Dust-acoustic Solitary Waves in Space Dusty Plasmas with Nonequilibrium Distribution

Document Type : Research Article

Authors

1 Assistant Professor, Department of Physics, Faculty of Basic Sciences, University of Neyshabur, Neyshabur, Iran

2 M.Sc. Graduated, Department of Physics, Faculty of Basic Sciences, University of Neyshabur, Neyshabur, Iran

Abstract

In this paper by using the most recent findings in the field of the Kappa distribution statistics for the non-equilibrium space plasmas, dust-acoustic waves have been studied in a dusty plasma comprising of the inertial dust particles with negative charges and suprahermal distributions of electrons and positrons. The velocity distribution function for stationay state of the plasma in this model is labeled by an invariant Kappa index () which is independent of the numbers of degrees of freedom, and the parameter  which represents the the numbers of degrees of freedom. In linear analysis, the dispersion relation of dust-acoustic waves is studied, whrere the true sound speed of the problem is derived. The derived dust-sound speed is a generalized one which depends on the polytropic index of Kappa distributed paricles ( ), which itself depends on the spectral index  and the potential degrees of freedom ( ). Generally, the dust-sound speed has its maximum in an equilibrium plamsa with Maxwellian distribution or isothermal electrons ( ), and it reduces by approaching to the anti-equilibrium regions with sub-isothermal electrons
( ).
On the other hand, in the non-linear analysis, the dust-acoustic solitary waves have been studied by deriving an energy-integral equation, where we have used the true dust-sound speed for defining the true Mach number (the fractional wave speed to the sound speed). The formation conditions of the potential well, the true Mach number domains, and the effects of the parameters of soliton speed, the spectral index  and the potential degrees of freedom via the perturbation ( ) in the propagation of dust-acoustic solitary waves have been studied analytically and numerically.
 In such a plasma, only the negative polarity solitons are possible. The reason is the negative charge of dust paricles via the attracted electrons, which causes the formation of negative potential solitons.
The structure of dust-acoustic solitons are examined in the near-equilibrium states, where the spectral indices are distributed with the values of , and also in the far-from-thermal equilibrium states which are labeled by the spectral indices with the values of .
It is found that the threshold Mach nmber is proportional to the square root of the polytropic index of Kappa distributed paricles which vaies in the range . So, the threshold Mach number increases by approaching to the equilibrium state and it reduces in far-from-thermal equilibrium states. 
It is shown that the subsonic solitons are possible in the far-from-thermal equilibrium plasmas. On the other hand, in an equilibrium plasma, corresponding to the asymptotic limit of , only the altrasonic solitons are possible which confirms the classical theory of solitons in equilibrium statistical mechanics.
It is found that the amplitude and steepening of the dust-acoustic solitons grows in far-from-thermal equilibrium states, which corresponds to the lower values of the spectral index . It is because of the impact the suprathermal particles on dust-acoustic solitons in that regions. Furthermore, an increase in Mach number results in the propagation of dust-acoustic solitons with more amplitude and steepening, in agreement with the standard theory of solitary waves. Moreover, decreasing the potential degrees of freedom causes an increase in the maximum amplitude and pulse steepening of dust-acoustic solitons.

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References

Adnan, M., Mahmood, S. and Qamar, A., 2014, Small amplitude ion acoustic solitons in a weakly magnetized plasma with anisotropic ion pressure and kappa distributed electrons, Advances in Space Research, 53, 845-852.
Baluku, T. K. and Hellberg, M. A., 2012, Ion acoustic solitons in a plasma with two-temperature kappa-distributed electrons, Phys. Plasmas, 19, 012106.
Baluku, T. K., Hellberg, M. A. and Mace, R. L., 2011, Electron acoustic waves in double‐kappa plasmas: Application to Saturn's magnetosphere, J. Geophys. Res., 116, A04227.
Chen, F. F., 2016, Introduction to Plasma Physics and Controlled Fusion, 3rd ed., Springer.
Daniel, J. and Tajima, T., 1998, Outbursts from a black hole via alfvén wave to electromagnetic wave mode conversion, Astrophys. J., 498, 296.
Davidson, R.C., 1972, Methods in nonlinear plasma theory, Academic Press.
Dialynas, K., Roussos, E., Regoli, L., Paranicas, C.P., Krimigis, S.M., Kane, M., Mitchell, D.G., Hamilton, D.C., Krupp, N. and Carbary, J.F., 2018, Energetic Ion Moments and Polytropic Index in Saturn’s Magnetosphere using Cassini/MIMI Measurements: A Simple Model Based on κ‐Distribution Functions, J. Geophys. Res: Space Phys., 123, 8066.
Dubinov, A. E., 2009, On a Widespread Inaccuracy in Defining the Mach Number of Solitons in a Plasma, Plasma Phys. Rep., 35, 991.
El-Awady, E. I., El-Tantawy, S.A., Moslem, W.M., and Shukla, P.K., 2010, Electron–positron–ion plasma with kappa distribution: Ion acoustic soliton propagation, Phys. Letters A, 374, 3216 – 3219.
Feldman, W. C., Asbridge, J. R., Bame, S. J., Montgomery, M. D. and Gary, S. P., 1975, Solar wind electrons, J. Geophys. Res., 80, 4181.
Gibbons, G. W., Hawking, S. W. and Siklos, S., 1983, The Very Early Universe, Cambridge University Press, Cambridge, UK.
Goldreich, P. and Julian, W. H., 1969, Pulsar Electrodynamics, Astrophys. J., 157, 869.
Grandi, S. and Molendi, S., 2002, Temperature Profiles of Nearby Clusters of Galaxies, Astrophys. J., 567, 163.
Kim, S. H. and Merlino, R. 2007, Electron attachment to C7F14 and SF6 in a thermally ionized potassium plasma, Phys. Rev. E. 76, 035401(R).
Livadiotis, G., 2017, Kappa distributions: Theory and applications in Plasmas, Elsevier.
Livadiotis, G. and McComas, D. J., 2011, Invariant Kappa Distribution in Space Plasmas Out of Equilibrium, Astrophys. J., 741, 88.
Livadiotis, G., 2019, On the Origin of Polytropic Behavior in Space and Astrophysical Plasmas, Astrophys. J., 874, 10.
Maksimovic, M., Pierrard, V. and Riley, P., 1997, Ulysses electron distributions fitted with Kappa functions, Geophys. Res. Lett., 24, 1151.
Mamun, A. A., 1997, Effects of ion temperature on electrostatic solitary structures in nonthermal plasmas, Phys. Rev. E, 55, 1852-1857.
Mamun, A. and Shukla, P. K., 2002, The role of dust charge fluctuations on nonlinear dust ion-acoustic waves, IEEE Transactions on Plasma Science, 30, 720-724.
Max, C. and Perkins, F.W., 1972, Instability of a Relativistically Strong Electromagnetic Wave of Circular Polarization, Phys. Rev. Lett. 29, 1731.
Mendis, D. A. and Rosenberg, M., Analysis of Nonlinear Dust-Acoustic Shock Waves in an Unmagnetized Dusty Plasma with q-Nonextensive Electrons Where Dust Is Arbitrarily Charged Fluid, 1994, Anu. Rev. Astron. Astrophys, 32, 419.
Michael, M., Willington, N. T., Jayakumar, N., Sebastian, S., Sreekala, G. and Venugopal, C., 2016, J. Theor. Appl. Phys., 10, 289.
Miller, H. R. and Witta, P. J., 1987, Active galactic nuclei, Springer-Verlag, Berlin, Germany.
Mishra, K. and Chhabra, R. S., 1996, Ion‐acoustic compressive and rarefactive solitons in a warm multicomponent plasma with negative ions, Phys. Plasmas. 3, 4446.
Nasim, M. H., Mirza, A. M., Qaisar, M. S. and Murtaz, G., 1998, Energy loss of charged projectiles in dusty plasmas, Phys. Plasmas, 5, 3581.
Nicolaou, G., Livadiotis, G. and Moussas, X., 2014, Long-Term Variability of the Polytropic Index of Solar Wind Protons at 1 AU, Soalr Phys., 289, 1371.
Northrop, T. G., 1992, Dusty Plasmas, Physica Scripta, 45, 475.
Oohara, W. and Hatakeyama, R., 2003, Pair-Ion Plasma Generation using Fullerenes, Phys. Rev. Lett., 91, 205005.
Oohara, W., Date, D. and Hatakeyama, R., 2005, Electrostatic Waves in a Paired Fullerene-Ion Plasma, Phys. Rev. Lett. 95, 175003.
Orsoz, J. R., Remillard, R. A., Bailyn, C. D. and McClin-tock, J. E., 1997, An Optical Precursor to the Recent X-Ray Outburst of the Black Hole Binary GRO J1655-40, Astrophys. J., 478, L83
Pierrard, V. and Lazar, M., 2010, Kappa Distributions: Theory and Applications in Space Plasmas, Sol Phys., 267, 153-174.
Pilipp, W. G., Miggenrieder, H., Montgomery, M.D., Mühlhäuser, K.H., Rosenbauer, H. and Schwenn, R., 1987, Characteristics of electron velocity distribution functions in the solar wind derived from the Helios Plasma Experiment, J. Geophys. Res., 92, 1075.
Prasad, S. K., Raes, J. O., Van Doorsselaere, T., Magyar, N. and Jess, D. B., 2018, The Polytropic Index of Solar Coronal Plasma in Sunspot Fan Loops and Its Temperature Dependenc, Astrophys. J, 868, 149.
Rao, N. N., Shukla, P. K. and Yu, M. Y., 1990, dust-acoustic waves in dusty plasmas, Planetary and Space Science, 38, 543-546.
Saberian, E., Esfandyari-Kalejahi, A., Afsari-Ghazi, M. and Rastakar-Ebrahimzadeh, A., 2013, Propagation of ion-acoustic solitons in an electron beam-superthermal plasma system with finite ion-temperature: Linear and fully nonlinear investigation, Phys. Plasmas, 20, 032307.
Saberian, E., Esfandyari-Kalejahi, A. and Afsari-Ghazi, M, 2017, Nonlinear Dust-Acoustic Structures in Space Plasmas with Superthermal Electrons, Positrons and Ions, Plasma Phys. Rep., 43, 83-93.
Saberian, E., 2019a, The Generalized Ion-sound Speed in Space and Astrophysical Plasmas, Astrophys. J., 887, 121.
Saberian, E., 2019b, Ion-acoustic Solitons in Solar Winds Plasma Out of Thermal Equilibrium, J. Earth and Space Phys., 45, 235-246.
Saini, N. S., Kourakis, I. and Hellberg, M. A., 2009, Arbitrary amplitude ion-acoustic solitary excitations in the presence of excess superthermal electrons, Phys. Plasmas, 16, 062903.
Sauer, K., Dubinin, E., Baumgärte, K. and Tarasov, V., 1998, Low-frequency electromagnetic waves and instabilities within the Martian bi-ion plasma, Earth Planets and Space. 50, 269.
Shah, A. and Saeed, R., 2011, Nonlinear Korteweg–de Vries–Burger equation for ion-acoustic shock waves in the presence of kappa distributed electrons and positrons, Plasma Physics and Controlled Fusion, 53, 095006.
Shukla, P. K. and Marklund, M., 2004, Dust acoustic wave in a strongly magnetized pair-dust plasma, Physica Scripta, 36, T113.
Sultana, S., Kourakis, I., Saini, N. S. and Hellberg, M. A., 2010, Oblique electrostatic excitations in a magnetized plasma in the presence of excess superthermal electrons, Phys. Plasmas, 17, 032310.
Tajima, T. and Shibata, K., 1997, Plasma Astrophysics, Addison-Wesley.
Tandberg-Hansen, E. and Emslie, A. G., 1988, The physics of solar flares, Cambridge University Press, Cambridge, UK.
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, 2839-2884.
Verheest, F., Hellberg, M. A. and Lakhina, G. S., 2007, Necessary conditions for the generation of acoustic solitons in magnetospheric and space plasmas with hot ions, Astrophys. Space Sci. Transactions, 3, 15-20.
Wang, T., Ofman, L., Sun, X., Provornikova, E. and Davila, J. M., 2015, Evidence of thermal conduction suppression in a solar flaring loop by coronal seismology of slow-mode waves, Astrophys. J. Lett., 811, L13.
Wardle, J. F. C., Homan, D. C., Ojha, R. and Roberts, D. H., 1998, Electron–positron jets associated with the quasar 3C279, Nature 395, 457.
Whipple, E. C.,1981, Potentials of surfaces in space, Rep. Progr. Physics, 44, 1197.
Winterhalter, D., Kivelson, M. G., Walker, R. J. and Russell, C. T., 1984, The MHD Rankine-Hugoniot jump conditions and the terrestrial bow shock: A statistical comparison, Advances in Space Res., 4, 287.
Zouganelis, I., 2008, Measuring suprathermal electron parameters in space plasmas: Implementation of the quasi-thermal noise spectroscopy with kappa distributions using in situ Ulysses/URAP radio measurements in the solar wind, J. Geophys. Res., 113, A08111.
Journal of the Earth and Space Physics
Volume 46, Issue 2
July 2020
Pages 377-394

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