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A kinetic model of plasma turbulence

Part of: Focus on Space Plasmas Present Achievements in SpacePlasmas

Published online by Cambridge University Press:  10 October 2014

S. Servidio ,
F. Valentini ,
D. Perrone ,
A. Greco ,
F. Califano ,
W. H. Matthaeus  and
P. Veltri
S. Servidio*
Affiliation:
Dipartimento di Fisica, Universitá della Calabria, Cosenza, 87036, Italy
F. Valentini
Affiliation:
Dipartimento di Fisica, Universitá della Calabria, Cosenza, 87036, Italy
D. Perrone
Affiliation:
LESIA, Observatoire de Paris, 92190 Meudon, France
A. Greco
Affiliation:
Dipartimento di Fisica, Universitá della Calabria, Cosenza, 87036, Italy
F. Califano
Affiliation:
Dipartimento di Fisica and CNISM, Universitá di Pisa, Pisa, 56127, Italy
W. H. Matthaeus
Affiliation:
Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA
P. Veltri
Affiliation:
Dipartimento di Fisica, Universitá della Calabria, Cosenza, 87036, Italy
*
†Email address for correspondence: [email protected]
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Abstract

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A Hybrid Vlasov–Maxwell (HVM) model is presented and recent results about the link between kinetic effects and turbulence are reviewed. Using five-dimensional (2D in space and 3D in the velocity space) simulations of plasma turbulence, it is found that kinetic effects (or non-fluid effects) manifest through the deformation of the proton velocity distribution function (DF), with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The direction of the proper temperature anisotropy, calculated in the main reference frame of the distribution itself, has a finite probability of being along or across the ambient magnetic field, in general agreement with the classical definition of anisotropy T⊥/T∥ (where subscripts refer to the magnetic field direction). Adopting the latter conventional definition, by varying the global plasma beta (β) and fluctuation level, simulations explore distinct regions of the space given by T⊥/T∥ and β∥, recovering solar wind observations. Moreover, as in the solar wind, HVM simulations suggest that proton anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. The role of alpha particles is reviewed using multi-ion kinetic simulations, revealing a similarity between proton and helium non-Maxwellian effects. The techniques presented here are applied to 1D spacecraft-like analysis, establishing a link between non-fluid phenomena and solar wind magnetic discontinuities. Finally, the dimensionality of turbulence is investigated, for the first time, via 6D HVM simulations (3D in both spaces). These preliminary results provide support for several previously reported studies based on 2.5D simulations, confirming several basic conclusions. This connection between kinetic features and turbulence open a new path on the study of processes such as heating, particle acceleration, and temperature-anisotropy, commonly observed in space plasmas.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 1 , January 2015 , 325810107
Copyright
Copyright © Cambridge University Press 2014 

References

REFERENCES

Alexandrova, O., Carbone, V., Veltri, P. and Sorriso-Valvo, L. 2008 Small-scale energy cascade of the solar wind turbulence. Astrophys. J. 674, 1153.CrossRefGoogle Scholar
Alexandrova, O., Chen, C. H. K., Sorriso-Valvo, L., Horbury, T. S. and Bale, S. D. 2013 Solar wind turbulence and the role of ion instabilities. Space Sci. Rev. 178, 101.Google Scholar
Alexandrova, O., Saur, J., Lacombe, C., Mangeney, A., Mitchell, J., Schwartz, S. J. and Robert, P. 2009 Universality of solar-wind turbulent spectrum from MHD to electron scales. Phys. Rev. Lett. 103, 165 003.CrossRefGoogle ScholarPubMed
Araneda, J. A., Maneva, Y. and Marsch, E. 2009 Preferential heating and acceleration of α particles by Alfvén-Cyclotron waves. Phys. Rev. Lett. 102, 175 001.Google Scholar
Araneda, J. A., Marsch, E. and Viñas, A. F. 2008 Proton core heating and beam formation via parametrically unstable Alfvén-Cyclotron waves. Phys. Rev. Lett. 100, 125 003.Google Scholar
Bale, S. D., Kasper, J. C., Howes, G. G., Quataert, E., Salem, C. and Sundkvist, D. 2009 Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind. Phys. Rev. Lett. 103, 211 101.Google Scholar
Bale, S. D., Kellogg, P. J., Mozer, F. S., Horbury, T. S. and Réme, H. 2005 Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 94, 215 002.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence, Cambridge: Cambridge University Press.Google Scholar
Birdsall, C. K. and Langdon, A. B. 1985 Plasma Physics via Computer Simulation. New York: McGraw-Hill.Google Scholar
Birn, J. et al. 2001 Geospace environmental modeling (GEM) magnetic reconnection challenge. J. Geophys. Res. 106, 3715.Google Scholar
Biskamp, D. 2000 Magnetic Reconnection in Plasmas. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Biskamp, D. 2003 Magnetohydrodynamic Turbulence. Cambridge: Cambridge University Press.Google Scholar
Bourouaine, S., Marsch, E., and Neubauer, F. M. 2010 Correlations between the proton temperature anisotropy and transverse high-frequency waves in the solar wind. Geophys. Res. Lett. 37, L14 104.Google Scholar
Bourouaine, S., Marsch, E. and Neubauer, F. M. 2011a On the relative speed and temperature ratio of solar wind alpha particles and protons: collisions versus wave effects. Astrophys. J. Lett. 728, L3.Google Scholar
Bourouaine, S., Marsch, E., and Neubauer, F. M. 2011b Temperature anisotropy and differential streaming of solar wind ions. Correlations with transverse fluctuations. Astron. Astrophys. 536, A39.CrossRefGoogle Scholar
Breech, B., Matthaeus, W. H., Minnie, J., Bieber, J. W., Oughton, S., Smith, C. W. and Isenberg, P. A. 2008 Turbulence transport throughout the heliosphere. J. Geophys. Res. 113, A08 105.Google Scholar
Bruno, R. and Carbone, V. 2005 The solar wind as a turbulence laboratory. Living Rev. Solar Phys. 2, 4.CrossRefGoogle Scholar
Bruno, R., Carbone, V., Veltri, P., Pietropaolo, E. and Bavassano, B. 2001 Identifying intermittency events in the solar wind. Planet. Space. Sci. 49, 1201.CrossRefGoogle Scholar
Burlaga, L. F. 1969 Directional discontinuities in the interplanetary magnetic field. Solar Phys. 7, 54.CrossRefGoogle Scholar
Camporeale, E. and Burgess, D. 2011 The dissipation of solar wind turbulent fluctuations at electron scales. Astrophys. J. 730, 114.CrossRefGoogle Scholar
Chandran, B. D. G., Li, B., Rogers, B. N., Quataert, E. and Germaschewski, K. 2010 Perpendicular ion heating by low-frequency Alfvén-wave turbulence in the solar wind. Astrophys. J. 720, 503.Google Scholar
Chen, C. Z. and Knorr, G. 1976 The integration of the Vlasov equation in configuration space. J. Comput. Phys. 22, 330.Google Scholar
Cranmer, S. R., Field, G. B. and Kohl, J. L. 1999 Spectroscopic constraints on models of ion cyclotron resonance heating in the polar solar corona and high-speed solar wind. Astrophys. J. 518, 937.Google Scholar
Daughton, W., Roytershteyn, V., Karimabadi, H., Yin, L., Albright, B. J., Bergen, B. and Bowers, K. J. 2011 Role of electron physics in the development of turbulent magnetic reconnection in collisionless plasmas. Nature Phys. 7, 539.Google Scholar
Davidson, R. C. 1990 Physics of Nonneutral Plasmas. Redwood City, CA, USA: Addison-Wesley.Google Scholar
Dendy, R. O. and Chapman, S. C. 2006 Characterization and interpretation of strongly nonlinear phenomena in fusion, space and astrophysical plasmas. Plasma Phys. Control. Fusion 48, B313.Google Scholar
Dendy, R. O., Chapman, S. C. and Paczuski, M. 2007 Fusion, space and solar plasmas as complex systems. Plasma Phys. Control. Fusion 49, A95.Google Scholar
Dmitruk, P., Matthaeus, W. H. and Seenu, N. 2004 Test particle energization by current sheets and nonuniform fields in magnetohydrodynamic turbulence. Astrophys. J. 617, 667.Google Scholar
Dobrowolny, M., Mangeney, A. and Veltri, P. 1980 Fully developed anisotropic hydromagnetic turbulence in interplanetary space. Phys. Rev. Lett. 45, 144.Google Scholar
Donato, S., Servidio, S., Dmitruk, P., Carbone, V., Shay, M. A., Cassak, P. A. and Matthaeus, W. H. 2012 Reconnection events in two-dimensional Hall magnetohydrodynamic turbulence. Phys. Plasmas 19, 092 307.Google Scholar
Drake, J. F., Opher, M., Swisdak, M. and Chamoun, J. N. 2010 A magnetic reconnection mechanism for the generation of anomalous cosmic rays. Astrophys J. 709, 963.Google Scholar
Dudok de Wit, T. T., 2004 Can high-order moments be meaningfully estimated from experimental turbulence measurements? Phys. Rev. E 70, 055 302.Google Scholar
Frisch, U. 1995 Turbulence. Cambridge: Cambridge University Press.Google Scholar
Galtier, S. and Buchlin, E. 2007 Multiscale hall-magnetohydrodynamic turbulence in the solar wind. Astrophys. J. 656, 560.Google Scholar
Gary, S. P. 1993 Theory of Space Plasma Microinstabilities. Cambridge: Cambridge University Press.Google Scholar
Gary, S. P., Saito, S. and Li, H. 2008 Cascade of whistler turbulence: particle-in-cell simulations. Geophys. Res. Lett. 35, L02 104.Google Scholar
Greco, A., Chuychai, P., Matthaeus, W. H., Servidio, S. and Dmitruk, P. 2008 Intermittent MHD structures and classical discontinuities. Geophys. Res. Lett. 35, L19 111.CrossRefGoogle Scholar
Greco, A., Matthaeus, W. H., Servidio, S., Chuychai, P. and Dmitruk, P. 2009 Statistical analysis of discontinuities in solar wind ACE data and comparison with intermittent MHD turbulence. Astrophys. J. Lett. 691, L111.Google Scholar
Greco, A. and Perri, S. 2014 Identification of high shears and compressive discontinuities in the inner heliosphere. Astrophys. J. 784, 163.Google Scholar
Greco, A., Valentini, F., Servidio, S. and Matthaeus, W. H. 2012 Inhomogeneous kinetic effects related to intermittent magnetic discontinuities. Phys. Rev. E 86, 066 405.Google Scholar
Hada, T., Koga, D., and Yamamoto, E. 2003 Phase coherence of MHD waves in the solar wind. Space Sci. Rev. 107, 463.Google Scholar
Hansteen, V. H., Leer, E. and Holzer, T. E. 1997 The role of helium in the outer solar atmosphere. Astrophys. J. 482, 498.CrossRefGoogle Scholar
Haynes, C. T., Burgess, D. and Camporeale, E. 2014 Reconnection and electron temperature anisotropy in sub-proton scale plasma turbulence. Astrophys. J. 783, 38.Google Scholar
Hellinger, P., Trávníček, P., Kasper, J. C. and Lazarus, A. J. 2006 Solar wind proton temperature anisotropy: linear theory and WIND/SWE observations. Geophys. Res. Lett. 33, L09 101.Google Scholar
Hellinger, P. and Trávníček, P. M. 2014 Solar wind protons at 1 AU: trends and bounds, constraints and correlations. Astrophys. J. Lett. 784, L15.Google Scholar
Heuer, M. and Marsch, E. 2007 Diffusion plateaus in the velocity distributions of fast solar wind protons. J. Geophys. Res. 112, A03 102.Google Scholar
Hollweg, J. V. and Isenberg, P. A. 2002 Generation of the fast solar wind: a review with emphasis on the resonant cyclotron interaction. J. Geophys. Res. 107, 1147.Google Scholar
Howes, G. G., Dorland, W., Cowley, S. C., Hammett, G. W., Quataert, E., Schekochihin, A. A. and Tatsuno, T. 2008 Kinetic simulations of magnetized turbulence in astrophysical plasmas. Phys. Rev. Lett. 100, 065 004.Google Scholar
Howes, G. G., Klein, K. G. and TenBarge, J. M. 2014 The quasilinear premise for the modeling of plasma turbulence. ArXiv e-prints.Google Scholar
Hunana, P., Goldstein, M. L., Passot, T., Sulem, P. L., Laveder, D. and Zank, G. P. 2013 Polarization and compressibility of oblique kinetic Alfvén waves. Astrophys. J. 766, 93.CrossRefGoogle Scholar
Karimabadi, H. et al. 2013 Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas. Phys. Plasmas 20, 012 303.Google Scholar
Kasper, J. C., Lazarus, A. J. and Gary, S. P. 2002 Wind/SWE observations of firehose constraint on solar wind proton temperature anisotropy. Geophys. Res. Lett. 29, 1839.Google Scholar
Kasper, J. C., Lazarus, A. J., and Gary, S. P. 2008 Hot solar-wind helium: direct evidence for local heating by Alfven-cyclotron dissipation. Phys. Rev. Lett. 101, 261 103.Google Scholar
Kennel, C. F. and Engelmann, F. 1966 Velocity space diffusion from weak plasma turbulence in a magnetic field. Phys. Fluids 9, 2377–2388.Google Scholar
Kerr, R. M. 1987 Histograms of helicity and strain in numerical turbulence. Phys. Rev. Lett. 59, 783.Google Scholar
Kiyani, K. H., Chapman, S. C., Khotyaintsev, Y. V., Dunlop, M. W. and Sahraoui, F. 2009 Global scale-invariant dissipation in collisionless plasma turbulence. Phys. Rev. Lett. 103, 075 006.Google Scholar
Laveder, D., Marradi, L., Passot, T. and Sulem, P. L. 2011 Fluid simulations of mirror constraints on proton temperature anisotropy in solar wind turbulence. Geophys. Res. Lett. 38, 17 108.Google Scholar
Laveder, D., Passot, T. and Sulem, P. L. 2013 Intermittent dissipation and lack of universality in one-dimensional Alfvénic turbulence. Phys. Lett. A 377, 1535.Google Scholar
Lesieur, M., Yaglom, A. and David, F. 2001 New Trends in Turbulence. Spinger.CrossRefGoogle Scholar
Maksimovic, M., Pierrard, V. and Lemaire, J. F. 1997 A kinetic model of the solar wind with Kappa distribution functions in the corona. Astron. Astrophys. 324, 725.Google Scholar
Malaspina, D. M., Newmann, D. L., Willson III, L. B., Goets, K., Kellog, P. J. and Kerstin, K. 2013 Electrostatic solitary waves in the solar wind: evidence for instability at solar wind current sheets. J. Geophys. Res. 118, 591.Google Scholar
Mariani, F., Bavassano, B., Villante, U. and Ness, N. F. 1973 Variations of the occurrence rate of discontinuities in the interplanetary magnetic field. J. Geophys. Res. 78, 8011.Google Scholar
Markovskii, S. A. and Vasquez, B. J. 2011a A short-timescale channel of dissipation of the strong solar wind turbulence. Astrophys. J. 739, 22.Google Scholar
Markovskii, S. A. and Vasquez, B. J. 2011b A short-timescale channel of dissipation of the strong solar wind turbulence. Astrophys. J. 739, 22.Google Scholar
Marsch, E. 2006 Kinetic physics of the solar corona and solar wind. Living Rev. Solar Phys. 3, 1.Google Scholar
Marsch, E., Ao, X.-Z. and Tu, C.-Y. 2004 On the temperature anisotropy of the core part of the proton velocity distribution function in the solar wind. J. Geophys. Res. 109, 4102.Google Scholar
Marsch, E., Muhlhauser, K.-H., Rosenbauer, H., Schwenn, R., and Neubauer, F.-M. 1982 Solar wind helium ions: observations of the Helios solar probes between 0.3 and 1 AU. J. Geophys. Res. 87, 35.Google Scholar
Marsch, E., Schwenn, R., Rosenbauer, H., Muehlhaeuser, K.-H., Pilipp, W. and Neubauer, F. M. 1982 Solar wind protons - three-dimensional velocity distributions and derived plasma parameters measured between 0.3 and 1 AU. J. Geophys. Res. 87, 52.Google Scholar
Maruca, B. A., Kasper, J. C. and Bale, S. D. 2011 What are the relative roles of heating and cooling in generating solar wind temperature anisotropies? Phys. Rev. Lett. 107, 201 101.CrossRefGoogle ScholarPubMed
Maruca, B. A., Kasper, J. C. and Gary, S. P. 2012 Instability-driven limits on helium temperature anisotropy in the solar wind: observations and linear Vlasov analysis. Astrophys. J. 748, 137.Google Scholar
Matteini, L., Landi, S., Hellinger, P., Pantellini, F., Maksimovic, M., Velli, M., Goldstein, B. E. and Marsch, E. 2007 Evolution of the solar wind proton temperature anisotropy from 0.3 to 2.5 AU. Geophys. Res. Lett. 34, L20 105.Google Scholar
Matteini, L., Landi, S., Velli, M. and Matthaeus, W. H. 2013 Proton temperature anisotropy and magnetic reconnection in the solar wind: effects of kinetic instabilities on current sheet stability. Astrophys. J. 763, 142.Google Scholar
Matthaeus, W. H. and Goldstein, M. L. 1982 Stationarity of magnetohydrodynamic fluctuations in the solar wind. J. Geophys. Res. 87, 10 347.Google Scholar
Matthaeus, W. H., Goldstein, M. L. and Roberts, D. A. 1990 Evidence for the presence of quasi-two-dimensional, nearly incompressible fluctuations in the solar wind. J. Geophys. Res. 95, 20 673.Google Scholar
Matthaeus, W. H. and Montgomery, D. 1980 Selective decay hypothesis at high mechanical and magnetic Reynolds numbers. Ann. New York Acad. Sci. 357, 203.Google Scholar
Matthaeus, W. H. and Montgomery, D. 1981 Nonlinear evolution of the sheet pinch. J. Plasma Phys. 25, 11.Google Scholar
Matthaeus, W. H., Servidio, S. and Dmitruk, P. 2008 Comment on “kinetic simulations of magnetized turbulence in astrophysical plasmas”. Phys. Rev. Lett. 101, 149 501.Google Scholar
Matthaeus, W. H., Servidio, S., Dmitruk, P., Carbone, V., Oughton, S., Wan, M. and Osman, K. T. 2012 Local anisotropy, higher order statistics, and turbulence spectra. Astrophys. J. 750, 103.Google Scholar
Matthaeus, W. H. et al. 2014 Nonlinear and linear timescales near kinetic scales in solar wind turbulence. ArXiv e-prints.Google Scholar
Matthews, A. P. 1994 Current advance method and cyclic leapfrog for 2D multispecies hybrid plasma simulations. J. Comput. Phys. 112, 102.Google Scholar
Mikhailovskii, A. B. 1974 Theory of plasma instabilities. In: Instabilities in an Inhomogeneous Plasma, Vol. 2. New York: Plenum.Google Scholar
Mininni, P. D. and Pouquet, A. 2009 Finite dissipation and intermittency in magnetohydrodynamics. Phys. Rev. E 80, 025 401.Google Scholar
Narita, Y., Gary, S. P., Saito, S., Glassmeier, K.-H. and Motschmann, U. 2011 Dispersion relation analysis of solar wind turbulence. Geophys. Res. Lett. 38, 5101.Google Scholar
Neugebauer, M. 2006 Comment on the abundances of rotational and tangential discontinuities in the solar wind. J. Geophys. Res. 111, 4103.Google Scholar
Osman, K. T., Matthaeus, W. H., Gosling, J. T., Greco, A., Servidio, S., Hnat, B., Chapman, S. C. and Phan, T. D. 2014 Magnetic reconnection and intermittent turbulence in the solar wind. Phys. Rev. Lett. 112, 215 002.CrossRefGoogle Scholar
Osman, K. T., Matthaeus, W. H., Greco, A. and Servidio, S. 2011 Evidence for inhomogeneous heating in the solar wind. Astrophys. J. Lett. 727, L11.Google Scholar
Osman, K. T., Matthaeus, W. H., Wan, M. and Rappazzo, A. F. 2012a Intermittency and local heating in the solar wind. Phys. Rev. Lett. 108, 261 102.Google Scholar
Osman, K. T., Matthaeus, W. H., Hnat, B. and Chapman, S. C. 2012b Kinetic signatures and intermittent turbulence in the solar wind plasma. Phys. Rev. Lett. 108, 261 103.CrossRefGoogle ScholarPubMed
Parashar, T. N., Servidio, S., Breech, B., Shay, M. A. and Matthaeus, W. H. 2010 Kinetic driven turbulence: structure in space and time. Phys. Plasmas 17, 102 304.Google Scholar
Parashar, T. N., Servidio, S., Shay, M. A., Breech, B. and Matthaeus, W. H. 2011 Effect of driving frequency on excitation of turbulence in a kinetic plasma. Phys. Plasmas 18, 092 302.Google Scholar
Parker, E. N. 1988 Nanoflares and the solar X-ray corona. Astrophys. J. 330, 474.CrossRefGoogle Scholar
Perri, S., Goldstein, M. L., Dorelli, L. J. and Sahraoui, F. 2012 Detection of small-scale structures in the dissipation regime of solar-wind turbulence. Phys. Rev. Lett. 109, 191 101.CrossRefGoogle ScholarPubMed
Perrone, D., Valentini, F., Servidio, S., Dalena, S. and Veltri, P. 2013 Vlasov simulations of multi-ion plasma turbulence in the solar wind. Astrophys. J. 762, 99.Google Scholar
Perrone, D., Valentini, F., Servidio, S., Dalena, S. and Veltri, P. 2014 Analysis of intermittent heating in a multi-component turbulent plasma. Europhys. J.D. 68, 7.Google Scholar
Perrone, D., Valentini, F. and Veltri, P. 2011 The role of alpha particles in the evolution of the solar-wind turbulence toward short spatial scales. Astrophys. J. 741, 43.Google Scholar
Perrone, D. et al. 2013 Nonclassical transport and particle-field coupling: from laboratory plasmas to the solar wind. Space Sci. Rev. 178, 233.Google Scholar
Sahraoui, F., Goldstein, M. L., Belmont, G., Canu, P. and Rezeau, L. 2010 Three dimensional anisotropic k spectra of turbulence at subproton scales in the solar wind. Phys. Rev. Lett. 105, 131 101.Google Scholar
Sahraoui, F., Goldstein, M. L., Robert, P. and Khotyaintsev, Yu. V. 2009 Evidence of a cascade and dissipation of solar wind turbulence at electron scales. Phys. Rev. Lett. 102, 231 102.Google Scholar
Saito, S., Gary, S. P., Li, H. and Narita, Y. 2008 Whistler turbulence: particle-in-cell simulations. Phys. Plasmas 15, 102 305.Google Scholar
Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, G. W., Howes, G. G., Quataert, E. and Tatsuno, T. 2009 Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophys. J. Suppl. 182, 310.CrossRefGoogle Scholar
Servidio, S., Carbone, V., Primavera, L., Veltri, P. and Stasiewicz, K. 2007 Compressible turbulence in hall magnetohydrodynamics. Planet. Space Sci. 55, 2239.Google Scholar
Servidio, S., Matthaeus, W. H., Shay, M. A., Cassak, P. A. and Dmitruk, P. 2009 Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 102, 115 003.CrossRefGoogle ScholarPubMed
Servidio, S., Matthaeus, W. H., Shay, M. A., Dmitruk, P., Cassak, P. A. and Wan, M. 2010 Statistics of magnetic reconnection in two-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 17, 032 315.Google Scholar
Servidio, S., Osman, K. T., Valentini, F., Perrone, D., Califano, F., Chapman, S., Matthaeus, W. H. and Veltri, P. 2014 Proton kinetic effects in Vlasov and solar wind turbulence. Astrophys. J. Lett. 781, L27.Google Scholar
Servidio, S., Valentini, F., Califano, F. and Veltri, P. 2012 Local kinetic effects in two-dimensional plasma turbulence. Phys. Rev. Lett. 108, 045 001.Google Scholar
Shay, M. A., Drake, J. F., Denton, R. E. and Biskamp, D. 1998 Structure of the dissipation region during collisionless magnetic reconnection. J. Geophys. Res. 103, 9165.Google Scholar
She, Z.-S., Jackson, E. and Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226.Google Scholar
Siggia, E. D. 1981 Numerical study of small-scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375.Google Scholar
Smith, C. W., Vasquez, B. J. and Hamilton, K. 2006 Interplanetary magnetic fluctuation anisotropy in the inertial range. J. Geophys. Res. 111, A09 111.Google Scholar
Sonnerup, B. U. O. and Cahill, L. J. Jr., 1967 Magnetopause structure and attitude from explorer 12 observations. J. Geophys. Res. 72, 171.Google Scholar
Sorriso-Valvo, L., Carbone, V., Veltri, P., Consolini, G. and Bruno, R. 1999 Intermittency in the solar wind turbulence through probability distribution functions of fluctuations. Geophys. Res. Lett. 26, 1801.Google Scholar
Sreenivasan, K. R. and Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435.Google Scholar
Sundkvist, D., Retinó, A., Vaivads, A. and Bale, S. D. 2007 Dissipation in turbulent plasma due to reconnection in thin current sheets. Phys. Rev. Lett. 99, 025 004.Google Scholar
TenBarge, J. M., Howes, G. G. and Dorland, W. 2013 Collisionless damping at electron scales in solar wind turbulence. Astrophys. J. 774, 139.CrossRefGoogle Scholar
Tessein, J. A., Matthaeus, W. H., Wan, M., Osman, K. T., Ruffolo, D., and Giacalone, J. 2013 Association of suprathermal particles with coherent structures and shocks. Astrophys. J. Lett. 776, L8.Google Scholar
Tsurutani, B. T. and Smith, E. J. 1979 Interplanetary discontinuities -temporal variations and the radial gradient from 1 to 8.5 AU. J. Geophys. Res. 84, 2773.Google Scholar
Tu, C.-Y., Marsch, E. and Qin, Z.-R. 2004 Dependence of the proton beam drift velocity on the proton core plasma beta in the solar wind. J. Geophys. Res. (Space Physics) 109, 5101.Google Scholar
Tu, C. -Y., Wang, L. -H. and Marsch, E. 2002 Formation of the proton beam distribution in high-speed solar wind. J. Geophys. Res. 107, 1291.Google Scholar
Uritsky, V. M., Pouquet, A., Rosenberg, D., Mininni, P. D. and Donovan, E. F. 2010 Structures in magnetohydrodynamic turbulence: detection and scaling. Phys. Rev. E 82, 056 326.Google Scholar
Vainshtein, S. I., Du, Y. and Sreenivasan, K. R. 1994 Sign-singular measure and its association with turbulent scalings. Phys. Rev. E 49, 2521.Google Scholar
Valentini, F., Califano, F. and Veltri, P. 2010 Two-dimensional kinetic turbulence in the solar wind. Phys. Rev. Lett. 104, 205 002.CrossRefGoogle ScholarPubMed
Valentini, F., Perrone, D. and Veltri, P. 2011 Short-wavelength electrostatic fluctuations in the solar wind. Astrophys. J. 739, 54.Google Scholar
Valentini, F., Trávníček, P., Califano, F., Hellinger, P. and Mangeney, A. 2007 A hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma. J. Comput. Phys. 225, 753.Google Scholar
Valentini, F. and Veltri, P. 2009 Electrostatic short-scale termination of solar-wind turbulence. Phys. Rev. Lett. 102, 225 001.CrossRefGoogle ScholarPubMed
Valentini, F., Veltri, P., Califano, F. and Mangeney, A. 2008 Cross-scale effects in solar-wind turbulence. Phys. Rev. Lett. 101, 025 006.Google Scholar
Vasquez, B. J., Abramenko, V. I., Haggerty, D. K., and Smith, C. W. 2007 Numerous small magnetic field discontinuities of Bartels rotation 2286 and the potential role of Alfvénic turbulence. J. Geophys. Res. 112, 11 102.Google Scholar
Vasquez, B. J. and Markovskii, S. A. 2012 Velocity power spectra from cross-field turbulence in the proton kinetic regime. Astrophys. J. 747, 19.Google Scholar
Veltri, P. 1999 MHD turbulence in the solar wind: self-similarity, intermittency and coherent structures. Plasma Phys. Control. Fusion 41, A787.Google Scholar
Vincent, A. and Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1.Google Scholar
Wang, X., Tu, C., He, J., Marschand, E. and Wang, L. 2013 On intermittent turbulence heating of the solar wind: differences between tangential and rotational discontinuities. Astrophys. J. Lett. 772, L14.Google Scholar
Wu, C. C. and Chang, T. 2000 2D MHD simulation of the emergence and merging of coherent structures. Geophys. Res. Lett. 27, 863.Google Scholar
Wu, P., Perri, S., Osman, K. T., Wan, M., Matthaeus, W. H., Shay, M. A., Goldstein, M. L., Karimabadi, H. and Chapman, S. 2013 Intermittent heating in solar wind and kinetic simulations. Astrophys. J. Lett. 763, L30.Google Scholar
Zhdankin, V., Uzdensky, D. A., Perez, J. C. and Boldyrev, S. 2013 Statistical analysis of current sheets in three-dimensional magnetohydrodynamic turbulence. Astrophys. J. 771, 124.Google Scholar