Hostname: page-component-6b989bf9dc-94dtm Total loading time: 0 Render date: 2024-04-13T08:52:02.729Z Has data issue: false hasContentIssue false

Proton temperature-anisotropy-driven instabilities in weakly collisional plasmas: Hybrid simulations

Published online by Cambridge University Press:  28 August 2014

Petr Hellinger*
Astronomical Institute AS CR, Bocni II/1401, CZ-14131 Prague, Czech Republic Institute of Atmospheric Physics, AS CR, Bocni II/1401, CZ-14131 Prague, Czech Republic
Pavel M. Trávníček
Astronomical Institute AS CR, Bocni II/1401, CZ-14131 Prague, Czech Republic Institute of Atmospheric Physics, AS CR, Bocni II/1401, CZ-14131 Prague, Czech Republic Space Sciences Laboratory, UCB, Berkeley, USA
Email address for correspondence:


Kinetic instabilities in weakly collisional, high beta plasmas are investigated using two-dimensional hybrid expanding box simulations with Coulomb collisions modeled through the Langevin equation (corresponding to the Fokker-Planck one). The expansion drives a parallel or perpendicular temperature anisotropy (depending on the orientation of the ambient magnetic field). For the chosen parameters the Coulomb collisions are important with respect to the driver but are not strong enough to keep the system stable with respect to instabilities driven by the proton temperature anisotropy. In the case of the parallel temperature anisotropy the dominant oblique fire hose instability efficiently reduces the anisotropy in a quasilinear manner. In the case of the perpendicular temperature anisotropy the dominant mirror instability generates coherent compressive structures which scatter protons and reduce the temperature anisotropy. For both the cases the instabilities generate temporarily enough wave energy so that the corresponding (anomalous) transport coefficients dominate over the collisional ones and their properties are similar to those in collisionless plasmas.

Research Article
Copyright © Cambridge University Press 2014 

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.)



Bale, S. D., Kasper, J. C., Howes, G. G., Quataert, E., Salem, C. and Sundkvist, D. 2009 Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind. Phys. Rev. Lett. 103, 211101.Google Scholar
Barakat, A. R. and Schunk, R. W. 1981 Momentum and energy exchange collision terms for interpenetrating bi-Maxwellian gases. J. Phys. D: Appl. Phys. 14, 421438.CrossRefGoogle Scholar
Braginskii, S. I. 1965 Transport processes in a plasma. In Reviews of Plasma Physics, Vol. 1 (ed. Leontovich, M.). New York: Consultants Bureau, pp. 205.Google Scholar
Califano, F., Hellinger, P., Kuznetsov, E., Passot, T., Sulem, P.-L. and Trávníček, P. M. 2008 Nonlinear mirror mode dynamics: Simulations and modeling. J. Geophys. Res. 113, A08219.Google Scholar
Chandran, B. D. G., Dennis, T. J., Quataert, E. and 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.CrossRefGoogle Scholar
Chandrasekhar, S. A., Kaufman, A. N. and Watson, K. M. 1958 The stability of the pinch. Proc. R. Soc. London, Ser. A 245, 435.Google Scholar
Chew, G. F., Goldberger, M. L. and Low, F. E. 1956 The Boltzmann equation and the one fluid hydromagnetic equations in the absence of particle collisions. Proc. R. Soc. London A236, 112118.Google Scholar
Chirikov, B. V. 1979 A universal instability of many-dimensional oscillator systems. Phys. Rep. 52, 263379.Google Scholar
Denton, R. E., Anderson, B. J., Gary, S. P. and Fuselier, S. A. 1994 Bounded anisotropy fluid model for ion temperatures. J. Geophys. Res. 99, 1122511241.CrossRefGoogle Scholar
Gary, S. P. 1993 Theory of Space Plasma Microinstabilities. New York: Cambridge University Press.CrossRefGoogle Scholar
Génot, V., Budnik, E., Hellinger, P., Passot, T., Belmont, G., Trávníček, P. M., Sulem, P. L., Lucek, E. and Dandouras, I. 2009 Mirror structures above and below the linear instability threshold: Cluster observations, fluid model and hybrid simulations. Ann. Geophys. 27, 601615.Google Scholar
Grappin, R., Velli, M. and Mangeney, A. 1993 Nonlinear-wave evolution in the expanding solar wind. Phys. Rev. Lett. 70, 21902193.Google Scholar
Hasegawa, A. 1969 Drift mirror instability in the magnetosphere. Phys. Fluids 12, 26422650.Google Scholar
Hellinger, P. 2007 Comment on the linear mirror instability near the threshold. Phys. Plasmas 14, 082105.Google Scholar
Hellinger, P., Kuznetsov, E. A., Passot, T., Sulem, P. L. and Trávníček, P. M. 2009 Mirror instability: From quasi-linear diffusion to coherent structures. Geophys. Res. Lett. 36, L06103.Google Scholar
Hellinger, P. and Matsumoto, H. 2000 New kinetic instability: Oblique Alfvén fire hose. J. Geophys. Res. 105, 1051910526.Google Scholar
Hellinger, P. and Matsumoto, H. 2001 Nonlinear competition between the whistler and Alfvén fire hoses. J. Geophys. Res. 106, 1321513218.Google Scholar
Hellinger, P., Passot, T., Sulem, P.-L. and Trávníček, P. M. 2013 Quasi-linear heating and acceleration in bi-Maxwellian plasmas. Phys. Plasmas 20, 122306.Google Scholar
Hellinger, P. and Trávníček, P. 2005 Magnetosheath compression: Role of characteristic compression time, alpha particle abundances and alpha/proton relative velocity. J. Geophys. Res. 110, A04210.Google Scholar
Hellinger, P. and Trávníček, P. M. 2008 Oblique proton fire hose instability in the expanding solar wind: Hybrid simulations. J. Geophys. Res. 113, A10109.Google Scholar
Hellinger, P. and Trávníček, P. M. 2009 On Coulomb collisions in bi-Maxwellian plasmas. Phys. Plasmas 16, 054501.Google Scholar
Hellinger, P. and Trávníček, P. M. 2010 Langevin representation of Coulomb collisions for bi-Maxwellian plasmas. J. Comput. Phys. 229, 54325439.CrossRefGoogle Scholar
Hellinger, P. and Trávníček, P. M. 2012 On the quasi-linear diffusion in collisionless plasmas (to say nothing about landau damping). Phys. Plasmas 19, 062307.Google Scholar
Hellinger, P. and Trávníček, P. M. 2014 Solar wind protons at 1 AU: Trends and bounds, constraints and correlations. Astrophys. J. Lett. 784, L15.CrossRefGoogle Scholar
Hellinger, P., Trávníček, P., Kasper, J. C. and Lazarus, A. J. 2006 Solar wind proton temperature anisotropy: Linear theory and WIND/SWE observations. Geophys. Res. Lett. 33, L09101.CrossRefGoogle Scholar
Kennel, C. F. and Engelmann, F. 1966 Velocity space diffusion from weak plasma turbulence in a magnetic field. Phys. Fluids 9, 23772388.CrossRefGoogle Scholar
Kunz, M. W., Schekochihin, A. A. and Stone, J. M. 2014 Firehose and mirror instabilities in a collisionless shearing plasma. Phys. Rev. Lett. 112, 205003.CrossRefGoogle Scholar
Kuznetsov, E. A., Passot, T. and Sulem, P. L. 2007a Nonlinear theory of mirror instability near threshold. JETP Lett. 86, 637642.Google Scholar
Kuznetsov, E. A., Passot, T. and Sulem, P. L. 2007b Dynamical model for nonlinear mirror modes near threshold. Phys. Rev. Lett. 98, 235003.CrossRefGoogle ScholarPubMed
Manheimer, W. M., Lampe, M. and Joyce, G. 1997 Langevin representation of Coulomb collisions in PIC simulations. J. Comput. Phys. 138, 563584.Google Scholar
Matteini, L., Landi, S., Hellinger, P. and Velli, M. 2006 Parallel proton fire hose instability in the expanding solar wind: Hybrid simulations. J. Geophys. Res. 111, A10101.Google Scholar
Matthews, A. 1994 Current advance method and cyclic leapfrog for 2D multispecies hybrid plasma simulations. J. Comput. Phys. 112, 102116.Google Scholar
Mogavero, F. and Schekochihin, A. A. 2014 Models of magnetic field evolution and effective viscosity in weakly collisional extragalactic plasmas. Mon. Not. R. Astron. Soc. 440, 32263242.CrossRefGoogle Scholar
Porazik, P. and Johnson, J. R. 2013 Gyrokinetic particle simulation of nonlinear evolution of mirror instability. J. Geophys. Res. 118, 72117218.Google Scholar
Rosin, M. S., Schekochihin, A. A., Rincon, F. and Cowley, S. C. 2011 A nonlinear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma. Mon. Not. R. Astron. Soc. 413, 738.Google Scholar
Santos-Lima, R., de Gouveia Dal Pino, E. M., Kowal, G., Falceta-Gonçalves, D., Lazarian, A. and Nakwacki, M. S. 2014 Magnetic field amplification and evolution in turbulent collisionless magnetohydrodynamics: An application to the intracluster medium. Astrophys. J. 781, 84.Google Scholar
Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, G. W., Howes, G. G., Plunk, G. G., Quataert, E. and Tatsuno, T. 2008 Gyrokinetic turbulence: a nonlinear route to dissipation through phase space. Plasma Phys. Control. Fusion 50, 124024.CrossRefGoogle Scholar
Shoub, E. C. 1987 Failure of the Fokker-Planck approximation to the Boltzmann integral for (1/r) potentials. Phys. Fluids 30, 13401352.Google Scholar
Trávníček, P., Hellinger, P., Taylor, M. G. G. T., Escoubet, C. P., Dandouras, I. and Lucek, E. 2007 Magnetosheath plasma expansion: Hybrid simulations. Geophys. Res. Lett. 34, L15104.CrossRefGoogle Scholar
Wicks, R. T., Matteini, L., Horbury, T. S., Hellinger, P. and Roberts, A. D. 2013 Temperature anisotropy instabilities; combining plasma and magnetic field data at different distances from the sun. In Proceedings of the 13th International Solar Wind Conferences, Vol. 1539. AIP, pp. 303306.Google Scholar
Yoon, P. H. and Seough, J. 2012 Quasilinear theory of anisotropy-beta relation for combined mirror and proton cyclotron instabilities. J. Geophys. Res. 117, A08102.Google Scholar