Solar Physics

, Volume 289, Issue 1, pp 369–378

The Electron Firehose and Ordinary-Mode Instabilities in Space Plasmas



Self-generated wave fluctuations are particularly interesting in the solar wind and magnetospheric plasmas, where Coulomb collisions are rare and cannot explain the observed states of quasi-equilibrium. Linear theory predicts that firehose and ordinary-mode instabilities can develop under the same conditions, which makes it challenging to separate the role of these instabilities in conditioning the space-plasma properties. The hierarchy of these two instabilities is reconsidered here for nonstreaming plasmas with an electron-temperature anisotropy T>T, where ∥ and ⊥ denote directions with respect to the local mean magnetic field. In addition to the previously reported comparative analysis, here the entire 3D wave-vector spectrum of the competing instabilities is investigated, with a focus on the oblique firehose instability and the relatively poorly known ordinary-mode instability. Results show a dominance of the oblique firehose instability with a threshold lower than the parallel firehose instability and lower than the ordinary-mode instability. For stronger anisotropies, the ordinary mode can grow faster, with maximum growth rates exceeding those of the oblique firehose instability. In contrast to previous studies that claimed a possible activity of the ordinary-mode in the low β [< 1] regimes, here it is rigorously shown that only the high β [> 1] regimes are susceptible to these instabilities.


Corona Flares, dynamics Solar wind Instabilities Waves, plasma 


  1. Bale, S., Kasper, J.C., Howes, G.G., Quataert, E., Salem, E., Sundkvist, D.: 2009, Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind. Phys. Rev. Lett. 103, 211101. doi:10.1103/PhysRevLett.103.211101. ADSCrossRefGoogle Scholar
  2. Camporeale, E., Burgess, D.: 2008, Electron firehose instability: kinetic linear theory and two-dimensional particle-in-cell simulations. J. Geophys. Res. 113, A07107. doi:10.1029/2008JA013043. ADSCrossRefGoogle Scholar
  3. Fried, B.D.: 1959, Mechanism for instability of transverse plasma waves. Phys. Fluids 2, 337. doi:10.1063/1.1705933. MathSciNetADSCrossRefGoogle Scholar
  4. Gary, S.P.: 1993, Theory of Space Plasma Microinstabilities, Cambridge University Press, Cambridge. CrossRefGoogle Scholar
  5. Gary, S.P., Karimabadi, H.: 2006, Linear theory of electron temperature anisotropy instabilities: Whistler, mirror, and Weibel. J. Geophys. Res. 111, A11224. doi:10.1029/2006JA011764. ADSCrossRefGoogle Scholar
  6. Gary, S.P., Madland, D.: 1985, Electromagnetic electron temperature anisotropy instabilities. J. Geophys. Res. 90, 7607 – 7610. doi:10.1029/JA090iA08p07607. ADSCrossRefGoogle Scholar
  7. Gary, S.P., Nishimura, K.: 2003, Resonant electron firehose instability: particle-in-cell simulations. Phys. Plasmas 10, 3571 – 3576. doi:10.1063/1.1590982. ADSCrossRefGoogle Scholar
  8. Gary, S.P., Neagu, E., Skoug, R.M., Goldstein, B.E.: 1999, Solar wind electrons: parametric constraints. J. Geophys. Res. 104, 19843 – 19849. doi:10.1029/1999JA900244. ADSCrossRefGoogle Scholar
  9. Hamasaki, S.: 1968, Electromagnetic microinstabilities of plasmas in a uniform magnetic induction. Phys. Fluids 11, 2724 – 2727. doi:10.1063/1.1691879. ADSCrossRefGoogle Scholar
  10. Hellinger, P., Travnicek, P., Kasper, J.C., Lazarus, A.J.: 2006, Solar wind proton temperature anisotropy: linear theory and WIND/SWE observations. Geophys. Res. Lett. 33, L09101. doi:10.1029/2006GL025925. ADSCrossRefGoogle Scholar
  11. Ibscher, D., Lazar, M., Schlickeiser, R.: 2012, On the existence of Weibel instability in a magnetized plasma. II. Perpendicular wave propagation: the ordinary mode. Phys. Plasmas 19, 072116. doi:10.1063/1.4736992. ADSCrossRefGoogle Scholar
  12. Lazar, M., Poedts, S.: 2009, Limits for the firehose instability in space plasmas. Solar Phys. 258, 119 – 128. doi:10.1007/s11207-009-9405-y. ADSCrossRefGoogle Scholar
  13. Lazar, M., Schlickeiser, R., Poedts, S.: 2010, Nonresonant electromagnetic instabilities in space plasmas: interplay of Weibel and firehose instabilities. In: AIP Conf. Proc. 1216, 280 – 283. doi:10.1063/1.3395855. Google Scholar
  14. Li, X., Habbal, S.R.: 2000, Electron kinetic firehose instability. J. Geophys. Res. 105, 27377 – 27385. doi:10.1029/2000JA000063. ADSCrossRefGoogle Scholar
  15. Marsch, E.: 2006, Kinetic physics of the solar corona and solar wind. Living Rev. Solar Phys. 3, 1. doi:10.12942/lrsp-2006-1. ADSCrossRefGoogle Scholar
  16. Messmer, P.: 2002, Temperature isotropization in solar flare plasmas due to the electron firehose instability. Astron. Astrophys. 382, 301 – 311. doi:10.1051/0004-6361:20011583. ADSCrossRefGoogle Scholar
  17. Paesold, G., Benz, A.O.: 1999, Electron firehose instability and acceleration of electrons in solar flares. Astron. Astrophys. 351, 741 – 746. ADSGoogle Scholar
  18. Paesold, G., Benz, A.O.: 2003, Test particle simulation of the electron firehose instability. Astron. Astrophys. 401, 711 – 720. doi:10.1051/0004-6361:20030113. ADSCrossRefGoogle Scholar
  19. Pokhotelov, O.A., Treumann, R.A., Sagdeev, R.Z., Balikhin, M.A., Onishchenko, O.G., Pavlenko, V.P., Sandberg, I.: 2002, Linear theory of the mirror instability in non-Maxwellian space plasmas. J. Geophys. Res. 107, 1312. doi:10.1029/2001JA009125. CrossRefGoogle Scholar
  20. 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. doi:10.1088/2041-8205/745/1/L9. ADSCrossRefGoogle Scholar
  21. Schlickeiser, R., Lazar, M., Skoda, T.: 2011, Spontaneously growing, weakly propagating, transverse fluctuations in anisotropic magnetized thermal plasmas. Phys. Plasmas 18, 012103. doi:10.1063/1.3532787. ADSCrossRefGoogle Scholar
  22. Stverak, S., Travnicek, P., Maksimovic, M., Marsch, E., Fazakerley, A.N., Scime, E.E.: 2008, Electron temperature anisotropy constraints in the solar wind. J. Geophys. Res. 113, A03103. doi:10.1029/2007JA012733. ADSCrossRefGoogle Scholar
  23. Swanson, D.G.: 2003, Plasma Waves, 2nd edn., IOP Publishing Ltd., Bristol. Google Scholar
  24. Weibel, E.S.: 1959, Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys. Rev. Lett. 2, 83 – 84. doi:10.1103/PhysRevLett.2.83. ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • M. Lazar
    • 1
    • 2
  • S. Poedts
    • 1
  • R. Schlickeiser
    • 2
  • D. Ibscher
    • 2
  1. 1.Center for Mathematical Plasma AstrophysicsK.U. LeuvenLeuvenBelgium
  2. 2.Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und AstrophysikRuhr-Universität BochumBochumGermany

Personalised recommendations