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Part of the book series: Atmosphere, Earth, Ocean & Space ((AEONS))

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Abstract

Plasma turbulence is a stochastic state of the plasma and its electromagnetic fluctuations in spatial and temporal structures. Unlike the randomness of thermal fluctuations (or i.e., thermal noise) that is caused by the discrete randomness of microscopic particles (or i.e., the hypothesis of molecular chaos), however, the turbulent stochasticity of the plasma turbulence should be attributed to the chaotic nondeterminacy of plasma collective modes when dynamically evolving into the chaos state via their nonlinear coupling (Ruelle and Takens 1971; Gollub and Swinney 1975). Plasmas, consisting of charged particles, are intrinsically different from neutral fluids, consisting of neutral atoms or molecules, and can have a number of various collective eigenmodes due to the interparticle electromagnetic interaction.

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References

  • Abel, I. G., Barnes, M., Cowley, S. C., et al. (2008). Linearized model fokker-planck collision operators for gyrokinetic simulations. I. theory. Physics of Plasmas, 15, 122509.

    Article  ADS  Google Scholar 

  • Acuña, M. H., Curtis, D., Scheifele, J. L., et al. (2008). The STEREO/IMPACT magnetic field experiment. Space Science Reviews, 136, 203–226.

    Article  ADS  Google Scholar 

  • Alexandrova, O., Saur, J., Lacombe, C., et al. (2009). Universality of solar-wind turbulent spectrum from MHD to electron scales. Physical Review Letters, 103, 165003.

    Article  ADS  Google Scholar 

  • Bale, S. D., Kellogg, P. J., Mozer, F. S., et al. (2005). Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence. Physical Review Letters, 94, 215002.

    Article  ADS  Google Scholar 

  • Barnes, M., Abel, I. G., Dorland, W., et al. (2009). Linearized model fokker-planck collision operators for gyrokinetic simulations. II. numerical implementation and tests. Physics of Plasmas, 16, 128.

    Article  ADS  Google Scholar 

  • Beresnyak, A., & Lazarian, A. (2006). Polarization intermittency and its influence on MHD turbulence. The Astrophysical Journal, 640, L175–L178.

    Article  ADS  Google Scholar 

  • Biskamp, D. (2003). Magnetohydrodynamic turbulence. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Biskamp, D., & Müller, W. C. (2000). Scaling properties of three-dimensional isotropic magnetohydrodynamic turbulence. Physical Review Letters, 7, 4889–4900.

    MathSciNet  Google Scholar 

  • Biskamp, D., Schwarz, E., & Drake, J. F. (1996). Two-dimensional electron magnetohydrodynamic turbulence. Physical Review Letters, 76, 1264–1267.

    Article  ADS  Google Scholar 

  • Biskamp, D., Schwarz, E., Zeiler, A., et al. (1999). Electron magnetohydrodynamic turbulence. Physics of Plasmas, 6, 751–758.

    Article  ADS  MathSciNet  Google Scholar 

  • Boldyrev, S. (2005). On the spectrum of magnetohydrodynamic turbulence. The Astrophysical Journal, 626, L37.

    Article  ADS  Google Scholar 

  • Boldyrev, S. (2006). Spectrum of magnetohydrodynamic turbulence. Physical Review Letters, 96, 115002.

    Article  ADS  Google Scholar 

  • Boldyrev, S., & Perez, J. C. (2012). Spectrum of kinetic-Alfvén turbulence. The Astrophysical Journal Letters, 758, L44.

    Article  ADS  Google Scholar 

  • Boldyrev, S., Horaites, K., Xia, Q., & Perez, J. C. (2013). Toward a theory of astrophysical plasma turbulence at subproton scales. The Astrophysical Journal, 777, 41.

    Article  ADS  Google Scholar 

  • Bruno, R., & Carbone, V. (2005). The solar wind as a turbulence laboratory. Living Reviews in Solar Physics, 2, 4.

    Article  ADS  Google Scholar 

  • Bruno, R., & Carbone, V. (2013). The solar wind as a turbulence laboratory. Living Reviews in Solar Physics, 10, 2.

    Article  ADS  Google Scholar 

  • Cerri, S. S., Servidio, S., & Califano, F. (2017). Kinetic cascade in solar-wind turbulence: 3D3V hybrid-kinetic simulations with electron inertia. The Astrophysical Journal Letters, 846, L18.

    Article  ADS  Google Scholar 

  • Chandran, B. D. G., Schekochihin, A. A., & Mallet, A. (2015). Intermittency and alignment in strong RMHD turbulence. The Astrophysical Journal, 807, 39.

    Article  ADS  Google Scholar 

  • Chen, C. H. K., Boldyrev, S., Xia, Q., & Perez, J. C. (2013). Nature of subproton scale turbulence in the solar wind. Physical Review Letters, 110, 225002.

    Article  ADS  Google Scholar 

  • Chen, C. H. K., Horbury, T. S., Schekochihin, A. A., et al. (2010). Anisotropy of solar wind turbulence between ion and electron scales. Physical Review Letters, 104, 255002.

    Article  ADS  Google Scholar 

  • Chen, L., & Wu, D. J. (2011a). Exact solutions of dispersion equation for MHD waves with short-wavelength modification. Chinese Science Bulletin, 56, 955–961.

    Article  ADS  Google Scholar 

  • Chen, L., & Wu, D. J. (2011b). Polarizations of coupling kinetic Alfvén and slow waves. Physics of Plasmas, 18, 072110.

    Article  ADS  Google Scholar 

  • Chen, L., & Zonca, F. (2016). Physics of Alfvén waves and energetic particles in burning plasmas. Reviews of Modern Physics, 88, 015008.

    Article  ADS  Google Scholar 

  • Cho, J., & Lazarian, A. (2004). The anisotropy of electron magnetohydrodynamic turbulence. The Astrophysical Journal, 615, L41–L44.

    Article  ADS  Google Scholar 

  • Cho, J., & Vishniac, E. T. (2000). The anisotropy of MHD Alfvénic turbulence. The Astrophysical Journal, 539, 273–282.

    Article  ADS  Google Scholar 

  • Coleman, P. J, Jr. (1968). Turbulence, viscosity, and dissipation in the solar-wind plasma. The Astrophysical Journal, 153, 371–388.

    Article  ADS  Google Scholar 

  • Dobrowolny, M., Mangeney, A., & Veltri, P. (1980). Properties of magnetohydrodynamic turbulence in the solar wind. Astronomy & Astrophysics, 83, 26–32.

    ADS  Google Scholar 

  • Fonseca, R. A., Martins, S. F., Silva, L. O., et al. (2008). One-to-one direct modeling of experiments and astrophysical scenario: Pushing the envelope on kinetic plasma simulations. Plasma Physics and Controlled Fusion, 50, 124034.

    Article  ADS  Google Scholar 

  • Fonseca, R. A., Silva, L. O., Tsung, F. S., et al. (2002). OSIRIS: A Three-Dimensional, fully relativistic particle in cell code for modeling plasma based accelerators. Lecture Notes in Computer Science, 2331, 342–351.

    Article  MATH  Google Scholar 

  • Forman, M. A., Wicks, R. T., & Horbury, T. S. (2011). Detailed fit of critical balance theory to solar wind turbulence measurements. The Astrophysical Journal, 733, 76.

    Article  ADS  Google Scholar 

  • Frieman, E. A., & Chen, L. (1982). Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Physics of Fluids, 25, 502.

    Article  ADS  MATH  Google Scholar 

  • Frisch, U. (1995). Turbulence: The legacy of A. N. Kolmogorov. Cambridge: Cambridge University Press.

    Google Scholar 

  • Gary, S. P., & Smith, C. W. (2009). Short-wavelength turbulence in the solar wind: Linear theory of whistler and kinetic Alfvén fluctuations. Journal of Geophysical Research, 114, A12105.

    Article  ADS  Google Scholar 

  • Goldreich, P., & Sridhar, S. (1995). Toward a theory of interstellar turbulence. 2: Strong Alfvénic turbulence. The Astrophysical Journal, 438, 763–775.

    Article  ADS  Google Scholar 

  • Goldreich, P., & Sridhar, S. (1997). Magnetohydrodynamic turbulence revisited. The Astrophysical Journal, 485, 680–688.

    Article  ADS  Google Scholar 

  • Goldstein, M. L., Roberts, D. A., & Fitch, C. A. (1994). Properties of the fluctuating magnetic helicity in the inertial and dissipation ranges of solar wind turbulence. Journal of Geophysical Research, 99, 11519–11538.

    Article  ADS  Google Scholar 

  • Goldstein, M. L., Wicks, R. T., Perri, S., & Sahraoui, F. (2015). Kinetic scale turbulence and dissipation in the solar wind: Key observational results and future outlook. Philosophical Transactions of the Royal Society A, 373, 20140147.

    Article  ADS  Google Scholar 

  • Gollub, J. P., & Swinney, H. L. (1975). Onset of turbulence in a rotating fluid. Physical Review Letters, 35, 927–930.

    Article  ADS  Google Scholar 

  • Grappin, R., Frisch, U., Pouquet, A., & Leorat, J. (1982). Alfvénic fluctuations as asymptotic states of MHD turbulence. Astronomy & Astrophysics, 105, 6–14.

    ADS  MATH  Google Scholar 

  • Grošelj, D., Mallet, A., Loureiro, N. F., & Jenko, F. (2018). Fully kinetic simulation of 3D kinetic Klfvén turbulence. Physical Review Letters, 120, 105101.

    Article  ADS  Google Scholar 

  • Hamilton, K., Smith, C. W., Vasquez, B. J., & Leamon, R. J. (2008). Anisotropies and helicities in the solar wind inertial and dissipation ranges at 1 AU. Journal of Geophysical Research, 113, A01106.

    Article  ADS  Google Scholar 

  • He, J., Marsch, E., Tu, C., et al. (2011). Possible evidence of Alfvén-cyclotron waves in the angle distribution of magnetic helicity of solar wind turbulence. The Astrophysical Journal, 731, 85.

    Article  ADS  Google Scholar 

  • He, J., Tu, C., Marsch, E., & Yao, S. (2012a). Do oblique Alfvén/ion-cyclotron or fast-mode/whistler waves dominant the dissipation of solar wind turbulence near the proton inertial length? The Astrophysical Journal Letters, 745, L8.

    Article  ADS  Google Scholar 

  • He, J., Tu, C., Marsch, E., & Yao, S. (2012b). Reproduction of the observed two-component magnetic helicity in solar wind turbulence by a superposition of parallel and oblique Alfvén waves. The Astrophysical Journal, 749, 86.

    Article  ADS  Google Scholar 

  • Hollweg, J. V. (1999). Kinetic Alfvén wave revisited. Journal of Geophysical Research, 104, 14811–14820.

    Article  ADS  Google Scholar 

  • Hopf, E. (1948). A mathematical example displaying features of turbulence. Communications on Pure and Applied Mathematics, 1, 303–322.

    Article  MathSciNet  MATH  Google Scholar 

  • Horbury, T. S., Forman, M., & Oughton, S. (2008). Anisotropic scaling of magnetohydrodynamic turbulence. Physical Review Letters, 101, 175005.

    Article  ADS  Google Scholar 

  • Howes, G. G., & Quataert, E. (2010). On the interpretation of magnetic helicity signatures in the dissipation range of solar wind turbulence. The Astrophysical Journal Letters, 709, L49–L52.

    Article  ADS  Google Scholar 

  • Howes, G. G., Cowley, S. C., Dorland, W., et al. (2006). Astrophysical gyrokinetics: Basic equations and linear theory. The Astrophysical Journal, 651, 590–614.

    Article  ADS  Google Scholar 

  • Howes, G. G., Cowley, S. C., Dorland, W., et al. (2008b). A model of turbulence in magnetized plasmas: Implications for the dissipation range in the solar wind. Journal of Geophysical Research, 113, A05103.

    Article  ADS  Google Scholar 

  • Howes, G. G., Dorland, W., Cowley, S. C., et al. (2008a). Kinetic simulations of magnetized turbulence in astrophysical plasmas. Physical Review Letters, 100, 065004.

    Article  ADS  Google Scholar 

  • Howes, G. G., Tenbarge, J. M., Dorland, W., et al. (2011). Gyrokinetic simulations of solar wind turbulence from ion to electron scales. Physical Review Letters, 107, 035004.

    Article  ADS  Google Scholar 

  • Howes, G., Dorland, W., Schekochihin, A., et al. (2010). A weakened cascade model for solar wind turbulence. In 52nd Annual Meeting of the APS Division of Plasma Physics, 8–12 Nov, APS.

    Google Scholar 

  • Iroshnikov, R. S. (1963), The turbulence of a conducting fluid in a strong magnetic field, Astron. Zh.40, 742–750. (English Translation: Sov. Astron. 1964, 7, 566).

    Google Scholar 

  • Kingsep, A. S., Chukbar, K. V., & Yan’kov, V. V. (1990). Electron magnetohydrodynamics. In B. B. Kadomtsev (Ed.), Reviews of plasma physics (pp. 243–291). NY: Consultants Bureau.

    Google Scholar 

  • Kiyani, K. H., Chapman, S. C., Khotyaintsev, Yu V., et al. (2009). Global scale-invariant dissipation in collisionless plasma turbulence. Physical Review Letters, 103, 075006.

    Google Scholar 

  • Klein, K. G., Howes, G. G., TenBarge, J. M., & Podesta, J. J. (2014). Physical interpretation of the angle-dependent magnetic helicity spectrum in the solar wind: The nature of turbulent fluctuations near the proton gyroradius scale. The Astrophysical Journal, 785, 138.

    Article  ADS  Google Scholar 

  • Kolmogorov, A. N. (1941). The local structure turbulence in incompressible viscous fluids for very large Reynolds numbers, Dokl. Akad. Nauk. SSSR 30, 301–305. Reprinted in 1991. Proceedings of the Royal Society of London Series A, 434, 9–13.

    Article  ADS  Google Scholar 

  • Kraichnan, R. H. (1965). Inertial range spectrum of hyromagnetic turbulence. Physics of Fluids, 8, 1385–1387.

    Article  ADS  MathSciNet  Google Scholar 

  • López, R. A., Viñas, A. F., Araneda, J. A., & Yoon, P. H. (2017). Kinetic scale structure of low-frequency waves and fluctuations. The Astrophysical Journal, 845, 60.

    Google Scholar 

  • Landau, L. (1944). Stability of tangential discontinuities in compressible fluid. In Proceedings of the USSR Academy of Sciences (Vol. 44, pp. 139–141).

    Google Scholar 

  • Leamon, R. J., Matthaeus, W. H., Smith, C. W., & Wong, H. K. (1998b). Contribution of cyclotron-resonant damping to kinetic dissipation of interplanetary turbulence. The Astrophysical Journal, 507, L181–L184.

    Article  ADS  Google Scholar 

  • Leamon, R. J., Smith, C. W., Ness, N. F., et al. (1998a). Observational constraints on the dynamics of the interplanetary magnetic field dissipation range. Journal of Geophysical Research, 103, 4775–4787.

    Article  ADS  Google Scholar 

  • Lumley, J. L., & Yaglom, A. M. (2001). A century of turbulence. Flow, Turbulence and Combustion, 66, 241–286.

    Article  MATH  Google Scholar 

  • Luo, Q. Y., & Wu, D. J. (2010). Observations of anisotropic scaling of solar wind turbulence. The Astrophysical Journal Letters, 714, L138–L141.

    Article  ADS  Google Scholar 

  • Luo, Q. Y., Wu, D. J., & Yang, L. (2011). Measurement of intermittency of anisotropic magnetohydrodynamic turbulence in high-speed solar wind. The Astrophysical Journal Letters, 733, L22.

    Article  ADS  Google Scholar 

  • Müller, W. C., Biskamp, D., & Grappin, R. (2003). Statistical anisotropy of magnetohydrodynamic turbulence. Physical Review E, 67, 066302.

    Article  ADS  MathSciNet  Google Scholar 

  • Maron, J., & Goldreich, P. (2001). Simulations of incompressible magnetohydrodynamic turbulence. The Astrophysical Journal, 554, 1175–1196.

    Article  ADS  Google Scholar 

  • Mason, J., Cattaneo, F., & Boldyrev, S. (2006). Dynamic alignment in driven magnetohydrodynamic turbulence. Physical Review Letters, 97, 255002.

    Article  ADS  Google Scholar 

  • Matthaeus, W. H., Wan, M., Servidio, S., et al. (2015). Intermittency, nonlinear dynamics and dissipation in the solar wind and astrophysical plasmas. Philosophical Transactions of the Royal Society A, 373, 20140154.

    Article  ADS  Google Scholar 

  • Mithaiwala, M., Rudakov, L., Crabtree, C., & Ganguli, G. (2012). Co-existence of whistler waves with kinetic Alfvén wave turbulence for the high-beta solar wind plasma. Physics of Plasmas, 19, 102902.

    Article  ADS  Google Scholar 

  • Ng, C. S., & Bhattacharjee, A. (1996). Interaction of shear-Alfvén wave packets: Implication for weak magnetohydrodynamic turbulence in astrophysical plasmas. The Astrophysical Journal, 465, 845.

    Article  ADS  Google Scholar 

  • Numata, R., Howes, G. G., Tatsuno, T., et al. (2010). AstroGK: Astrophysical gyrokinetics code. Journal of Computational Physics, 229, 9347–9372.

    Article  ADS  MATH  Google Scholar 

  • Parker, E. N. (1979). Cosmical magnetic fields: Their origin and their activity. New York: Oxford University Press.

    Google Scholar 

  • Pincon, J. L. (1995). Cluster and the K-filtering. In K.-H. Glassmeier, U. Motschmann, & R. Schmidt (Eds.), Proceedings of the Cluster Workshops, Data Analysis Tools and Physical Measurements and Mission-Oriented Theory (p. 87). European Space Agency.

    Google Scholar 

  • Podesta, J. J. (2009). Dependence of solar-wind power spectra on the direction of the local mean magnetic field. The Astrophysical Journal, 698, 986–999.

    Article  ADS  Google Scholar 

  • Podesta, J. J. (2013). Evidence of kinetic Alfvén waves in the solar wind at 1 AU. Solar Physics, 286, 529–548.

    Article  ADS  Google Scholar 

  • Podesta, J. J., & Gary, S. P. (2011). Magnetic helicity spectrum of solar wind fluctuations as a function of the angle with respect to the local mean magnetic field. The Astrophysical Journal, 734, 15.

    Article  ADS  Google Scholar 

  • Podesta, J. J., & TenBarge, J. M. (2012). Scale dependence of the variance anisotropy near the proton gyroradius scale: Additional evidence for kinetic Alfvén waves in the solar wind at 1 AU. Journal of Geophysical Research, 117, A10106.

    ADS  Google Scholar 

  • Podesta, J. J., Borovsky, J. E., & Gary, S. P. (2010). A kinetic Alfvén wave cascade subject to collisionless damping cannot reach electron scales in the solar wind at 1 AU. The Astrophysical Journal, 712, 685–691.

    Article  ADS  Google Scholar 

  • Pouquet, A., Meneguzzi, M., & Frisch, U. (1986). Growth of correlations in magnetohydrodynamic turbulence. Physical Review A, 33, 4266–4276.

    Article  ADS  Google Scholar 

  • Reynolds, O. (1883). An experimental investigation of the circumstances which determine whether the motion of water shall he direct or sinuous, and of the law of resistance in parallel channels. Proceedings of the Royal Society, 35, 84–99.

    Article  ADS  MATH  Google Scholar 

  • Ruelle, D., & Takens, F. (1971). On the nature of turbulence. Communications in Mathematical Physics, 23, 343–344.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Rutherford, P. H., & Frieman, E. A. (1968). Drift instabilities in general magnetic field configurations. Physics of Fluids, 11, 569.

    Article  ADS  Google Scholar 

  • Sahraoui, F., Goldstein, M. L., Belmont, G., et al. (2010). Three dimensional anisotropic k spectra of turbulence at subproton scales in the solar wind. Physical Review Letters, 105, 131101.

    Article  ADS  Google Scholar 

  • Sahraoui, F., Goldstein, M. L., Robert, P., & Khotyaintsev, Yu V. (2009). Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale. Physical Review Letters, 102, 231102.

    Article  ADS  Google Scholar 

  • Salem, C. S., Howes, G. G., Sundkvist, D., et al. (2012). Identification of kinetic Alfvén wave turbulence in the solar wind. The Astrophysical Journal Letters, 745, L9.

    Article  ADS  Google Scholar 

  • Schekochihin, A. A., Cowley, S. C., Dorland, W., et al. (2009). Astrophysical gyrokinetics: Kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. The Astrophysical Journal Supplement Series, 182, 310–377.

    Article  ADS  Google Scholar 

  • Smale, S. (1967). Differentiable dynamical systems. Bulletin of the American Mathematical Society, 73, 747–817.

    Article  MathSciNet  MATH  Google Scholar 

  • Sridhar, S., & Goldreich, P. (1994). Toward a theory of interstellar turbulence 1: Weak Alfvénic turbulence. The Astrophysical Journal, 432, 612–621.

    Article  ADS  Google Scholar 

  • Tatsuno, T., Dorland, W., Schekochihin, A. A., et al. (2009). Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence. Physical Review Letters, 103, 015003.

    Article  ADS  Google Scholar 

  • Taylor, G. I. (1938). Production and dissipation of vorticity in a turbulent fluid. Proceedings of the Royal Society of London Series A, 164, 15–23.

    Article  ADS  MATH  Google Scholar 

  • TenBarge, J. M., & Howes, G. G. (2012). Evidence of critical balance in kinetic Alfvén wave turbulence simulations. Physics of Plasmas, 19, 419–763.

    Article  Google Scholar 

  • TenBarge, J. M., Howes, G. G., & Dorland, W. (2013). Collisionless damping at electron scales in solar wind turbulence. The Astrophysical Journal, 774, 1201–1205.

    Article  Google Scholar 

  • TenBarge, J. M., Podesta, J. J., Klein, K. G., & Howes, G. G. (2012). Interpreting magnetic variance anisotropy measurements in the solar wind. The Astrophysical Journal, 753, 107.

    Article  ADS  Google Scholar 

  • Told, D., Jenko, F., TenBarge, J. M., et al. (2015). Multiscale nature of the dissipation range in gyrokinetic simulations of Alfvénic turbulence. Physical Review Letters, 115, 025003.

    Article  ADS  Google Scholar 

  • Torrence, C., & Compo, G. P. (1998). A practical guide to wavelet analysis. Bulletin of the American Meteorological Society, 79, 61–78.

    Article  ADS  Google Scholar 

  • Tu, C. Y., & Marsch, E. (1995). MHD structures, waves and turbulence in the solar wind: Observations and theories. Space Science Reviews, 73, 1–210.

    Article  ADS  Google Scholar 

  • Voitenko, Yu M, & Keyser, J. D. (2011). Turbulent spectra and spectral kinks in the transition range from MHD to kinetic Alfvén turbulence. Nonlinear Processes in Geophysics, 18, 587–597.

    Article  ADS  Google Scholar 

  • Voitenko, Yu M. (1998a). Three-wave coupling and parametric decay of kinetic Alfvén waves. Journal of Plasma Physics, 60, 497–514.

    Article  ADS  Google Scholar 

  • Voitenko, Yu M. (1998b). Three-wave coupling and weak turbulence of kinetic Alfvén waves. Journal of Plasma Physics, 60, 515–527.

    Article  ADS  Google Scholar 

  • Wicks, R. T., Horbury, T. S., Chen, C. H. K., & Schekochihin, A. A. (2010). Power and spectral index anisotropy of the entire inertial range of turbulence in the fast solar wind. Monthly Notices of the Royal Astronomical Society, 407, L31–L35.

    Article  ADS  Google Scholar 

  • Zhao, J. S., Voitenko, Y. M., Wu, D. J., & Yu, M. Y. (2016). Kinetic Alfvén turbulence below and above ion cyclotron frequency. Journal of Geophysical Research, 121, 5–18.

    Google Scholar 

  • Zhao, J. S., Wu, D. J., & Lu, J. Y. (2013). Kinetic Alfvén turbulence and parallel electric fields in flare loops. The Astrophysical Journal, 767, 109.

    Article  ADS  Google Scholar 

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Wu, DJ., Chen, L. (2020). KAW Turbulence in Solar Wind. In: Kinetic Alfvén Waves in Laboratory, Space, and Astrophysical Plasmas. Atmosphere, Earth, Ocean & Space. Springer, Singapore. https://doi.org/10.1007/978-981-13-7989-5_5

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