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The development of magnetic field line wander by plasma turbulence

  • Gregory G. Howes (a1) and Sofiane Bourouaine (a1)

Abstract

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

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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.
Alexandrova, O., Lacombe, C., Mangeney, A., Grappin, R. & Maksimovic, M. 2012 Solar wind turbulent spectrum at plasma kinetic scales. Astrophys. J. 760, 121.
Alexandrova, O., Saur, J., Lacombe, C., Mangeney, A., Mitchell, J., Schwartz, S. J. & Robert, P. 2009 Universality of solar-wind turbulent spectrum from MHD to electron scales. Phys. Rev. Lett. 103 (16), 165003.
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.
Belcher, J. W. & Davis, L. 1971 Large-amplitude Alfvén waves in the interplanetary medium, 2. J. Geophys. Res. 76, 35343563.
Bian, N. H., Kontar, E. P. & MacKinnon, A. L. 2011 Turbulent cross-field transport of non-thermal electrons in coronal loops: theory and obser vations. Astron. Astrophys. 535, A18.
Bieber, J. W., Wanner, W. & Matthaeus, W. H. 1996 Dominant two-dimensional solar wind turbulence with implications for cosmic ray transport. J. Geophys. Res. 101, 25112522.
Boozer, A. H. 2014 Formation of current sheets in magnetic reconnection. Phys. Plasmas 21 (7), 072907.
Bourouaine, S., Alexandrova, O., Marsch, E. & Maksimovic, M. 2012 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.
Bourouaine, S. & Howes, G. G. 2017 The development of magnetic field line wander in gyrokinetic plasma turbulence: dependence on amplitude of turbulence. J. Plasma Phys. 83 (3), 905830301.
Bruno, R. & Carbone, V. 2005 The solar wind as a turbulence laboratory. Living Reviews Solar Phys. 2, 4.
del-Castillo-Negrete, D. & Blazevski, D. 2014 Heat pulse propagation in chaotic three-dimensional magnetic fields. Nucl. Fusion 54 (6), 064009.
del-Castillo-Negrete, D. & Blazevski, D. 2016 Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields. Phys. Plasmas 23 (4), 042505.
Chandran, B. D. G. 2000 Scattering of energetic particles by anisotropic magnetohydrodynamic turbulence with a Goldreich–Sridhar power spectrum. Phys. Rev. Lett. 85, 46564659.
Chandran, B. D. G. & Cowley, S. C. 1998 Thermal conduction in a tangled magnetic field. Phys. Rev. Lett. 80, 30773080.
Chandrasekhar, S. 1951 The invariant theory of isotropic turbulence in magneto-hydrodynamics. Proc. R. Soc. Lond. A 204, 435449.
Chen, C. H. K., Horbury, T. S., Schekochihin, A. A., Wicks, R. T., Alexandrova, O. & Mitchell, J. 2010 Anisotropy of solar wind turbulence between ion and electron scales. Phys. Rev. Lett. 104 (25), 255002.
Cho, J. & Lazarian, A. 2004 The anisotropy of electron magnetohydrodynamic turbulence. Astrophys. J. Lett. 615, L41L44.
Cho, J. & Lazarian, A. 2009 Simulations of electron magnetohydrodynamic turbulence. Astrophys. J. 701, 236252.
Cho, J. & Vishniac, E. T. 2000 The anisotropy of magnetohydrodynamic Alfvénic turbulence. Astrophys. J. 539, 273282.
Dombre, T., Frisch, U., Henon, M., Greene, J. M. & Soward, A. M. 1986 Chaotic streamlines in the ABC flows. J. Fluid Mech. 167, 353391.
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.
Eyink, G., Vishniac, E., Lalescu, C., Aluie, H., Kanov, K., Bürger, K., Burns, R., Meneveau, C. & Szalay, A. 2013 Flux-freezing breakdown in high-conductivity magnetohydrodynamic turbulence. Nature 497, 466469.
Filonenko, N. N., Sagdeev, R. Z. & Zaslavsky, G. M. 1967 Destruction of magnetic surfaces by magnetic field irregularities. 2. Nucl. Fusion 7 (4), 253.
Frieman, E. A. & Chen, L. 1982 Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Phys. Fluids 25, 502508.
Galeev, A. A. & Zeleny, L. M. 1981 Anomalous electron thermal conductivity across the destroyed magnetic surfaces. Physica D 2, 90101.
Galtier, S., Nazarenko, S. V., Newell, A. C. & Pouquet, A. 2000 A weak turbulence theory for incompressible magnetohydrodynamics. J. Plasma Phys. 63, 447488.
Giacalone, J. & Jokipii, J. R. 1999 The transport of cosmic rays across a turbulent magnetic field. Astrophys. J. 520, 204214.
Goldreich, P. & Sridhar, S. 1995 Toward a theory of interstellar turbulence II. Strong Alfvénic turbulence. Astrophys. J. 438, 763775.
Gruzinov, A. V., Isichenko, M. B. & Kalda, I. L. 1990 Two-dimensional turbulent diffusion. Sov. Phys. JETP 97, 476488.
Guest, B. & Shalchi, A. 2012 Random walk of magnetic field lines in dynamical turbulence: A field line tracing method. II. Two-dimensional turbulence. Phys. Plasmas 19 (3), 032902.
Guo, F. & Giacalone, J. 2010 The effect of large-scale magnetic turbulence on the acceleration of electrons by perpendicular collisionless shocks. Astrophys. J. 715, 406411.
Guo, F. & Giacalone, J. 2013 The acceleration of thermal protons at parallel collisionless shocks: three-dimensional hybrid simulations. Astrophys. J. 773, 158.
Guo, F. & Giacalone, J. 2015 The acceleration of electrons at collisionless shocks moving through a turbulent magnetic field. Astrophys. J. 802, 97.
Haas, F. A. & Thyagaraja, A. 1986 Conceptual and experimental bases of theories of anomalous transport in Tokamaks. Phys. Rep. 143, 241276.
Hatch, D. R., Pueschel, M. J., Jenko, F., Nevins, W. M., Terry, P. W. & Doerk, H. 2012 Origin of magnetic stochasticity and transport in plasma microturbulence. Phys. Rev. Lett. 108 (23), 235002.
Hatch, D. R., Pueschel, M. J., Jenko, F., Nevins, W. M., Terry, P. W. & Doerk, H. 2013 Magnetic stochasticity and transport due to nonlinearly excited subdominant microtearing modes. Phys. Plasmas 20 (1), 012307.
Hauff, T., Jenko, F., Shalchi, A. & Schlickeiser, R. 2010 Scaling theory for cross-field transport of cosmic rays in turbulent fields. Astrophys. J. 711, 9971007.
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., 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., 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.
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., 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. & 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.
Howes, G. G., TenBarge, J. M. & Dorland, W. 2011 A weakened cascade model for turbulence in astrophysical plasmas. Phys. Plasmas 18, 102305.
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.
Huang, Y.-M., Bhattacharjee, A. & Boozer, A. H. 2014 Rapid change of field line connectivity and reconnection in stochastic magnetic fields. Astrophys. J. 793, 106.
Isichenko, M. B. 1992 Percolation, statistical topography, and transport in random media. Rev. Mod. Phys. 64, 9611043.
Jokipii, J. R. 1966 Cosmic-ray propagation. I. Charged particles in a random magnetic field. Astrophys. J. 146, 480.
Jokipii, J. R. & Parker, E. N. 1968 Random walk of magnetic lines of force in astrophysics. Phys. Rev. Lett. 21, 4447.
Kiyani, K. H., Chapman, S. C., Khotyaintsev, Y. V., Dunlop, M. W. & Sahraoui, F. 2009 Global scale-invariant dissipation in collisionless plasma turbulence. Phys. Rev. Lett. 103, 075006.
Kiyani, K. H., Osman, K. T. & Chapman, S. C. 2015 Introduction: Dissipation and heating in solar wind turbulence: from the macro to the micro and back again. Phil. Trans. R. Soc. Lond. A 373, 40155.
Klein, K. G., Howes, G. G. & TenBarge, J. M. 2014 The violation of the taylor hypothesis in measurements of solar wind turbulence. Astrophys. J. Lett. 790, L20.
Kolmogorov, A. N. 1941 Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16.
Kowal, G., Lazarian, A., Vishniac, E. T. & Otmianowska-Mazur, K. 2009 Numerical tests of fast reconnection in weakly stochastic magnetic fields. Astrophys. J. 700, 6385.
Kowal, G., Lazarian, A., Vishniac, E. T. & Otmianowska-Mazur, K. 2012 Reconnection studies under different types of turbulence driving. Nonlin. Process. Geophys. 19, 297314.
Kraichnan, R. H. 1965 Inertial range spectrum of hyromagnetic turbulence. Phys. Fluids 8, 13851387.
Krommes, J. A., Oberman, C. & Kleva, R. G. 1983 Plasma transport in stochastic magnetic fields. Part 3. Kinetics of test particle diffusion. J. Plasma Phys. 30, 1156.
Laval, G. 1993 Particle diffusion in stochastic magnetic fields. Phys. Fluids B 5, 711721.
Lazarian, A. & Vishniac, E. T. 1999 Reconnection in a weakly stochastic field. Astrophys. J. 517, 700718.
Maron, J. & Goldreich, P. 2001 Simulations of incompressible magnetohydrodynamic turbulence. Astrophys. J. 554, 11751196.
Matthaeus, W. H., Gray, P. C., Pontius, D. H. Jr. & Bieber, J. W. 1995 Spatial structure and field-line diffusion in transverse magnetic turbulence. Phys. Rev. Lett. 75, 21362139.
Matthaeus, W. H., Oughton, S., Pontius, D. H. Jr. & Zhou, Y. 1994 Evolution of energy-containing turbulent eddies in the solar wind. J. Geophys. Res. 99, 19267.
Montgomery, D. & Matthaeus, W. H. 1995 Anisotropic modal energy transfer in interstellar turbulence. Astrophys. J. 447, 706.
Montgomery, D. & Turner, L. 1981 Anisotropic magnetohydrodynamic turbulence in a strong external magnetic field. Phys. Fluids 24, 825831.
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.
Nevins, W. M., Wang, E. & Candy, J. 2011 Magnetic stochasticity in gyrokinetic simulations of plasma microturbulence. Phys. Rev. Lett. 106 (6), 065003.
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.
Politano, H. & Pouquet, A. 1998 von Kármán–Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions. Phys. Rev. E 57, 21.
Pueschel, M. J., Kammerer, M. & Jenko, F. 2008 Gyrokinetic turbulence simulations at high plasma beta. Phys. Plasmas 15 (10), 102310.
Qin, G. & Shalchi, A. 2013 The role of the Kubo number in two-component turbulence. Phys. Plasmas 20 (9), 092302.
Ragot, B. R. 2001 Magnetic field line wandering and shock-front acceleration: application to the radio emission of SN 1987A. Astrophys. J. 547, 10101023.
Ragot, B. R. 2011 Statistics of field-line dispersal: random-walk characterization and supradiffusive regime. Astrophys. J. 728, 50.
Rappazzo, A. F. & Parker, E. N. 2013 Current sheets formation in tangled coronal magnetic fields. Astrophys. J. Lett. 773, L2.
Rechester, A. B. & Rosenbluth, M. N. 1978 Electron heat transport in a tokamak with destroyed magnetic surfaces. Phys. Rev. Lett. 40, 3841.
Richardson, I. G., von Rosenvinge, T. T., Cane, H. V., Christian, E. R., Cohen, C. M. S., Labrador, A. W., Leske, R. A., Mewaldt, R. A., Wiedenbeck, M. E. & Stone, E. C. 2014 ${>}$ 25 MeV proton events observed by the high energy telescopes on the STEREO A and B spacecraft and/or at earth during the first seven years of the STEREO mission. Solar Phys. 289, 30593107.
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.
Robinson, D. C. & Rusbridge, M. G. 1971 Structure of turbulence in the zeta plasma. Phys. Fluids 14, 24992511.
Rosenbluth, M. N., Sagdeev, R. Z., Taylor, J. B. & Zaslavsky, G. M. 1966 Destruction of magnetic surfaces by magnetic field irregularities. Nucl. Fusion 6 (4), 297.
Ruffolo, D. & Matthaeus, W. H. 2013 Theory of magnetic field line random walk in noisy reduced magnetohydrodynamic turbulence. Phys. Plasmas 20 (1), 012308.
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.
Sahraoui, F., Goldstein, M. L., Robert, P. & Khotyaintsev, Y. V. 2009 Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale. Phys. Rev. Lett. 102 (23), 231102.
Sahraoui, F., Huang, S. Y., Belmont, G., Goldstein, M. L., Rétino, A., Robert, P. & De Patoul, J. 2013 Scaling of the electron dissipation range of solar wind turbulence. Astrophys. J. 777, 15.
Schlickeiser, R. 1989 Cosmic-ray transport and acceleration. I – Derivation of the kinetic equation and application to cosmic rays in static cold media. II – Cosmic rays in moving cold media with application to diffusive shock wave acceleration. Astrophys. J. 336, 243293.
Schlickeiser, R. & Miller, J. A. 1998 Quasi-linear theory of cosmic-ray transport and acceleration: the role of oblique magnetohydrodynamic waves and transit-time damping. Astrophys. J. 492, 352378.
Servidio, S., Matthaeus, W. H., Wan, M., Ruffolo, D., Rappazzo, A. F. & Oughton, S. 2014 Complexity and diffusion of magnetic flux surfaces in anisotropic turbulence. Astrophys. J. 785, 56.
Shalchi, A. 2010a A unified particle diffusion theory for cross-field scattering: subdiffusion, recovery of diffusion, and diffusion in three-dimensional turbulence. Astrophys. J. Lett. 720, L127L130.
Shalchi, A. 2010b Random walk of magnetic field lines in dynamical turbulence: A field line tracing method. I. Slab turbulence. Phys. Plasmas 17 (8), 082902.
Shalchi, A. & Kolly, A. 2013 Analytical description of field-line random walk in Goldreich–Sridhar turbulence. Mon. Not. R. Astron. Soc. 431, 19231928.
Shalchi, A. & Kourakis, I. 2007a Analytical description of stochastic field-line wandering in magnetic turbulence. Phys. Plasmas 14 (9), 092903.
Shalchi, A. & Kourakis, I. 2007b Random walk of magnetic field-lines for different values of the energy range spectral index. Phys. Plasmas 14 (11), 112901.
Shebalin, J. V., Matthaeus, W. H. & Montgomery, D. 1983 Anisotropy in MHD turbulence due to a mean magnetic field. J. Plasma Phys. 29, 525547.
Similon, P. L. & Sudan, R. N. 1989 Energy dissipation of Alfven wave packets deformed by irregular magnetic fields in solar-coronal arches. Astrophys. J. 336, 442453.
Spatschek, K. H. 2008 Aspects of stochastic transport in laboratory and astrophysical plasmas. Plasma Phys. Control Fusion 50 (12), 124027.
Sridhar, S. & Goldreich, P. 1994 Toward a theory of interstellar turbulence. 1: Weak Alfvenic turbulence. Astrophys. J. 432, 612621.
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476490.
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.
TenBarge, J. M., Howes, G. G. & Dorland, W. 2013 Collisionless damping at electron scales in solar wind turbulence. Astrophys. J. 774, 139.
TenBarge, J. M., Howes, G. G., Dorland, W. & Hammett, G. W. 2014 An oscillating Langevin antenna for driving plasma turbulence simulations. Comput. Phys. Commun. 185, 578589.
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.
Tu, C.-Y. & Marsch, E. 1995 MHD structures, waves and turbulence in the solar wind: Observations and theories. Space Sci. Rev. 73, 12.
Vishniac, E. T., Pillsworth, S., Eyink, G., Kowal, G., Lazarian, A. & Murray, S. 2012 Reconnection current sheet structure in a turbulent medium. Nonlin. Process. Geophys. 19, 605610.
Wang, Y., Boldyrev, S. & Perez, J. C. 2011 Residual energy in magnetohydrodynamic turbulence. Astrophys. J. Lett. 740, L36.
Yousef, T. A., Rincon, F. & Schekochihin, A. A. 2007 Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence. J. Fluid Mech. 575, 111.
Zimbardo, G., Pommois, P. & Veltri, P. 2006 Superdiffusive and subdiffusive transport of energetic particles in solar wind anisotropic magnetic turbulence. Astrophys. J. Lett. 639, L91L94.
Zimbardo, G., Veltri, P., Basile, G. & Principato, S. 1995 Anomalous diffusion and Lévy random walk of magnetic field lines in three dimensional turbulence. Phys. Plasmas 2, 26532663.
Zimbardo, G., Veltri, P. & Pommois, P. 2000 Anomalous, quasilinear, and percolative regimes for magnetic-field-line transport in axially symmetric turbulence. Phys. Rev. E 61, 1940.
Zweben, S. J., Menyuk, C. R. & Taylor, R. J. 1979 Small-scale magnetic fluctuations inside the macrotor tokamak. Phys. Rev. Lett. 42, 12701274.
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The development of magnetic field line wander by plasma turbulence

  • Gregory G. Howes (a1) and Sofiane Bourouaine (a1)

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