Abstract
A sequence of in situ measurements points the presence of non-thermal species in the profile of particle distributions. This study highlights the role of such energetic electrons on the wave-spectrum. Using Vlasov–Maxwell’s model, the dispersion relations of the parallel propagating modes along with the space scale of damping are discussed using non-relativistic bi-Maxwellian and bi-Kappa distribution functions under the weak field approximation, i.e.,
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
[1] S. P. Gary, R. M. Skoug, J. T. Steinberg, and C. W. Smith, “Proton temperature anisotropy constraint in the solar wind: ACE observations,” Geophys. Res. Lett., vol. 28, p. 2759, 2001. https://doi.org/10.1029/2001gl013165.Search in Google Scholar
[2] J. C. Kasper, A. J. Lazarus, and S. P. Gary, “Wind/SWE observations of firehose constraint on solar wind proton temperature anisotropy,” Geophys. Res. Lett., vol. 29, p. 1839, 2002. https://doi.org/10.1029/2002gl015128.Search in Google Scholar
[3] E. Marsch, X. -Z. Ao, and C. -Y. Tu, “On the temperature anisotropy of the core part of the proton velocity distribution function in the solar wind,” J. Geophys. Res., vol. 109, p. A04102, 2004. https://doi.org/10.1029/2003ja010330.Search in Google Scholar
[4] P. Hellinger, P. Travnıcek, J. C. Kasper, and A. J. Lazarus, “Solar wind proton temperature anisotropy: linear theory and WIND/SWE observations,” Geophys. Res. Lett., vol. 33, p. 9101, 2006. https://doi.org/10.1029/2006gl025925.Search in Google Scholar
[5] L. Matteini, S. Landi, P. Hellinger, et al.., “Evolution of the solar wind proton temperature anisotropy from 0.3 to 2.5 AU,” Geophys. Res. Lett., vol. 34, p. L20105, 2007. https://doi.org/10.1029/2007gl030920.Search in Google Scholar
[6] S. D. Bale, J. C. Kasper, G. G. Howes, E. Quataert, C. Salem, and D. Sundkvist, “Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind,” Phys. Rev. Lett., vol. 103, p. 211101, 2009. https://doi.org/10.1103/physrevlett.103.211101.Search in Google Scholar
[7] S. Stverak, P. Travnıcek, M. Maksimovic, E. Marsch, A. N. Fazakerley, and E. E. Scime, “Electron temperature anisotropy constraints in the solar wind,” J. Geophys. Res., vol. 113, p. A03103, 2008.10.1029/2007JA012733Search in Google Scholar
[8] B. A. Maruca, J. C. Kasper, and S. D. Bale, “What Are the Relative Roles of Heating and Cooling in Generating Solar Wind Temperature Anisotropies?” Phys. Rev. Lett., vol. 107, p. 201101, 2011. https://doi.org/10.1103/physrevlett.107.201101.Search in Google Scholar
[9] X. H. Wei, J. B. Cao, G. C. Zhou, et al.., “Generation mechanism of the whistler-mode waves in the plasma sheet prior to magnetic reconnection,” Adv. Space Res., vol. 52, p. 205, 2013. https://doi.org/10.1016/j.asr.2013.02.016.Search in Google Scholar
[10] S. S. A. Gillani, N. L. Tsintsadze, H. A. Shah, and M. Razzaq, “Instabilities and generation of a quasistationary magnetic field by the interaction of relativistically intense electromagnetic wave with a plasma,” Phys. Plasmas, vol. 17, p. 083103, 2010. https://doi.org/10.1063/1.3466848.Search in Google Scholar
[11] A. Bret and C. Deutsch, “Stabilization of the filamentation instability and the anisotropy of the background plasma,” Phys. Plasmas, vol. 13, p. 022110, 2006. https://doi.org/10.1063/1.2172362.Search in Google Scholar
[12] A. Sid, A. Ghezal, A. Soudani, and M. Bekhouche, “Weibel instability in a bi-Maxwellian laser fusion plasma,” Plasma Fusion Res., vol. 5, p. 007, 2010. https://doi.org/10.1585/pfr.5.007.Search in Google Scholar
[13] A. A. Andreev, E. G. Gamaly, V. N. Novikov, A. N. Semakhin, and V. T. Tikhonchuk, “Heating of a dense plasma by an ultrashort laser in the anomalous skin-effect regime,” Z. Eksp. Teor. Fiz., vol. 101, p. 1303, 1992.Search in Google Scholar
[14] A. Hasegawa, K. Mima, and M. Duong-van, “Plasma distribution function in a superthermal radiation field,” Phys. Rev. Lett., vol. 54, p. 2608, 1985. https://doi.org/10.1103/physrevlett.54.2608.Search in Google Scholar
[15] R. A. Treumann, “Kinetic theoretical foundation of Lorentzian statistical mechanics,” Phys. Scripta, vol. 59, p. 19, 1999. https://doi.org/10.1238/physica.regular.059a00019.Search in Google Scholar
[16] C. Vocks and G. Mann, “Generation of suprathermal electrons by resonant wave‐particle interaction in the solar corona and wind,” APJ (Acta Pathol. Jpn.), vol. 593, p. 1134, 2003. https://doi.org/10.1086/376682.Search in Google Scholar
[17] R. L. Mace, “Whistler instability enhanced by suprathermal electrons within the Earth’s foreshock,” J. Geophys. Res., vol. 103, p. 14643, 1998. https://doi.org/10.1029/98ja00616.Search in Google Scholar
[18] G. Gloeckler, J. Geiss, H. Balsiger, et al.., “The solar wind ion composition spectrometer,” Astron. AstroPhys. Suppl. Ser., vol. 92, p. 267, 1992.Search in Google Scholar
[19] S. J. Bame, J. R. Asbridge, H. E. Felthauser, E. W. Hones, and I. B. Strong, “Characteristics of the plasma sheet in the Earth’s magnetotail,” J. Geophys. Res., vol. 72, p. 113, 1967. https://doi.org/10.1029/jz072i001p00113.Search in Google Scholar
[20] G. Gloeckler and D. C. Hamilton, “AMPTE ion composition results,” Phys. Scripta, vol. T18, p. 73, 1987. https://doi.org/10.1088/0031-8949/1987/t18/009.Search in Google Scholar
[21] V. Formisano, G. Moreno, F. Palmiotto, and P. C. Hedgecock, “Solar wind interaction with the Earth’s magnetic field: 1. Magnetosheath,” J. Geophys. Res., vol. 78, p. 3714, 1973. https://doi.org/10.1029/ja078i019p03714.Search in Google Scholar
[22] V. Pierrard and J. Lemaire, “Fitting the AE-8 energy spectra with two Maxwellian functions,” Radiat. Meas., vol. 26, p. 333, 1996. https://doi.org/10.1016/1350-4487(96)00057-1.Search in Google Scholar
[23] S. M. Krimigis, T. P. Armstrong, W. I. Axford, et al.., “The magnetosphere of Uranus: hot plasma and radiation environment,” Science, vol. 233, p. 97, 1986. https://doi.org/10.1126/science.233.4759.97.Search in Google Scholar
[24] B. H. Mauk, E. P. Keath, M. Kane, et al.., “The magnetosphere of Neptune: hot plasmas and energetic particles,” J. Geophys. Res., vol. 96, p. 19061, 1991. https://doi.org/10.1029/91ja01820.Search in Google Scholar
[25] V. A. Godyak and R. B. Piejak, “Abnormally low electron energy and heating-mode transition in a low-pressure argon rf discharge at 13.56 MHz,” Phys. Rev. Lett., vol. 65, p. 996, 1990. https://doi.org/10.1103/physrevlett.65.996.Search in Google Scholar
[26] V. A. Godyak, R. B. Piejak, and B. M. Alexandrovich, “Evolution of the electron-energy-distribution function during rf discharge transition to the high-voltage mode,” Phys. Rev. Lett., vol. 68, p. 40, 1992. https://doi.org/10.1103/physrevlett.68.40.Search in Google Scholar
[27] M. M. Turner, R. A. Doyle, and M. B. Hopkins, “Measured and simulated electron energy distribution functions in a low‐pressure radio frequency discharge in argon,” Appl. Phys. Lett., vol. 62, p. 3247, 1993. https://doi.org/10.1063/1.109088.Search in Google Scholar
[28] E. S. Weibel, “Anomalous skin effect in a plasma,” Phys. Fluids, vol. 10, p. 741, 1967. https://doi.org/10.1063/1.1762185.Search in Google Scholar
[29] A. F. Alexandrov, A. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics, Berlin/Heidelberg, Springer-Verlag, 1984.10.1007/978-3-642-69247-5Search in Google Scholar
[30] G. E. H. Reuter and E. H. Sondheimer, “The theory of the anomalous skin effect in metals,” Proc. R. Soc. London, Ser. A, vol. 195, p. 336, 1948.10.1038/161394a0Search in Google Scholar
[31] I. F. Voloshin, S. V. Kravchenko, L. M. Fisher, and V. A. Yampol’skii, “Nonlinear anomalous skin effect in metals,” Zh. Eksp. Teor. Fiz., vol. 88, p. 1460, 1985.Search in Google Scholar
[32] B. B. L. Witte, P. Sperling, M. French, V. Recoules, S. H. Glenzer, and R. Redmer “Observations of non-linear plasmon damping in dense plasmas,” Phys. Plasmas, vol. 25, p. 056901, 2018.10.1063/1.5017889Search in Google Scholar
[33] A. A. Andreev, K. Y. Platonov, and J. C. Gauthier, “Skin effect in strongly inhomogeneous laser plasmas with weakly anisotropic temperature distribution,” Phys. Rev. E, vol. 58, p. 2424, 1998. https://doi.org/10.1103/physreve.58.2424.Search in Google Scholar
[34] G. Ferrante, M. Zarcone, and S. A. Urypin, “Anomalous transmission of an ultrashort ionizing laser pulse through a thin foil,” Phys. Rev. Lett., vol. 91, p. 085005, 2003. https://doi.org/10.1103/physrevlett.91.085005.Search in Google Scholar
[35] I. Kaganovich, E. Startsev, and G. Shvets, “Anomalous skin effect for anisotropic electron velocity distribution function,” Phys. Plasmas, vol. 11, p. 6, 2004. https://doi.org/10.1063/1.1723461.Search in Google Scholar
[36] Z. Iqbal, A. Hussain, G. Murtaza, and M. Ali, “On the damping of right hand circularly polarized waves in spin quantum plasmas,” Phys. Plasmas, vol. 21, p. 122118, 2014. https://doi.org/10.1063/1.4904816.Search in Google Scholar
[37] P. M. Platzman and S. J. Buchsbaum, “Transmission of electromagnetic waves through plasma slabs,” Phys. Rev., vol. 132, p. 2, 1963. https://doi.org/10.1103/physrev.132.2.Search in Google Scholar
[38] N. Sternberg, V. Godyak, and D. Hoffma, “Magnetic field effects on gas discharge plasmas,” Phys. Plasmas, vol. 13, p. 063511, 2006.10.1063/1.2214537Search in Google Scholar
[39] S. S. Kim, C. S. Chang, N. S. Yoon, and K. W. Whang, “Inductively coupled plasma heating in a weakly magnetized plasma,” Phys. Plasmas, vol. 6, p. 2926, 1999. https://doi.org/10.1063/1.873250.Search in Google Scholar
[40] G. Abbas, M. F. Bashir, and G. Murtaza, “Anomalous skin effects in relativistic parallel propagating weakly magnetized electron plasma waves,” Phys. Plasmas, vol. 18, p. 102115, 2011. https://doi.org/10.1063/1.3652694.Search in Google Scholar
[41] G. Abbas, M. Sarfraz, and H. A. Shah, “Anomalous skin effects in a weakly magnetized degenerate electron plasma,” Phys. Plasmas, vol. 21, p. 092108, 2014. https://doi.org/10.1063/1.4894698.Search in Google Scholar
[42] I. B. Bernstein, “Waves in a plasma in a magnetic field,” Phys. Rev., vol. 109, p. 10, 1958. https://doi.org/10.1103/physrev.109.10.Search in Google Scholar
[43] D. C. Montgomery and D. A. Tidman, Plasma Kinetic Theory, New York, McGraw-Hill, 1964, p. 142.Search in Google Scholar
[44] B. Buti, “Relativistic effects on plasma oscillations and two-stream instability. I,” Phys. Fluids, vol. 6, p. 89, 1963. https://doi.org/10.1063/1.1724513.Search in Google Scholar
[45] A. Sagiv and E. Waxman, “Collective processes in relativistic plasma and their implications for gamma‐ray burst afterglows,” APJ (Acta Pathol. Jpn.), vol. 574, p. 861, 2002. https://doi.org/10.1086/340948.Search in Google Scholar
[46] S. P. Gary, Theory of Space Plasma Microinstabilities, Cambridge, Cambridge University Press, 1993.10.1017/CBO9780511551512Search in Google Scholar
[47] D. Summers and R. M. Thorne, “The modified plasma dispersion function,” Phys. Fluid. Plasma Phys., vol. 3, p. 1835, 1991. https://doi.org/10.1063/1.859653.Search in Google Scholar
[48] M. N. S. Qureshi, H. A. Shah, G. Murtaza, S. J. Schwartz, and F. Mahmood, “Parallel propagating electromagnetic modes with the generalized (r,q) distribution function,” Phys. Plasmas, vol. 11, p. 3819, 2004. https://doi.org/10.1063/1.1688329.Search in Google Scholar
[49] M. Maksimovic, I. Zouganelis, J. -Y. Chaufray, et al.., “Radial evolution of the electron distribution functions in the fast solar wind between 0.3 and 1.5 AU,” J. Geophys. Res., vol. 110, p. A09104, 2005. https://doi.org/10.1029/2005ja011119.Search in Google Scholar
[50] M. Lazar and S. Poedts, “Firehose instability in space plasmas with bi-kappa distributions,” Astron. Astrophys., vol. 494, p. 311, 2009. https://doi.org/10.1051/0004-6361:200811109.10.1051/0004-6361:200811109Search in Google Scholar
[51] A. F. Viñas, P. S. Moya, R. E. Navarro, J. A. Valdivia, J. A. Araneda, and V. Muñoz, “Electromagnetic fluctuations of the whistler-cyclotron and firehose instabilities in a Maxwellian and Tsallis-kappa-like plasma,” J. Geophys. Res.: Space Phys., vol. 120, p. 3307, 2015. https://doi.org/10.1002/2014ja020554.Search in Google Scholar
[52] M. Lazar, S. M. Shaaban, S. Poedts, and Š. Štverák, “Firehose constraints of the bi-Kappa-distributed electrons: a zero-order approach for the suprathermal electrons in the solar wind,” Mon. Not. Roy. Astron. Soc., vol. 464, p. 564, 2017. https://doi.org/10.1093/mnras/stw2336.Search in Google Scholar
[53] T. H. Khokhar, M. F. Bashir, P. H. Yoon, R. A. López, and G. Murtaza, “Spatial damping of parallel propagating electromagnetic waves in magnetized plasmas,” Phys. Plasmas, vol. 25, p. 084501, 2018. https://doi.org/10.1063/1.5035285.Search in Google Scholar
[54] T. H. Khokhar, P. H. Yoon, R. A. López, and G. Murtaza, “Spatial propagation and damping of ordinary electromagnetic mode,” Phys. Plasmas, vol. 25, p. 082114, 2018. https://doi.org/10.1063/1.5043356.Search in Google Scholar
[55] G. Abbas, M. F. Bashir, and G. Murtaza, “Anomalous skin effects in relativistic parallel propagating weakly magnetized electron plasma waves,” Phys. Plasmas, vol. 18, p. 102115, 2011. https://doi.org/10.1063/1.3652694.Search in Google Scholar
[56] G. Abbas, G. Murtaza, and R. J. Kingham, “High frequency electromagnetic modes in a weakly magnetized relativistic electron plasma,” Phys. Plasmas, vol. 17, p. 072105, 2010. https://doi.org/10.1063/1.3460345.Search in Google Scholar
[57] G. Abbas, M. F. Bashir, M. Ali, and G. Murtaza, “Study of high frequency parallel propagating modes in a weakly magnetized relativistic degenerate electron plasma,” Phys. Plasmas, vol. 19, p. 032103, 2012. https://doi.org/10.1063/1.3690099.Search in Google Scholar
[58] S. Noureen, G. Abbas, and M. Sarfraz, “On the dispersion characteristics of extraordinary mode in a relativistic fully degenerate electron plasma,” Phys. Plasmas, vol. 25, p. 012123, 2018. https://doi.org/10.1063/1.4894698.Search in Google Scholar
[59] M. Hellberg, R. Mace, and T. Cattaert, “Effects of superthermal particles on waves in magnetized space plasmas,” Space Sci. Rev., vol. 121, p. 127, 2005. https://doi.org/10.1007/s11214-006-5024-1.Search in Google Scholar
[60] V. Pierrard and M. Lazar, “Kappa distributions: theory and applications in space plasmas,” Sol. Phys., vol. 267, p. 153, 2010. https://doi.org/10.1007/s11207-010-9640-2.Search in Google Scholar
[61] M. P. Leubner and N. Schupfer, “Mirror instability thresholds in suprathermal space plasmas,” J. Geophys. Res., vol. 105, p. 27387, 2000. https://doi.org/10.1029/1999ja000447.Search in Google Scholar
[62] M. P. Leubner and N. Schupfer, “A general kinetic mirror instability criterion for space applications,” J. Geophys. Res., vol. 106, p. 12993, 2001. https://doi.org/10.1029/2000ja000425.Search in Google Scholar
[63] M. Lazar, S. Poedts, and H. Fichtner, “Destabilizing effects of the suprathermal populations in the solar wind,” Astron. Astrophys., vol. 582, p. A124, 2015. https://doi.org/10.1051/0004-6361/201526509.Search in Google Scholar
[64] M. Lazar and P. H. Yoon, “On the interpretation and applicability of κ-distributions,” Astron. Astrophys., vol. 589, p. A39, 2016. https://doi.org/10.1051/0004-6361/201527593.Search in Google Scholar
[65] B. Fried and S. D. Conte, The Plasma Dispersion Function, New York and London, Academic Press, 1961.Search in Google Scholar
[66] M. Lazar, S. Poedts, R. Schlickeiser, and P. K. Shukla, “Proton Firehose instability in bi-Kappa distributed plasmas,” Astron. Astrophys., vol. 534, p. A116, 2011. https://doi.org/10.1051/0004-6361/201116982.Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- General
- Temperature-insensitive intensity-modulation liquid refractive index sensor based on fiber-optic Michelson probe structure
- Dynamical Systems & Nonlinear Phenomena
- Impact of non-thermal electrons on spatial damping: a kinetic model for the parallel propagating modes
- Role of entropy in ηi-mode driven nonlinear structures obtained by homotopy perturbation method in electron–positron–ion plasma
- Study of ferrofluid flow and heat transfer between cone and disk
- Solid State Physics & Materials Science
- Structural, electronic, magnetic and mechanical properties of the full-Heusler compounds Ni2Mn(Ge,Sn) and Mn2NiGe
- Exothermic behaviour of aluminium and graphene as a fuel in Fe2O3 based nanothermite
- Surface levels of organic conductors in a tilted in-plane magnetic field
- Thermodynamics & Statistical Physics
- Adiabatic compressibility of biphasic salt melts
- Stochastic thermodynamics of a finite quantum system coupled to a heat bath
Articles in the same Issue
- Frontmatter
- General
- Temperature-insensitive intensity-modulation liquid refractive index sensor based on fiber-optic Michelson probe structure
- Dynamical Systems & Nonlinear Phenomena
- Impact of non-thermal electrons on spatial damping: a kinetic model for the parallel propagating modes
- Role of entropy in ηi-mode driven nonlinear structures obtained by homotopy perturbation method in electron–positron–ion plasma
- Study of ferrofluid flow and heat transfer between cone and disk
- Solid State Physics & Materials Science
- Structural, electronic, magnetic and mechanical properties of the full-Heusler compounds Ni2Mn(Ge,Sn) and Mn2NiGe
- Exothermic behaviour of aluminium and graphene as a fuel in Fe2O3 based nanothermite
- Surface levels of organic conductors in a tilted in-plane magnetic field
- Thermodynamics & Statistical Physics
- Adiabatic compressibility of biphasic salt melts
- Stochastic thermodynamics of a finite quantum system coupled to a heat bath