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Kinetic Turbulence

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Magnetic Fields in Diffuse Media

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 407))

Abstract

The weak collisionality typical of turbulence in many diffuse astrophysical plasmas invalidates an MHD description of the turbulent dynamics, motivating the development of a more comprehensive theory of kinetic turbulence. In particular, a kinetic approach is essential for the investigation of the physical mechanisms responsible for the dissipation of astrophysical turbulence and the resulting heating of the plasma. This chapter reviews the limitations of MHD turbulence theory and explains how kinetic considerations may be incorporated to obtain a kinetic theory for astrophysical plasma turbulence. Key questions about the nature of kinetic turbulence that drive current research efforts are identified. A comprehensive model of the kinetic turbulent cascade is presented, with a detailed discussion of each component of the model and a review of supporting and conflicting theoretical, numerical, and observational evidence.

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Notes

  1. 1.

    Here T s is expressed in units of energy, absorbing the Boltzmann constant.

  2. 2.

    Note that condition (4) is not generally independent of condition (3). For MHD Alfvén waves, the condition \(\omega \ll \varOmega _{i}\) may be alternatively written \(\rho _{i}/l_{\parallel }\ll \sqrt{\beta _{i}}\), where the ion plasma beta is \(\beta _{i} = 8\pi n_{i}T_{i}/B^{2}\). Thus, if \(\sqrt{\beta _{i}} \sim \mathcal{O}(1)\), then condition (4) is roughly equivalent to condition (3).

  3. 3.

    The Lorentz force limits the perpendicular motion of plasma particles to the particle Larmor radius. Since typical astrophysical conditions yield \(\rho _{i} \ll \lambda _{i}\), the plasma is essentially always collisionless in the perpendicular direction. Note, however, that because plasma particles cannot move beyond the Larmor radius in the perpendicular direction from the magnetic field, this embodies the large-scale perpendicular motions, \(l_{\perp }\gg \rho _{i}\), with a fluid-like behavior, even under weakly collisional conditions.

  4. 4.

    In the limit that the turbulent astrophysical fluctuations satisfy the gyrokinetic approximation, \(k_{\parallel }\ll k_{\perp }\) and ω ≪ Ω i (Frieman and Chen 1982; Howes et al. 2006; Schekochihin et al. 2009), the linear physics depends on only three dimensionless parameters, \(\overline{\omega }_{\text{GK}} =\omega /(k_{\parallel }v_{A}) = \overline{\omega }_{\text{GK}}(k_{\perp }\rho _{i},\beta _{i},T_{i}/T_{e})\) (Howes et al. 2006).

References

  • Alexandrova, O., Saur, J., Lacombe, C., Mangeney, A., Mitchell, J., Schwartz, S.J., Robert, P.: Universality of solar-wind turbulent spectrum from MHD to electron scales. Phys. Rev. Lett. 103(16), 165003 (2009)

    Article  ADS  Google Scholar 

  • Alexandrova, O., Lacombe, C., Mangeney, A., Grappin, R., Maksimovic, M.: Solar wind turbulent spectrum at plasma kinetic scales. Astrophys. J. 760, 121 (2012)

    Article  ADS  Google Scholar 

  • Armstrong, J.W., Cordes, J.M., Rickett, B.J.: Density power spectrum in the local interstellar medium. Nature 291, 561–564 (1981)

    Article  ADS  Google Scholar 

  • Armstrong, J.W., Rickett, B.J., Spangler, S.R.: Electron density power spectrum in the local interstellar medium. Astrophys. J. 443, 209–221 (1995)

    Article  ADS  Google Scholar 

  • Balbus, S.A., Hawley, J.F.: A powerful local shear instability in weakly magnetized disks. i. Linear analysis. Astrophys. J. 376, 214–222 (1991)

    Google Scholar 

  • Balbus, S.A., Hawley, J.F.: Instability, turbulence, and enhanced transport in accretion disks. Rev. Mod. Phys. 70, 1–53 (1998)

    Article  ADS  Google Scholar 

  • Bale, S.D., Kellogg, P.J., Mozer, F.S., Horbury, T S., Reme, H.: Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 94(21):215002 (2005)

    Google Scholar 

  • Bale, S.D., Kasper, J.C., Howes, G.G., Quataert, E., Salem, C., Sundkvist, D.: Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind. Phys. Rev. Lett. 103(21), 211101 (2009)

    Article  ADS  Google Scholar 

  • Barnes, A.: Collisionless damping of hydromagnetic waves. Phys. Fluids 9, 1483–1495 (1966)

    Article  ADS  Google Scholar 

  • Belcher, J.W., Davis, L.: Large-amplitude Alfvén waves in the interplanetary medium, 2: J. Geophys. Res. 76, 3534–3563 (1971)

    Article  ADS  Google Scholar 

  • Birn, J., Priest, E.R.: Reconnection of Magnetic Fields. Cambriodge University Press, Cambriodge (2006)

    Google Scholar 

  • Biskmap, D., Schwarz, E., Zeiler, A., Celani, A., Drake, J.F.: Electron magnetohydrodynamic turbulence. Phys. Plasmas 6, 751–758 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  • Boldyrev, S.: Spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 96(11), 115002 (2006)

    Article  ADS  Google Scholar 

  • Boldyrev, S., Perez, J.C., Borovsky, J.E., Podesta, J.J.: Spectral scaling laws in magnetohydrodynamic turbulence simulations and in the solar wind. Astrophys. J. Lett. 741, L19 (2011)

    Article  ADS  Google Scholar 

  • Boldyrev, S., Perez, J.C., Wang, Y.: Residual energy in weak and strong MHD turbulence. (2012). ArXiv e-prints

    Google Scholar 

  • Bourouaine, S., Alexandrova, O., Marsch, E., Maksimovic, M.: On spectral breaks in the power spectra of magnetic fluctuations in fast solar wind between 0.3 and 0.9 AU. Astrophys. J. 749, 102 (2012)

    Google Scholar 

  • Braginskii, S.I.: Transport processes in a plasma. Rev. Plasma Phys. 1, 205 (1965)

    ADS  Google Scholar 

  • Breech, B., Matthaeus, W.H., Cranmer, S.R., Kasper, J.C., Oughton, S.: Electron and proton heating by solar wind turbulence. J. Geophys. Res. (Space Phys.), 114(A13), 9103 (2009)

    Google Scholar 

  • Bruno, R., Carbone, V.: The solar wind as a turbulence laboratory. Living Rev. Solar Phys. 2, 4 (2005)

    Article  ADS  Google Scholar 

  • Chen, C.H.K., Horbury, T.S., Schekochihin, A.A., Wicks, R.T., Alexandrova, O., Mitchell, J.: Anisotropy of solar wind turbulence between ion and electron scales. Phys. Rev. Lett. 104(25), 255002 (2010)

    Article  ADS  Google Scholar 

  • Cho, J., Lazarian, A.: Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications. Mon. Not. Roy. Astron. Soc. 345, 325–339 (2003)

    Article  ADS  Google Scholar 

  • Cho, J., Lazarian, A.: The anisotropy of electron magnetohydrodynamic turbulence. Astrophys. J. Lett. 615, L41–L44 (2004)

    Article  ADS  Google Scholar 

  • Cho, J., Lazarian, A.: Simulations of electron magnetohydrodynamic turbulence. Astrophys. J. 701, 236–252 (2009)

    Article  ADS  Google Scholar 

  • Cranmer, S.R., Matthaeus, W.H., Breech, B.A., Kasper, J.C.: Empirical constraints on proton and electron heating in the fast solar wind. Astrophys. J. 702, 1604–1614 (2009)

    Article  ADS  Google Scholar 

  • Dmitruk, P., Matthaeus, W.H.: Test particle acceleration in three-dimensional Hall MHD turbulence. J. Geophys. Res. (Space Phys.) 111, 12110 (2006)

    Article  ADS  Google Scholar 

  • Dmitruk, P., Matthaeus, W.H., Seenu, N.: Test particle energization by current sheets and nonuniform fields in magnetohydrodynamic turbulence. Astrophys. J. 617, 667–679 (2004)

    Article  ADS  Google Scholar 

  • Dorland, W., Hammett, G.W.: Gyrofluid turbulence models with kinetic effects. Phys. Fluids B 5, 812–835 (1993)

    Article  ADS  Google Scholar 

  • Frieman, E.A., Chen, L.: Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Phys. Fluids 25, 502–508 (1982)

    Article  ADS  MATH  Google Scholar 

  • Galtier, S.: Wave turbulence in incompressible Hall magnetohydrodynamics. J. Plasma Phys. 72, 721–769 (2006)

    Article  ADS  Google Scholar 

  • Galtier, S., Nazarenko, S.V., Newell, A.C., Pouquet, A.: A weak turbulence theory for incompressible magnetohydrodynamics. J. Plasma Phys. 63, 447–488 (2000)

    Article  ADS  Google Scholar 

  • Gary, S.P., Saito, S., Narita, Y.: Whistler turbulence wavevector anisotropies: particle-in-cell simulations Astrophys. J. 716, 1332–1335 (2010)

    ADS  Google Scholar 

  • Goldreich, P., Sridhar, S.: Toward a theory of interstellar turbulence II. Strong Alfvénic turbulence. Astrophys. J. 438, 763–775 (1995)

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Goldstein, M.L., Roberts, D.A., Matthaeus, W.H.: Magnetohydrodynamic turbulence in the solar wind. Ann. Rev. Astron. Astrophys. 33, 283–326 (1995)

    Article  ADS  Google Scholar 

  • Gruzinov, A.V.: Radiative efficiency of collisionless accretion. Astrophys. J. 501, 787 (1998)

    Article  ADS  Google Scholar 

  • Hasegawa, A., Sato, T.: Space plasma physics. 1. Stationary processes. Physics and Chemistry in Space, vol. 16. Springer-Verlag: Berlin (1989)

    Book  Google Scholar 

  • He, J., Marsch, E., Tu, C., Yao, S., Tian, H.: Possible evidence of Alfvén-cyclotron waves in the angle distribution of magnetic helicity of solar wind turbulence. Astrophys. J. 731, 85 (2011)

    Article  ADS  Google Scholar 

  • Hollweg, J.V.: Kinetic Alfvén wave revisited. J. Geophys. Res. 104, 14811–14820 (1999)

    Article  ADS  Google Scholar 

  • Howes, G.G.: Inertial range turbulence in kinetic plasmas. Phys. Plasmas 15(5), 055904 (2008)

    Article  ADS  Google Scholar 

  • Howes, G.G.: A prescription for the turbulent heating of astrophysical plasmas. Mon. Not. R. Astron. Soc. 409, L104–L108 (2010)

    Article  ADS  Google Scholar 

  • Howes, G.G.: Prediction of the proton-to-total turbulent heating in the solar wind. Astrophys. J. 738, 40 (2011)

    Article  ADS  Google Scholar 

  • Howes, G.G., Quataert, E.: On the interpretation of magnetic helicity signatures in the dissipation range of solar wind turbulence. Astrophys. J. Lett. 709, L49–L52 (2010)

    Article  ADS  Google Scholar 

  • Howes, G.G., Cowley, S.C., Dorland, W., Hammett, G.W., Quataert, E., Schekochihin, A.A.: Astrophysical gyrokinetics: basic equations and linear theory. Astrophys. J. 651, 590–614 (2006)

    Article  ADS  Google Scholar 

  • Howes, G.G., Cowley, S.C., Dorland, W., Hammett, G.W., Quataert, E., Schekochihin, A.A.: A model of turbulence in magnetized plasmas: Implications for the dissipation range in the solar wind. J. Geophys. Res. 113(A12), A05103 (2008)

    ADS  Google Scholar 

  • Howes, G.G., Dorland, W., Cowley, S.C., Hammett, G.W., Quataert, E., Schekochihin, A.A., Tatsuno, T.: Kinetic simulations of magnetized turbulence in astrophysical plasmas. Phys. Rev. Lett. 100(6), 065004 (2008)

    Article  ADS  Google Scholar 

  • Howes, G.G., Tenbarge, J.M., Dorland, W.: A weakened cascade model for turbulence in astrophysical plasmas. Phys. Plasmas 18(10), 102305 (2011)

    Article  ADS  Google Scholar 

  • Howes, G.G., TenBarge, J.M., Dorland, W., Quataert, E., Schekochihin, A.A. Numata, R., Tatsuno, T.: Gyrokinetic simulations of solar wind turbulence from ion to electron scales. Phys. Rev. Lett. 107(3), 035004 (2011)

    Article  ADS  Google Scholar 

  • Howes, G.G., Bale, S.D., Klein, K.G., Chen, C.H.K., Salem, C.S., TenBarge, J.M.: The slow-mode nature of compressible wave power in solar wind turbulence. Astrophys. J. Lett. 753, L19, (2012)

    Article  ADS  Google Scholar 

  • Jian, L.K., Russell, C.T., Luhmann, J.G., Strangeway, R.J., Leisner, J.S., Galvin, A.B.: Ion cyclotron waves in the solar wind observed by STEREO near 1 AU. Astrophys. J. Lett. 701, L105–L109 (2009)

    Article  ADS  Google Scholar 

  • Kellogg, P.J., Horbury, T.S.: Rapid density fluctuations in the solar wind. Ann. Geophys. 23, 3765–3773 (2005)

    Article  ADS  Google Scholar 

  • Kiyani, K.H., Chapman, S.C., Khotyaintsev, Y.V., Dunlop, M.W., Sahraoui, F.: Global scale-invariant dissipation in collisionless plasma turbulence. Phys. Rev. Lett. 103, 075006 (2009)

    Article  ADS  Google Scholar 

  • Klein, K.G., Howes, G.G., TenBarge, J.M., Bale, S.D., Chen, C.H.K., Salem, C.S.: Using synthetic spacecraft data to interpret compressible fluctuations in solar wind turbulence. Astrophys. J. 755, 159 (2012)

    Article  ADS  Google Scholar 

  • Kolmogorov, A.N.: The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers. Dokl. Akad. Nauk SSSR 30, 9– (1941). [English Translation: Proc. R. Soc. London A 434, 9 (1991)]

    Google Scholar 

  • Krishan, V., Mahajan, S.M.: Magnetic fluctuations and Hall magnetohydrodynamic turbulence in the solar wind. J. Geophys. Res. 109(A18), A11105 (2004)

    Article  ADS  Google Scholar 

  • Leamon, R.J., Smith, C.W., Ness, N.F., Matthaeus, W.H., Wong, H.K.: Observational constraints on the dynamics of the interplanetary magnetic field dissipation range. J. Geophys. Res. 103, 4775–4787 (1998)

    Article  ADS  Google Scholar 

  • Leamon, R.J., Smith, C.W., Ness, N.F., Wong, H.K.: Dissipation range dynamics: Kinetic alfvén waves and the importance of β e . J. Geophys. Res. 104, 22331–22344 (1999)

    Article  ADS  Google Scholar 

  • Leamon, R.J., Matthaeus, W.H., Smith, C.W., Zank, G.P., Mullan, D.J., Oughton, S.: MHD-driven kinetic dissipation in the solar wind and corona. Astrophys. J. 537, 1054–1062 (2000)

    Article  ADS  Google Scholar 

  • Lithwick, Y., Goldreich, P.: Compressible magnetohydrodynamic turbulence in interstellar plasmas. Astrophys. J. 562, 279–296 (2001)

    Article  ADS  Google Scholar 

  • Markovskii, S.A., Vasquez, B.J.: A short-timescale channel of dissipation of the strong solar wind turbulence. Astrophys. J. 739, 22 (2011)

    Article  ADS  Google Scholar 

  • Maron, J., Goldreich, P.: Simulations of incompressible magnetohydrodynamic turbulence. Astrophys. J. 554, 1175–1196 (2001)

    Article  ADS  Google Scholar 

  • Narita, Y., Gary, S.P.: Inertial-range spectrum of whistler turbulence. Ann. Geophys. 28, 597–601 (2010)

    Article  ADS  Google Scholar 

  • Osman, K.T., Matthaeus, W.H., Greco, A., Servidio, S.: Evidence for inhomogeneous heating in the solar wind. Astrophys. J. Lett. 727, L11+ (2011)

    Google Scholar 

  • Osman, K.T., Matthaeus, W.H., Wan, M., Rappazzo, A.F.: Intermittent dissipation and local heating in the solar wind. ArXiv e-prints (2011)

    Google Scholar 

  • Parashar, T.N., Shay, M.A., Cassak, P.A., Matthaeus, W.H.: Kinetic dissipation and anisotropic heating in a turbulent collisionless plasma. Phys. Plasmas 16(3), 032310 (2009)

    Article  ADS  Google Scholar 

  • Parashar, T.N., Servidio, S., Breech, B., Shay, M.A., Matthaeus, W.H.: Kinetic driven turbulence: Structure in space and time. Phys. Plasmas 17(10), 102304 (2010)

    Article  ADS  Google Scholar 

  • Perri, S., Carbone, V., Veltri, P.: Where does fluid-like turbulence break down in the solar wind? Astrophys. J. Lett. 725, L52–L55 (2010)

    Article  ADS  Google Scholar 

  • Plunk, G.G., Tatsuno, T.: Energy transfer and dual cascade in kinetic magnetized plasma turbulence. Phys. Rev. Lett. 106(16), 165003 (2011)

    Article  ADS  Google Scholar 

  • Plunk, G.G., Cowley, S.C., Schekochihin, A.A., Tatsuno T.: Two-dimensional gyrokinetic turbulence. J. Fluid Mech. 664, 407–435 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Podesta, J.J., Roberts, D.A., Goldstein, M.L.: Spectral exponents of kinetic and magnetic energy spectra in solar wind turbulence. Astrophys. J. 664, 543–548 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Quataert, E., Gruzinov, A.: Turbulence and particle heating in advection-dominated accretion flows. Astrophys. J. 520, 248–255 (1999)

    Article  ADS  Google Scholar 

  • Sahraoui, F., Goldstein, M.L., Robert, P., Khotyaintsev, Y.V.: Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale. Phys. Rev. Lett. 102(23), 231102 (2009)

    Article  ADS  Google Scholar 

  • Sahraoui, F., Goldstein, M.L., Belmont, G., Canu, P., Rezeau, L.: Three dimensional anisotropic k spectra of turbulence at subproton scales in the solar wind. Phys. Rev. Lett. 105(13), 131101 (2010)

    Article  ADS  Google Scholar 

  • Sahraoui, F., Belmont, G., Goldstein, M.L.: New insight into short-wavelength solar wind fluctuations from vlasov theory. Astrophys. J. 748, 100 (2012)

    Article  ADS  Google Scholar 

  • Salem, C.S., Howes, G.G, Sundkvist, D., Bale, S.D., Chaston, C.C., Chen, C.H.K., Mozer, F.S.: Identification of kinetic Alfvén wave turbulence in the solar wind. Astrophys. J. Lett. 745, L9 (2012)

    Article  ADS  Google Scholar 

  • Schekochihin, A.A., Cowley, S.C., Dorland, W., Hammett, G.W., Howes, G.G., Quataert, E., Tatsuno, T.: Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophys. J. Supp. 182, 310–377 (2009)

    Article  ADS  Google Scholar 

  • Servidio, S., Matthaeus, W.H., Shay, M.A., Cassak, P.A., Dmitruk, P.: Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 102(11), 115003 (2009)

    Article  ADS  Google Scholar 

  • Servidio, S., Matthaeus, W.H., Shay, M.A., Dmitruk, P., Cassak, P.A., Wan, M.: Statistics of magnetic reconnection in two-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 17(3), 032315 (2010)

    Article  ADS  Google Scholar 

  • Servidio, S., Dmitruk, P., Greco, A., Wan, M., Donato, S., Cassak, P.A., Shay, M.A., Carbone, V., Matthaeus, W.H.: Magnetic reconnection as an element of turbulence. Nonlin. Proc. Geophys. 18, 675–695 (2011)

    Article  ADS  Google Scholar 

  • Servidio, S., Valentini, F., Califano, F., Veltri, P.: Local kinetic effects in two-dimensional plasma turbulence. Phys. Rev. Lett. 108(4), 045001 (2012)

    Article  ADS  Google Scholar 

  • Shaikh, D., Zank, G.P.: Driven dissipative whistler wave turbulence. Phys. Plasmas 12(12), 122310 (2005)

    Article  ADS  Google Scholar 

  • Shaikh, D., Zank. G.P.: Spectral features of solar wind turbulent plasma. Mon. Not. R. Astron. Soc. 400, 1881–1891 (2009)

    Google Scholar 

  • Smith, C.W., Mullan, D.J., Ness, N.F., Skoug, R.M., Steinberg, J.: Day the solar wind almost disappeared: magnetic field fluctuations, wave refraction and dissipation. J. Geophys. Res. 106, 18625–18634 (2001)

    Article  ADS  Google Scholar 

  • Smith, C.W., Vasquez, B.J., Hollweg, J.V.: Observational constraints on the role of cyclotron damping and kinetic alfvén waves in the solar wind. Astrophys. J. 745, 8 (2012)

    Article  ADS  Google Scholar 

  • Sridhar, S., Goldreich, P.: Toward a theory of interstellar turbulence I. Weak Alfvénic turbulence. Astrophys. J. 433, 612–621 (1994)

    ADS  Google Scholar 

  • Stawicki, O., Gary, S.P., Li, H.: Solar wind magnetic fluctuation spectra: dispersion versus damping. J. Geophys. Res. 106, 8273–8282 (2001)

    Article  ADS  Google Scholar 

  • Stix, T.H.: Waves in Plasmas. American Institute of Physics, New York (1992)

    Google Scholar 

  • Strauss, H.R.: Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks. Phys. Fluids 19, 134–140 (1976)

    Article  ADS  Google Scholar 

  • Tatsuno, T., Schekochihin, A.A., Dorland, W., Plunk, G., Barnes, M.A., Cowley, S.C., Howes, G.G.: Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence. Phys. Rev. Lett. 103(1), 015003 (2009)

    Article  ADS  Google Scholar 

  • Taylor, G.I.: The spectrum of turbulence. Proc. R. Soc. A 164, 476–490 (1938)

    Article  ADS  Google Scholar 

  • TenBarge, J.M., Howes, G.G.: Current sheets and collisionless damping in kinetic plasma turbulence. Astrophys. J. 771, L27 (2013a)

    Article  ADS  Google Scholar 

  • TenBarge, J.M., Podesta, J.J., Klein, K.G., Howes, G.G.: Interpreting magnetic variance anisotropy measurements in the solar wind. Astrophys. J. 774, 139 (2013b)

    Article  ADS  Google Scholar 

  • Tenbarge, J.M., Howes, G.G.: Evidence of critical balance in kinetic Alfvén wave turbulence simulations. Phys. Plasmas 19, 055901 (2012c)

    Article  ADS  Google Scholar 

  • TenBarge, J.M., Podesta, J.J., Klein, K.G., Howes, G.G.: Interpreting magnetic variance anisotropy measurements in the solar wind. Astrophys. J. 753, 107 (2012b)

    Article  ADS  Google Scholar 

  • Terry, P.W., et al.: Dissipation range turbulent cascades in plasmas. Phys. Plasmas 19, 055906 (2012)

    Article  ADS  Google Scholar 

  • Tu, C.-Y., Marsch, E.: On the nature of compressive fluctuations in the solar wind. J. Geophys. Res. 99, 21481 (1994)

    Article  ADS  Google Scholar 

  • Tu, C.-Y., Marsch, E.: MHD structures, waves and turbulence in the solar wind: observations and theories. Space Sci. Rev. 73, 1–2 (1995)

    Article  ADS  Google Scholar 

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Acknowledgements

I would like to thank Steve Cowley, Bill Dorland, and Eliot Quataert for their invaluable guidance, steering my career toward the study of turbulence in kinetic astrophysical plasmas. Alex Schekochihin, Tomo Tatsuno, Ryusuke Numata, and Jason TenBarge have contributed tremendously to my efforts to understand kinetic turbulence. Financial support has been provided by NSF grant PHY-10033446, NSF CAREER Award AGS-1054061, and NASA grant NNX10AC91G.

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  1. Department of Physics and Astronomy, University of Iowa, Iowa City, IA, 52242, USA

    Gregory G. Howes

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  1. Gregory G. Howes
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Editors and Affiliations

  1. Department of Astronomy, University of Wisconsin-Madison, Madison, Wisconsin, USA

    Alexander Lazarian

  2. Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, São Paulo, Brazil

    Elisabete M. de Gouveia Dal Pino

  3. Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, São Paulo, Brazil

    Claudio Melioli

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Howes, G.G. (2015). Kinetic Turbulence. In: Lazarian, A., de Gouveia Dal Pino, E., Melioli, C. (eds) Magnetic Fields in Diffuse Media. Astrophysics and Space Science Library, vol 407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44625-6_6

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