Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-23T18:18:48.971Z Has data issue: false hasContentIssue false
  • English
  • Français

General dispersion properties of magnetized plasmas with drifting bi-Kappa distributions. DIS-K: Dispersion Solver for Kappa Plasmas

Published online by Cambridge University Press:  11 June 2021

R.A. López Open the ORCID record for R.A. López [Opens in a new window] ,
S.M. Shaaban Open the ORCID record for S.M. Shaaban [Opens in a new window]  and
M. Lazar Open the ORCID record for M. Lazar [Opens in a new window]
R.A. López*
Affiliation:
Departamento de Física, Universidad de Santiago de Chile, Usach, 9170124Santiago, Chile
S.M. Shaaban
Affiliation:
Institute of Experimental and Applied Physics, University of Kiel, Leibnizstrasse 11, D-24118Kiel, Germany Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, 35516Mansoura, Egypt
M. Lazar
Affiliation:
Centre for Mathematical Plasma Astrophysics, KU Leuven, Celestijnenlaan 200B, B-3001Leuven, Belgium Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, D-44780Bochum, Germany
*
†Email address for correspondence: rlopez186@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Space plasmas are known to be out of (local) thermodynamic equilibrium, as observations show direct or indirect evidences of non-thermal velocity distributions of plasma particles. Prominent are the anisotropies relative to the magnetic field, anisotropic temperatures, field-aligned beams or drifting populations, but also, the suprathermal populations enhancing the high-energy tails of the observed distributions. Drifting bi-Kappa distribution functions can provide a good representation of these features and enable for a kinetic fundamental description of the dispersion and stability of these collision-poor plasmas, where particle–particle collisions are rare but wave–particle interactions appear to play a dominant role in the dynamics. In the present paper we derive the full set of components of the dispersion tensor for magnetized plasma populations modelled by drifting bi-Kappa distributions. A new solver called DIS-K (DIspersion Solver for Kappa plasmas) is proposed to solve numerically the dispersion relations of high complexity. The solver is validated by comparing with the damped and unstable wave solutions obtained with other codes, operating in the limits of drifting Maxwellian and non-drifting Kappa models. These new theoretical tools enable more realistic characterizations, both analytical and numerical, of wave fluctuations and instabilities in complex kinetic configurations measured in-situ in space plasmas.

Keywords

plasma wavesplasma instabilitiesspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 3 , June 2021 , 905870310
Check for updates
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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.)

References

REFERENCES

Alexandrova, O., Chen, C.H.K., Sorriso-Valvo, L., Horbury, T.S. & Bale, S.D. 2013 Solar wind turbulence and the role of ion instabilities. Space Sci. Rev. 178 (2), 101–139.CrossRefGoogle Scholar
Astfalk, P. 2018 Linear and quasilinear studies of kinetic instabilities in non-Maxwellian space plasmas. Dissertation, Technische Universität, München, München.Google Scholar
Astfalk, P., Görler, T. & Jenko, F. 2015 DSHARK: a dispersion relation solver for obliquely propagating waves in bi-kappa-distributed plasmas. J. Geophys. Res.: Space 120 (9), 7107–7120.CrossRefGoogle Scholar
Bale, S.D., Kasper, J.C., Howes, G.G., Quataert, E., Salem, C. & Sundkvist, D. 2009 Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind. Phys. Rev. Lett. 103, 211101.CrossRefGoogle ScholarPubMed
Basu, B. 2009 Hydromagnetic waves and instabilities in kappa distribution plasma. Phys. Plasmas 16 (5), 052106.CrossRefGoogle Scholar
Bian, N.H., Emslie, A.G., Stackhouse, D.J. & Kontar, E.P. 2014 The formation of Kappa-distribution accelerated electron populations in solar flares. Astrophys. J. 796 (2), 142.CrossRefGoogle Scholar
Bowen, T.A., Mallet, A., Huang, J., Klein, K.G., Malaspina, D.M., Stevens, M., Bale, S.D., Bonnell, J.W., Case, A.W., Chandran, B.D.G., et al. 2020 Ion-scale electromagnetic waves in the inner heliosphere. Astrophys. J. Suppl. 246 (2), 66.CrossRefGoogle Scholar
Cattaert, T., Hellberg, M.A. & Mace, R.L. 2007 Oblique propagation of electromagnetic waves in a kappa-Maxwellian plasma. Phys. Plasmas 14 (8), 082111.CrossRefGoogle Scholar
Collier, M.R., Hamilton, D., Gloeckler, G., Bochsler, P. & Sheldon, R. 1996 Neon-20, oxygen-16, and helium-4 densities, temperatures, and suprathermal tails in the solar wind determined with wind/mass. Geophys. Res. Lett. 23 (10), 1191–1194.CrossRefGoogle Scholar
Fried, B. & Conte, S. 1961 The Plasma Dispersion Function: The Hilbert Transform of the Gaussian. Academic Press.Google Scholar
Gaelzer, R. & Ziebell, L.F. 2016 Obliquely propagating electromagnetic waves in magnetized kappa plasmas. Phys. Plasmas 23 (2), 022110.CrossRefGoogle Scholar
Gaelzer, R., Ziebell, L.F. & Meneses, A.R. 2016 The general dielectric tensor for bi-kappa magnetized plasmas. Phys. Plasmas 23 (6), 062108.CrossRefGoogle Scholar
Gary, S.P. 1993 Theory of Space Plasma Microinstabilities. Cambridge University Press.CrossRefGoogle Scholar
Gary, S.P., Jian, L.K., Broiles, T.W., Stevens, M.L., Podesta, J.J. & Kasper, J.C. 2016 Ion-driven instabilities in the solar wind: wind observations of 19 March 2005. J. Geophys. Res.: Space 121, 30–41.CrossRefGoogle Scholar
Hammond, C.M., Feldman, W.C., McComas, D.J., Phillips, J.L. & Forsyth, R.J. 1996 Variation of electron-strahl width in the high-speed solar wind: ULYSSES observations. Astron. Astrophys. 316, 350–354.Google Scholar
Hellberg, M.A. & Mace, R.L. 2002 Generalized plasma dispersion function for a plasma with a kappa-Maxwellian velocity distribution. Phys. Plasmas 9 (5), 1495.CrossRefGoogle Scholar
Isenberg, P.A. & Vasquez, B.J. 2019 Perpendicular ion heating by cyclotron resonant dissipation of turbulently generated kinetic Alfvén waves in the solar wind. Astrophys. J. 887 (1), 63.CrossRefGoogle Scholar
Jeong, S.-Y., Verscharen, D., Wicks, R.T. & Fazakerley, A.N. 2020 A quasi-linear diffusion model for resonant wave-particle instability in homogeneous plasma. Astrophys. J. 902 (2), 128.CrossRefGoogle Scholar
Kasper, J.C., Lazarus, A.J., Gary, S.P. & Szabo, A. 2003 Solar wind temperature anisotropies. AIP Conf. Proc. 679 (1), 538–541.CrossRefGoogle Scholar
Kim, S., Lazar, M., Schlickeiser, R., López, R.A. & Yoon, P.H. 2018 Low frequency electromagnetic fluctuations in Kappa magnetized plasmas. Plasma Phys. Control. Fusion 60 (7), 075010.CrossRefGoogle Scholar
Kim, S., Schlickeiser, R., Yoon, P.H., López, R.A. & Lazar, M. 2017 Spontaneous emission of electromagnetic fluctuations in Kappa magnetized plasmas. Plasma Phys. Control. Fusion 59 (12), 125003.CrossRefGoogle Scholar
Klein, K.G. & Howes, G.G. 2015 Predicted impacts of proton temperature anisotropy on solar wind turbulence. Phys. Plasmas 22 (3), 032903.CrossRefGoogle Scholar
Lazar, M., Fichtner, H. & Yoon, P.H. 2016 On the interpretation and applicability of $\kappa$-distributions. Astron. Astrophys. 589, A39.CrossRefGoogle Scholar
Lazar, M., López, R.A., Shaaban, S.M., Poedts, S. & Fichtner, H. 2019 Whistler instability stimulated by the suprathermal electrons present in space plasmas. Astrophys. Space Sci. 364 (10), 171.CrossRefGoogle Scholar
Lazar, M., Pierrard, V., Shaaban, S., Fichtner, H. & Poedts, S. 2017 Dual Maxwellian-kappa modeling of the solar wind electrons: new clues on the temperature of kappa populations. Astron. Astrophys. 602, A44.CrossRefGoogle Scholar
Lazar, M. & Poedts, S. 2009 Firehose instability in space plasmas with bi-kappa distributions. Astron. Astrophys. 494 (1), 311–315.CrossRefGoogle Scholar
Lazar, M., Poedts, S. & Fichtner, H. 2015 Destabilizing effects of the suprathermal populations in the solar wind. Astron. Astrophys. 582, A124.CrossRefGoogle Scholar
Lazar, M., Scherer, K., Fichtner, H. & Pierrard, V. 2020 a Toward a realistic macroscopic parametrization of space plasmas with regularized ${\kappa }$-distributions. Astron. Astrophys. 634, A20.CrossRefGoogle Scholar
Leamon, R.J., Smith, C.W., Ness, N.F. & Wong, H.K. 1999 Dissipation range dynamics: kinetic Alfvé waves and the importance of $\beta _e$. J. Geophys. Res.: Space 104 (A10), 22331–22344.CrossRefGoogle Scholar
Liu, Y., Liu, S.Q., Dai, B. & Xue, T.L. 2014 Dispersion and damping rates of dispersive Alfvén wave in a nonextensive plasma. Phys. Plasmas 21 (3), 032125.CrossRefGoogle Scholar
López, R.A., Lazar, M., Shaaban, S.M., Poedts, S. & Moya, P.S. 2020 Alternative high-plasma beta regimes of electron heat-flux instabilities in the solar wind. Astrophys. J. Lett. 900 (2), L25.CrossRefGoogle Scholar
López, R.A., Lazar, M., Shaaban, S.M., Poedts, S., Yoon, P.H., Viñas, A.F. & Moya, P.S. 2019 Particle-in-cell simulations of firehose instability driven by bi-kappa electrons. Astrophys. J. Lett. 873 (2), L20.CrossRefGoogle Scholar
Mace, R.L. & Hellberg, M.A. 1995 A dispersion function for plasmas containing superthermal particles. Phys. Plasmas 2 (6), 2098.CrossRefGoogle Scholar
Maksimovic, M., Zouganelis, I., Chaufray, J.-Y., Issautier, K., Scime, E., Littleton, J., Marsch, E., McComas, D., Salem, C., Lin, R., et al. 2005 Radial evolution of the electron distribution functions in the fast solar wind between 0.3 and 1.5 au. J. Geophys. Res.: Space 110 (A9), A09104.Google Scholar
Marsch, E. 2006 Kinetic physics of the solar corona and solar wind. Living Rev. Sol. Phys. 3 (1), 1–100.CrossRefGoogle Scholar
Mason, G.M. & Gloeckler, G. 2012 Power law distributions of suprathermal ions in the quiet solar wind. Space Sci. Rev. 172 (1–4), 241–251.CrossRefGoogle Scholar
Micera, A., Zhukov, A.N., López, R.A., Innocenti, M.E., Lazar, M., Boella, E. & Lapenta, G. 2020 Particle-in-cell simulation of whistler heat-flux instabilities in the solar wind: heat-flux regulation and electron halo formation. Astrophys. J. Lett. 903 (1), L23.CrossRefGoogle Scholar
Pierrard, V. & Lazar, M. 2010 Kappa distributions: theory and applications in space plasmas. Sol. Phys. 267 (1), 153–174.Google Scholar
Piessens, R., de Doncker-Kapenga, E., Ueberhuber, C.W. & Kahaner, D.K. 1983 Quadpack: A Subroutine Package for Automatic Integration. Computational Mathematics Series. Springer.CrossRefGoogle Scholar
Pilipp, W.G., Miggenrieder, H., Montgomery, M.D., Mühlhäuser, K.H., Rosenbauer, H. & Schwenn, R. 1987 Characteristics of electron velocity distribution functions in the solar wind derived from the Helios Plasma Experiment. J. Geophys. Res. 92 (A2), 1075.Google Scholar
Roennmark, K. 1982 Waves in homogeneous, anisotropic multicomponent plasmas (whamp). Rep. No. 179, ISSN: 0347-6406. Kiruna, Sweden: Kiruna Geophysical Institute.Google Scholar
Shaaban, S., Lazar, M., López, R. & Wimmer-Schweingruber, R. 2021 a On the interplay of solar wind proton and electron instabilities: linear and quasi-linear approaches. Mon. Not. R. Astron Soc. 503 (3), 3134.CrossRefGoogle Scholar
Shaaban, S., Lazar, M., Yoon, P. & Poedts, S. 2019 Quasilinear approach of the cumulative whistler instability in fast solar wind: constraints of electron temperature anisotropy. Astron. Astrophys. 627, A76.Google Scholar
Shaaban, S.M. & Lazar, M. 2020 Whistler instabilities from the interplay of electron anisotropies in space plasmas: a quasi-linear approach. Mon. Not. R. Astron Soc. 492 (3), 3529–3539.CrossRefGoogle Scholar
Shaaban, S.M., Lazar, M., López, R.A., Fichtner, H. & Poedts, S. 2019 Firehose instabilities triggered by the solar wind suprathermal electrons. Mon. Not. R. Astron. Soc. 483 (4), 5642–5648.CrossRefGoogle Scholar
Shaaban, S.M., Lazar, M., López, R.A. & Poedts, S. 2020 Electromagnetic ion–ion instabilities in space plasmas: effects of suprathermal populations. Astrophys. J. 899 (1), 20.CrossRefGoogle Scholar
Shaaban, S.M., Lazar, M. & Poedts, S. 2018 Clarifying the solar wind heat flux instabilities. Mon. Not. R. Astron Soc. 480 (1), 310–319.CrossRefGoogle Scholar
Shaaban, S.M., Lazar, M. & Schlickeiser, R. 2021 b Electromagnetic ion cyclotron instability stimulated by the suprathermal ions in space plasmas: a quasi-linear approach. Phys. Plasmas 28 (2), 022103.CrossRefGoogle Scholar
Stix, T.H. 1992 Waves in Plasmas. AIP-Press.Google Scholar
Štverák, Š., Trávnıček, P., Maksimovic, M., Marsch, E., Fazakerley, A.N. & Scime, E.E. 2008 Electron temperature anisotropy constraints in the solar wind. J. Geophys. Res.: Space 113, A03103.Google Scholar
Summers, D. & Thorne, R.M. 1991 The modified plasma dispersion function. Phys. Fluids B 3 (8), 1835.CrossRefGoogle Scholar
Summers, D., Xue, S. & Thorne, R.M. 1994 Calculation of the dielectric tensor for a generalized Lorentzian (kappa) distribution function. Phys. Plasmas 1 (6), 2012–2025.CrossRefGoogle Scholar
Tong, Y., Vasko, I.Y., Artemyev, A.V., Bale, S.D. & Mozer, F.S. 2019 Statistical study of whistler waves in the solar wind at 1 au. Astrophys. J. 878 (1), 41.Google Scholar
Vasyliunas, V.M. 1968 A survey of low-energy electrons in the evening sector of the magnetosphere with OGO 1 and OGO 3. J. Geophys. Res. 73 (9), 2839–2884.CrossRefGoogle Scholar
Verscharen, D. & Chandran, B.D.G. 2018 NHDS: the new Hampshire dispersion relation solver. Res. Notes AAS 2 (2), 13.Google Scholar
Verscharen, D., Chandran, B.D.G., Jeong, S.-Y., Salem, C.S., Pulupa, M.P. & Bale, S.D. 2019 b Self-induced scattering of Strahl electrons in the solar wind. Astrophys. J. 886 (2), 136.Google Scholar
Verscharen, D., Klein, K.G. & Maruca, B.A. 2019 a The multi-scale nature of the solar wind. Living Rev. Sol. Phys. 16 (1), 5.Google ScholarPubMed
Viñas, A.F., Gaelzer, R., Moya, P. S., Mace, R. & Araneda, J.A. 2017 Linear kinetic waves in plasmas described by kappa distributions. In Kappa Distributions, chap. 7, pp. 329–361. Elsevier.Google Scholar
Viñas, A.F., Wong, H. K. & Klimas, A. J. 2000 Generation of electron suprathermal tails in the upper solar atmosphere: implications for coronal heating. Astrophys. J. 528 (1), 509–523.CrossRefGoogle Scholar
Wilson, L.B., Chen, L.-J., Wang, S., Schwartz, S.J., Turner, D.L., Stevens, M.L., Kasper, J.C., Osmane, A., Caprioli, D., Bale, S.D., et al. 2019b Electron energy partition across interplanetary shocks. II. Statistics. Astrophys. J. Suppl. 245 (2), 24.CrossRefGoogle Scholar
Wilson, L.B., Chen, L.-J., Wang, S., Schwartz, S.J., Turner, D.L., Stevens, M.L., Kasper, J.C., Osmane, A., Caprioli, D., Bale, S.D., Pulupa, M.P., Salem, C.S. & Goodrich, K.A. 2019 a Electron energy partition across interplanetary shocks. I. Methodology and data product. Astrophys. J. Suppl. 243 (1), 8.CrossRefGoogle ScholarPubMed
Wilson, L.B., Koval, A., Szabo, A., Breneman, A., Cattell, C.A., Goetz, K., Kellogg, P.J., Kersten, K., Kasper, J.C. & Maruca, B.A. 2013 Electromagnetic waves and electron anisotropies downstream of supercritical interplanetary shocks. J. Geophys. Res.: Space 118, 5–16.CrossRefGoogle Scholar
Woodham, L.D., Wicks, R.T., Verscharen, D., Owen, C.J., Maruca, B.A. & Alterman, B.L. 2019 Parallel-propagating fluctuations at proton-kinetic scales in the solar wind are dominated by kinetic instabilities. Astrophys. J. 884 (2), L53.Google Scholar
Yoon, P.H. 2017 Kinetic instabilities in the solar wind driven by temperature anisotropies. Rev. Mod. Plasma Phys. 1 (1), 4.CrossRefGoogle Scholar
Yoon, P.H. 2019 Classical Kinetic Theory of Weakly Turbulent Nonlinear Plasma Processes. Cambridge University Press.CrossRefGoogle Scholar