Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-17T06:13:14.224Z Has data issue: false hasContentIssue false
  • English
  • Français

Imbalanced kinetic Alfvén wave turbulence: from weak turbulence theory to nonlinear diffusion models for the strong regime

Part of: Focus on Space Plasmas

Published online by Cambridge University Press:  16 May 2019

T. Passot  and
P. L. Sulem
T. Passot*
Affiliation:
Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire J.L. Lagrange, Boulevard de l’Observatoire, CS 34229, 06304 Nice CEDEX 4, France
P. L. Sulem
Affiliation:
Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire J.L. Lagrange, Boulevard de l’Observatoire, CS 34229, 06304 Nice CEDEX 4, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A two-field Hamiltonian gyrofluid model for kinetic Alfvén waves retaining ion finite Larmor radius corrections, parallel magnetic field fluctuations and electron inertia, is used to study turbulent cascades from the magnetohydrodynamic (MHD) to the sub-ion scales. Special attention is paid to the case of imbalance between waves propagating along or opposite to the ambient magnetic field. For weak turbulence in the absence of electron inertia, kinetic equations for the spectral density of the conserved quantities (total energy and generalized cross-helicity) are obtained. They provide a global description, matching between the regimes of reduced MHD at large scales and electron reduced MHD at small scales, previously considered in the literature. In the limit of ultra-local interactions, Leith-type nonlinear diffusion equations in the Fourier space are derived and heuristically extended to the strong turbulence regime by modifying the transfer time appropriately. Relations with existing phenomenological models for imbalanced MHD and balanced sub-ion turbulence are discussed. It turns out that in the presence of dispersive effects, the dynamics is sensitive on the way turbulence is maintained in a steady state. Furthermore, the total energy spectrum at sub-ion scales becomes steeper as the generalized cross-helicity flux is increased.

Keywords

plasma nonlinear phenomenaplasma wavesspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 85 , Issue 3 , June 2019 , 905850301
Copyright
© Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abdelhamid, H. M., Lingam, M. & Mahajan, S. M. 2016 Extended MHD turbulence and its applications to the solar wind. Astrophys. J. 829, 87.Google Scholar
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.Google Scholar
Belcher, J. W. & Davis, L. Jr 1971 Large-amplitude Alfvén waves in the interplanetary medium, 2. J. Geophys. Res. 76, 3534.Google Scholar
Benney, D. J. & Newell, A. C. 1969 Random wave closures. Stud. Appl. Maths 48, 29–53.Google Scholar
Beresnyak, A. 2014 Spectra of strong magnetohydrodynamic turbulence from high-resolution simulations. Astrophys. J. Lett. 784, L20.Google Scholar
Beresnyak, A. & Lazarian, A. 2008 Strong imbalanced turbulence. Astrophys. J 682, 1070–1075.Google Scholar
Beresnyak, A. & Lazarian, A. 2009 Structure of stationary strong imbalanced turbulence. Astrophys. J 702, 460–471.Google Scholar
Beresnyak, A. & Lazarian, A. 2010 Scaling laws and diffuse locality of balanced and imbalanced magnetohydrodynamic turbulence. Astrophys. J. Lett. 722, L110–L113.Google Scholar
Bian, N. H. & Tsiklauri, D. 2009 Compressible Hall magnetohydrodynamics in a strong magnetic field. Phys. Plasmas 16 (6), 064503.Google Scholar
Biskamp, D., Schwarz, E., Zeiler, A., Celani, A. & Drake, J. F. 1999 Electron magnetohydrodynamic turbulence. Phys. Plasmas 6, 751–758.Google Scholar
Boldyrev, S., Horaites, K., Xia, Q. & Perez, J. C. 2013 Toward a theory of astrophysical plasma turbulence at subproton scales. Astrophys. J. 777, 41.Google Scholar
Boldyrev, S. & Perez, J. C. 2012 Spectrum of kinetic-Alfvén turbulence. Astrophys. J. Lett. 758, L44.Google Scholar
Brizard, A. 1992 Nonlinear gyrofluid description of turbulent magnetized plasmas. Phys. Fluids B 4, 1213–1228.Google Scholar
Bruno, R. & Carbone, V. 2013 The solar wind as a turbulence laboratory. Living Rev. Solar Phys. 10, 2.Google Scholar
Bruno, R. & Carbone, V. 2016 Turbulence in the Solar Wind, Lectures Notes in Physics, vol. 928. Springer.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. 061102.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
Chandran, B. D. G. 2008 Strong anisotropic MHD turbulence with cross helicity. Astrophys. J. 685, 646–658.Google Scholar
Chen, C. H. K. 2016 Recent progress in astrophysical plasma turbulence for solar wind observations. J. Plasma Phys. 82, 535820602.Google Scholar
Chen, C. H. K. & Boldyrev, S. 2017 Nature of kinetic scale turbulence in the Earth’s magnetosheath. Astrophys. J. 842, 122.Google Scholar
Cho, J. & Kim, H. 2016 Spectral evolution of helical electron magnetohydrodynamics turbulence. J. Geophys. Res. Space Phys. 121, 6157–6167.Google Scholar
Clark, T. T., Rubinstein, R. & Weinstock, J. 2009 Reassessment of the classical turbulence closures: the Leith diffusion model. J. Turbul. 10, 35.Google Scholar
Connaughton, C. & Nazarenko, S. 2004 Warm cascades and anomalous scaling in a diffusion model of turbulence. Phys. Rev. Lett. 92 (4), 044501.Google Scholar
Cranmer, S. R. & van Ballegooijen, A. A. 2003 Alfvénic turbulence in the extended solar corona: kinetic effects and proton heating. Astrophys. J. 594, 573–591.Google Scholar
Dyachenko, S., Newell, A. C., Pushkarev, A. & Zakharov, V. E. 1992 Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation. Physica D 57, 96–160.Google Scholar
Fjørtoft, R. 1953 On changes in the spectral distribution of kinetic energy for two-dimensional nondivergent flow. Tellus 5, 225.Google Scholar
Fox, N. J., Velli, M. C., Bale, S. D., Decker, R., Driesman, A., Howard, R. A., Kasper, J. C., Kinnison, J., Kusterer, M., Lario, D. et al. 2016 The solar probe plus mission: humanity’s first visit to our star. Space Sci. Rev. 204, 7–48.Google Scholar
Galtier, S. 2006 Wave turbulence in incompressible Hall magnetohydrodynamics. J. Plasma Phys. 72, 721–769.Google Scholar
Galtier, S. & Bhattacharjee, A. 2003 Anisotropic weak whistler wave turbulence in electron magnetohydrodynamics. Phys. Plasmas 10, 3065–3075.Google Scholar
Galtier, S. & Buchlin, E. 2010 Nonlinear diffusion equations for anisotropic magnetohydrodynamic turbulence with cross helicity. Astrophys. J. 722, 1977–1983.Google Scholar
Galtier, S. & Meyrand, R. 2015 Entanglement of helicity and energy in kinetic Alfvén wave/whistler turbulence. J. Plasma Phys. 81, 325810106.Google Scholar
Galtier, S., Nazarenko, S. V., Newell, A. C. & Pouquet, A. 2002 Anisotropic turbulence of shear Alfvén waves. Astrophys. J. Lett. 564, L49–L52.Google Scholar
Goldreich, P. & Sridhar, S. 1997 Magnetohydrodynamic turbulence revisited. Astrophys. J. 485, 680–688.Google Scholar
Grappin, R., Pouquet, A. & Léorat, J. 1983 Dependence of MHD turbulence spectra on the velocity-field magnetic correlation. Astron. Astrophys. 126, 51–58.Google Scholar
Grasso, D., Pegoraro, F., Porcelli, F. & Califano, F. 1999 Hamiltonian magnetic reconnection. Plasma Phys. Control. Fusion 41, 1497–1515.Google Scholar
Grošelj, D., Mallet, A., Loureiro, N. F. & Jenko, F. 2018 Fully kinetic simulation of 3D kinetic Alfvén turbulence. Phys. Rev. Lett. 120 (10), 105101.Google Scholar
Howes, G. G., Cowley, S. C., Dorland, W., Hammett, G. W., Quataert, E. & Schekochihin, A. A. 2006 Astrophysical gyrokinetics: basic equations and linear theory. Astrophys. J. 651, 590–614.Google Scholar
Howes, G. G., Tenbarge, J. M. & Dorland, W. 2011 A weakened cascade model for turbulence in astrophysical plasmas. Phys. Plasmas 18 (10), 102305–102305.Google Scholar
Kim, H. & Cho, J. 2015 Inverse cascade in imbalanced electron magnetohydrodynamic turbulence. Astrophys. J. 801, 75.Google Scholar
Kraichnan, R. H. 1971 Inertial-range transfer in two- and three-dimensional turbulence. J. Fluid Mech. 47, 525–535.Google Scholar
Leith, C. E. 1967 Diffusion approximation to inertial energy transfer in isotropic turbulence. Phys. Fluids 10, 1409–1416.Google Scholar
Lithwick, Y. & Goldreich, P. 2003 Imbalanced weak magnetohydrodynamic turbulence. Astrophys. J. 582, 1220–1240.Google Scholar
Lithwick, Y., Goldreich, P. & Sridhar, S. 2007 Imbalanced strong MHD turbulence. Astrophys. J. 655, 269–274.Google Scholar
Lucek, E. A. & Balogh, A 1998 The identification and characterization of Alfvénic fluctuations in Ulysses data at midlatitudes. Astrophys. J. 507, 984–990.Google Scholar
Lyutikov, M. 2013 Electron magnetohydrodynamics: dynamics and turbulence. Phys. Rev. E 88, 053103.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, 1644–1660.Google Scholar
Mallet, A., Schekochihin, A. A. & Chandran, B. D. G. 2017 Disruption of sheet-like structures in Alfvénic turbulence by magnetic reconnection. MNRAS 468, 4862–4871.Google Scholar
Marino, R., Sorriso-Valvo, L., Carbone, V., Noullez, A., Bruno, R. & Bavassano, B. 2009 The energy cascade in solar wind MHD turbulence. Earth Moon Planets 104, 115–119.Google Scholar
Marsch, E. & Tu, C.-Y. 1990 On the radial evolution of MHD turbulence in the inner heliosphere. J. Geophys. Res. 95 (A6), 8211–8229.Google Scholar
Matthaeus, W. H., Oughton, S. & Zhou, Y. 2009 Anisotropic magnetohydrodynamic spectral transfer in the diffusion approximation. Phys. Rev. E 79, 035401(R).Google Scholar
Meyrand, R., Galtier, S. & Kiyani, K. H. 2016 Direct evidence of the transition from weak to strong magnetohydrodynamic turbulence. Phys. Rev. Lett. 116, 105002.Google Scholar
Meyrand, R., Kiyani, K. H. & Galtier, S. 2015 Weak magnetohydrodynamic turbulence and intermittency. J. Fluid Mech. 770, R1.Google Scholar
Meyrand, R., Kiyani, K. H., Gürcan, Ö. D. & Galtier, S. 2018 Coexistence of weak and strong wave turbulence in incompressible Hall magnetohydrodynamics. Phys. Rev. X 8, 031066.Google Scholar
Moya, P. S., Pinto, V. A., Viñas, A. F., Sibeck, D. G., Kurth, W. S., Hospodarsky, G. B. & Wygant, J. R. 2015 Weak kinetic Alfvén waves turbulence during the 14 November 2012 geomagnetic storm: Van Allen probes observations. J. Geophys. Res. 120 (A7), 5504–5523.Google Scholar
Nazarenko, S. 2011 Wave Turbulence, Lectures Notes in Physics, vol. 825. Springer.Google Scholar
Newell, A. C., Nazarenko, S. & Biven, L. 2001 Wave turbulence and intermittency. Physica D 152–153, 520–550.Google Scholar
Ng, C. S. & Bhattacharjee, A. 1996 Interaction of shear-Alfvén wave packets: implication for weak magnetohydrodynamic turbulence in astrophysical plasmas. Astrophys. J. 465, 845–854.Google Scholar
Passot, T., Sulem, P. L. & Tassi, E. 2018 Gyrofluid modeling and phenomenology of low- $\unicode[STIX]{x1D6FD}_{e}$ Alfvén wave turbulence. Phys. Plasmas 25, 042107.Google Scholar
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.Google Scholar
Passot, T., Sulem, P. L. & Tassi, E. 2017 Electron-scale reduced fluid models with gyroviscous effects. J. Plasma Phys. 83, 715830402.Google Scholar
Perez, J. C. & Boldyrev, S. 2009 Role of cross-helicity in magnetohydrodynamic turbulence. Phys. Rev. Lett. 102, 025003.Google Scholar
Perez, J. C. & Chandran, B. D. G. 2013 Direct numerical simulations of reflection-driven, reduced magnetohydrodynamic turbulence from the sun to the Alfvén critical point. Astrophys. J. 776 (2), 124.Google Scholar
Perez, J. C., Mason, J., Boldyrev, S. & Cattaneo, F. 2012 On the energy spectrum of strong magnetohydrodynamic turbulence. Phys. Rev. X 2, 041005.Google Scholar
Podesta, J. J. 2013 Evidence of kinetic Alfvén waves in the solar wind at 1 AU. Solar Phys. 286, 529–548.Google Scholar
Podesta, J. J. & Bhattacharjee, A. 2010 Theory of incompressible magnetohydrodynamic turbulence with scale-dependent alignment and cross-helicity. Astrophys. J. 718, 11511157.Google Scholar
Podesta, J. J. & Borovsky, J. E. 2010 Scale invariance of normalized cross-helicity throughout the inertial range of solar wind turbulence. Phys. Plasmas 17 (11), 112905.Google Scholar
Pouquet, A., Frisch, U. & Leorat, J. 1976 Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77, 321–354.Google Scholar
Roberts, D. A., Goldstein, M. L., Klein, L. W. & Matthaeus, W. H. 1987 Origin and evolution of fluctuations in the solar wind: Helios observations and Helios–Voyager comparisons. J. Geophys. Res. 92 (A11), 12023–12035.Google Scholar
Roytershteyn, V., Boldyrev, S., Delzanno, G. L., Chen, C. H. K., Grošelj, D. & Loureiro, N. F. 2019 Numerical study of inertial kinetic-Alfvén turbulence. Astrophys. J. 870, 103.Google Scholar
Sahraoui, F., Goldstein, M. L., Belmont, G., Canu, P. & Rezeau, L. 2010 Three dimensional anisotropic $k$ spectra of turbulence at subproton scales in the solar wind. Phys. Rev. Lett. 105, 131101.Google Scholar
Sahraoui, F., Goldstein, M. L., Robert, P. & Khotyaintsev, Y. U. 2009 Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale. Phys. Rev. Lett. 102, 231102.Google Scholar
Salem, C. S., Howes, G. G., Sundkvist, D., Bale, S. D., Chaston, C. C., Chen, C. H. K. & Mozer, F. S. 2012 Identification of kinetic Alfvén wave turbulence in the solar wind. Astrophys. J. Lett. 745, L9.Google Scholar
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. 182, 310–377.Google Scholar
Schekochihin, A. A., Nazarenko, S. V. & Yousef, T. A. 2012 Weak Alfvén-wave turbulence revisited. Phys. Rev. E 85, 036406.Google Scholar
Schep, T. J., Pegoraro, F. & Kuvshinov, B. N. 1994 Generalized two-fluid theory of nonlinear magnetic structures. Phys. Plasmas 1, 2843–2852.Google Scholar
Stansby, D., Horbury, T. S. & Matteini, L. 2019 Diagnosing solar wind origins using in situ measurements in the inner heliosphere. MNRAS 482, 1706–1714.Google Scholar
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.Google Scholar
Tassi, E. 2017 Hamiltonian closures in fluid models for plasmas. Euro. Phys. J. D 71, 269.Google Scholar
Tassi, E., Sulem, P. L. & Passot, T. 2016 Reduced models accounting for parallel magnetic perturbations: gyrofluid and finite Larmor radius-Landau fluid approaches. J. Plasma Phys. 82, 705820601.Google Scholar
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.Google Scholar
Tronko, N., Nazarenko, S. V. & Galtier, S. 2013 Weak turbulence in two-dimensional magnetohydrodynamics. Phys. Rev. E 87, 033103.Google Scholar
Tu, C. Y., March, E. & Rausenbauer, H. 1990 The dependence of MHD turbulence spectra on the inner solar wind stream structure near solar minimum. Geophys. Res. Lett. 17, 283–286.Google Scholar
Tu, C.-Y., Marsch, E. & Thieme, K. M. 1989 Basic properties of solar wind MHD turbulence near 0.3 AU analyzed by means of elsasser variables. J. Geophys. Res. 94 (A9), 11739–11759.Google Scholar
Voitenko, Y. & De Keyser, J. 2016 MHD-kinetic transition in imbalanced Alfvénic turbulence. Astrophys. J. Lett. 832, L20.Google Scholar
Voitenko, Y. M. 1998 Three-wave coupling and parametric decay of kinetic Alfvén waves. J. Plasma Phys. 60, 497–514.Google Scholar
Wicks, R. T., Roberts, D. A., Mallet, A., Schekochihin, A. A., Horbury, T. S. & Chen, C. H. K. 2013 Correlations at large scales and the onset of turbulence in the fast solar wind. Astrophys. J. 778, 177.Google Scholar
Zhou, Ye. & Matthaeus, W. H. 1990 Models of inertial range spectra of interplanetary magnetohydrodynamic turbulence. J. Geophys. Res. 95 (A9), 14881–14892.Google Scholar