magnetopause during strongly dawnward interplanetary magnetic field conditions. J. Geophys. Res. (Space Phys.) 117, 8233 (2012). doi: 10.1029/2011JA017256 ADSGoogle Scholar
  81. D. Iraji, I. Furno, A. Fasoli, C. Theiler, Imaging of turbulent structures and tomographic reconstruction of TORPEX plasma emissivity. Phys. Plasmas 17, 122304 (2010). doi: 10.1063/1.3523052 ADSGoogle Scholar
  82. B.V. Jackson, P.P. Hick, A. Buffington, M.M. Bisi, J.M. Clover, M. Tokumaru, M. Kojima, K. Fujiki, Three-dimensional reconstruction of heliospheric structure using iterative tomography: a review. J. Atmos. Sol.-Terr. Phys. 73, 1214–1227 (2011). doi: 10.1016/j.jastp.2010.10.007 ADSGoogle Scholar
  83. H. Johnsen, H.L. Pécseli, J. Trulsen, Conditional eddies in plasma turbulence. Phys. Fluids 30, 2239–2254 (1987). doi: 10.1063/1.866158 ADSGoogle Scholar
  84. H. Kantz, T. Schreiber, Nonlinear Time Series Analysis, 2nd edn. Cambridge Nonlinear Science Series, vol. 7 (Cambridge University Press, Cambridge, 2000) Google Scholar
  85. N. Katz, J. Egedal, W. Fox, A. Le, M. Porkolab, Experiments on the propagation of plasma filaments. Phys. Rev. Lett. 101(1), 015003 (2008). doi: 10.1103/PhysRevLett.101.015003 ADSGoogle Scholar
  86. C.F. Kennel, H.E. Petschek, Limit on stably trapped particle fluxes. J. Geophys. Res. 71, 1 (1966) ADSGoogle Scholar
  87. L. Kersley, S.E. Pryse, I.K. Walker, J.A.T. Heaton, C.N. Mitchell, M.J. Williams, C.A. Willson, Imaging of electron density troughs by tomographic techniques. Radio Sci. 32(4), 1607–1621 (1997). doi: 10.1029/97RS00310 ADSGoogle Scholar
  88. Y. Khotyaintsev, S. Buchert, K. Stasiewicz, A. Vaivads, S. Savin, V.O. Papitashvili, C.J. Farrugia, B. Popielawska, Y.-K. Tung, Transient reconnection in the cusp during strongly negative IMF By. J. Geophys. Res. (Space Phys.) 109, 4204 (2004). doi: 10.1029/2003JA009908 ADSGoogle Scholar
  89. J.S. Kim, R.J. Fonck, R.D. Durst, E. Fernandez, P.W. Terry, S.F. Paul, M.C. Zarnstorff, Measurements of nonlinear energy transfer in turbulence in the tokamak fusion test reactor. Phys. Rev. Lett. 79, 841–844 (1997). doi: 10.1103/PhysRevLett.79.841 ADSGoogle Scholar
  90. J.S. Kim, D.H. Edgell, J.M. Greene, E.J. Strait, M.S. Chance, MHD mode identification of tokamak plasmas from Mirnov signals. Plasma Phys. Control. Fusion 41, 1399–1420 (1999). doi: 10.1088/0741-3335/41/11/307 ADSGoogle Scholar
  91. Y.C. Kim, E.J. Powers, Digital bispectral analysis and its applications to nonlinear wave interactions. IEEE Trans. Plasma Sci. PS-7, 120–131 (1979) ADSGoogle Scholar
  92. A. Kirk, N. Ben Ayed, G. Counsell, B. Dudson, T. Eich, A. Herrmann, B. Koch, R. Martin, A. Meakins, S. Saarelma, R. Scannell, S. Tallents, M. Walsh, H.R. Wilson, M. Team, Filament structures at the plasma edge on MAST. Plasma Phys. Control. Fusion 48(12B, SI), 433–441 (2006). doi: 10.1088/0741-3335/48/12B/S41 Google Scholar
  93. K.H. Kiyani, S.C. Chapman, N.W. Watkins, Pseudononstationarity in the scaling exponents of finite-interval time series. Phys. Rev. E 79(3), 036109 (2009). doi: 10.1103/PhysRevE.79.036109 ADSGoogle Scholar
  94. 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
  95. K. Kiyani, S.C. Chapman, B. Hnat, R.M. Nicol, Self-similar signature of the active solar corona within the inertial range of solar-wind turbulence. Phys. Rev. Lett. 98(21), 211101 (2007). doi: 10.1103/PhysRevLett.98.211101 ADSGoogle Scholar
  96. A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305 (1941). Reprinted in Proc. R. Soc. Lond., Ser. A 434, 9–13 (1991) ADSGoogle Scholar
  97. A.N. Kolmogorov, A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82–85 (1962). doi: 10.1017/S0022112062000518 MathSciNetADSzbMATHGoogle Scholar
  98. S.I. Krasheninnikov, D.A. D’Ippolito, J.R. Myra, Recent theoretical progress in understanding coherent structures in edge and SOL turbulence. J. Plasma Phys. 74, 679–717 (2008) ADSGoogle Scholar
  99. V. Kravtchenko-Berejnoi, F. Lefeuvre, V. Krasnoselskikh, D. Lagoutte, On the use of tricoherent analysis to detect non-linear wave-wave interactions. Signal Process. 42(3), 291–309 (1995). doi: 10.1016/0165-1684(94)00136-N zbMATHGoogle Scholar
  100. A. Lazurenko, G. Coduti, S. Mazouffre, G. Bonhomme, Dispersion relation of high-frequency plasma oscillations in hall thrusters. Phys. Plasmas 15(3), 034502 (2008). doi: 10.1063/1.2889424 ADSGoogle Scholar
  101. M.P. Leubner, Z. Vörös, A nonextensive entropy approach to solar wind intermittency. Astrophys. J. 618(1), 547 (2005). doi: 10.1086/425893 ADSGoogle Scholar
  102. R.P. Lin, Non-relativistic solar electrons. Space Sci. Rev. 16, 189–256 (1974). doi: 10.1007/BF00240886 ADSGoogle Scholar
  103. E.T. Lundberg, P.M. Kintner, S.P. Powell, K.A. Lynch, Multipayload interferometric wave vector determination of auroral hiss. J. Geophys. Res. (Space Phys.) 117, 2306 (2012). doi: 10.1029/2011JA017037 ADSGoogle Scholar
  104. A. Madon, T. Klinger, Spatio-temporal bifurcations in plasma drift-waves. Physica D 91(3), 301–316 (1996). doi: 10.1016/0167-2789(95)00266-9 zbMATHGoogle Scholar
  105. 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
  106. A. Manini, J. Moret, F. Ryter, the ASDEX Upgrade Team, Signal processing techniques based on singular value decomposition applied to modulated ECH experiments. Nucl. Fusion 43, 490–511 (2003). doi: 10.1088/0029-5515/43/6/312 ADSGoogle Scholar
  107. R.J. Maqueda, D.P. Stotler, N. Team, Intermittent divertor filaments in the national spherical torus experiment and their relation to midplane blobs. Nucl. Fusion 50(7), 075002 (2010). doi: 10.1088/0029-5515/50/7/075002 ADSGoogle Scholar
  108. E. Marsch, C.-Y. Tu, Intermittency, non-Gaussian statistics and fractal scaling of MHD fluctuations in the solar wind. Nonlinear Process. Geophys. 4, 101–124 (1997) ADSGoogle Scholar
  109. W.H. Matthaeus, M.L. Goldstein, Stationarity of magnetohydrodynamic fluctuations in the solar wind. J. Geophys. Res. (Space Phys.) 87, 10347–10354 (1982). doi: 10.1029/JA087iA12p10347 ADSGoogle Scholar
  110. W.H. Matthaeus, M. Velli, Who needs turbulence? Space Sci. Rev. 160(1–4), 145–168 (2011). doi: 10.1007/s11214-011-9793-9 ADSGoogle Scholar
  111. N. Meunier, J. Zhao, Observations of photospheric dynamics and magnetic fields: from large-scale to small-scale flows. Space Sci. Rev. 144, 127–149 (2009). doi: 10.1007/s11214-008-9472-7 ADSGoogle Scholar
  112. J.A. Mier, R. Sánchez, L. García, B.A. Carreras, D.E. Newman, Characterization of nondiffusive transport in plasma turbulence via a novel Lagrangian method. Phys. Rev. Lett. 101, 165001 (2008). doi: 10.1103/PhysRevLett.101.165001 ADSGoogle Scholar
  113. S.H. Müller, A. Diallo, A. Fasoli, I. Furno, B. Labit, G. Plyushchev, M. Podestà, F.M. Poli, Probabilistic analysis of turbulent structures from two-dimensional plasma imaging. Phys. Plasmas 13(10), 100701 (2006). doi: 10.1063/1.2351960 Google Scholar
  114. S.L. Musher, A.M. Rubenchik, V.E. Zakharov, Weak langmuir turbulence. Phys. Rep. 252, 177–274 (1995). doi: 10.1016/0370-1573(94)00071-A ADSGoogle Scholar
  115. J.F. Muzy, E. Bacry, A. Arneodo, Multifractal formalism for fractal signals: the structure-function approach versus the wavelet-transform modulus-maxima method. Phys. Rev. E 47, 875–884 (1993). doi: 10.1103/PhysRevE.47.875 ADSGoogle Scholar
  116. C. Nardone, Multichannel fluctuation data analysis by the singular value decomposition method. Application to MHD modes in JET. Plasma Phys. Control. Fusion 34(9), 1447 (1992). doi: 10.1088/0741-3335/34/9/001 ADSGoogle Scholar
  117. D.E. Newman, B.A. Carreras, P.H. Diamond, T.S. Hahm, The dynamics of marginality and self-organized criticality as a paradigm for turbulent transport. Phys. Plasmas 3, 1858–1866 (1996). doi: 10.1063/1.871681 ADSGoogle Scholar
  118. R. Nguyen van yen, D. del-Castillo-Negrete, K. Schneider, M. Farge, G. Chen, Wavelet-based density estimation for noise reduction in plasma simulations using particles. J. Comput. Phys. 229(8), 2821–2839 (2010). doi: 10.1016/ MathSciNetADSzbMATHGoogle Scholar
  119. S. Niedner, H.-G. Schuster, T. Klinger, G. Bonhomme, Symmetry breaking in ionization wave turbulence. Phys. Rev. E 59, 52–59 (1999). doi: 10.1103/PhysRevE.59.52 ADSGoogle Scholar
  120. G. Paschmann, P.W. Daly (eds.), Analysis Methods for Multi-spacecraft Data, 2nd edn. ISSI Scientific Report SR-001 (Springer, Amsterdam, 2000). Google Scholar
  121. G. Paschmann, P.W. Daly (eds.), Multi-Spacecraft Analysis Methods Revisited. ISSI Scientific Report SR-008 (Springer, Amsterdam, 2008). Google Scholar
  122. S. Perri, A. Balogh, Characterization of transitions in the solar wind parameters. Astrophys. J. 710, 1286–1294 (2010a). doi: 10.1088/0004-637X/710/2/1286 ADSGoogle Scholar
  123. S. Perri, A. Balogh, Stationarity in solar wind flows. Astrophys. J. 714, 937–943 (2010b). doi: 10.1088/0004-637X/714/1/937 ADSGoogle Scholar
  124. S. Perri, G. Zimbardo, Evidence of superdiffusive transport of electrons accelerated at interplanetary shocks. Astrophys. J. Lett. 671, 177–180 (2007). doi: 10.1086/525523 ADSGoogle Scholar
  125. S. Perri, G. Zimbardo, Superdiffusive transport of electrons accelerated at corotating interaction regions. J. Geophys. Res. (Space Phys.) 113, 3107 (2008). doi: 10.1029/2007JA012695 ADSGoogle Scholar
  126. S. Perri, G. Zimbardo, Ion and electron superdiffusive transport in the interplanetary space. Adv. Space Res. 44, 465–470 (2009a). doi: 10.1016/j.asr.2009.04.017 ADSGoogle Scholar
  127. S. Perri, G. Zimbardo, Ion superdiffusion at the solar wind termination shock. Astrophys. J. Lett. 693, 118–121 (2009b). doi: 10.1088/0004-637X/693/2/L118 ADSGoogle Scholar
  128. S. Perri, G. Zimbardo, Magnetic variances and pitch-angle scattering times upstream of interplanetary shocks. Astrophys. J. 754, 8 (2012a). doi: 10.1088/0004-637X/754/1/8 ADSGoogle Scholar
  129. S. Perri, G. Zimbardo, Superdiffusive shock acceleration. Astrophys. J. 750, 87 (2012b) ADSGoogle Scholar
  130. D. Perrone, R.O. Dendy, I. Furno, G. Zimbardo, Nonclassical transport and particle-field coupling: from laboratory plasmas to the solar wind. Space Sci. Rev. (2013, accepted) Google Scholar
  131. J.L. Pinçon, F. Lefeuvre, Local characterization of homogeneous turbulence in a space plasma from simultaneous measurements of field components at several points in space. J. Geophys. Res. 96, 1789–1802 (1991) ADSGoogle Scholar
  132. F.M. Poli, S. Brunner, A. Diallo, A. Fasoli, I. Furno, B. Labit, S.H. Müller, G. Plyushchev, M. Podestà, Experimental characterization of drift-interchange instabilities in a simple toroidal plasma. Phys. Plasmas 13(10), 102104 (2006). doi: 10.1063/1.2356483 ADSGoogle Scholar
  133. D.V. Reames, Particle acceleration at the Sun and in the heliosphere. Space Sci. Rev. 90, 413–491 (1999). doi: 10.1023/A:1005105831781 ADSGoogle Scholar
  134. A. Retinò, D. Sundkvist, A. Vaivads, F. Mozer, M. André, C.J. Owen, In situ evidence of magnetic reconnection in turbulent plasma. Nat. Phys. 3, 236–238 (2007). doi: 10.1038/nphys574 Google Scholar
  135. C.P. Ritz, E.J. Powers, Estimation of nonlinear transfer functions for fully developed turbulence. Physica D Nonlinear Phenom. 20, 320–334 (1986). doi: 10.1016/0167-2789(86)90036-9 ADSzbMATHGoogle Scholar
  136. C.P. Ritz, E.J. Powers, T.L. Rhodes, R.D. Bengtson, K.W. Gentle, H. Lin, P.E. Phillips, A.J. Wootton, D.L. Brower, N.C. Luhmann Jr., W.A. Peebles, P.M. Schoch, R.L. Hickok, Advanced plasma fluctuation analysis techniques and their impact on fusion research. Rev. Sci. Instrum. 59, 1739–1744 (1988). doi: 10.1063/1.1140098 ADSGoogle Scholar
  137. F. Sahraoui, Diagnosis of magnetic structures and intermittency in space-plasma turbulence using the technique of surrogate data. Phys. Rev. E 78(2), 026402 (2008). doi: 10.1103/PhysRevE.78.026402 ADSGoogle Scholar
  138. F. Sahraoui, G. Belmont, L. Rezeau, N. Cornilleau-Wehrlin, J.L. Pinçon, A. Balogh, Anisotropic turbulent spectra in the terrestrial magnetosheath as seen by the cluster spacecraft. Phys. Rev. Lett. 96(7), 075002 (2006). doi: 10.1103/PhysRevLett.96.075002 ADSGoogle Scholar
  139. F. Sahraoui, M.L. Goldstein, G. Belmont, A. Roux, L. Rezeau, P. Canu, P. Robert, N. Cornilleau-Wehrlin, O. Le Contel, T. Dudok de Wit, J. Pinçon, K. Kiyani, Multi-spacecraft investigation of space turbulence: lessons from cluster and input to the cross-scale mission. Planet. Space Sci. 59, 585–591 (2011). doi: 10.1016/j.pss.2010.06.001 ADSGoogle Scholar
  140. T. Schreiber, A. Schmitz, Surrogate time series. Physica D 142, 346–382 (2000). doi: 10.1016/S0167-2789(00)00043-9 MathSciNetADSzbMATHGoogle Scholar
  141. A. Shalchi, I. Kourakis, A new theory for perpendicular transport of cosmic rays. Astron. Astrophys. 470, 405–409 (2007). doi: 10.1051/0004-6361:20077260 ADSzbMATHGoogle Scholar
  142. C. Shen, X. Li, M. Dunlop, Z.X. Liu, A. Balogh, D.N. Baker, M. Hapgood, X. Wang, Analyses on the geometrical structure of magnetic field in the current sheet based on cluster measurements. J. Geophys. Res. (Space Phys.) 108, 1168 (2003). doi: 10.1029/2002JA009612 ADSGoogle Scholar
  143. M.F. Shlesinger, G.M. Zaslavsky, J. Klafter, Strange kinetics. Nature 363, 31–37 (1993). doi: 10.1038/363031a0 ADSGoogle Scholar
  144. B.U.Ö. Sonnerup, M. Scheible, Minimum and maximum variance analysis. In: ISSI Scientific Reports Series vol. 1 (1998), pp. 185–220 Google Scholar
  145. 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
  146. 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). doi: 10.1016/S0032-0633(01)00060-5 ADSGoogle Scholar
  147. J. Souček, T. Dudok de Wit, V. Krasnoselskikh, A. Volokitin, Statistical analysis of nonlinear wave interactions in simulated langmuir turbulence data. Ann. Geophys. 21, 681–692 (2003) ADSGoogle Scholar
  148. U. Stroth, F. Greiner, C. Lechte, N. Mahdizadeh, K. Rahbarnia, M. Ramisch, Study of edge turbulence in dimensionally similar laboratory plasmas. Phys. Plasmas 11, 2558–2564 (2004). doi: 10.1063/1.1688789 ADSGoogle Scholar
  149. D. Sundkvist, V. Krasnoselskikh, P.K. Shukla, A. Vaivads, M. André, S. Buchert, H. Rème, In situ multi-satellite detection of coherent vortices as a manifestation of Alfvénic turbulence. Nature 436, 825–828 (2005). doi: 10.1038/nature03931 ADSGoogle Scholar
  150. J. Svensson, A. Werner, J. Contributors, Current tomography for axisymmetric plasmas. Plasma Phys. Control. Fusion 50(8), 085002 (2008). doi: 10.1088/0741-3335/50/8/085002 ADSGoogle Scholar
  151. J. Terry, S. Zweben, K. Hallatschek, B. LaBombard, R. Maqueda, B. Bai, C. Boswell, M. Greenwald, D. Kopon, W. Nevins, C. Pitcher, B. Rogers, D. Stotler, X. Xu, Observations of the turbulence in the scrape-off-layer of Alcator C-Mod and comparisons with simulation. Phys. Plasmas 10(5, Part 2), 1739–1747 (2003). doi: 10.1063/1.1564090 ADSGoogle Scholar
  152. C. Theiler, I. Furno, P. Ricci, A. Fasoli, B. Labit, S.H. Mueller, G. Plyushchev, Cross-field motion of plasma blobs in an open magnetic field line configuration. Phys. Rev. Lett. 103, 065001 (2009). doi: 10.1103/PhysRevLett.103.065001 ADSGoogle Scholar
  153. A. Tjulin, J.-L. Pinçon, F. Sahraoui, M. André, N. Cornilleau-Wehrlin, The k-filtering technique applied to wave electric and magnetic field measurements from the cluster satellites. J. Geophys. Res. (Space Phys.) 110, 11224 (2005). doi: 10.1029/2005JA011125 ADSGoogle Scholar
  154. C. Torrence, G.P. Compo, A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79, 61–78 (1998). doi: 10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2 ADSGoogle Scholar
  155. 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
  156. G.R. Tynan, A. Fujisawa, G. McKee, A review of experimental drift turbulence studies. Plasma Phys. Control. Fusion 51(11), 113001 (2009). doi: 10.1088/0741-3335/51/11/113001 ADSGoogle Scholar
  157. M. Škorić, M. Rajković, Characterization of intermittency in plasma edge turbulence. Contrib. Plasma Phys. 48, 37–41 (2008). doi: 10.1002/ctpp.200810006 ADSGoogle Scholar
  158. J.C. van den Berg (ed.), Wavelets in Physics (Cambridge University Press, Cambridge, 2004) zbMATHGoogle Scholar
  159. D. Vassiliadis, Systems theory for geospace plasma dynamics. Rev. Geophys. 44, 2002 (2006). doi: 10.1029/2004RG000161 ADSGoogle Scholar
  160. J. Vega, A. Pereira, A. Portas, S. Dormido-Canto, G. Farias, R. Dormido, J. Sánchez, N. Duro, M. Santos, E. Sanchez, G. Pajares, Data mining technique for fast retrieval of similar waveforms in fusion massive databases. Fusion Eng. Des. 83(1), 132–139 (2008). doi: 10.1016/j.fusengdes.2007.09.011 Google Scholar
  161. 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
  162. 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
  163. J. Vogt, A. Albert, O. Marghitu, Analysis of three-spacecraft data using planar reciprocal vectors: methodological framework and spatial gradient estimation. Ann. Geophys. 27, 3249–3273 (2009) ADSGoogle Scholar
  164. U. von Toussaint, Bayesian inference in physics. Rev. Mod. Phys. 83, 943–999 (2011). doi: 10.1103/RevModPhys.83.943 ADSGoogle Scholar
  165. A. Wernik, Methods of data analysis for resolving nonlinear phenomena, in Modern Ionospheric Science, ed. by H. Kohl, R. Rüster, K. Schlegel (European Geophysical Society, Katlenburg-Lindau, 1996), pp. 322–345 Google Scholar
  166. T. Windisch, O. Grulke, T. Klinger, Radial propagation of structures in drift wave turbulence. Phys. Plasmas 13(12), 122303 (2006). doi: 10.1063/1.2400845 ADSGoogle Scholar
  167. C.X. Yu, M. Gilmore, W.A. Peebles, T.L. Rhodes, Structure function analysis of long-range correlations in plasma turbulence. Phys. Plasmas 10, 2772–2779 (2003). doi: 10.1063/1.1583711 ADSGoogle Scholar
  168. G.M. Zaslavskii, R.Z. Sagdeev, D.K. Chaikovskii, A.A. Chernikov, Chaos and two-dimensional random walk in periodic and quasi-periodic fields. J. Exp. Theor. Phys. 95, 1723–1733 (1989) Google Scholar
  169. G.M. Zaslavsky, D. Stevens, H. Weitzner, Self-similar transport in incomplete chaos. Phys. Rev. E 48, 1683–1694 (1993). doi: 10.1103/PhysRevE.48.1683 MathSciNetADSGoogle Scholar
  170. G. Zimbardo, Anomalous particle diffusion and Lévy random walk of magnetic field lines in three-dimensional solar wind turbulence. Plasma Phys. Control. Fusion 47, 755–767 (2005). doi: 10.1088/0741-3335/47/12B/S57 Google Scholar
  171. G. Zimbardo, P. Pommois, P. Veltri, Superdiffusive and subdiffusive transport of energetic particles in solar wind anisotropic magnetic turbulence. Astrophys. J. 639, 91–94 (2006). doi: 10.1086/502676 ADSGoogle Scholar
  172. G. Zimbardo, A. Greco, L. Sorriso-Valvo, S. Perri, Z. Vörös, G. Aburjania, K. Chargazia, O. Alexandrova, Magnetic turbulence in the geospace environment. Space Sci. Rev. 156, 89–134 (2010). doi: 10.1007/s11214-010-9692-5 ADSGoogle Scholar
  173. G. Zimbardo, S. Perri, P. Pommois, P. Veltri, Anomalous particle transport in the heliosphere. Adv. Space Res. 49, 1633–1642 (2012). doi: 10.1016/j.asr.2011.10.022 ADSGoogle Scholar
  174. G. Zumofen, J. Klafter, Scale-invariant motion in intermittent chaotic systems. Phys. Rev. E 47, 851–863 (1993). doi: 10.1103/PhysRevE.47.851 ADSGoogle Scholar
  175. S.J. Zweben, Search for coherent structure within tokamak plasma turbulence. Phys. Fluids 28, 974–982 (1985). doi: 10.1063/1.865069 ADSGoogle Scholar
  176. S.J. Zweben, J.A. Boedo, O. Grulke, C. Hidalgo, B. La Bombard, R.J. Maqueda, P. Scarin, J.L. Terry, Edge turbulence measurements in toroidal fusion devices. Plasma Phys. Control. Fusion 49, 1–23 (2007). doi: 10.1088/0741-3335/49/7/S01 ADSGoogle Scholar
  177. S.J. Zweben, J.L. Terry, B. LaBombard, M. Agostini, M. Greenwald, O. Grulke, J.W. Hughes, D.A. D’Ippolito, S.I. Krasheninnikov, J.R. Myra, D.A. Russell, D.P. Stotler, M. Umansky, Estimate of convective radial transport due to SOL turbulence as measured by GPI in Alcator C-Mod. J. Nucl. Mater. 415(1, S), 463–466 (2011). doi: 10.1016/j.jnucmat.2010.08.018 ADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • T. Dudok de Wit
    • 1
    Email author
  • O. Alexandrova
    • 2
  • I. Furno
    • 3
  • L. Sorriso-Valvo
    • 4
    • 5
  • G. Zimbardo
    • 6
  1. 1.LPC2ECNRS and University of OrléansOrléans cedex 2France
  2. 2.LESIAObservatoire de ParisMeudonFrance
  3. 3.EPFL SB CRPPLausanneSwitzerland
  4. 4.Dipartimento di FisicaIPCF-CNR, UOS di CosenzaArcavacata di Rende (CS)Italy
  5. 5.Space Sciences LaboratoryUniversity of California, BerkeleyBerkeleyUSA
  6. 6.Dipartimento di FisicaUniversità della CalabriaArcavacata di Rende (CS)Italy

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