Advertisement

Space Science Reviews

, Volume 178, Issue 2–4, pp 233–270 | Cite as

Nonclassical Transport and Particle-Field Coupling: from Laboratory Plasmas to the Solar Wind

  • D. PerroneEmail author
  • R. O. Dendy
  • I. Furno
  • R. Sanchez
  • G. Zimbardo
  • A. Bovet
  • A. Fasoli
  • K. Gustafson
  • S. Perri
  • P. Ricci
  • F. Valentini
Article

Abstract

Understanding transport of thermal and suprathermal particles is a fundamental issue in laboratory, solar-terrestrial, and astrophysical plasmas. For laboratory fusion experiments, confinement of particles and energy is essential for sustaining the plasma long enough to reach burning conditions. For solar wind and magnetospheric plasmas, transport properties determine the spatial and temporal distribution of energetic particles, which can be harmful for spacecraft functioning, as well as the entry of solar wind plasma into the magnetosphere. For astrophysical plasmas, transport properties determine the efficiency of particle acceleration processes and affect observable radiative signatures. In all cases, transport depends on the interaction of thermal and suprathermal particles with the electric and magnetic fluctuations in the plasma. Understanding transport therefore requires us to understand these interactions, which encompass a wide range of scales, from magnetohydrodynamic to kinetic scales, with larger scale structures also having a role. The wealth of transport studies during recent decades has shown the existence of a variety of regimes that differ from the classical quasilinear regime. In this paper we give an overview of nonclassical plasma transport regimes, discussing theoretical approaches to superdiffusive and subdiffusive transport, wave–particle interactions at microscopic kinetic scales, the influence of coherent structures and of avalanching transport, and the results of numerical simulations and experimental data analyses. Applications to laboratory plasmas and space plasmas are discussed.

Keywords

Transport Wave–particle interaction Laboratory plasmas Space plasmas Anomalous diffusion 

Notes

Acknowledgements

This work was part-funded by the RCUK Energy Programme under grant EP/I501045 and the European Communities under the contract of Association between EURATOM and CCFE. The views and opinions expressed herein do not necessarily reflect those of the European Commission. The TORPEX experiments and simulations were supported in part by the Swiss National Science Foundation. The authors wish to acknowledge the valuable support of the CRPP technical team. K.G. was supported by US-NSF IRFP grant OISE-0853498. The hybrid Vlasov-Maxwell numerical simulations discussed in the present work were performed on the Fermi supercomputer at Cineca (Bologna, Italy), within the project ASWTURB 2011 (HP10BO2REM), supported by the Italian Super-computing research allocation (ISCRA), and within the European project PRACE Pra04-771 (Partnership for advanced computing in Europe). D.P. is supported by the Italian Ministry for University and Research (MIUR) PRIN 2009 funds (grant number 20092YP7EY). G.Z. acknowledges support from the European Union FP7, Marie Curie project 269198 – Geoplasmas. S. P.’s research has been supported by “Borsa Post-doc POR Calabria FSE 2007/2013 Asse IV Capitale Umano - Obiettivo Operativo M.2”.

References

  1. S. Abdullaev, Structure of motion near saddle points and chaotic transport in Hamiltonian systems. Phys. Rev. E 62, 3508 (2000) MathSciNetADSGoogle Scholar
  2. O. Adriani et al. (PAMELA collaboration), PAMELA measurements of cosmic-ray proton and helium spectra. Science 332, 69 (2011) ADSGoogle Scholar
  3. O. Alexandrova, J. Saur, C. Lacombe et al., Universality of the solar wind turbulent spectrum from MHD to electron scales. Phys. Rev. Lett. 103, 165003 (2009) ADSGoogle Scholar
  4. F. Anderegg, C.F. Driscoll, D.H. Dubin et al., Electron acoustic waves in pure ion plasmas. Phys. Plasmas 16, 055705 (2009) ADSGoogle Scholar
  5. S.V. Annibaldi, G. Manfredi, R.O. Dendy et al., Evidence for strange kinetics in Hasegawa-Mima turbulent transport. Plasma Phys. Control. Fusion 42, L13 (2000) ADSGoogle Scholar
  6. S.V. Annibaldi, G. Manfredi, R.O. Dendy, Non-Gaussian transport in strong plasma turbulence. Phys. Plasmas 9, 791 (2002) ADSGoogle Scholar
  7. J.A. Araneda, E. Marsch, A.F. Viñas, Proton core heating and beam formation via parametrically unstable Alfvén-cyclotron waves. Phys. Rev. Lett. 100, 125003 (2008) ADSGoogle Scholar
  8. J.A. Araneda, Y. Maneva, E. Marsch, Preferential heating and acceleration of α particles by Alfvén-cyclotron waves. Phys. Rev. Lett. 102, 175001 (2009) ADSGoogle Scholar
  9. P. Bak, C. Tang, K. Wiesenfeld, Self-organized criticality: an explanation of 1/f noise. Phys. Rev. Lett. 59, 381 (1987) MathSciNetADSGoogle Scholar
  10. P. Bak, C. Tang, K. Wiesenfeld, Self-organized criticality. Phys. Rev. A 38, 364 (1988) MathSciNetADSzbMATHGoogle Scholar
  11. S.D. Bale, P.J. Kellogg, F.S. Mozer et al., Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 94, 215002 (2005) ADSGoogle Scholar
  12. J.W. Bieber, W.H. Matthaeus, C.W. Smith, Proton and electron mean free paths: the Palmer consensus revisited. Astrophys. J. 420, 294 (1994) ADSGoogle Scholar
  13. C.K. Birdsall, A.B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985) Google Scholar
  14. R. Bitane, G. Zimbardo, P. Veltri, Electron transport in coronal loops: the influence of the exponential separation of magnetic field lines. Astrophys. J. 719, 1912 (2010) ADSGoogle Scholar
  15. 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, L14104 (2010) ADSGoogle Scholar
  16. S. Bourouaine, E. Marsch, F.M. Neubauer, On the relative speed and temperature ratio of solar wind alpha particles and protons: collisions versus wave effects. Astrophys. J. 728, L3 (2011a) ADSGoogle Scholar
  17. S. Bourouaine, E. Marsch, F.M. Neubauer, Temperature anisotropy and differential streaming of solar wind ions. Correlations with transverse fluctuations. Astron. Astrophys. 536, A39 (2011b) ADSGoogle Scholar
  18. A. Bovet, A. Fasoli, I. Furno et al., Investigation of fast ion transport in TORPEX. Nucl. Fusion 52, 094017 (2012) ADSGoogle Scholar
  19. R. Bruno, V. Carbone, The solar wind as a turbulence laboratory. Living Rev. Sol. Phys. 2, 4 (2005) ADSGoogle Scholar
  20. G.S. Burillo, B.P. van Milligen, A. Thyagaraja, Analysis of the radial transport of tracers in a turbulence simulation. Phys. Plasmas 16, 042319 (2009) ADSGoogle Scholar
  21. E. Camporeale, D. Burgess, The dissipation of solar wind turbulent fluctuations at electron scales. Astrophys. J. 730, 114 (2011) ADSGoogle Scholar
  22. B.A. Carreras, V.E. Lynch, D.E. Newman, A model realization of self-organized criticality for plasma confinement. Phys. Plasmas 3, 2903 (1996) ADSGoogle Scholar
  23. S.C. Chapman, N. Watkins, R.O. Dendy et al., A simple avalanche model as an analogue for magnetospheric activity. Geophys. Res. Lett. 25, 2397 (1998) ADSGoogle Scholar
  24. S.C. Chapman, R.O. Dendy, G. Rowlands, A sandpile model with dual scaling regimes for laboratory, space and astrophysical plasmas. Phys. Plasmas 6, 4169 (1999) ADSGoogle Scholar
  25. S.C. Chapman, R.O. Dendy, B. Hnat, A sandpile model with tokamak-like enhanced confinement phenomenology. Phys. Rev. Lett. 86, 2814 (2001a) ADSGoogle Scholar
  26. S.C. Chapman, R.O. Dendy, B. Hnat, A simple avalanche model for astroplasma and laboratory confinement systems. Phys. Plasmas 8, 1969 (2001b) ADSGoogle Scholar
  27. S.C. Chapman, R.O. Dendy, B. Hnat, Self organisation of edge and internal pedestals in a sandpile. Plasma Phys. Control. Fusion 45, 301 (2003) ADSGoogle Scholar
  28. C.H.K. Chen, A. Mallet, T.A. Yousef et al., Anisotropy of Alfvénic turbulence in the solar wind and numerical simulations. Mon. Not. R. Astron. Soc. 415, 3219 (2011) ADSGoogle Scholar
  29. R.-B. Decker, S.M. Krimigis, E.C. Roelof et al., Mediation of the solar wind termination shock by non-thermal ions. Nature 454, 67 (2008) ADSGoogle Scholar
  30. D. del-Castillo-Negrete, Asymmetric transport and non-Gaussian statistics of passive scalars in vortices in shear. Phys. Fluids 10, 576 (1998) MathSciNetADSzbMATHGoogle Scholar
  31. D. del-Castillo-Negrete, B.A. Carreras, V.E. Lynch, Fractional diffusion in plasma turbulence. Phys. Plasmas 11, 3854 (2004a) ADSGoogle Scholar
  32. D. del-Castillo-Negrete, B.A. Carreras, V.E. Lynch, Nondiffusive transport in plasma turbulence: a fractional diffusion approach. Phys. Rev. Lett. 94, 065003 (2004b) ADSGoogle Scholar
  33. R.O. Dendy, P. Helander, Sandpiles, silos and tokamak phenomenology: a brief review. Plasma Phys. Control. Fusion 39, 1947 (1997) ADSGoogle Scholar
  34. R.O. Dendy, P. Helander, On the appearance and non-appearance of self-organised criticality in sandpiles. Phys. Rev. E 57, 3641 (1998) ADSGoogle Scholar
  35. R.O. Dendy, P. Helander, M. Tagger, On the role of self-organised criticality in accretion systems. Astron. Astrophys. 337, 962 (1998) ADSGoogle Scholar
  36. R.O. Dendy, S.C. Chapman, Characterisation and interpretation of strongly nonlinear phenomena in fusion, space, and astrophysical plasmas. Plasma Phys. Control. Fusion 48, B313 (2006) Google Scholar
  37. R.O. Dendy, S.C. Chapman, M. Paczuski, Fusion, space, and solar plasmas as complex systems. Plasma Phys. Control. Fusion 49, A95 (2007) ADSGoogle Scholar
  38. J.M. Dewhurst, B. Hnat, R.O. Dendy, The effects of nonuniform magnetic field strength on density flux and test particle transport in drift wave turbulence. Phys. Plasmas 16, 072306 (2009) ADSGoogle Scholar
  39. J.M. Dewhurst, B. Hnat, R.O. Dendy, Finite Larmor radius effects on test particle transport in drift wave-zonal flow turbulence. Plasma Phys. Control. Fusion 52, 025004 (2010). doi: 10.1088/0741-3335/52/2/025004 ADSGoogle Scholar
  40. A. Diallo, A. Fasoli, I. Furno et al., Dynamics of plasma blobs in a shear flow. Phys. Rev. Lett. 101, 115005 (2008) ADSGoogle Scholar
  41. P.H. Diamond, S.-I. Itoh, T.S. Hahm, Zonal flows in plasmas—a review. Plasma Phys. Control. Fusion 47, R35 (2005) ADSGoogle Scholar
  42. P.H. Diamond, A. Hasegawa, K. Mima, Vorticity dynamics, drift wave turbulence, and zonal flows: a look back and a look ahead. Plasma Phys. Control. Fusion 53, 124001 (2011) ADSGoogle Scholar
  43. A. Dosch, A. Shalchi, Diffusive shock acceleration at interplanetary perpendicular shock waves: influence of the large scale structure of turbulence on the maximum particle energy. Adv. Space Res. 46, 1208 (2010) ADSGoogle Scholar
  44. P. Duffy, J.-G. Kirk, Y.-A. Gallant et al., Anomalous transport and particle acceleration at shocks. Astron. Astrophys. 302, L21 (1995) ADSGoogle Scholar
  45. A. Fasoli, B. Labit, M. McGrath et al., Electrostatic turbulence and transport in a simple magnetized plasma. Phys. Plasmas 13, 055902 (2006) ADSGoogle Scholar
  46. A. Fasoli, A. Burckel, L. Federspiel et al., Electrostatic instabilities, turbulence and fast ion interactions in the TORPEX device. Plasma Phys. Control. Fusion 52, 124020 (2010) ADSGoogle Scholar
  47. J. Feder, Fractals (Plenum, New York, 1988) zbMATHGoogle Scholar
  48. L.A. Fisk, M.A. Lee, Shock acceleration of energetic particles in corotating interaction regions in the solar wind. Astrophys. J. 237, 620 (1980) ADSGoogle Scholar
  49. V. Florinski, R.B. Decker, J.A. le Roux et al., An energetic-particle-mediated termination shock observed by Voyager 2. Geophys. Res. Lett. 36, L12101 (2009) ADSGoogle Scholar
  50. A. Fujisawa, Experimental studies of mesoscale structure and its interactions with microscale waves in plasma turbulence. Plasma Phys. Control. Fusion 53, 124015 (2011) ADSGoogle Scholar
  51. I. Furno, B. Labit, M. Podestà et al., Experimental observation of the blob-generation mechanism from interchange waves in a plasma. Phys. Rev. Lett. 100, 055004 (2008a) ADSGoogle Scholar
  52. I. Furno, B. Labit, A. Fasoli et al., Mechanism for blob generation in the TORPEX toroidal plasma. Phys. Plasmas 15, 055903 (2008b) ADSGoogle Scholar
  53. I. Furno, M. Spolaore, C. Theiler et al., Direct two-dimensional measurements of the field-aligned current associated with plasma blobs. Phys. Rev. Lett. 106, 245001 (2011) ADSGoogle Scholar
  54. S.P. Gary, S. Saito, H. Li, Cascade of whistler turbulence: particle-in-cell simulations. Geophys. Res. Lett. 35, L02104 (2008) ADSGoogle Scholar
  55. J. Giacalone, Large-scale hybrid simulations of particle acceleration at a parallel shock. Astrophys. J. 609, 452 (2004) ADSGoogle Scholar
  56. J. Giacalone, Cosmic-ray transport and interaction with shocks. Space Sci. Rev. (2011). doi: 10.1007/s11214-011-9763-2 Google Scholar
  57. J.P. Graves, R.O. Dendy, K.I. Hopcraft et al., The role of clustering effects in non-diffusive transport in tokamaks. Phys. Plasmas 9, 1596 (2002) ADSGoogle Scholar
  58. S. Günter, C. Angioni, M. Apostoliceanu et al., Overview of ASDEX upgrade results—development of integrated operating scenarios for ITER. Nucl. Fusion 45, S98 (2005) Google Scholar
  59. D.A. Gurnett, E. Marsch, W. Pilipp et al., Ion-acoustic waves and related plasma observations in the solar wind. J. Geophys. Res. 84, 2029 (1979) ADSGoogle Scholar
  60. K. Gustafson, D. Del-Castillo-Negrete, W. Dorland, Finite Larmor radius effects on nondiffusive tracer transport in a zonal flow. Phys. Plasmas 15, 102309 (2008) ADSGoogle Scholar
  61. K. Gustafson, P. Ricci, A. Bovet et al., Suprathermal ion transport in simple magnetized torus configurations. Phys. Plasmas 19, 062306 (2012a) ADSGoogle Scholar
  62. K. Gustafson, P. Ricci, I. Furno et al., Nondiffusive suprathermal ion transport in simple magnetized toroidal plasmas. Phys. Rev. Lett. 108, 035006 (2012b) ADSGoogle Scholar
  63. K. Gustafson, P. Ricci, Lévy walk description of suprathermal ion transport. Phys. Plasmas 19, 032304 (2012) ADSGoogle Scholar
  64. T. Hauff, F. Jenko, S. Eule, Intermediate non-Gaussian transport in plasma core turbulence. Phys. Plasmas 14, 102316 (2007) ADSGoogle Scholar
  65. T. Hauff, F. Jenko, Mechanisms and scalings of energetic ion transport via tokamak microturbulence. Phys. Plasmas 15, 2307 (2008) Google Scholar
  66. P. Helander, S.C. Chapman, R.O. Dendy et al., Exactly solvable sandpile with fractal avalanching. Phys. Rev. 59, 6356 (1999) ADSGoogle Scholar
  67. W.A. Hornsby, A.R. Bell, R.J. Kingham et al., A code to solve the Vlasov Fokker-Planck equation applied to particle transport in magnetic turbulence. Plasma Phys. Control. Fusion 52, 075011 (2010) ADSGoogle Scholar
  68. D. Hughes, M. Paczuski, R.O. Dendy et al., Solar flares as cascades of reconnecting magnetic loops. Phys. Rev. Lett. 90, 131101 (2003) ADSGoogle Scholar
  69. S. Inagaki, T. Tokuzawa, K. Itoh et al., Observations of long-distance radial correlation in toroidal plasma turbulence. Phys. Rev. Lett. 107, 115001 (2011) ADSGoogle Scholar
  70. J.R. Jokipii, Cosmic-ray propagation. I. Charged particles in a random magnetic field. Astrophys. J. 146, 480 (1966) ADSGoogle Scholar
  71. J.G. Kirk, P. Duffy, Y.A. Gallant, Stochastic particle acceleration at shocks in the presence of braided magnetic fields. Astron. Astrophys. 314, 1010 (1996) ADSGoogle Scholar
  72. J.G. Kirk, R.O. Dendy, Shock acceleration of cosmic rays: a critical review. J. Phys. G 27, 1589 (2001) ADSGoogle Scholar
  73. J. Klafter, A. Blumen, M.F. Shlesinger, Stochastic pathway to anomalous diffusion. Phys. Rev. A 35, 3081 (1987) MathSciNetADSGoogle Scholar
  74. A.J. Klimas, J.A. Valdivia, D. Vassiliadis et al., Self-organized criticality in the substorm phenomenon and its relation to localized reconnection in the magnetospheric plasma sheet. J. Geophys. Res. 105(A8), 18765 (2000) ADSGoogle Scholar
  75. J. Kóta, J.R. Jokipii, Velocity correlation and the spatial diffusion coefficients of cosmic rays: compound diffusion. Astrophys. J. 531, 1067 (2000) ADSGoogle Scholar
  76. J.A. Krommes, C. Oberman, R.B. Kleva, Plasma transport in stochastic magnetic fields. Part 3. Kinetics of test particle diffusion. J. Plasma Phys. 30, 11 (1983) ADSGoogle Scholar
  77. B. Labit, C. Theiler, A. Fasoli et al., Blob-induced toroidal momentum transport in simple magnetized plasmas. Phys. Plasmas 18, 032308 (2011) ADSGoogle Scholar
  78. P.O. Lagage, C.J. Cesarsky, Cosmic-ray shock acceleration in the presence of self-excited waves. Astron. Astrophys. 118, 223 (1983a) ADSzbMATHGoogle Scholar
  79. P.O. Lagage, C.J. Cesarsky, The maximum energy of cosmic rays accelerated by supernova shocks. Astron. Astrophys. 125, 249 (1983b) ADSzbMATHGoogle Scholar
  80. L.D. Landau, On the vibrations of the electronic plasma. J. Phys. (Moscow) 10, 25 (1946) zbMATHGoogle Scholar
  81. M.A. Lee, L.A. Fisk, Shock acceleration of energetic particles in the heliosphere. Space Sci. Rev. 32, 205 (1982) ADSGoogle Scholar
  82. R.E. Lee, S.C. Chapman, R.O. Dendy, Ion acceleration processes at reforming collisionless shocks. Phys. Plasmas 12, 012901 (2005a) ADSGoogle Scholar
  83. R.E. Lee, S.C. Chapman, R.O. Dendy, Reforming perpendicular shocks in the presence of pickup protons: initial ion acceleration. Ann. Geophys. 23, 643 (2005b) ADSGoogle Scholar
  84. R.P. Lin, Non-relativistic solar electrons. Space Sci. Rev. 16, 189 (1974) ADSGoogle Scholar
  85. R.P. Lin, Relationship of solar flare accelerated particles to solar energetic particles (SEPs) observed in the interplanetary medium. Adv. Space Res. 35, 1857 (2005) ADSGoogle Scholar
  86. E. Lu, R. Hamilton, Avalanches of the distribution of solar flares. Astrophys. J. 380, L89 (1991) ADSGoogle Scholar
  87. F. Mainardi, Y. Luchko, G. Pagnini, The fundamental solution of the space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 4, 153–192 (1996) MathSciNetGoogle Scholar
  88. M.A. Malkov, P.H. Diamond, Weak hysteresis in a simplified model of the L-H transition. Phys. Plasmas 16, 012504 (2009) ADSGoogle Scholar
  89. B.B. Mandelbrot, J.W. van Ness, Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10, 422 (1968) MathSciNetADSzbMATHGoogle Scholar
  90. G. Manfredi, R.O. Dendy, Test-particle transport in strong electrostatic drift turbulence with finite Larmor radius effects. Phys. Rev. Lett. 76, 4360 (1996) ADSGoogle Scholar
  91. G. Manfredi, M. Shoucri, R.O. Dendy et al., Vlasov gyrokinetic simulations of ion-temperature-gradient driven instabilities. Phys. Plasmas 3, 202 (1996) ADSGoogle Scholar
  92. G. Manfredi, R.O. Dendy, Transport properties of energetic particles in a turbulent electrostatic field. Phys. Plasmas 4, 628 (1997) ADSGoogle Scholar
  93. G. Manfredi, C.M. Roach, R.O. Dendy, Zonal flow and streamer generation in drift turbulence. Plasma Phys. Control. Fusion 43, 825 (2001) ADSGoogle Scholar
  94. A. Mangeney, F. Califano, C. Cavazzoni et al., A numerical scheme for the integration of the Vlasov-Maxwell system of equations. J. Comput. Phys. 179, 405 (2002) MathSciNetGoogle Scholar
  95. E. Marsch, K.-H. Mühlhäuser, R. Schwenn et al., Solar wind protons: three-dimensional velocity distributions and derived plasma parameters measured between 0.3 and 1 AU. J. Geophys. Res. 87, A1 (1982a) Google Scholar
  96. E. Marsch, K.-H. Mühlhäuser, R. Schwenn et al., Solar wind helium ions: observations of the Helios solar probes between 0.3 and 1 AU. J. Geophys. Res. 35, A1 (1982b) Google Scholar
  97. E. Marsch, Kinetic physics of the solar corona and solar wind. Living Rev. Sol. Phys. 3, 1 (2006) ADSGoogle Scholar
  98. J.A. Mier, R. Sanchez, L. Garcia et al., Characterization of non-diffusive transport in plasma turbulence via a novel Lagrangian method. Phys. Rev. Lett. 101, 165001 (2008) ADSGoogle Scholar
  99. J.A. Miller, Particle acceleration in impulsive solar flares. Space Sci. Rev. 86, 79 (1998) ADSGoogle Scholar
  100. E.W. Montroll, G.H. Weiss, Random walks on lattices. II. J. Math. Phys. 6, 167 (1965) MathSciNetADSGoogle Scholar
  101. S.H. Müller, A. Diallo, A. Fasoli et al., Plasma blobs in a basic toroidal experiment: origin, dynamics, and induced transport. Phys. Plasmas 14, 110704 (2007) Google Scholar
  102. D.E. Newman, B.A. Carreras, P.H. Diamond et al., The dynamics of marginality and self-organized criticality as a paradigm for turbulent transport. Phys. Plasmas 3, 1858 (1996) ADSGoogle Scholar
  103. T.N. Parashar, S. Servidio, B. Breech et al., Kinetic driven turbulence: structure in space and time. Phys. Plasmas 17, 102304 (2010) ADSGoogle Scholar
  104. T.N. Parashar, S. Servidio, M.A. Shay et al., Effect of driving frequency on excitation of turbulence in a kinetic plasma. Phys. Plasmas 18, 092302 (2011) ADSGoogle Scholar
  105. S. Perri, G. Zimbardo, Evidence of superdiffusive transport of electrons accelerated at interplanetary shocks. Astrophys. J. 671, L177 (2007) ADSGoogle Scholar
  106. S. Perri, F. Lepreti, V. Carbone et al., Position and velocity space diffusion of test particles in stochastic electromagnetic fields. Europhys. Lett. 78, 40003 (2007) ADSGoogle Scholar
  107. S. Perri, G. Zimbardo, Superdiffusive transport of electrons accelerated at corotating interaction regions. J. Geophys. Res. 113, A03107 (2008a). doi: 10.1029/2007JA012695 ADSGoogle Scholar
  108. S. Perri, G. Zimbardo, Observations of anomalous transport of energetic electrons in the heliosphere. Astrophys. Space Sci. Trans. 4, 27 (2008b) ADSGoogle Scholar
  109. S. Perri, G. Zimbardo, Ion and electron superdiffusive transport in the interplanetary space. Adv. Space Res. 44, 465 (2009a) ADSGoogle Scholar
  110. S. Perri, G. Zimbardo, Ion superdiffusion at the solar wind termination shock. Astrophys. J. 693, L118 (2009b) ADSGoogle Scholar
  111. S. Perri, G. Zimbardo, A. Greco, On the energization of protons interacting with 3-D time-dependent electromagnetic fields in the Earth’s magnetotail. J. Geophys. Res. 116, A05221 (2011). doi: 10.1029/2010JA016328 ADSGoogle Scholar
  112. S. Perri, G. Zimbardo, Superdiffusive shock acceleration. Astrophys. J. 750, 87 (2012) ADSGoogle Scholar
  113. D. Perrone, F. Valentini, P. Veltri, The role of alpha particles in the evolution of the solar-wind turbulence toward short spatial scales. Astrophys. J. 741, 43 (2011) ADSGoogle Scholar
  114. 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) ADSGoogle Scholar
  115. G. Plyushchev, A. Diallo, A. Fasoli et al., Fast ion source and detector for investigating the interaction of turbulence with suprathermal ions in a low temperature toroidal plasma. Rev. Sci. Instrum. 77, 10F503 (2006) Google Scholar
  116. M. Podestà, A. Fasoli, B. Labit et al., Cross-field transport by instabilities and blobs in a magnetized toroidal plasma. Phys. Rev. Lett. 101, 045001 (2008) ADSGoogle Scholar
  117. P. Pommois, P. Veltri, G. Zimbardo, Anomalous and Gaussian transport regimes in anisotropic three-dimensional magnetic turbulence. Phys. Rev. E 59, 2244 (1999) ADSGoogle Scholar
  118. P. Pommois, P. Veltri, G. Zimbardo, Field line diffusion in solar wind magnetic turbulence and energetic particle propagation across heliographic latitudes. J. Geophys. Res. 106, 24965 (2001) ADSGoogle Scholar
  119. P. Pommois, G. Zimbardo, P. Veltri, Anomalous, non-Gaussian transport of charged particles in anisotropic magnetic turbulence. Phys. Plasmas 14, 012311 (2007) ADSGoogle Scholar
  120. G. Qin, W.H. Matthaeus, J.W. Bieber, Subdiffusive transport of charged particles perpendicular to the large scale magnetic field. Geophys. Res. Lett. 29, 1048 (2002a). doi: 10.1029/2001GL014035 ADSGoogle Scholar
  121. G. Qin, W.H. Matthaeus, J.W. Bieber, Perpendicular transport of charged particles in composite model turbulence: recovery of diffusion. Astrophys. J. 578, L117 (2002b) ADSGoogle Scholar
  122. B.R. Ragot, J.G. Kirk, Anomalous transport of cosmic ray electrons. Astron. Astrophys. 327, 432 (1997) ADSGoogle Scholar
  123. D.V. Reames, Particle acceleration at the Sun and in the heliosphere. Space Sci. Rev. 90, 413 (1999) ADSGoogle Scholar
  124. A.B. Rechester, M.N. Rosenbluth, Electron heat transport in a Tokamak with destroyed magnetic surfaces. Phys. Rev. Lett. 40, 38 (1978) ADSGoogle Scholar
  125. P. Ricci, C. Theiler, A. Fasoli et al., Langmuir probe-based observables for plasma-turbulence code validation and application to the TORPEX basic plasma physics experiment. Phys. Plasmas 16, 055703 (2009) ADSGoogle Scholar
  126. P. Ricci, B.N. Rogers, Transport scaling in interchange-driven toroidal plasmas. Phys. Plasmas 16, 062303 (2009) ADSGoogle Scholar
  127. P. Ricci, B.N. Rogers, Turbulence phase space in simple magnetized toroidal plasmas. Phys. Rev. Lett. 104, 145001 (2010) ADSGoogle Scholar
  128. P. Ricci, C. Theiler, A. Fasoli et al., Methodology for turbulence code validation: quantification of simulation-experiment agreement and application to the TORPEX experiment. Phys. Plasmas 18, 032109 (2011) ADSGoogle Scholar
  129. D. Ruffolo, W.H. Matthaeus, P. Chuychai, Trapping of solar energetic particles by the small-scale topology of solar wind turbulence. Astrophys. J. 597, L169 (2003) ADSGoogle Scholar
  130. F. Sahraoui, M.L. Goldstein, G. Belmont et al., Three dimensional anisotropic k spectra of turbulence at subproton scales in the solar wind. Phys. Rev. Lett. 105, 131101 (2010) ADSGoogle Scholar
  131. S. Saito, S.P. Gary, H. Li et al., Whistler turbulence: particle-in-cell simulations. Phys. Plasmas 15, 102305 (2008) ADSGoogle Scholar
  132. G. Samorodnitsky, M.S. Taqqu, Stable Non-Gaussian Distributions (Chapman & Hall, New York, 1994) Google Scholar
  133. R. Sanchez, B.A. Carreras, B. ph. van Milligen, Fluid limits of nonintegrable CTRWs in terms of fractional differential equations. Phys. Rev. E 71, 011111 (2005) MathSciNetADSGoogle Scholar
  134. R. Sanchez, B.A. Carreras, D.E. Newman et al., Renormalization of tracer turbulence leading to fractional differential equations. Phys. Rev. E 74, 016305 (2006) MathSciNetADSGoogle Scholar
  135. R. Sanchez, D.E. Newman, J.-N. Leboeuf et al., Nature of transport across sheared zonal flows in electrostatic ion-temperature-gradient gyrokinetic plasma turbulence. Phys. Rev. Lett. 101, 205002 (2008) ADSGoogle Scholar
  136. R. Sanchez, D.E. Newman, J.-N. Leboeuf et al., Nature of turbulent transport across sheared zonal flows: insights from gyrokinetic simulations. Plasma Phys. Control. Fusion 53, 074018 (2011) ADSGoogle Scholar
  137. H. Schmitz, S.C. Chapman, R.O. Dendy, Electron pre-acceleration mechanisms in the foot region of high Alfvénic Mach number shocks. Astron. Astrophys. 579, 327 (2002b) ADSGoogle Scholar
  138. H. Schmitz, S.C. Chapman, R.O. Dendy, The influence of electron temperature and magnetic field on cosmic ray injection at high Mach number shocks. Astron. Astrophys. 570, 637 (2002a) ADSGoogle Scholar
  139. S. Servidio, F. Valentini, F. Califano et al., Local kinetic effects in two-dimensional plasma turbulence. Phys. Rev. Lett. 108, 045001 (2012) ADSGoogle Scholar
  140. A. Shalchi, I. Kourakis, A new theory for perpendicular transport of cosmic rays. Astron. Astrophys. 470, 405 (2007) ADSzbMATHGoogle Scholar
  141. A. Shalchi, Applicability of the Taylor-Green-Kubo formula in particle diffusion theory. Phys. Rev. E 83, 046402 (2011) ADSGoogle Scholar
  142. M.F. Shlesinger, J. Klafter, Y.M. Wong, Random walks with infinite spatial and temporal moments. J. Stat. Phys. 27, 499 (1982) MathSciNetADSzbMATHGoogle Scholar
  143. W.J. Shugard, H. Reiss, Transient nucleation in H2O–H2SO4 mixtures: a stochastic approach. J. Chem. Phys. 65, 2827 (1976) ADSGoogle Scholar
  144. T. Sugiyama, D. Shiota, Sign for super-diffusive transport of energetic ions associated with a coronal-mass-ejection-driven interplanetary shock. Astrophys. J. 731, L34 (2011) ADSGoogle Scholar
  145. R.C. Tautz, Simulation results on the influence of magneto-hydrodynamic waves on cosmic ray particles. Plasma Phys. Control. Fusion 52, 045016 (2010) ADSGoogle Scholar
  146. R.C. Tautz, A. Shalchi, On the diffusivity of cosmic ray transport. J. Geophys. Res. 115, A03104 (2010). doi: 10.1029/2009JA014944 ADSGoogle Scholar
  147. C. Theiler, A. Diallo, A. Fasoli et al., The role of the density gradient on intermittent cross-field transport events in a simple magnetized toroidal plasma. Phys. Plasmas 15, 042303 (2008) ADSGoogle Scholar
  148. C. Theiler, I. Furno, P. Ricci et al., Cross-field motion of plasma blobs in an open magnetic field line configuration. Phys. Rev. Lett. 103, 065001 (2009) ADSGoogle Scholar
  149. G.R. Tynan, A. Fujisawa, G. McKee, A review of experimental drift turbulence studies. Plasma Phys. Control. Fusion 51, 113001 (2009) ADSGoogle Scholar
  150. F. Valentini, P. Veltri, A. Mangeney, A numerical scheme for the integration of the Vlasov–Poisson system of equations, in the magnetized case. J. Comput. Phys. 210, 730 (2005) ADSzbMATHGoogle Scholar
  151. F. Valentini, P. Trávníček, F. Califano et al., A hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma. J. Comput. Phys. 225, 753 (2007) MathSciNetADSzbMATHGoogle Scholar
  152. F. Valentini, P. Veltri, F. Califano et al., Cross-scale effects in solar-wind turbulence. Phys. Rev. Lett. 101, 025006 (2008) ADSGoogle Scholar
  153. F. Valentini, P. Veltri, Electrostatic short-scale termination of solar-wind turbulence. Phys. Rev. Lett. 102, 225001 (2009) ADSGoogle Scholar
  154. F. Valentini, F. Califano, P. Veltri, Two-dimensional kinetic turbulence in the solar wind. Phys. Rev. Lett. 104, 205002 (2010) ADSGoogle Scholar
  155. F. Valentini, F. Califano, D. Perrone et al., New ion-wave path in the energy cascade. Phys. Rev. Lett. 106, 165002 (2011a) ADSGoogle Scholar
  156. F. Valentini, F. Califano, D. Perrone et al., Excitation of nonlinear electrostatic waves with phase velocity close to the ion-thermal speed. Plasma Phys. Control. Fusion 53, 105017 (2011b) ADSGoogle Scholar
  157. F. Valentini, D. Perrone, P. Veltri, Short-wavelength electrostatic fluctuations in the solar wind. Astrophys. J. 739, 54 (2011c) ADSGoogle Scholar
  158. B.Ph. van Milligen, R. Sanchez, B.A. Carreras, Probabilistic finite-size transport models for fusion: anomalous transport and scaling laws. Phys. Plasmas 11, 2272 (2004) ADSGoogle Scholar
  159. F. Wagner, A quarter-century of H-mode studies. Plasma Phys. Control. Fusion 49, B1 (2007) ADSGoogle Scholar
  160. N.W. Watkins, S.C. Chapman, R.O. Dendy et al., Robustness of collective behaviour in strongly driven avalanche models: magnetospheric implications. Geophys. Res. Lett. 26, 2617 (1999) ADSGoogle Scholar
  161. N.W. Watkins, M.P. Freeman, S.C. Chapman et al., Testing the SOC hypothesis for the magnetosphere. J. Atmos. Sol.-Terr. Phys. 63, 1435 (2001) ADSGoogle Scholar
  162. G.M. Webb, G.P. Zank, E.Kh. Kaghashvili et al., Compound and perpendicular diffusion of cosmic rays and random walk of the field lines. I. Parallel particle transport models. Astrophys. J. 651, 211 (2006) ADSGoogle Scholar
  163. T. Yamada, S.-I. Itoh, T. Maruta et al., Anatomy of plasma turbulence. Nat. Phys. 4, 721 (2008) Google Scholar
  164. G.M. Zaslavsky, Chaos, fractional kinetics, and anomalous transport. Phys. Rep. 371, 461 (2002) MathSciNetADSzbMATHGoogle Scholar
  165. S. Zhou, W.W. Heidbrink, H. Boehmer et al., Turbulent transport of fast ions in the large plasma device. Phys. Plasmas 17, 092103 (2010) ADSGoogle Scholar
  166. S. Zhou, W.W. Heidbrink, H. Boehmer et al., Dependence of fast-ion transport on the nature of the turbulence in the large plasma device. Phys. Plasmas 18, 082104 (2011) ADSGoogle Scholar
  167. G. Zimbardo, P. Veltri, P. Pommois, Anomalous, quasilinear, and percolative regimes for magnetic-field-line transport in axially symmetric turbulence. Phys. Rev. E 61, 1940 (2000a) ADSGoogle Scholar
  168. G. Zimbardo, A. Greco, P. Veltri, Superballistic transport in tearing driven magnetic turbulence. Phys. Plasmas 7, 1071 (2000b) ADSGoogle Scholar
  169. G. Zimbardo, P. Pommois, P. Veltri, Magnetic flux tube evolution in solar wind anisotropic magnetic turbulence. J. Geophys. Res. 109, A02113 (2004). doi: 10.1029/2003JA010162 ADSGoogle 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, B755 (2005) 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, L91 (2006) ADSGoogle Scholar
  172. G. Zimbardo, R. Bitane, P. Pommois et al., Kolmogorov entropy of magnetic field lines in the percolation regime. Plasma Phys. Control. Fusion 51, 015005 (2009) ADSGoogle Scholar
  173. G. Zimbardo, A. Greco, L. Sorriso-Valvo et al., Magnetic turbulence in the geospace environment. Space Sci. Rev. 156, 89 (2010) ADSGoogle Scholar
  174. G. Zimbardo, S. Perri, P. Pommois et al., Anomalous particle transport in the heliosphere. Adv. Space Res. 49, 1633 (2012) ADSGoogle Scholar
  175. G. Zumofen, A. Blumen, J. Klafter et al., Lévy-walks for turbulence: a numerical study. J. Stat. Phys. 54, 1519 (1989) MathSciNetADSGoogle Scholar
  176. G. Zumofen, J. Klafter, Scale-invariant motion in intermittent chaotic systems. Phys. Rev. E 47, 851 (1993) ADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • D. Perrone
    • 1
    Email author
  • R. O. Dendy
    • 2
    • 3
  • I. Furno
    • 4
  • R. Sanchez
    • 5
  • G. Zimbardo
    • 1
  • A. Bovet
    • 4
  • A. Fasoli
    • 4
  • K. Gustafson
    • 4
  • S. Perri
    • 1
  • P. Ricci
    • 4
  • F. Valentini
    • 1
  1. 1.Department of PhysicsUniversity of CalabriaRendeItaly
  2. 2.Culham Science CentreEuratom/CCFE Fusion AssociationAbingdonUK
  3. 3.Centre for Fusion, Space and Astrophysics, Department of PhysicsWarwick UniversityCoventryUK
  4. 4.Centre de Recherches en Physique des Plasmas (CRPP), Ecole Polytechnique Fédérale de Lausanne (EPFL)Association Euratom-SuisseLausanneSwitzerland
  5. 5.Department of PhysicsUniversidad Carlos IIILeganésSpain

Personalised recommendations