Skip to main content Accessibility help

Plasma turbulence at ion scales: a comparison between particle in cell and Eulerian hybrid-kinetic approaches

  • S. S. Cerri (a1), L. Franci (a2) (a3), F. Califano (a1), S. Landi (a2) (a4) and P. Hellinger (a5)...


Kinetic-range turbulence in magnetized plasmas and, in particular, in the context of solar wind turbulence has been extensively investigated over the past decades via numerical simulations. Among others, one of the widely adopted reduced plasma models is the so-called hybrid-kinetic model, where the ions are fully kinetic and the electrons are treated as a neutralizing (inertial or massless) fluid. Within the same model, different numerical methods and/or approaches to turbulence development have been employed. In the present work, we present a comparison between two-dimensional hybrid-kinetic simulations of plasma turbulence obtained with two complementary approaches spanning approximately two decades in wavenumber – from the magnetohydrodynamics inertial range to scales well below the ion gyroradius – with a state-of-the-art accuracy. One approach employs hybrid particle-in-cell simulations of freely decaying Alfvénic turbulence, whereas the other consists of Eulerian hybrid Vlasov–Maxwell simulations of turbulence continuously driven with partially compressible large-scale fluctuations. Despite the completely different initialization and injection/drive at large scales, the same properties of turbulent fluctuations at $k_{\bot }\unicode[STIX]{x1D70C}_{i}\gtrsim 1$ are observed, where $k_{\bot }$ is the fluctuations’ wavenumber perpendicular to the background magnetic field and $\unicode[STIX]{x1D70C}_{i}$ is the ion Larmor radius. The system indeed self-consistently ‘reprocesses’ the turbulent fluctuations while they are cascading towards smaller and smaller scales, in a way which actually depends on the plasma beta parameter ( $\unicode[STIX]{x1D6FD}$ is the ratio between the thermal and the magnetic pressures). Small-scale turbulence has been found to be mainly populated by kinetic Alfvén wave (KAW) fluctuations for $\unicode[STIX]{x1D6FD}\geqslant 1$ , whereas KAW fluctuations are only sub-dominant for low- $\unicode[STIX]{x1D6FD}$ .


Corresponding author

Email addresses for correspondence:,


Hide All
Alexandrova, O., Saur, J., Lacombe, C., Mangeney, A., Mitchell, J., Schwartz, S. J. & Robert, P. 2009 Universality of solar-wind turbulent spectrum from MHD to electron scales. Phys. Rev. Lett. 103 (16), 165003.
Bale, S. D., Kellogg, P. J., Mozer, F. S., Horbury, T. S. & Reme, H. 2005 Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 94 (21), 215002.
Biskamp, D. 2003 Magnetohydrodynamic Turbulence. Cambridge University Press.
Boldyrev, S., Chen, C. H. K., Xia, Q. & Zhdankin, V. 2015 Spectral breaks of Alfvénic turbulence in a collisionless plasma. Astrophys. J. 806, 238.
Boldyrev, S., Horaites, K., Xia, Q. & Perez, J. C. 2013 Toward a theory of astrophysical plasma turbulence at subproton scales. Astrophys. J. 777, 41.
Boldyrev, S. & Perez, J. C. 2012 Spectrum of kinetic-Alfvén turbulence. Astrophys. J. Lett. 758, L44.
Bruno, R. & Carbone, V. 2013 The solar wind as a turbulence laboratory. Living Rev. Sol. Phys. 10, 2.
Bruno, R., Trenchi, L. & Telloni, D. 2014 Spectral slope variation at proton scales from fast to slow solar wind. Astrophys. J. Lett. 793, L15.
Cerri, S. S. & Califano, F. 2017 Reconnection and small-scale fields in 2D-3V hybrid-kinetic driven turbulence simulations. New J. Phys. 19 (2), 025007.
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.
Chasapis, A., Retinò, A., Sahraoui, F., Vaivads, A., Khotyaintsev, Y. V., Sundkvist, D., Greco, A., Sorriso-Valvo, L. & Canu, P. 2015 Thin current sheets and associated electron heating in turbulent space plasma. Asotrophys. J. Lett. 804, L1.
Chen, C. H. K., Boldyrev, S., Xia, Q. & Perez, J. C. 2013 Nature of subproton scale turbulence in the solar wind. Phys. Rev. Lett. 110 (22), 225002.
Cheng, C. Z. & Knorr, G. 1976 The integration of the Vlasov equation in configuration space. J. Comput. Phys. 22, 330351.
Franci, L., Hellinger, P., Matteini, L., Verdini, A. & Landi, S. 2016a Two-dimensional Hybrid Simulations of Kinetic Plasma Turbulence: Current and Vorticity Versus Proton Temperature, American Institute of Physics Conference Series, vol. 1720, p. 040003.
Franci, L., Landi, S., Matteini, L., Verdini, A. & Hellinger, P. 2015a High-resolution hybrid simulations of kinetic plasma turbulence at proton scales. Astrophys. J. 812, 21.
Franci, L., Landi, S., Matteini, L., Verdini, A. & Hellinger, P. 2016b Plasma beta dependence of the ion-scale spectral break of solar wind turbulence: high-resolution 2D hybrid simulations. Astrophys. J. 833, 91.
Franci, L., Verdini, A., Matteini, L., Landi, S. & Hellinger, P. 2015b Solar wind turbulence from MHD to sub-ion scales: high-resolution hybrid simulations. Astrophys. J. Lett. 804, L39.
Galtier, S. & Bhattacharjee, A. 2003 Anisotropic weak whistler wave turbulence in electron magnetohydrodynamics. Phys. Plasmas 10, 30653076.
Gary, S. P. & Smith, C. W. 2009 Short-wavelength turbulence in the solar wind: linear theory of whistler and kinetic Alfvén fluctuations. J. Geophys. Res. Space Phys. 114, A12105.
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.
Howes, G. G., Cowley, S. C., Dorland, W., Hammett, G. W., Quataert, E. & Schekochihin, A. A. 2008a A model of turbulence in magnetized plasmas: implications for the dissipation range in the solar wind. J. Geophys. Res. Space Phys. 113, A05103.
Howes, G. G., Dorland, W., Cowley, S. C., Hammett, G. W., Quataert, E., Schekochihin, A. A. & Tatsuno, T. 2008b Kinetic simulations of magnetized turbulence in astrophysical plasmas. Phys. Rev. Lett. 100 (6), 065004.
Howes, G. G., Tenbarge, J. M., Dorland, W., Quataert, E., Schekochihin, A. A., Numata, R. & Tatsuno, T. 2011 Gyrokinetic simulations of solar wind turbulence from ion to electron scales. Phys. Rev. Lett. 107 (3), 035004.
Karimabadi, H., Roytershteyn, V., Daughton, W. & Liu, Y.-H. 2013a Recent evolution in the theory of magnetic reconnection and its connection with turbulence. Space Sci. Rev. 178, 307323.
Karimabadi, H., Roytershteyn, V., Wan, M., Matthaeus, W. H., Daughton, W., Wu, P., Shay, M., Loring, B., Borovsky, J., Leonardis, E. et al. 2013b Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas. Phys. Plasmas 20 (1), 012303.
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 1642.
Li, T. C., Howes, G. G., Klein, K. G. & TenBarge, J. M. 2016 Energy dissipation and Landau damping in two- and three-dimensional plasma turbulence. Astrophys. J. Lett. 832, L24.
Lion, S., Alexandrova, O. & Zaslavsky, A. 2016 Coherent events and spectral shape at ion kinetic scales in the fast solar wind turbulence. Astrophys. J. 824, 47.
Mangeney, A., Califano, F., Cavazzoni, C. & Travnicek, P. 2002 A numerical scheme for the integration of the Vlasov–Maxwell system of equations. J. Comput. Phys. 179, 495538.
Matthaeus, W. H. & Lamkin, S. L. 1986 Turbulent magnetic reconnection. Phys. Fluids 29, 25132534.
Matthews, A. P. 1994 Current advance method and cyclic leapfrog for 2D multispecies hybrid plasma simulations. J. Comput. Phys. 112, 102116.
Mininni, P. D. & Pouquet, A. 2009 Finite dissipation and intermittency in magnetohydrodynamics. Phys. Rev. E 80 (2), 025401.
Navarro, A. B., Teaca, B., Told, D., Groselj, D., Crandall, P. & Jenko, F. 2016 Structure of plasma heating in gyrokinetic Alfvénic turbulence. Phys. Rev. Lett. 117 (24), 245101.
Parashar, T. N., Salem, C., Wicks, R. T., Karimabadi, H., Gary, S. P. & Matthaeus, W. H. 2015 Turbulent dissipation challenge: a community-driven effort. J. Plasma Phys. 81 (5), 905810513.
Parashar, T. N., Servidio, S., Breech, B., Shay, M. A. & Matthaeus, W. H. 2010 Kinetic driven turbulence: structure in space and time. Phys. Plasmas 17 (10), 102304.
Parashar, T. N., Servidio, S., Shay, M. A., Breech, B. & Matthaeus, W. H. 2011 Effect of driving frequency on excitation of turbulence in a kinetic plasma. Phys. Plasmas 18 (9), 092302.
Passot, T., Henri, P., Laveder, D. & Sulem, P.-L. 2014 Fluid simulations of ion scale plasmas with weakly distorted magnetic fields. FLR-Landau fluid simulations. Eur. Phys. J. D 68, 207.
Passot, T. & Sulem, P. L. 2015 A model for the non-universal power law of the solar wind sub-ion-scale magnetic spectrum. Astrophys. J. Lett. 812, L37.
Perri, S., Goldstein, M. L., Dorelli, J. C. & Sahraoui, F. 2012 Detection of small-scale structures in the dissipation regime of solar-wind turbulence. Phys. Rev. Lett. 109 (19), 191101.
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.
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.
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, 38703881.
Roberts, O. W., Li, X. & Li, B. 2013 Kinetic plasma turbulence in the fast solar wind measured by cluster. Astrophys. J. 769, 58.
Sahraoui, F., Goldstein, M. L., Robert, P. & Khotyaintsev, Y. V. 2009 Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale. Phys. Rev. Lett. 102 (23), 231102.
Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, G. W., Howes, G. G., Quataert, E. & Tatsuno, T. 2009 Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophys. J. Suppl. Series 182, 310377.
Servidio, S., Dmitruk, P., Greco, A., Wan, M., Donato, S., Cassak, P. A., Shay, M. A., Carbone, V. & Matthaeus, W. H. 2011 Magnetic reconnection as an element of turbulence. Nonlinear Process. Geophys. 18, 675695.
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.
Servidio, S., Valentini, F., Califano, F. & Veltri, P. 2012 Local kinetic effects in two-dimensional plasma turbulence. Phys. Rev. Lett. 108 (4), 045001.
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 (1), 325810107.
Shaikh, D. & Zank, G. P. 2009 Spectral features of solar wind turbulent plasma. Mon. Not. R. Astron. Soc. 400, 18811891.
Stawicki, O., Gary, S. P. & Li, H. 2001 Solar wind magnetic fluctuation spectra: dispersion versus damping. J. Geophys. Res. 106, 82738282.
Sulem, P. L., Passot, T., Laveder, D. & Borgogno, D. 2016 Influence of the nonlinearity parameter on the solar wind sub-ion magnetic energy spectrum: FLR-Landau fluid simulations. Astrophys. J. 818, 66.
Told, D., Jenko, F., TenBarge, J. M., Howes, G. G. & Hammett, G. W. 2015 Multiscale nature of the dissipation range in gyrokinetic simulations of Alfvénic turbulence. Phys. Rev. Lett. 115 (2), 025003.
Valentini, F., Califano, F. & Veltri, P. 2010 Two-dimensional kinetic turbulence in the solar wind. Phys. Rev. Lett. 104 (20), 205002.
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 (12), 125001.
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 (8), 082307.
Valentini, F., Trávníček, 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, 753770.
Wan, M., Matthaeus, W. H., Roytershteyn, V., Parashar, T. N., Wu, P. & Karimabadi, H. 2016 Intermittency, coherent structures and dissipation in plasma turbulence. Phys. Plasmas 23 (4), 042307.
Winske, D. 1985 Hybrid simulation codes with application to shocks and upstream waves. Space Sci. Rev. 42, 5366.
MathJax is a JavaScript display engine for mathematics. For more information see


Plasma turbulence at ion scales: a comparison between particle in cell and Eulerian hybrid-kinetic approaches

  • S. S. Cerri (a1), L. Franci (a2) (a3), F. Califano (a1), S. Landi (a2) (a4) and P. Hellinger (a5)...


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed