Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T16:15:25.815Z Has data issue: false hasContentIssue false

Diagnosing collisionless energy transfer using field–particle correlations: Vlasov–Poisson plasmas

Published online by Cambridge University Press:  12 January 2017

Gregory G. Howes*
Affiliation:
Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA
Kristopher G. Klein
Affiliation:
Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI 48109, USA Space Science Center, University of New Hampshire, Durham, NH 03824, USA
Tak Chu Li
Affiliation:
Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA
*
Email address for correspondence: gregory-howes@uiowa.edu

Abstract

Turbulence plays a key role in the conversion of the energy of large-scale fields and flows to plasma heat, impacting the macroscopic evolution of the heliosphere and other astrophysical plasma systems. Although we have long been able to make direct spacecraft measurements of all aspects of the electromagnetic field and plasma fluctuations in near-Earth space, our understanding of the physical mechanisms responsible for the damping of the turbulent fluctuations in heliospheric plasmas remains incomplete. Here we propose an innovative field–particle correlation technique that can be used to measure directly the secular energy transfer from fields to particles associated with collisionless damping of the turbulent fluctuations. Furthermore, this novel procedure yields information about the collisionless energy transfer as a function of particle velocity, providing vital new information that can help to identify the dominant collisionless mechanism governing the damping of the turbulent fluctuations. Kinetic plasma theory is used to devise the appropriate correlation to diagnose Landau damping, and the field–particle correlation technique is thoroughly illustrated using the simplified case of the Landau damping of Langmuir waves in a 1D-1V (one dimension in physical space and one dimension in velocity space) Vlasov–Poisson plasma. Generalizations necessary to apply the field–particle correlation technique to diagnose the collisionless damping of turbulent fluctuations in the solar wind are discussed, highlighting several caveats. This novel field–particle correlation technique is intended to be used as a primary analysis tool for measurements from current, upcoming and proposed spacecraft missions that are focused on the kinetic microphysics of weakly collisional heliospheric plasmas, including the Magnetospheric Multiscale (MMS), Solar Probe Plus, Solar Orbiter and Turbulence Heating ObserveR (THOR) missions.

Type
Research Article
Copyright
© Cambridge University Press 2017 

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

Anderson, R. R. & Maeda, K. 1977 VLF emissions associated with enhanced magnetospheric electrons. J. Geophys. Res. 82, 135146.Google Scholar
Bale, S. D., Goetz, K., Harvey, P. R., Turin, P., Bonnell, J. W., Dudok de Wit, T., Ergun, R. E., MacDowall, R. J., Pulupa, M., Andre, M. et al. 2016 The FIELDS Instrument Suite for Solar Probe Plus. Space Sci. Rev 204 (1), 4982.CrossRefGoogle ScholarPubMed
Barnes, A. 1966 Collisionless damping of hydromagnetic waves. Phys. Fluids 9, 14831495.CrossRefGoogle Scholar
Borovsky, J. E. & Denton, M. H. 2011 No evidence for heating of the solar wind at strong current sheets. Astrophys. J. Lett. 739, L61.Google Scholar
Bourouaine, S. & Chandran, B. D. G. 2013 Observational test of stochastic heating in low- $\unicode[STIX]{x1D6FD}$ fast-solar-wind streams. Astrophys. J. 774, 96.Google Scholar
Bourouaine, S., Marsch, E. & Vocks, C. 2008 On the efficiency of nonresonant ion heating by coronal Alfvén waves. Astrophys. J. Lett. 684, L119L122.Google Scholar
Burch, J. L., Moore, T. E., Torbert, R. B. & Giles, B. L. 2016 Magnetospheric multiscale overview and science objectives. Space Sci. Rev. 199, 521.CrossRefGoogle Scholar
Burke, W. J., Gough, M. P., Gentile, L. C., Huang, C. Y., Machuzak, J. S. & Rubin, A. G. 1999 MHz and kHz modulations of particle fluxes during beam experiments of the tethered satellite system missions. Adv. Space Res. 24, 10471054.Google Scholar
Burton, R. K. & Holzer, R. E. 1974 The origin and propagation of chorus in the outer magnetosphere. J. Geophys. Res. 79, 10141023.Google Scholar
Chandran, B. D. G. 2010 Alfvén-wave turbulence and perpendicular ion temperatures in coronal holes. Astrophys. J. 720, 548554.Google Scholar
Chandran, B. D. G., Dennis, T. J., Quataert, E. & Bale, S. D. 2011 Incorporating kinetic physics into a two-fluid solar-wind model with temperature anisotropy and low-frequency Alfvén-wave turbulence. Astrophys. J. 743, 197.Google Scholar
Chandran, B. D. G., Li, B., Rogers, B. N., Quataert, E. & Germaschewski, K. 2010 Perpendicular ion heating by low-frequency Alfvén-wave turbulence in the solar wind. Astrophys. J. 720, 503515.Google Scholar
Chaston, C. C. 2006 ULF waves and auroral electrons. In Magnetospheric ULF Waves: Synthesis and New Directions (ed. Takahashi, K., Chi, P. J., Denton, R. E. & Lysak, R. L.), Washington DC American Geophysical Union Geophysical Monograph Series, vol. 169, p. 239. American Geophysical Union.Google Scholar
Chaston, C. C., Bonnell, J. W., Carlson, C. W., Mcfadden, J. P., Ergun, R. E. & Strangeway, R. J. 2003 Properties of small-scale Alfvén waves and accelerated electrons from FAST. J. Geophys. Res. 108, 8003.Google Scholar
Chaston, C. C., Carlson, C. W., Mcfadden, J. P., Ergun, R. E. & Strangeway, R. J. 2007 How important are dispersive Alfvén waves for auroral particle acceleration? Geophys. Res. Lett. 34, 7101.Google Scholar
Chen, C. H. K., Bale, S. D., Salem, C. & Mozer, F. S. 2011 Frame dependence of the electric field spectrum of solar wind turbulence. Astrophys. J. Lett. 737, L41.Google Scholar
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.Google ScholarPubMed
Chen, L., Lin, Z. & White, R. 2001 On resonant heating below the cyclotron frequency. Phys. Plasmas 8, 47134716.Google Scholar
Coleman, P. J. Jr. 1968 Turbulence, viscosity, and dissipation in the solar-wind plasma. Astrophys. J. 153, 371388.Google Scholar
Denskat, K. U., Beinroth, H. J. & Neubauer, F. M. 1983 Interplanetary magnetic field power spectra with frequencies from 2.4 $\times$ 10 to the -5th HZ to 470 HZ from HELIOS-observations during solar minimum conditions. J. Geophys. Zeit. Geophys. 54, 6067.Google Scholar
Dmitruk, P., Matthaeus, W. H. & Seenu, N. 2004 Test particle energization by current sheets and nonuniform fields in magnetohydrodynamic turbulence. Astrophys. J. 617, 667679.CrossRefGoogle Scholar
Ergun, R. E., Carlson, C. W., Mcfadden, J. P., Clemmons, J. H. & Boehm, M. H. 1991a Langmuir wave growth and electron bunching – results from a wave–particle correlator. J. Geophys. Res. 96, 225238.Google Scholar
Ergun, R. E., Carlson, C. W., Mcfadden, J. P., Tonthat, D. M. & Clemmons, J. H. 1991b Observation of electron bunching during Landau growth and damping. J. Geophys. Res. 96, 11.Google Scholar
Ergun, R. E., Carlson, C. W., Mozer, F. S., Delory, G. T., Temerin, M., Mcfadden, J. P., Pankow, D., Abiad, R., Harvey, P., Wilkes, R. et al. 2001 The FAST satellite fields instrument. Space Sci. Rev. 98, 6791.Google Scholar
Ergun, R. E., Mcfadden, J. P. & Carlson, C. W. 1998 Wave–Particle Correlator Instrument Design, Washington DC American Geophysical Union Geophysical Monograph Series, vol. 102, p. 325. American Geophysical Union.Google Scholar
Fredricks, R. W. & Scarf, F. L. 1973 Recent studies of magnetospheric electric field emissions above the electron gyrofrequency. J. Geophys. Res. 78, 310314.Google Scholar
Fried, B. D. & Conte, S. D. 1961 The Plasma Dispersion Function. Academic.Google Scholar
Fukuhara, H., Kojima, H., Ueda, Y., Omura, Y., Katoh, Y. & Yamakawa, H. 2009 A new instrument for the study of wave–particle interactions in space: one-chip wave–particle interaction analyzer. Earth Planets Space 61, 765778.Google Scholar
Gary, S. P. 1999 Collisionless dissipation wavenumber: linear theory. J. Geophys. Res. 104, 67596762.CrossRefGoogle Scholar
Goertz, C. K. & Boswell, R. W. 1979 Magnetosphere-ionosphere coupling. J. Geophys. Res. 84, 72397246.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. J. Geophys. Res. 99, 1151911538.CrossRefGoogle Scholar
Gough, M. P. 1980 A technique for rocket-borne detection of electron bunching at megahertz frequencies. Nucl. Instrum. Meth. 177, 581587.Google Scholar
Gough, M. P., Buckley, A. M., Carozzi, T. & Beloff, N. 2003 Experimental studies of wave–particle interactions in space using particle correlators: results and future developments. Adv. Space Res. 32, 407416.CrossRefGoogle Scholar
Gough, M. P., Burke, W. J., Hardy, D. A., Huang, C. Y., Gentile, L. C., Rubin, A. G., Oberhardt, M. R., Drobot, A. T., Thompson, D. C. & Raitt, W. J. 1998a Megahertz electron modulations during TSS 1R. Geophys. Res. Lett. 25, 441444.Google Scholar
Gough, M. P., Christiansen, P. J. & Wilhelm, K. 1990 Auroral beam-plasma interactions – particle correlator investigations. J. Geophys. Res. 95, 1228712294.Google Scholar
Gough, M. P., Hardy, D. A., Burke, W. J., Oberhardt, M. R., Gentile, L. C., Huang, C. Y., Cooke, D. L., Raitt, W. J., Thompson, D. C. & Mcneil, W. 1997 Heating and low-frequency modulation of electrons observed during electron beam operations on TSS 1. J. Geophys. Res. 102, 1733517358.Google Scholar
Gough, M. P., Hardy, D. A. & James, H. G. 1998b First results from the energetic particle instrument on the OEDIPUS-C sounding rocket. Adv. Space Res. 21, 705708.Google Scholar
Gough, M. P., Hardy, D. A., Oberhardt, M. R., Burke, W. J., Gentile, L. C., Mcneil, B., Bounar, K., Thompson, D. C. & Raitt, W. J. 1995 Correlator measurements of megahertz wave–particle interactions during electron beam operations on STS 46. J. Geophys. Res. 100, 2156121576.Google Scholar
Gough, M. P., Hardy, D. A., Oberhardt, M. R., Burke, W. J., Gentile, L. C., Thompson, D. C. & Raitt, W. J. 1998c Spree measurements of wave–particle interactions generated by the electron guns on TSS-1 and TSS-1R. Adv. Space Res. 21, 729733.CrossRefGoogle Scholar
Gough, M. P., Martelli, G., Smith, P. N., Maehlum, B. N. & Ventura, G. 1980 Bunching of 8–10 keV auroral electrons near an artificial electron beam. Nature 287, 1517.CrossRefGoogle Scholar
Gough, M. P. & Urban, A. 1983 Auroral beam/plasma interaction observed directly. Planet. Space Sci. 31, 875883.Google Scholar
Hasegawa, A. 1976 Particle acceleration by MHD surface wave and formation of aurora. J. Geophys. Res. 81, 50835090.Google Scholar
Hollweg, J. V. & Isenberg, P. A. 2002 Generation of the fast solar wind: a review with emphasis on the resonant cyclotron interaction. J. Geophys. Res. (Space Physics) 107, 1147.Google Scholar
Howes, G. G. 2015 A dynamical model of plasma turbulence in the solar wind. Phil. Trans. R. Soc. Lond. A 373 (2041), 20140145.Google ScholarPubMed
Howes, G. G. 2015 Kinetic turbulence. In Magnetic Fields in Diffuse Media, Springer.Google 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., Bale, S. D., Klein, K. G., Chen, C. H. K., Salem, C. S. & Tenbarge, J. M. 2012 The slow-mode nature of compressible wave power in solar wind turbulence. Astrophys. J. Lett. 753, L19.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, 590614.CrossRefGoogle Scholar
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. 113 (A12), A05103.Google Scholar
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.CrossRefGoogle ScholarPubMed
Howes, G. G., Klein, K. G. & Tenbarge, J. M. 2014 Validity of the Taylor hypothesis for linear kinetic waves in the weakly collisional solar wind. Astrophys. J. 789, 106.CrossRefGoogle Scholar
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, 035004.Google Scholar
Huang, C. Y., Burke, W. J., Hardy, D. A., Gough, M. P., James, H. G., Villalón, E. & Gentile, L. C. 2001 Electron acceleration by megahertz waves during OEDIPUS C. J. Geophys. Res. 106, 18351848.Google Scholar
Huang, C. Y., Burke, W. J., Hardy, D. A., Gough, M. P., Olson, D. G., Gentile, L. C., Gilchrist, B. E., Bonifazi, C., Raitt, W. J. & Thompson, D. C. 1998 Cerenkov emissions of ion acoustic-like waves generated by electron beams emitted during TSS 1R. Geophys. Res. Lett. 25, 721724.CrossRefGoogle Scholar
Hui, C.-H. & Seyler, C. E. 1992 Electron acceleration by Alfven waves in the magnetosphere. J. Geophys. Res. 97, 39533963.Google Scholar
Isenberg, P. A. & Hollweg, J. V. 1983 On the preferential acceleration and heating of solar wind heavy ions. J. Geophys. Res. 88, 39233935.Google Scholar
Isenberg, P. A., Lee, M. A. & Hollweg, J. V. 2001 The kinetic shell model of coronal heating and acceleration by ion cyclotron waves: 1. Outward propagating waves. J. Geophys. Res. 106, 56495660.Google Scholar
Johnson, J. R. & Cheng, C. Z. 2001 Stochastic ion heating at the magnetopause due to kinetic Alfvén waves. Geophys. Res. Lett. 28, 44214424.CrossRefGoogle Scholar
Karimabadi, H., Roytershteyn, V., Wan, M., Matthaeus, W. H., Daughton, W., Wu, P., Shay, M., Loring, B., Borovsky, J., Leonardis, E. et al. 2013 Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas. Phys. Plasmas 20 (1), 012303.Google Scholar
Kasper, J. C., Abiad, R., Austin, G., Balat-Pichelin, M., Bale, S. D., Belcher, J. W., Berg, P., Bergner, H., Berthomier, M., Bookbinder, J. et al. 2015 Solar wind electrons alphas and protons (SWEAP) investigation: design of the solar wind and coronal plasma instrument suite for solar probe plus. Space Sci. Rev. 204, 131186. doi:10.1007/s11214-015-0206-3.Google Scholar
Katoh, Y., Kitahara, M., Kojima, H., Omura, Y., Kasahara, S., Hirahara, M., Miyoshi, Y., Seki, K., Asamura, K., Takashima, T. et al. 2013 Significance of wave–particle interaction analyzer for direct measurements of nonlinear wave–particle interactions. Ann. Geophys. 31 (3), 503512.CrossRefGoogle Scholar
Keiling, A. 2009 Alfvén waves and their roles in the dynamics of the earth’s magnetotail: a review. Space Sci. Rev. 142, 73156.Google Scholar
Keiling, A., Wygant, J. R., Cattell, C., Peria, W., Parks, G., Temerin, M., Mozer, F. S., Russell, C. T. & Kletzing, C. A. 2002 Correlation of Alfvén wave Poynting flux in the plasma sheet at 4–7 $R_{E}$ with ionospheric electron energy flux. J. Geophys. Res. 107, 1132.Google Scholar
Kennel, C. F. & Petschek, H. E. 1966 Limit on stably trapped particle fluxes. J. Geophys. Res. 71, 1.Google Scholar
Kennel, C. F., Scarf, F. L., Fredricks, R. W., Mcgehee, J. H. & Coroniti, F. V. 1970 VLF electric field observations in the magnetosphere. J. Geophys. Res. 75, 61366152.CrossRefGoogle Scholar
Kimura, I., Hashimoto, K., Matsumoto, H., Mukai, T., Bell, T. F., Inan, U. S., Helliwell, R. A. & Katsufrakis, J. P. 1983 EXOS-B/Siple station VLF wave–particle interaction experiments. I – general description and wave–particle correlations. J. Geophys. Res. 88, 282294.Google Scholar
Klein, K. G., Howes, G. G., Tenbarge, J. M., Bale, S. D., Chen, C. H. K. & Salem, C. S. 2012 Using synthetic spacecraft data to interpret compressible fluctuations in solar wind turbulence. Astrophys. J. 755, 159.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. Astrophys. J. 785, 138.CrossRefGoogle Scholar
Kletzing, C. A. 1994 Electron acceleration by kinetic Alfvén waves. J. Geophys. Res. 99, 1109511104.Google Scholar
Kletzing, C. A., Bounds, S. R., Labelle, J. & Samara, M. 2005 Observation of the reactive component of Langmuir wave phase-bunched electrons. Geophys. Res. Lett. 32, L05106.Google Scholar
Kletzing, C. A. & Muschietti, L. 2006 Phase correlation of electrons and Langmuir waves. In Geospace Electromagnetic Waves and Radiation (ed. Labelle, J. W. & Treumann, R. A.), Lecture Notes in Physics, vol. 687, p. 313. Springer.Google Scholar
Kruskal, M. D. & Oberman, C. R. 1958 On the stability of plasma in static equilibrium. Phys. Fluids 1, 275280.Google Scholar
Kulsrud, R. M. 1983 Mhd description of plasma. In Basic Plasma Physics I (ed. Galeev, A. A. & Sudan, R. N.), Handbook of Plasma Physics, vol. 1, chap. 1.4, pp. 115145. North Holland.Google Scholar
Landau, L. D. 1946 On the vibrations of the electronic plasma. J. Phys. 10, 25.Google Scholar
Leamon, R. J., Matthaeus, W. H., Smith, C. W. & Wong, H. K. 1998a Contribution of cyclotron-resonant damping to kinetic dissipation of interplanetary turbulence. Astrophys. J. 507, L181L184.CrossRefGoogle Scholar
Leamon, R. J., Matthaeus, W. H., Smith, C. W., Zank, G. P., Mullan, D. J. & Oughton, S. 2000 MHD-driven kinetic dissipation in the solar wind and corona. Astrophys. J. 537, 10541062.Google Scholar
Leamon, R. J., Smith, C. W., Ness, N. F., Matthaeus, W. H. & Wong, H. K. 1998b Observational constraints on the dynamics of the interplanetary magnetic field dissipation range. J. Geophys. Res. 103, 47754787.Google Scholar
Leamon, R. J., Smith, C. W., Ness, N. F. & Wong, H. K. 1999 Dissipation range dynamics: kinetic alfvén waves and the importance of $\unicode[STIX]{x1D6FD}_{e}$ . J. Geophys. Res. 104, 2233122344.Google Scholar
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 (2), L24.Google Scholar
Lysak, R. L. & Dum, C. T. 1983 Dynamics of magnetosphere-ionosphere coupling including turbulent transport. J. Geophys. Res. 88, 365380.Google Scholar
Lysak, R. L. & Lotko, W. 1996 On the kinetic dispersion relation for shear Alfvén waves. J. Geophys. Res. 101, 50855094.Google Scholar
Manfredi, G. 1997 Long-time behavior of nonlinear landau damping. Phys. Rev. Lett. 79, 28152818.Google Scholar
Markovskii, S. A. & Vasquez, B. J. 2011 A short-timescale channel of dissipation of the strong solar wind turbulence. Astrophys. J. 739, 22.Google Scholar
Matthaeus, W. H. & Velli, M. 2011 Who needs turbulence? A review of turbulence effects in the heliosphere and on the fundamental process of reconnection. Space Sci. Rev. 160, 145168.Google Scholar
Melrose, D. B. 1986 Instabilities in Space and Laboratory Plasmas. Cambridge University Press.Google Scholar
Morrison, P. J. 1994 The energy of perturbations for Vlasov plasmas. Phys. Plasmas 1, 14471451.CrossRefGoogle Scholar
Müller, D., Marsden, R. G., St. Cyr, O. C. & Gilbert, H. R. 2013 Solar orbiter. Exploring the sun-heliosphere connection. Sol. Phys. 285, 2570.Google Scholar
Muschietti, L., Roth, I. & Ergun, R. 1994 Interaction of Langmuir wave packets with streaming electrons: phase-correlation aspects. Phys. Plasmas 1, 10081024.Google Scholar
Oliven, M. N. & Gurnett, D. A. 1968 Microburst phenomena: 3. An association between microbursts and VLF chorus. J. Geophys. Res. 73, 23552362.Google Scholar
O’Neil, T. 1965 Collisionless damping of nonlinear plasma oscillations. Phys. Fluids 8, 22552262.Google Scholar
Osman, K. T., Kiyani, K. H., Chapman, S. C. & Hnat, B. 2014a Anisotropic intermittency of magnetohydrodynamic turbulence. Astrophys. J. Lett. 783, L27.Google Scholar
Osman, K. T., Matthaeus, W. H., Gosling, J. T., Greco, A., Servidio, S., Hnat, B., Chapman, S. C. & Phan, T. D. 2014b Magnetic reconnection and intermittent turbulence in the solar wind. Phys. Rev. Lett. 112 (21), 215002.Google 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.Google Scholar
Osman, K. T., Matthaeus, W. H., Hnat, B. & Chapman, S. C. 2012a Kinetic signatures and intermittent turbulence in the solar wind plasma. Phys. Rev. Lett. 108 (26), 261103.Google Scholar
Osman, K. T., Matthaeus, W. H., Wan, M. & Rappazzo, A. F. 2012b Intermittency and local heating in the solar wind. Phys. Rev. Lett. 108 (26), 261102.Google Scholar
Park, C. G., Parks, G. K. & Lin, C. S. 1981 A ground-satellite study of wave–particle correlations. J. Geophys. Res. 86, 3753.CrossRefGoogle Scholar
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.Google Scholar
Pezzi, O., Camporeale, E. & Valentini, F. 2016 Collisional effects on the numerical recurrence in Vlasov–Poisson simulations. Phys. Plasmas 23, 022103.Google Scholar
Quataert, E. 1998 Particle heating by Alfvénic turbulence in hot accretion flows. Astrophys. J. 500, 978991.CrossRefGoogle Scholar
Quataert, E. & Gruzinov, A. 1999 Turbulence and particle heating in advection-dominated accretion flows. Astrophys. J. 520, 248255.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, 236238.Google Scholar
Rosenberg, T. J., Helliwell, R. A. & Katsufrakis, J. P. 1971 Electron precipitation associated with discrete very-low-frequency emissions. J. Geophys. Res. 76, 84458452.Google Scholar
Rubin, A. G., Burke, W. J., Gough, M. P., Machuzak, J. S., Gentile, L. C., Huang, C. Y., Hardy, D. A., Thompson, D. C. & Raitt, W. J. 1999 Beam-induced electron modulations observed during TSS 1R. J. Geophys. Res. 104, 1725117262.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
Scarf, F. L., Fredricks, R. W., Kennel, C. F. & Coroniti, F. V. 1973 Satellite studies of magnetospheric substorms on August 15, 1968: 8. Ogo 5 plasma wave observations. J. Geophys. Res. 78, 3119.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, 310377.CrossRefGoogle Scholar
Schriver, D., Ashour-Abdalla, M., Strangeway, R. J., Richard, R. L., Klezting, C., Dotan, Y. & Wygant, J. 2003 FAST/polar conjunction study of field-aligned auroral acceleration and corresponding magnetotail drivers. J. Geophys. Res. 108, 8020.Google Scholar
Schroeder, J. W. R., Skiff, F., Kletzing, C. A., Howes, G. G., Carter, T. A. & Dorfman, S. 2016 Direct measurement of electron sloshing of an inertial Alfvén wave. Geophys. Res. Lett. 43, 47014707.Google Scholar
Servidio, S., Greco, A., Matthaeus, W. H., Osman, K. T. & Dmitruk, P. 2011 Statistical association of discontinuities and reconnection in magnetohydrodynamic turbulence. J. Geophys. Res. 116, 9102.Google Scholar
Shaw, R. R. & Gurnett, D. A. 1975 Electrostatic noise bands associated with the electron gyrofrequency and plasma frequency in the outer magnetosphere. J. Geophys. Res. 80, 42594271.CrossRefGoogle Scholar
Spiger, R. J., Murphree, J. S., Anderson, H. R. & Loewenstein, R. F. 1976 Modulation of auroral electron fluxes in the frequency range 50 kHz to 10 MHz. J. Geophys. Res. 81, 12691278.Google Scholar
Spiger, R. J., Oehme, D., Loewenstein, R. F., Murphree, J., Anderson, H. R. & Anderson, R. 1974 A detector for high frequency modulation in auroral particle fluxes. Rev. Sci. Instrum. 45, 12141220.Google Scholar
Stasiewicz, K., Bellan, P., Chaston, C., Kletzing, C., Lysak, R., Maggs, J., Pokhotelov, O., Seyler, C., Shukla, P., Stenflo, L. et al. 2000 Small scale Alfvénic structure in the aurora. Space Sci. Rev. 92, 423533.Google Scholar
Stix, T. H. 1992 Waves in Plasmas. American Institute of Physics.Google Scholar
Sundkvist, D., Retinò, A., Vaivads, A. & Bale, S. D. 2007 Dissipation in turbulent plasma due to reconnection in thin current sheets. Phys. Rev. Lett. 99 (2), 025004.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476490.Google Scholar
Tenbarge, J. M. & Howes, G. G. 2013 Current sheets and collisionless damping in kinetic plasma turbulence. Astrophys. J. Lett. 771, L27.Google Scholar
Tenbarge, J. M., Podesta, J. J., Klein, K. G. & Howes, G. G. 2012 Interpreting magnetic variance anisotropy measurements in the solar wind. Astrophys. J. 753, 107.CrossRefGoogle 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
Uritsky, V. M., Pouquet, A., Rosenberg, D., Mininni, P. D. & Donovan, E. F. 2010 Structures in magnetohydrodynamic turbulence: detection and scaling. Phys. Rev. E 82 (5), 056326.Google Scholar
Vaivads, A., Retin, A., Soucek, J., Khotyaintsev, Yu. V., Valentini, F., Escoubet, C. P., Alexandrova, O., Andr, M., Bale, S. D., Balikhin, M. et al. 2016 Turbulence heating observer satellite mission proposal. J. Plasma Phys. 82 (5), 905820501.Google Scholar
Villani, C. 2014 Particle systems and nonlinear Landau dampinga. Phys. Plasmas 21 (3), 030901.Google Scholar
Voitenko, Y. & Goossens, M. 2004 Excitation of kinetic Alfvén turbulence by MHD waves and energization of space plasmas. Nonlinear Process. Geophys. 11, 535543.CrossRefGoogle Scholar
Wan, M., Matthaeus, W. H., Karimabadi, H., Roytershteyn, V., Shay, M., Wu, P., Daughton, W., Loring, B. & Chapman, S. C. 2012 Intermittent dissipation at kinetic scales in collisionless plasma turbulence. Phys. Rev. Lett. 109 (19), 195001.CrossRefGoogle ScholarPubMed
Wang, X., Tu, C., He, J., Marsch, E. & Wang, L. 2013 On intermittent turbulence heating of the solar wind: differences between tangential and rotational discontinuities. Astrophys. J. Lett. 772, L14.Google Scholar
Watkins, N. W., Bather, J. A., Chapman, S. C., Mouikis, C. G., Gough, M. P., Wygant, J. R., Hardy, D. A., Collin, H. L., Johnstone, A. D. & Anderson, R. R. 1996 Suspected wave–particle interactions coincident with a pancake distribution as seen by the CRRES spacecraft. Adv. Space Res. 17, 8387.CrossRefGoogle Scholar
White, R., Chen, L. & Lin, Z. 2002 Resonant plasma heating below the cyclotron frequency. Phys. Plasmas 9, 18901897.Google Scholar
Woolliscroft, L. J. C., Alleyne, H. S. C., Dunford, C. M., Sumner, A., Thompson, J. A., Walker, S. N., Yearby, K. H., Buckley, A., Chapman, S. & Gough, M. P. 1997 The digital wave-processing experiment on cluster. Space Sci. Rev. 79, 209231.Google Scholar
Wu, P., Perri, S., Osman, K., Wan, M., Matthaeus, W. H., Shay, M. A., Goldstein, M. L., Karimabadi, H. & Chapman, S. 2013 Intermittent heating in solar wind and kinetic simulations. Astrophys. J. Lett. 763, L30.CrossRefGoogle Scholar
Zhdankin, V., Uzdensky, D. A. & Boldyrev, S. 2015a Temporal analysis of dissipative structures in magnetohydrodynamic turbulence. Astrophys. J. 811, 6.Google Scholar
Zhdankin, V., Uzdensky, D. A. & Boldyrev, S. 2015b Temporal intermittency of energy dissipation in magnetohydrodynamic turbulence. Phys. Rev. Lett. 114 (6), 065002.Google Scholar
Zhdankin, V., Uzdensky, D. A., Perez, J. C. & Boldyrev, S. 2013 Statistical analysis of current sheets in three-dimensional magnetohydrodynamic turbulence. Astrophys. J. 771, 124.Google Scholar