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Spatially localized particle energization by Landau damping in current sheets produced by strong Alfvén wave collisions

  • Gregory G. Howes (a1), Andrew J. McCubbin (a1) and Kristopher G. Klein (a2)

Abstract

Understanding the removal of energy from turbulent fluctuations in a magnetized plasma and the consequent energization of the constituent plasma particles is a major goal of heliophysics and astrophysics. Previous work has shown that nonlinear interactions among counterpropagating Alfvén waves – or Alfvén wave collisions – are the fundamental building block of astrophysical plasma turbulence and naturally generate current sheets in the strongly nonlinear limit. A nonlinear gyrokinetic simulation of a strong Alfvén wave collision is used to examine the damping of the electromagnetic fluctuations and the associated energization of particles that occurs in self-consistently generated current sheets. A simple model explains the flow of energy due to the collisionless damping and the associated particle energization, as well as the subsequent thermalization of the particle energy by collisions. The net particle energization by the parallel electric field is shown to be spatially localized, and the nonlinear evolution is essential in enabling spatial non-uniformity. Using the recently developed field–particle correlation technique, we show that particles resonant with the Alfvén waves in the simulation dominate the energy transfer, demonstrating conclusively that Landau damping plays a key role in the spatially localized damping of the electromagnetic fluctuations and consequent energization of the particles in this strongly nonlinear simulation.

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Corresponding author

Email address for correspondence: gregory-howes@uiowa.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.
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.
Bhattacharjee, A., Huang, Y. M., Yang, H. & Rogers, B. 2009 Fast reconnection in high-lundquist-number plasmas due to the plasmoid instability. Phys. Plasmas 16, 112102.
Birn, J., Drake, J. F., Shay, M. A., Rogers, B. N., Denton, R. E., Hesse, M., Kuznetsova, M., Ma, Z. W., Bhattacharjee, A., Otto, A. et al. 2001 Geospace environmental modeling (GEM) magnetic reconnection challenge. J. Geophys. Res. 106, 37153720.
Boldyrev, S. 2006 Spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 96 (11), 115002.
Borovsky, J. E. & Denton, M. H. 2011 No evidence for heating of the solar wind at strong current sheets. Astrophys. J. Lett. 739, L61.
Brandenburg, A. 2014 Magnetic Prandtl number dependence of the kinetic-to-magnetic dissipation ratio. Astrophys. J. 791, 12.
Brizard, A. J. & Hahm, T. S. 2007 Foundations of nonlinear gyrokinetic theory. Rev. Mod. Phys. 79, 421468.
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.
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.
Dorland, W. & Hammett, G. W. 1993 Gyrofluid turbulence models with kinetic effects. Phys. Fluids B 5, 812835.
Drake, D. J., Schroeder, J. W. R., Howes, G. G., Kletzing, C. A., Skiff, F., Carter, T. A. & Auerbach, D. W. 2013 Alfvén wave collisions, the fundamental building block of plasma turbulence. IV. Laboratory experiment. Phys. Plasmas 20 (7), 072901.
Drake, J. F., Shay, M. A. & Swisdak, M. 2008 The Hall fields and fast magnetic reconnection. Phys. Plasmas 15 (4), 042306.
Elsasser, W. M. 1950 The hydromagnetic equations. Phys. Rev. 79, 183.
Frieman, E. A. & Chen, L. 1982 Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Phys. Fluids 25, 502508.
Galtier, S., Nazarenko, S. V., Newell, A. C. & Pouquet, A. 2000 A weak turbulence theory for incompressible magnetohydrodynamics. J. Plasma Phys. 63, 447488.
Goldreich, P. & Sridhar, S. 1995 Toward a theory of interstellar turbulence II. Strong Alfvénic turbulence. Astrophys. J. 438, 763775.
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.
Howes, G. G. 2017 A prospectus on kinetic heliophysics. Phys. Plasmas 24 (5), 055907.
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.
Howes, G. G., Drake, D. J., Nielson, K. D., Carter, T. A., Kletzing, C. A. & Skiff, F. 2012 Toward astrophysical turbulence in the laboratory. Phys. Rev. Lett. 109 (25), 255001.
Howes, G. G., Klein, K. G. & Li, T. C. 2017 Diagnosing collisionless energy transfer using field-particle correlations: Vlasov–Poisson plasmas. J. Plasma Phys. 83 (1), 705830102.
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.
Howes, G. G. & Nielson, K. D. 2013 Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution. Phys. Plasmas 20 (7), 072302.
Howes, G. G., Nielson, K. D., Drake, D. J., Schroeder, J. W. R., Skiff, F., Kletzing, C. A. & Carter, T. A. 2013 Alfvén wave collisions, the fundamental building block of plasma turbulence. III. Theory for experimental design. Phys. Plasmas 20 (7), 072304.
Iroshnikov, R. S. 1963 The turbulence of a conducting fluid in a strong magnetic field. Astron. Zh. 40, 742: English translation: (1964) Sov. Astron. 7 566.
Isenberg, P. A. & Hollweg, J. V. 1983 On the preferential acceleration and heating of solar wind heavy ions. J. Geophys. Res. 88, 39233935.
Ji, H. & Daughton, W. 2011 Phase diagram for magnetic reconnection in heliophysical, astrophysical, and laboratory plasmas. Phys. Plasmas 18 (11), 111207.
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.
Kawamori, E. 2013 Experimental verification of entropy cascade in two-dimensional electrostatic turbulence in magnetized plasma. Phys. Rev. Lett. 110 (9), 095001.
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. 2015 Predicted impacts of proton temperature anisotropy on solar wind turbulence. Phys. Plasmas 22 (3), 032903.
Klein, K. G. & Howes, G. G. 2016 Measuring collisionless damping in heliospheric plasmas using field-particle correlations. Astrophys. J. Lett. 826, L30.
Klein, K. G., Howes, G. G. & TenBarge, J. M. 2017 Diagnosing collisionless energy transfer using field-particle correlations: gyrokinetic turbulence. J. Plasma Phys. 83 (4), 535830401.
Kraichnan, R. H. 1965 Inertial range spectrum of hyromagnetic turbulence. Phys. Fluids 8, 13851387.
Kruskal, M. D. & Oberman, C. R. 1958 On the stability of plasma in static equilibrium. Phys. Fluids 1, 275280.
Kulsrud, R. M. 1983 MHD description of plasma. In Handbook of Plasma Physics (ed. Galeev, A. A. & Sudan, R. N.), vol. 1, chap. 1.4, pp. 115145. North Holland.
Landau, L. D. 1946 On the vibrations of the electronic plasma. J. Phys. 10, 25.
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, L24.
Loureiro, N. F., Schekochihin, A. A. & Cowley, S. C. 2007 Instability of current sheets and formation of plasmoid chains. Phys. Plasmas 14, 100703.
Matthaeus, W. H. & Montgomery, D. 1980 Selective decay hypothesis at high mechanical and magnetic Reynolds numbers. Ann. N.Y. Acad. Sci. 357, 203222.
Meneguzzi, M., Frisch, U. & Pouquet, A. 1981 Helical and nonhelical turbulent dynamos. Phys. Rev. Lett. 47, 10601064.
Morrison, P. J. 1994 The energy of perturbations for Vlasov plasmas. Phys. Plasmas 1, 14471451.
Mouhot, C. & Villani, C. 2011 On Landau damping. Acta Mathematica 207 (1), 29201.
Navarro, A. B., Teaca, B., Told, D., Groselj, D., Crandall, P. & Jenko, F. 2016 Structure of plasma heating in gyrokinetic Alfvénic turbulence. Phys. Rev. Lett. 117 (24), 245101.
Ng, C. S. & Bhattacharjee, A. 1996 Interaction of Shear–Alfven wave packets: implication for weak magnetohydrodynamic turbulence in astrophysical plasmas. Astrophys. J. 465, 845.
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.
Numata, R., Howes, G. G., Tatsuno, T., Barnes, M. & Dorland, W. 2010 AstroGK: astrophysical gyrokinetics code. J. Comput. Phys. 229, 9347.
Osman, K. T., Matthaeus, W. H., Gosling, J. T., Greco, A., Servidio, S., Hnat, B., Chapman, S. C. & Phan, T. D. 2014 Magnetic reconnection and intermittent turbulence in the solar wind. Phys. Rev. Lett. 112 (21), 215002.
Osman, K. T., Matthaeus, W. H., Greco, A. & Servidio, S. 2011 Evidence for inhomogeneous heating in the solar wind. Astrophys. J. Lett. 727, L11.
Osman, K. T., Matthaeus, W. H., Wan, M. & Rappazzo, A. F. 2012 Intermittency and local heating in the solar wind. Phys. Rev. Lett. 108 (26), 261102.
Parker, E. N. 1958 Dynamics of the interplanetary gas and magnetic fields. Astrophys. J. 128, 664.
Parker, J. T., Highcock, E. G., Schekochihin, A. A. & Dellar, P. J. 2016 Suppression of phase mixing in drift-kinetic plasma turbulence. Phys. Plasmas 23 (7), 070703.
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.
Plunk, G. G. 2013 Landau damping in a turbulent setting. Phys. Plasmas 20 (3), 032304.
Plunk, G. G., Cowley, S. C., Schekochihin, A. A. & Tatsuno, T. 2010 Two-dimensional gyrokinetic turbulence. J. Fluid Mech. 664, 407435.
Plunk, G. G. & Tatsuno, T. 2011 Energy transfer and dual cascade in kinetic magnetized plasma turbulence. Phys. Rev. Lett. 106 (16), 165003.
Quataert, E. 1998 Particle heating by Alfvénic turbulence in hot accretion flows. Astrophys. J. 500, 978991.
Ricci, P., Brackbill, J. U., Daughton, W. & Lapenta, G. 2004 Collisionless magnetic reconnection in the presence of a guide field. Phys. Plasmas 11, 41024114.
Rutherford, P. H. & Frieman, E. A. 1968 Drift instabilities in general mangetic field configurations. Phys. Fluids 11, 569585.
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., 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.
Shay, M. A., Drake, J. F., Rogers, B. N. & Denton, R. E. 2001 Alfvénic collisionless magnetic reconnection and the Hall term. J. Geophys. Res. 106, 37593772.
Shibata, K. & Tanuma, S. 2001 Plasmoid-induced-reconnection and fractal reconnection. Earth Planets Space 53, 473.
Spitzer, L. 1962 Physics of Fully Ionized Gases, 2nd edn., p. 1962. Interscience.
Sridhar, S. & Goldreich, P. 1994 Toward a theory of interstellar turbulence. 1: weak Alfvenic turbulence. Astrophys. J. 432, 612621.
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. 2013 Current sheets and collisionless damping in kinetic plasma turbulence. Astrophys. J. Lett. 771, L27.
Treumann, R. A. & Baumjohann, W. 2015 Spontaneous magnetic reconnection. Collisionless reconnection and its potential astrophysical relevance. Astron. Astrophys. Rev. 23, 4.
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.
Verniero, J. L. & Howes, G. G. 2017 The Alfvénic nature of energy transfer mediation in localized, strongly nonlinear Alfvén wavepacket collisions. J. Plasma Phys. (accepted).
Verniero, J. L., Howes, G. G. & Klein, K. G. 2018 Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit. J. Plasma Phys. 84 (1), 905840103.
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.
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.
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.
Zhdankin, V., Uzdensky, D. A. & Boldyrev, S. 2015 Temporal analysis of dissipative structures in magnetohydrodynamic turbulence. Astrophys. J. 811, 6.
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.
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Keywords

Spatially localized particle energization by Landau damping in current sheets produced by strong Alfvén wave collisions

  • Gregory G. Howes (a1), Andrew J. McCubbin (a1) and Kristopher G. Klein (a2)

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