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Local energy transfer rate and kinetic processes: the fate of turbulent energy in two-dimensional hybrid Vlasov–Maxwell numerical simulations

Part of: Focus on Space Plasmas Professor Francesco Pegoraro

Published online by Cambridge University Press:  15 April 2018

Luca Sorriso-Valvo Open the ORCID record for Luca Sorriso-Valvo [Opens in a new window] ,
Denise Perrone ,
Oreste Pezzi ,
Francesco Valentini ,
Sergio Servidio ,
Ioannis Zouganelis  and
Pierluigi Veltri
Luca Sorriso-Valvo*
Affiliation:
Nanotec/CNR, Sede di Cosenza, Ponte P. Bucci, Cubo 31C, 87036 Rende, Italy
Denise Perrone
Affiliation:
European Space Agency, ESAC, 28692, Madrid, Spain Department of Physics, Imperial College London, London SW7 2AZ, UK
Oreste Pezzi
Affiliation:
Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, Cubo 31C, 87036 Rende, Italy
Francesco Valentini
Affiliation:
Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, Cubo 31C, 87036 Rende, Italy
Sergio Servidio
Affiliation:
Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, Cubo 31C, 87036 Rende, Italy
Ioannis Zouganelis
Affiliation:
European Space Agency, ESAC, 28692, Madrid, Spain
Pierluigi Veltri
Affiliation:
Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, Cubo 31C, 87036 Rende, Italy
*
†Email address for correspondence: lucasorriso@gmail.com
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Abstract

The nature of the cross-scale connections between the inertial-range turbulent energy cascade and the small-scale kinetic processes in collisionless plasmas is explored through the analysis of two-dimensional hybrid Vlasov–Maxwell numerical simulation (HVM), with $\unicode[STIX]{x1D6FC}$ particles, and through a proxy of the turbulent energy transfer rate, namely the local energy transfer (LET) rate. Correlations between pairs of variables, including those related to kinetic processes and to deviation from Maxwellian distributions, are first evidenced. Then, the general properties and the statistical scaling laws of the LET are described, confirming its reliability for the description of the turbulent cascade and revealing its textured topology. Finally, the connection between such proxy and the diagnostic variables is explored using conditional averaging, showing that several quantities are enhanced in the presence of large positive energy flux, and reduced near sites of negative flux. These observations can help in determining which processes are involved in the dissipation of energy at small scales, as for example the ion-cyclotron or mirror instabilities typically associated with perpendicular anisotropy of temperature.

Keywords

plasma nonlinear phenomenaplasma simulationspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 2 , April 2018 , 725840201
Copyright
© Cambridge University Press 2018 

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References

Alexandrova, O., Carbone, V., Veltri, P. & Sorriso-Valvo, L. 2008 Small-scale energy cascade of the solar wind turbulence. Astrophys. J. 674, 1153.Google Scholar
Alexandrova, O., Chen, C. H. K., Sorriso-Valvo, L., Horbury, T. S. & Bale, S. D. 2013 Solar wind turbulence and the role of ion instabilities. Space Sci. Rev. 178, 101.Google Scholar
Andrés, N., Galtier, S. & Sahraoui, F. 2018 Exact law for homogeneous compressible Hall magnetohydrodynamics turbulence. Phys. Rev. E 97, 013204.Google ScholarPubMed
Andrés, N. & Sahraoui, F. 2017 Alternative derivation of exact law for compressible and isothermal magnetohydrodynamics turbulence. Phys. Rev. E 96, 053205.Google Scholar
Araneda, J. A., Maneva, Y. & Marsch, E. 2009 Preferential heating and acceleration of alpha particles by Alfven-cyclotron waves. Phys. Rev. Lett. 102, 175001.CrossRefGoogle ScholarPubMed
Aunai, N., Hesse, M. & Kuznetsova, M. 2013 Electron nongyrotropy in the context of collisionless magnetic reconnection. Phys. Plasmas 20, 092903.Google Scholar
Breuillard, H., Yordanova, E., Vaivads, A. & Alexandrova, O. 2016 The effects of kinetic instabilities on small-scale turbulence in Earth’s magnetosheath. Astrophys. J. 829, 54.Google Scholar
Bruno, R., Bavassano, B., Pietropaolo, E., Carbone, V. & Veltri, P. 1999 Effects of intermittency on interplanetary velocity and magnetic field fluctuations anisotropy. Geophys. Res. Lett. 26, 3185–3188.Google Scholar
Bruno, R. & Carbone, V. 2013 The solar wind as a turbulence laboratory. Living Rev. Solar Phys. 10, 1.Google Scholar
Burch, J. L., Moore, T. E., Torbert, R. B. & Giles, B. L. 2016a Magnetospheric multiscale overview and science objectives. Space Sci. Rev. 199, 5.Google Scholar
Burch, J. L., Torbert, R. B., Phan, T. D., Chen, L.-J., Moore, T. E., Ergun, R. E., Eastwood, J. P., Gershman, D. J., Cassak, P. A., Argall, M. R. et al. 2016b Electron-scale measurements of magnetic reconnection in space. Science 352, 6290.CrossRefGoogle ScholarPubMed
Burlaga, L. F. 1991 Intermittent turbulence in the solar wind. J. Geophys. Res. 96, 5847.Google Scholar
Chasapis, A., Retinò, A., Sahraoui, F., Vaivads, A., Khotyaintsev, Yu. V., Sundkvist, D., Greco, A., Sorriso-Valvo, L. & Canu, P. 2015 Thin current sheets and associated electron heating in turbulent space plasma. Astrophys. J. Lett. 804, L1.Google Scholar
Camporeale, E. & Burgess, D. 2011 The dissipation of solar wind turbulent fluctuations at electron scales. Astrophys. J. 730, 114.Google Scholar
Carbone, V., Marino, R., Sorriso-Valvo, L., Noullez, A. & Bruno, R. 2009 Scaling laws of turbulence and heating of fast solar wind: the role of density fluctuations. Phys. Rev. Lett. 103, 115001.Google Scholar
Cerri, S. S., Califano, F., Jenko, F., Told, D. & Rincon, F. 2016 Subproton-scale cascades in solar wind turbulence: driven hybrid-kinetic simulations. Astrophys. J. Lett. 822, L12.CrossRefGoogle Scholar
Cerri, S. S., Kunz, M. W. & Califano, F. 2018 Dual phase-space cascades in 3D hybrid-Vlasov–Maxwell turbulence. Astrophys. J. Lett.; arXiv:1802.06133 (accepted).Google Scholar
Cerri, S. S., Servidio, S. & Califano, F. 2017 Kinetic cascade in solar-wind turbulence: 3D3V hybrid-kinetic simulations with electron inertia. Astrophys. J. Lett. 846, L18.Google Scholar
Chasapis, A., Matthaeus, W. H., Parashar, T. N., LeContel, O, Retinò, A., Breuillard, H., Khotyaintsev, Yu. V., Vaivads, A., Lavraud, B., Eriksson, E. et al. 2017 Electron heating at kinetic scales in magnetosheath turbulence. Astrophys. J. 836, 247.CrossRefGoogle Scholar
Chen, C. H. C. 2016 Recent progress in astrophysical plasma turbulence from solar wind observations. J. Plasma Phys. 82, 535820602.Google Scholar
Coburn, J. T., Smith, C. W., Vasquez, B. J., Forman, M. A. & Stawarz, J. E. 2014 Variable cascade dynamics and intermittency in the solar wind at 1 AU. Astrophys. J. 786, 52.Google Scholar
Del Sarto, D., Pegoraro, F. & Califano, F. 2016 Pressure anisotropy and small spatial scales induced by velocity shear. Phys. Rev. E 93, 053203.Google Scholar
Farge, M. 1992 Wavelet transfroms and their applications to turbulence. Annu. Rev. Fluid Mech. 24, 395.Google Scholar
Franci, L., Hellinger, P., Matteini, L., Verdini, A. & Landi, S. 2016 SOLAR WIND 14, Proc. Fourteenth International Solar Wind Conferance 1720. (ed. Wang, L. et al. ). AIP.Google Scholar
Franci, L., Landi, S., Verdini, A., Matteini, L. & Hellinger, P. 2018 Solar wind turbulent cascade from MHD to sub-ion scales: large-size 3D hybrid particle-in-cell simulations. Astrophys. J. 853, 26.CrossRefGoogle Scholar
Franci, L., Verdini, A., Matteini, L., Landi, S. & Hellinger, P. 2015 Solar wind turbulence from MHD to sub-ion scales: high resolution hybrid simulations. Astrophys. J. Lett. 804, L39.CrossRefGoogle Scholar
Frisch, U. P. 1995 Turbulence: the Legacy of A.N. Kolmogorov. Cambridge University Press.Google Scholar
Greco, A., Chuychai, P., Matthaeus, W. H., Servidio, S. & Dimitruk, P. 2008 Intermittent MHD structures and classical discontinuities. Geophys. Res. Lett. 35, L19111.Google Scholar
Greco, A. & Perri, S. 2014 Identification of high shear and compressive discontinuities in the inner heliosphere. Astrophys. J. 784, 163.Google Scholar
Greco, A., Perri, S., Servidio, S., Yordanova, E. & Veltri, P. 2016 The complex structure of magnetic field discontinuities in the turbulent solar wind. Astrophys. J. Lett. 823, L39.Google Scholar
Greco, A., Valentini, F., Servidio, S. & Matthaeus, W. H. 2012 Inhomogeneous kinetic effects related to intermittent magnetic discontinuities. Phys. Rev. E 86, 066405.Google Scholar
Groselj, D., Cerri, S. S., Navarro, A. B., Willmott, C., Told, D., Loureiro, N. F., Califano, F. & Jenko, F. 2017 Fully kinetic versus reduced-kinetic modeling of collisionless plasma turbulence. Astrophys. J. 847, 28.CrossRefGoogle Scholar
Haggerty, C. C., Parashar, T. N., Matthaeus, W. H., Shay, M. A., Yang, Y., Wan, M., Wu, P. & Servidio, S. 2017 Exploring the statistics of magnetic reconnection X-points in kinetic particle-in-cell turbulence. Phys. Plasmas 24, 102308.CrossRefGoogle Scholar
Howes, G. G. 2016 The dynamical generation of current sheets in astrophysical plasma turbulence. Astrophys. J. Lett. 827, L28.Google Scholar
Howes, G. G., McCubbin, A. J. & Klein, K. G. 2018 Spatially localized particle energization by Landau damping in current sheets produced by strong Alfvn wave collisions. J. Plasma Phys. 84, 905840105.CrossRefGoogle Scholar
Huba, J. 1996 The Kelvin–Helmholtz instability: finite Larmor radius magnetohydrodynamics. Geophys. Res. Lett. 23, 2907.CrossRefGoogle Scholar
Karimabadi, H., Roytershteyn, V., Wan, M., Matthaeus, W. H., Daughton, W., Wu, P., Shay, M., Loring, B., Borovsky, J., Leonardis, W. et al. 2013 Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas. Phys. Plasmas 20, 012303.Google Scholar
Kasper, J. C., Lazarus, A. J. & Gary, S. P. 2008 Hot solar-wind helium: direct evidence for local heating by Alfv-cyclotron dissipation. Phys. Rev. Lett. 101, 261103.Google Scholar
Kiyani, K. H., Chapman, S. C., Khotyaintsev, Yu. V., Dunlop, M. W. & Sahraoui, F. 2009 Global scale-invariant dissipation in collisionless plasma turbulence. Phys. Rev. Lett. 103, 075006.CrossRefGoogle ScholarPubMed
Lion, S., Alexandrova, O. & Zaslavsky, A. 2016 Coherent events and spectral shape at ion kinetic scales in fast solar wind turbulence. Astrophys. J. 824, 47.Google Scholar
MacBride, B. T., Forman, M. A. & Smith, C. W. 2005 Solar Wind 11/SOHO 16, Connecting Sun and Heliosphere. (ed. Fleck, B., Zurbuchen, T. H. & Lacoste, H.), European Space Agency, 592, p. 613.Google Scholar
MacBride, B. T., Smith, C. W. & Forman, M. A. 2008 The turbulent cascade at 1 AU: energy transfer and the third-order scaling for MHD. Astrophys. J. 679, 1644.CrossRefGoogle Scholar
Maneva, Y. G., Vinas, A. F., Moya, P. S., Wicks, R. & Poedts, S. 2015 Dissipation of parallel and oblique Alfvén-cyclotron waves – implications for heating of alpha particles in the solar wind. Astrophys. J. 814, 33.Google Scholar
Marino, R., Sorriso-Valvo, L., Carbone, V., Noullez, A., Bruno, R. & Bavassano, B. 2008 Heating the solar wind by a magnetohydrodynamic turbulent energy cascade. Astrophys. J. Lett. 667, L71.Google Scholar
Marino, R., Sorriso-Valvo, L., D’Amicis, R., Carbone, V., Bruno, R. & Veltri, V. 2012 On the occurrence of the third-order scaling in high latitude solar wind. Astrophys. J. 750, 41.CrossRefGoogle Scholar
Markovskii, S. A., Vasquez, B. J., Smith, C. W. & Hollweg, J. V. 2006 Dissipation of the perpendicular turbulent cascade in the solar wind. Astrophys. J. 639, 1177.Google Scholar
Marsch, E. 2006 Kinetic physics of the solar corona and solar wind. Living Rev. Solar Phys. 3, 1.CrossRefGoogle Scholar
Marsch, E. & Tu, C.-Y. 1997 Intermittency, non-Gaussian statistics and fractal scaling of MHD fluctuations in the solar wind. Nonlinear Process. Geophys. 4, 101.Google Scholar
Martin, L. N., De Vita, G., Sorriso-Valvo, L., Dimitruck, P., Nigro, G., Primavera, L. & Carbone, V. 2013 Cancellation properties in Hall magnetohydrodynamics with a strong guide magnetic field. Phys. Rev. E 88, 063107.Google Scholar
Maruca, B. A., Kasper, J. C. & Gary, S. P. 2012 Instability-drive limits on helium temperature anisotropy in the solar wind: observations and linear Vlasov analysis. Astrophys. J. 748, 137.Google Scholar
Matteini, L., Hellinger, P., Goldstein, B. E., Landi, S., Velli, M. & Neugebauer, M. 2013 Signatures of kinetic instabilities in the solar wind. J. Geophys. Res. Space Phys. 118, 2771.CrossRefGoogle Scholar
Osman, K. T., Matthaeus, W. H., Greco, A. & Servidio, S. 2011 Evidence for inhomogeneous heating in the solar wind. Astrophys. J. Lett. 727, L11.CrossRefGoogle Scholar
Osman, K. T., Matthaeus, W. H., Hnat, B. & Chapman, S. C. 2012 Kinetic signatures and Intermittent turbulence in the solar wind plasma. Phys. Rev. Lett. 108, 261103.CrossRefGoogle ScholarPubMed
Parashar, T. N. & Matthaeus, W. H. 2016 Propinquity of current and vortex structures: effects on collisionless plasma heating. Astrophys. J. 832, 57.Google Scholar
Parashar, T. N., Matthaeus, W. H., Shay, M. A. & Wan, M. 2015 Transition from kinetic to MHD behavior in a collisionless plasma. Astrophys. J. 811, 112.Google Scholar
Parashar, T. N., Shay, M. A., Cassak, P. A. & Matthaeus, W. H. 2009 Kinetic dissipation and anisotropic heating in a turbulent collisionless plasma. Phys. Plasmas 16, 032310.CrossRefGoogle Scholar
Perrone, D., Alexandrova, O., Mangeney, A., Maksimovic, M., Lacombe, C., Rakoto, V., Kasper, J. C. & Jovanovic, D. 2016 Compressive coherent structures at ion scales in the slow solar wind. Astrophys. J. 826, 196.CrossRefGoogle Scholar
Perrone, D., Alexandrova, O., Roberts, O. W., Lion, S., Lacombe, C., Walsh, A., Maksimovic, M. & Zouganelis, I. 2017 Coherent structures at ion scales in fast solar wind: cluster observations. Astrophys. J. 849, 49.Google Scholar
Perrone, D., Bourouaine, S., Valentini, F., Marsch, E. & Veltri, P. 2014a Generation of temperature anisotropy for alpha particle velocity distributions in solar wind at 0.3 AU: Vlasov simulations and Helios observations. J. Geophys. Res. Space Phys. 119, 2400.Google Scholar
Perrone, D., Valentini, F., Servidio, S., Dalena, S. & 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. & Veltri, P. 2014b Analysis of intermittent heating in a multi-component turbulent plasma. Eur. Phys. J. D 68, 209.Google Scholar
Perrone, D., Valentini, F. & 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
Peyret, R. & Taylor, T. D. 1986 Computational Methods for Fluid Flow. Springer.Google Scholar
Pezzi, O. 2017 Solar wind collisional heating. J. Plasma Phys. 83, 555830301.Google Scholar
Pezzi, O., Malara, F., Servidio, S., Valentini, F., Parashar, T. N., Matthaeus, W. H. & Veltri, P. 2017a Turbulence generation during the head-on collision of Alfvénic wave packets. Phys. Rev. E 96, 023201.Google Scholar
Pezzi, O., Parashar, T. N., Servidio, S., Valentini, F., Vásconez, C. L., Yang, Y., Malara, F., Matthaeus, W. H. & Veltri, P. 2017b Colliding Alfvénic wave packets in magnetohydrodynamics, Hall and kinetic simulations, Revisiting a classic: the Parker–Moffatt problem. J. Plasma Phys. 83, 905830105.Google Scholar
Pezzi, O., Parashar, T. N., Servidio, S., Valentini, F., Vásconez, C. L., Yang, Y., Malara, F., Matthaeus, W. H. & Veltri, P. 2017c Revisiting a classic: the Parker–Moffatt problem. Astrophys. J. 834, 166.CrossRefGoogle Scholar
Pezzi, O., Servidio, S., Perrone, D., Valentini, F., Sorriso-Valvo, L., Greco, A., Matthaeus, W. H. & Veltri, P. 2018 Velocity-space cascade in magnetized plasmas: numerical simulations. Phys. Plasmas; arXiv:1803.01633 (submitted).CrossRefGoogle Scholar
Pezzi, O., Valentini, F., Perrone, D. & Veltri, P. 2013 Eulerian simulations of collisional effects on electrostatic plasma waves. Phys. Plasmas 20, 092111.Google Scholar
Pezzi, O., Valentini, F., Perrone, D. & Veltri, P. 2014 Erratum: ‘Eulerian simulations of collisional effects on electrostatic plasma waves’ [Phys. Plasmas 20, 092111 (2013)]. Phys. Plasmas 21, 019901.Google Scholar
Pezzi, O., Valentini, F. & Veltri, P. 2015a Collisional relaxation: Landau versus Dougherty operator. J. Plasma Phys. 81, 305810107.Google Scholar
Pezzi, O., Valentini, F. & Veltri, P. 2015b Nonlinear regime of electrostatic waves ropagation in presence of electron-electron collisions. Phys. Plasmas 22, 042112.Google Scholar
Pezzi, O., Valentini, F. & Veltri, P. 2016 Collisional relaxation of fine velocity structures in plasmas. Phys. Rev. Lett. 116, 145001.Google Scholar
Politano, H. & Pouquet, A. 1998 Dynamical length scales for turbulent magnetized flows. Geophys. Res. Lett. 25, 273.Google Scholar
Pucci, F., Vasconez, C. L., Pezzi, O., Servidio, S., Valentini, F., Matthaeus, W. H. & Malara, F. 2016 From Alfvén waves to kinetic Alfvén waves in an inhomogeneous equilibrium structure. J. Geophys. Res. Space Phys. 121, 1024–1045.Google Scholar
Retinò, A., Sundkvist, D., Vaivads, A., Mozer, F., André, M. & Owen, C. J. 2007 In situ evidence of magnetic reconnection in turbulent plasma. Nat. Phys. 3, 235.CrossRefGoogle Scholar
Roberts, O. W., Li, X., Alexandrova, O. & Li, B. 2016 Observation of an MHD Alfvén vortex in the slow solar wind. J. Geophys. Res. Space Phys. 121, 3870.Google Scholar
Schekochihin, A. A., Parker, J. T., Highcock, E. G., Dellar, P. J., Dorland, W. & Hammett, G. W. 2016 Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence. J. Plasma Phys. 82, 905820212.Google Scholar
Scudder, J. & Daughton, W. 2008 ‘Illuminating’ electron diffusion regions of collisionless magnetic reconnection using electron agyrotropy. J. Geophys. Res. 113, A06222.Google Scholar
Schwartz, S. J., Hellinger, P., Bale, S. D., Owen, C., Nakamura, R., Vaivads, A., Sorriso-Valvo, L., Liu, W., Wimmer-Schweingruber, R., Fujimoto, M. et al. 2011 Special issue: cross-scale coupling in plasmas preface. Planet. Space Sci. 59, 447.Google Scholar
Servidio, S., Chasapis, A., Matthaeus, W. H., Perrone, D., Valentini, F., Parashar, T. N., Veltri, P., Gershman, D., Russell, C. T., Giles, B. et al. 2017 Magnetospheric multiscale observation of plasma velocity-space cascade: Hermite representation and theory. Phys. Rev. Lett. 119, 205101.Google Scholar
Servidio, S., Matthaeus, W. H. & Dmitruk, P. 2008 Depression of nonlinearity in decaying isotropic MHD turbulence. Phys. Rev. Lett. 100, 095005.Google Scholar
Servidio, S., Osman, K. T., Valentini, F., Perrone, D., Califano, F., Chapman, S., Matthaeus, W. H. & Veltri, P. 2014 Proton kinetic effects in Vlasov and solar wind turbulence. Astrophys. J. Lett. 781, L27.CrossRefGoogle Scholar
Servidio, S., Valentini, F., Califano, F. & Veltri, P. 2012 Local kinetic effects in two-dimensional plasma turbulence. Phys. Rev. Lett. 108, 045001.Google Scholar
Servidio, S., Valentini, F., Perrone, D., Greco, A., Califano, F., Matthaeus, W. H. & Veltri, P. 2015 A kinetic model of plasma turbulence. J. Plasma Phys. 81, 328510107.Google Scholar
Sorriso-Valvo, L., Carbone, F., Perri, S., Greco, A., Marino, R. & Bruno, R. 2018 On the statistical properties of turbulent energy transfer rate in the inner heliosphere. Solar Phys. 293, 10.Google Scholar
Sorriso-Valvo, L., Carbone, V., Noullez, A., Politano, H., Pouquet, A. & Veltri, P. 2002 Analysis of cancellation in two-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 9, 89.Google Scholar
Sorriso-Valvo, L., Carbone, V., Veltri, P., Consolini, G. & Bruno, R. 1999 Intermittency in the solar wind turbulence through probability distribution functions of fluctuations. Geophys. Res. Lett. 26, 1801.Google Scholar
Sorriso-Valvo, L., Marino, R., Carbone, V., Noullez, A., Lepreti, F., Veltri, P., Bruno, R., Bavassano, B. & Pietropaolo, E. 2007 Observation of inertial energy cascade in interplanetary space plasma. Phys. Rev. Lett. 99, 115001.Google Scholar
Sorriso-Valvo, L., Marino, R., Lijoi, L., Perri, S. & Carbone, V. 2015 Self-consistent castaing distribution of solar wind turbulent fluctuations. Astrophys. J. 807, 86.Google Scholar
Swisdak, M. 2016 Quantifying gyrotropy in magnetic reconnection. Geophys. Res. Lett. 43, 43.CrossRefGoogle Scholar
Tessein, J. A., Matthaeus, W. H., Wan, M., Osman, K. T., Ruffolo, D. & Giacalone, J. 2013 Association of suprathermal particles with coherent structures and shocks. Astrophys. J. Lett. 776, L8.Google Scholar
Vaivads, A., Retinó, A., Soucek, J., Khotyaintsev, Yu. V., Valentini, F., Escoubet, C. P. et al. 2016 Turbulence heating observeR – satellite mission proposal. J. Plasma Phys. 82, 905820501.CrossRefGoogle Scholar
Valentini, F., Califano, F., Perrone, D., Pegoraro, F. & Veltri, P. 2011a New ion-wave path in the energy cascade. Phys. Rev. Lett. 106, 165002.Google Scholar
Valentini, F., Califano, F. & Veltri, P. 2010 Two-dimensional kinetic turbulence in the solar wind. Phys. Rev. Lett. 104, 205002.Google Scholar
Valentini, F., Perrone, D., Stabile, S., Pezzi, O., Servidio, S., De Marco, R., Marcucci, F., Bruno, R., Lavraud, B., De Keyser, J. et al. 2016 Differential kinetic dynamics and heating of ions in the turbulent solar wind. New J. Phys. 18, 125001.Google Scholar
Valentini, F., Perrone, D. & Veltri, P. 2011b Short-wavelength electrostatic fluctuations in the solar wind. Astrophys. J. 739, 54.Google Scholar
Valentini, F., Servidio, S., Perrone, D., Califano, F., Matthaeus, W. H. & Veltri, P. 2014 Hybrid Vlasov–Maxwell simulations of two-dimensional turbulence in plasmas. Phys. Plasmas 21, 082307.Google Scholar
Valentini, F., Travnicek, P., Califano, F., Hellinger, P. & 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., Vasconez, C. L., Pezzi, O., Servidio, S., Malara, F. & Pucci, F. 2017 Transition to kinetic turbulence at proton scales driven by large-amplitude kinetic Alfvén fluctuations. Astron. Astrophys. 599, A8.Google Scholar
Valentini, F. & Veltri, P. 2009 Electrostatic short-scale termination of solar-wind turbulence. Phys. Rev. Lett. 102, 225001.Google Scholar
Valentini, F., Veltri, P., Califano, F. & Mangeney, A. 2008 Cross-scale effects in solar-wind turbulence. Phys. Rev. Lett. 101, 025006.Google Scholar
Vasconez, C. L., Pucci, F., Valentini, F., Servidio, S., Matthaeus, W. H. & Malara, F. 2015 Kinetic Alfvén wave generation by large-scale phase mixing. Astrophys. J. 815, 7.Google Scholar
Wan, M., Matthaeus, W. H., Roytershteyn, V., Karimabadi, H., Parashar, T., Wu, P. & Shay, M. 2015 Intermittent dissipation and heating in 3D kinetic plasma turbulence. Phys. Rev. Lett. 114, 175002.Google Scholar
Yang, Y., Matthaeus, W. H., Parashar, T., Wu, P., Wan, M., Shi, Y., Chen, S., Roytershteyn, V. & Daughton, W. 2017 Intermittent dissipation and heating in 3D kinetic plasma turbulence. Phys. Rev. E 95, 061201(R).Google Scholar