Abstract
A variety of nonthermal characteristics like kinetic, e.g., temperature, anisotropies and suprathermal populations (enhancing the high energy tails of the velocity distributions) are revealed by the in-situ observations in the solar wind indicating quasistationary states of plasma particles out of thermal equilibrium. Large deviations from isotropy generate kinetic instabilities and growing fluctuating fields which should be more efficient than collisions in limiting the anisotropy (below the instability threshold) and explain the anisotropy limits reported by the observations. The present paper aims to decode the principal instabilities driven by the temperature anisotropy of electrons and protons in the solar wind, and contrast the instability thresholds with the bounds observed at 1 AU for the temperature anisotropy. The instabilities are characterized using linear kinetic theory to identify the appropriate (fastest) instability in the relaxation of temperature anisotropies \(A_{e,p} = T_{e,p,\perp}/ T _{e,p,\parallel} \ne1\). The analysis focuses on the electromagnetic instabilities driven by the anisotropic protons (\(A_{p} \lessgtr1\)) and invokes for the first time a dynamical model to capture the interplay with the anisotropic electrons by correlating the effects of these two species of plasma particles, dominant in the solar wind.
Similar content being viewed by others
References
Bale, S., Kasper, J., Howes, G., Quataert, E., Salem, C., Sundkvist, D.: Phys. Rev. Lett. 103(21), 211101 (2009)
Christon, S.P., Williams, D.J., Mitchell, D.G., Frank, L.A., Huang, C.Y.: J. Geophys. Res. Space Phys. 94(A10), 13409 (1989)
Fried, B.D., Conte, S.D.: The Plasma Dispersion Function: the Hilbert Transform of the Gaussian. Elsevier, Amsterdam (1961)
Gary, S.P.: J. Geophys. Res. Space Phys. 97(A6), 8519 (1992)
Gary, S.P., Lee, M.A.: J. Geophys. Res. 99, 11 (1994)
Gary, S.P., McKean, M.E., Winske, D.: J. Geophys. Res. Space Phys. 98(A3), 3963 (1993)
Gary, S.P., Anderson, B.J., Denton, R.E., Fuselier, S.A., McKean, M.E.: Phys. Plasmas 1(5), 1676 (1994)
Gary, S.P., Jian, L.K., Broiles, T.W., Stevens, M.L., Podesta, J.J., Kasper, J.C.: J. Geophys. Res. Space Phys. 121(1), 30 (2016)
Hellinger, P., Trávníček, P., Kasper, J.C., Lazarus, A.J.: Geophys. Res. Lett. 33(9), L09101 (2006)
Hellinger, P., Trávníček, P.M., Štverák, Š., Matteini, L., Velli, M.: J. Geophys. Res. Space Phys. 118(4), 1351 (2013)
Kasper, J.C., Lazarus, A.J., Gary, S.P.: Geophys. Res. Lett. 29(17), 20 (2002)
Kasper, J., Lazarus, A., Gary, S., Szabo, A.: In: AIP Conference Proceedings, p. 538. IOP Publishing, Bristol (2003)
Kennel, C.F., Petschek, H.E.: J. Geophys. Res. 71(1), 1 (1966)
Kennel, C., Scarf, F.: J. Geophys. Res. 73(19), 6149 (1968)
Krall, N., Trivelpiece, A.: Principles of Plasma Physics. McGraw-Hill, New York (1973)
Lazar, M., Schlickeiser, R., Shukla, P.: Phys. Plasmas 15(4), 042103 (2008)
Lazar, M., Poedts, S., Schlickeiser, R.: Astron. Astrophys. 534, 116 (2011)
Lazar, M., Poedts, S., Fichtner, H.: Astron. Astrophys. 582, 124 (2015)
Lepping, R., Acũna, M., Burlaga, L., Farrell, W., Slavin, J., Schatten, K., Mariani, F., Ness, N., Neubauer, F., Whang, Y., et al.: Space Sci. Rev. 71(1–4), 207 (1995)
Leubner, M.P., Schupfer, N.: J. Geophys. Res. Space Phys. 105(A12), 27387 (2000)
Leubner, M.P., Schupfer, N.: J. Geophys. Res. Space Phys. 106(A7), 12993 (2001)
Maksimovic, M., Pierrard, V., Riley, P.: Geophys. Res. Lett. 24(9), 1151 (1997)
Matteini, L., Landi, S., Hellinger, P., Pantellini, F., Maksimovic, M., Velli, M., Goldstein, B.E., Marsch, E.: Geophys. Res. Lett. 34(20), 20105 (2007)
Matteini, L., Hellinger, P., Goldstein, B.E., Landi, S., Velli, M., Neugebauer, M.: J. Geophys. Res. Space Phys. 118(6), 2771 (2013)
McKean, M., Winske, D., Gary, S.: J. Geophys. Res. Space Phys. 97(A12), 19421 (1992)
McKean, M., Winske, D., Gary, S.: J. Geophys. Res. Space Phys. 99(A6), 11141 (1994)
Michno, M., Lazar, M., Yoon, P., Schlickeiser, R.: Astrophys. J. 781(1), 49 (2014)
Ogilvie, K., Chornay, D., Fritzenreiter, R., Hunsaker, F., Keller, J., Lobell, J., Miller, G., Scudder, J., Sittler Jr., E., Torbert, R., et al.: Space Sci. Rev. 71, 55 (1995)
Shaaban, S.M., Lazar, M., Poedts, S., Elhanbaly, A.: Astrophys. J. 814(1), 34 (2015)
Shaaban, S.M., Lazar, M., Poedts, S., Elhanbaly, A.: Astrophys. Space Sci. 361(6), 1 (2016)
Štverák, Š., Trávníček, P., Maksimovic, M., Marsch, E., Fazakerley, A.N., Scime, E.E.: J. Geophys. Res. Space Phys. 113(A3), A03103 (2008)
Summers, D., Thorne, R.M.: Phys. Fluids, B Plasma Phys. 3(8), 1835 (1991)
Vasyliunas, V.M.: J. Geophys. Res. 73(9), 2839 (1968)
Acknowledgements
The authors acknowledge the use of WIND SWE (Ogilvie et al. 1995) ion data, and WIND MFI (Lepping et al. 1995) magnetic field data from the SPDF CDAWeb service: http://cdaweb.gsfc.nasa.gov/. The authors acknowledge support from the Katholieke Universiteit Leuven. These results were obtained in the framework of the projects GOA/2015-014 (KU Leuven), G.0A23.16N (FWO-Vlaanderen), and C 90347 (ESA Prodex). The research leading to these results has also received funding from IAP P7/08 CHARM (Belspo). S.M. Shaaban would like to thank the Egyptian Ministry of Higher Education for supporting his research activities.
Author information
Authors and Affiliations
Corresponding author
Appendices
Appendix A: Distributions and dispersion functions
For a plasma of electrons and protons with bi-Maxwellian velocity distribution functions (VDFs)
where thermal velocities \(u_{\alpha,\parallel, \perp}\) are defined by the components of the anisotropic temperature
the plasma dispersion function in Eq. (1) takes the standard form (Fried and Conte 1961)
of argument \(\xi_{\alpha,M}^{\pm}= ( \omega\pm\varOmega_{ \alpha} ) / ( ku_{\alpha,\parallel,} ) \)
To include suprathermal population, the electrons can be described by a bi-Kappa VDF (Summers and Thorne 1991)
which is normalized to unity \(\int d^{3}vF_{e,\kappa}= 1\), and is written in terms of thermal velocities \(u_{e,\parallel, \perp}\) defined by the components of the effective temperature (for a power-index \(\kappa_{e} >3/2\))
Suprathermals enhance the electron temperature, and implicitly the plasma beta parameter (Leubner and Schupfer 2000, 2001; Lazar et al. 2015)
and for the modified Kappa dispersion function (8) we use in Eq. (1) the form (Lazar et al. 2008)
of argument \(\xi_{e,\kappa}^{\pm}= (\omega\pm\varOmega_{e})/(k u_{e,\parallel,})\).
Appendix B: Fitting parameters for Eq. (4)
Rights and permissions
About this article
Cite this article
Shaaban, S.M., Lazar, M., Poedts, S. et al. Shaping the solar wind temperature anisotropy by the interplay of electron and proton instabilities. Astrophys Space Sci 362, 13 (2017). https://doi.org/10.1007/s10509-016-2994-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10509-016-2994-7