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Collisionless energy transfer in kinetic turbulence: field–particle correlations in Fourier space

  • Tak Chu Li (a1), Gregory G. Howes (a2), Kristopher G. Klein (a3), Yi-Hsin Liu (a1) and Jason M. TenBarge (a4)...

Abstract

Turbulence is commonly observed in nearly collisionless heliospheric plasmas, including the solar wind and corona and the Earth’s magnetosphere. Understanding the collisionless mechanisms responsible for the energy transfer from the turbulent fluctuations to the particles is a frontier in kinetic turbulence research. Collisionless energy transfer from the turbulence to the particles can take place reversibly, resulting in non-thermal energy in the particle velocity distribution functions (VDFs) before eventual collisional thermalization is realized. Exploiting the information contained in the fluctuations in the VDFs is valuable. Here we apply a recently developed method based on VDFs, the field–particle correlation technique, to a $\unicode[STIX]{x1D6FD}=1$ , solar-wind-like, low-frequency Alfvénic turbulence simulation with well-resolved phase space to identify the field–particle energy transfer in velocity space. The field–particle correlations reveal that the energy transfer, mediated by the parallel electric field, results in significant structuring of the VDF in the direction parallel to the magnetic field. Fourier modes representing the length scales between the ion and electron gyroradii show that energy transfer is resonant in nature, localized in velocity space to the Landau resonances for each Fourier mode. The energy transfer closely follows the Landau resonant velocities with varying perpendicular wavenumber $k_{\bot }$ and plasma $\unicode[STIX]{x1D6FD}$ . This resonant signature, consistent with Landau damping, is observed in all diagnosed Fourier modes that cover the dissipation range of the simulation.

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Corresponding author

Email address for correspondence: tak.chu.li@dartmouth.edu

References

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Abel, I. G., Barnes, M., Cowley, S. C., Dorland, W. & Schekochihin, A. A. 2008 Linearized model Fokker–Planck collision operators for gyrokinetic simulations. I. Theory. Phys. Plasmas 15 (12), 122509; arXiv:0808.1300.
Adkins, T. & Schekochihin, A. A. 2018 A solvable model of vlasov-kinetic plasma turbulence in fourierhermite phase space. J. Plasma Phys. 84 (1), 905840107.
Alexandrova, O., Chen, C. H. K., Sorriso-Valvo, L., Horbury, T. S. & Bale, S. D. 2013 Solar wind turbulence and the role of ion instabilities. Space Sci. Rev. 178, 101139; arXiv:1306.5336.
Arzamasskiy, L., Kunz, M. W., Chandran, B. D. G. & Quataert, E. 2019 Hybrid-kinetic simulations of ion heating in Alfvénic turbulence. Astrophys. J. 53; doi:10.3847/1538-4357/ab20cc.
Barnes, A. 1966 Collisionless damping of hydromagnetic waves. Phys. Fluids 9, 14831495.
Barnes, M., Abel, I. G., Dorland, W., Ernst, D. R., Hammett, G. W., Ricci, P., Rogers, B. N., Schekochihin, A. A. & Tatsuno, T. 2009 Linearized model Fokker–Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests. Phys. Plasmas 16 (7), 072107.
Boldyrev, S., Horaites, K., Xia, Q. & Perez, J. C. 2013 Toward a theory of astrophysical plasma turbulence at subproton scales. Astrophys. J. 777, 41.
Brizard, A. J. & Hahm, T. S. 2007 Foundations of nonlinear gyrokinetic theory. Rev. Mod. Phys. 79, 421468.
Burch, J. L., Moore, T. E., Torbert, R. B. & Giles, B. L. 2016 Magnetospheric multiscale overview and science objectives. Space Sci. Rev. 199 (1), 521.
Cerri, S. S., Kunz, M. W. & Califano, F. 2018 Dual phase-space cascades in 3d hybrid-vlasovmaxwell turbulence. Astrophys. J. Lett. 856 (1), L13.
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.
Chang, O., Peter Gary, S. & Wang, J. 2014 Energy dissipation by whistler turbulence: three-dimensional particle-in-cell simulations. Phys. Plasmas 21 (5), 052305.
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; arXiv:1305.2950.
Chen, C. H. K., Klein, K. G. & Howes, G. G. 2019 Evidence for electron Landau damping in space plasma turbulence. Nat. Commun. 10, 740 arXiv:1902.05785.
Chen, L., Lin, Z. & White, R. 2001 On resonant heating below the cyclotron frequency. Phys. Plasmas 8, 47134716.
Coleman, P. J. Jr. 1968 Turbulence, viscosity, and dissipation in the solar-wind plasma. Astrophys. J. 153, 371388.
Dahlburg, R. B. & Picone, J. M. 1989 Evolution of the Orszag–Tang vortex system in a compressible medium. I – Initial average subsonic flow. Phys. Fluids B 1, 21532171.
Dahlin, J. T., Drake, J. F. & Swisdak, M. 2016 Parallel electric fields are inefficient drivers of energetic electrons in magnetic reconnection. Phys. Plasmas 23 (12), 120704.
Franci, L., Landi, S., Matteini, L., Verdini, A. & Hellinger, P. 2015 High-resolution hybrid simulations of kinetic plasma turbulence at proton scales. Astrophys. J. 812 (1), 21.
Frieman, E. A. & Chen, L. 1982 Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Phys. Fluids 25, 502508.
Gershman, D. J., F-Viñas, A., Dorelli, J. C., Boardsen, S. A., Avanov, L. A., Bellan, P. M., Schwartz, S. J., Lavraud, B., Coffey, V. N., Chandler, M. O. et al. 2017 Wave-particle energy exchange directly observed in a kinetic Alfvén-branch wave. Nat. Commun. 8, 14719.
Goldreich, P. & Sridhar, S. 1995 Toward a theery of interstellar turbulence II. Strong Alfvénic turbulence. Astrophys. J. 438, 763775.
Grauer, R. & Marliani, C. 2000 Current-sheet formation in 3D ideal incompressible magnetohydrodynamics. Phys. Rev. Lett. 84, 4850.
Grośelj, D., Cerri, S. S., Navarro, A. B., Willmott, C., Told, D., Loureiro, N. F., Califano, F. & Jenko, F. 2017 Fully kinetic versus reduced-kinetic modeling of collisionless plasma turbulence. Astrophys. J. 847 (1), 28.
Grośelj, D., Chen, C. H. K., Mallet, A., Samtaney, R., Schneider, K. & Jenko, F.2018 Kinetic turbulence in astrophysical plasmas: waves and/or structures? Preprint, arXiv:1806.05741.
He, J., Tu, C., Marsch, E. & Yao, S. 2012 Do oblique Alfvén/Ion-cyclotron or fast-mode/whistler waves dominate the dissipation of solar wind turbulence near the proton inertial length? Astrophys. J. Lett. 745, L8.
Howes, G. G. 2008 Inertial range turbulence in kinetic plasmas. Phys. Plasmas 15 (5), 055904.
Howes, G. G. 2015 A dynamical model of plasma turbulence in the solar wind. Phil. Trans. R. Soc. Lond. A 373 (2041), 20140145.
Howes, G. G. 2016 The dynamical generation of current sheets in astrophysical plasma turbulence. Astrophys. J. Lett. 82, L28 arXiv:1607.07465.
Howes, G. G. 2017 A prospectus on kinetic heliophysics. Phys. Plasmas 24 (5), 055907; arXiv:10.1063/1.4983993.
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; arXiv:astro-ph/0511812.
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; arXiv:0707.3147.
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., Klein, K. G. & Li, T. C. 2017 Diagnosing collisionless energy transfer using fieldparticle correlations: Vlasovpoisson plasmas. J. Plasma Phys. 83 (1), 705830102.
Howes, G. G., McCubbin, A. J. & Klein, K. G. 2018 Spatially localized particle energization by landau damping in current sheets produced by strong alfvén wave collisions. J. Plasma Phys. 84 (1), 905840105.
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.
Hughes, R. S., Gary, S. P., Wang, J. & Parashar, T. N. 2017 Kinetic alfvén turbulence: electron and ion heating by particle-in-cell simulations. Astrophys. J. Lett. 847 (2), L14.
Isenberg, P. A. & Hollweg, J. V. 1983 On the preferential acceleration and heating of solar wind heavy ions. J. Geophys. Res. 88, 39233935.
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.
Kawazura, Y., Barnes, M. & Schekochihin, A. A. 2019 Thermal disequilibration of ions and electrons by collisionless plasma turbulence. Proc. Natl Acad. Sci. 116, 771776; arXiv:1807.07702.
Klein, K. G. 2017 Characterizing fluid and kinetic instabilities using field–particle correlations on single-point time series. Phys. Plasmas 24 (5), 055901.
Klein, K. G. & Howes, G. G. 2016 Measuring collisionless damping in heliospheric plasmas using fieldparticle correlations. Astrophys. J. Lett. 826 (2), L30.
Klein, K. G., Howes, G. G. & TenBarge, J. M. 2017 Diagnosing collisionless energy transfer using fieldparticle correlations: gyrokinetic turbulence. J. Plasma Phys. 83 (4), 535830401.
Kobayashi, S., Rogers, B. N. & Numata, R. 2014 Gyrokinetic simulations of collisionless reconnection in turbulent non-uniform plasmas. Phys. Plasmas 21 (4), 040704.
Kruskal, M. D. & Oberman, C. R. 1958 On the stability of plasma in static equilibrium. Phys. Fluids 1, 275280.
Landau, L. D. 1946 On the vibrations of the electronic plasma. Zh. Eksp. Teor. Fiz. 16, 574.
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.
Mininni, P. D., Pouquet, A. G. & Montgomery, D. C. 2006 Small-scale structures in three-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 97 (24), 244503; arXiv:physics/0607269.
Morrison, P. J. 1994 The energy of perturbations for Vlasov plasmas. Phys. Plasmas 1, 14471451.
Narita, Y., Gary, S. P., Saito, S., Glassmeier, K.-H. & Motschmann, U. 2011 Dispersion relation analysis of solar wind turbulence. Geophys. Res. Lett. 38, L05101.
Narita, Y., Nakamura, R., Baumjohann, W., Glassmeier, K.-H., Motschmann, U., Giles, B., Magnes, W., Fischer, D., Torbert, R. B., Russell, C. T. et al. 2016 On electron-scale whistler turbulence in the solar wind. Astrophys. J. Lett. 827 (1), L8.
Navarro, A. B. n, Teaca, B., Told, D., Groselj, D., Crandall, P. & Jenko, F. 2016 Structure of plasma heating in gyrokinetic alfvénic turbulence. Phys. Rev. Lett. 117, 245101.
Nielson, K. D., Howes, G. G. & Dorland, W. 2013 Alfvén wave collisions, the fundamental building block of plasma turbulence. II. Numerical solution. Phys. Plasmas 20 (7), 072303; arXiv:1306.1456.
Numata, R., Dorland, W., Howes, G. G., Loureiro, N. F., Rogers, B. N. & Tatsuno, T. 2011 Gyrokinetic simulations of the tearing instability. Phys. Plasmas 18 (11), 112106; arXiv: 1107.5842.
Numata, R., Howes, G. G., Tatsuno, T., Barnes, M. & Dorland, W. 2010 AstroGK: astrophysical gyrokinetics code. J. Comput. Phys. 229, 9347 arXiv:1004.0279.
Numata, R. & Loureiro, N. F. 2015 Ion and electron heating during magnetic reconnection in weakly collisional plasmas. J. Plasma Phys. 81, 3001 arXiv:1406.6456.
Orszag, S. A. & Tang, C.-M. 1979 Small-scale structure of two-dimensional magnetohydrodynamic turbulence. J. Fluid Mech. 90, 129143.
Parashar, T. N. & Matthaeus, W. H. 2016 Propinquity of current and vortex structures: effects on collisionless plasma heating. Astrophys. J. 832 (1), 57.
Parashar, T. N., Shay, M. A., Cassak, P. A. & Matthaeus, W. H. 2009 Kinetic dissipation and anisotropic heating in a turbulent collisionless plasma. Phys. Plasmas 16 (3), 032310.
Parashar, T. N., Vasquez, B. J. & Markovskii, S. A. 2014 The role of electron equation of state in heating partition of protons in a collisionless plasma. Phys. Plasmas 21 (2), 022301.
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 (2), L37.
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 (2), 196.
Picone, J. M. & Dahlburg, R. B. 1991 Evolution of the Orszag–Tang vortex system in a compressible medium. II. Supersonic flow. Phys. Fluids B 3, 2944.
Politano, H., Pouquet, A. & Sulem, P. L. 1989 Inertial ranges and resistive instabilities in two-dimensional magnetohydrodynamic turbulence. Phys. Fluids B 1, 23302339.
Politano, H., Pouquet, A. & Sulem, P. L. 1995 Current and vorticity dynamics in three-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 2, 29312939.
Quataert, E. 1998 Particle heating by Alfvénic turbulence in hot accretion flows. Astrophys. J. 500, 978991; arXiv:astro-ph/9710127.
Roberts, O. W., Alexandrova, O., Kajdi, P., Turc, L., Perrone, D., Escoubet, C. P. & Walsh, A. 2017 Variability of the magnetic field power spectrum in the solar wind at electron scales. Astrophys. J. 850 (2), 120.
Roberts, O. W., Li, X. & Jeska, L. 2015 A statistical study of the solar wind turbulence at ion kinetic scales using the $k$ -filtering technique and cluster data. Astrophys. J. 802, 2.
Roberts, O. W., Li, X. & Li, B. 2013 Kinetic plasma turbulence in the fast solar wind measured by cluster. Astrophys. J. 769, 58 arXiv:1303.5129.
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 (13), 131101.
Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, G. W., Howes, G. G., Plunk, G. G., Quataert, E. & Tatsuno, T. 2008 Gyrokinetic turbulence: a nonlinear route to dissipation through phase space. Plasma Phys. Control. Fusion 50 (12), 124024; arXiv:0806.1069.
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.
Schekochihin, A. A., Kawazura, Y. & Barnes, M. A. 2019 Constraints on ion versus electron heating by plasma turbulence at low beta. J. Plasma Phys. 85 (3), 905850303; arXiv:1812.09792.
Schekochihin, A. A., Parker, J. T., Highcock, E. G., Dellar, P. J., Dorland, W. & Hammett, G. W. 2016 Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence. J. Plasma Phys. 82 (2), 905820212.
Schoeffler, K. M., Loureiro, N. F., Fonseca, R. A. & Silva, L. O. 2014 Magnetic-field generation and amplification in an expanding plasma. Phys. Rev. Lett. 112 (17), 175001; arXiv:1308.3421.
Servidio, S., Chasapis, A., Matthaeus, W. H., Perrone, D., Valentini, F., Parashar, T. N., Veltri, P., Gershman, D., Russell, C. T., Giles, B. et al. 2017 Magnetospheric multiscale observation of plasma velocity-space cascade: Hermite representation and theory. Phys. Rev. Lett. 119, 205101.
Tatsuno, T., Schekochihin, A. A., Dorland, W., Plunk, G., Barnes, M. A., Cowley, S. C. & Howes, G. G. 2009 Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence. Phys. Rev. Lett. 103 (1), 015003.
TenBarge, J. M., Daughton, W., Karimabadi, H., Howes, G. G. & Dorland, W. 2014 Collisionless reconnection in the large guide field regime: Gyrokinetic versus particle-in-cell simulations. Phys. Plasmas 21 (2), 020708.
TenBarge, J. M. & Howes, G. G. 2012 Evidence of critical balance in kinetic Alfvén wave turbulence simulations. Phys. Plasmas 19 (5), 055901.
TenBarge, J. M. & Howes, G. G. 2013 Current sheets and collisionless damping in kinetic plasma turbulence. Astrophys. J. Lett. 771, L27 arXiv:1304.2958.
TenBarge, J. M., Howes, G. G. & Dorland, W. 2013 Collisionless damping at electron scales in solar wind turbulence. Astrophys. J. 774, 139.
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; arXiv:1505.02204.
Vásconez, C. L., Valentini, F., Camporeale, E. & Veltri, P. 2014 Vlasov simulations of kinetic alfvén waves at proton kinetic scales. Phys. Plasmas 21 (11), 112107.
Vech, D., Klein, K. G. & Kasper, J. C. 2017 Nature of stochastic ion heating in the solar wind: testing the dependence on plasma beta and turbulence amplitude. Astrophys. J. Lett. 850 (1), L11.
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.
Wang, X., Tu, C.-Y., He, J.-S. & Wang, L.-H. 2018 Ion-scale spectral break in the normal plasma beta range in the solar wind turbulence. J. Geophys. Res. 123 (1), 6875.
Yang, Y., Matthaeus, W. H., Parashar, T. N., Haggerty, C. C., Roytershteyn, V., Daughton, W., Wan, M., Shi, Y. & Chen, S. 2017 Energy transfer, pressure tensor, and heating of kinetic plasma. Phys. Plasmas 24 (7), 072306.
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Keywords

Collisionless energy transfer in kinetic turbulence: field–particle correlations in Fourier space

  • Tak Chu Li (a1), Gregory G. Howes (a2), Kristopher G. Klein (a3), Yi-Hsin Liu (a1) and Jason M. TenBarge (a4)...

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