Abstract
The dust-acoustic shock waves have been theoretically investigated using reductive perturbation technique. An unmagnetized four-component dusty plasma system consisting of nonextensive q-distributed electrons, Boltzmann distributed ions, and negatively as well as positively charged dust particles has been considered. The solution of Burgers equation in planar geometry is numerically analyzed. It has been observed that the nonextensive q-distribution of electrons has a significant role in the formation of shock waves. The relevance of our results to astrophysics as well as laboratory plasmas are briefly discussed.
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References
Bains, A.S., Tribeche, M., Gill, T.S.: Phys. Plasmas 18, 022108 (2011)
Barkan, A., Merlino, R.L., D’Angelo, N.: Phys. Plasmas 2, 3563 (1995)
Bliokh, P.V., Yarashenko, V.V.: Sov. Astron. 29, 330 (1985)
Chatterjee, P., Kundu, S.K.: Indian J. Phys. 82, 4 (2008)
Chatterjee, P., Roy, K.: Z. Naturforsch. 63a, 393 (2008)
Chow, V.W., Mendis, D.A., Rosenberg, M.: J. Geophys. Res. 98, 19065 (1993)
D’Angelo, N.: J. Phys. D 37, 860 (2004)
Ellis, T.A., Neff, J.S.: Icarus 91, 280 (1991)
Eslami, P., Mottaghizadeh, M., Pakzad, H.R.: Astrophys. Space Sci. 333, 263 (2011)
Farokhi, B., Shukla, P.K., Tsindsadze, N.L., Tskhakaya, D.D.: Phys. Lett. A 264, 318 (1999)
Havnes, O., Trøim, J., Blix, T., Mortensen, W., Naecheim, L.I., Thrane, E., Tønnesen, T.: J. Geophys. Res. 101, 10839 (1996)
Horanyi, M.: Astron. Astrophys. Rev. 34, 383 (1996)
Horanyi, M., Morfill, G.E., Grun, E.: Nature 363, 144 (1993)
Kundu, S.K., Ghosh, D.K., Chatterjee, P., Das, B.: Bulg. J. Phys. 38, 409 (2011)
Mamun, A.A., Cairns, R.A., Shukla, P.K.: Phys. Plasmas 3, 702 (1996)
Mandal, G., Roy, K., Chatterjee, P.: Indian J. Phys. 83(3), 365 (2009)
Melandso, F.: Phys. Plasmas 3, 3890 (1996)
Mendis, D.A., Rosenberg, M.: Annu. Rev. Astron. Astrophys. 32, 419 (1994)
Merlino, R.L., Barken, A., Thompson, C., D’Angelo, N.: Phys. Plasmas 5, 1607 (1998)
Nakamura, Y.: Phys. Plasmas 9, 440 (2002)
Nakamura, Y., Bailung, H., Shukla, P.K.: Phys. Rev. Lett. 83, 1602 (1999)
Pakzad, H.R.: Astrophys. Space Sci. 331, 175 (2011a)
Pakzad, H.R.: Astrophys. Space Sci. 332, 269 (2011b)
Paul, A., Mandal, G., Mamun, A.A., Amin, M.R.: IEEE Trans. Plasma Sci. 39, 1254 (2011)
Rahmann, A., Mamun, A.A.: Chin. J. Phys. 46, 601 (2008)
Rao, N.N., Shukla, P.K., Yu, M.Y.: Planet. Space Sci. 38, 543 (1990)
Renyi, A.: Acta Math. Hung. 6, 285 (1995)
Rosenberg, M., Thomas, E., Merlino, R.L.: Phys. Plasmas 15, 073701 (2008)
Sahu, B.: Bulg. J. Phys. 38, 175 (2011a)
Sahu, B.: Phys. Plasmas 18, 082302 (2011b)
Sayed, F., Mamun, A.A.: Phys. Plasmas 14, 014501 (2007)
Shahmansouri, M., Tribeche, M.: Astrophys. Space Sci. 344, 99 (2013a)
Shahmansouri, M., Tribeche, M.: Astrophys. Space Sci. 346, 165 (2013b)
Shukla, P.K., Silin, V.P.: Phys. Scr. 45, 508 (1992)
Shukla, P.K., Verma, R.K.: Phys. Fluids B 5, 236 (1993)
Shukla, P.K., Yu, M.Y., Bharuthram, R.: J. Geophys. Res. 96, 21343 (1992)
Thomas, E. Jr., Fisher, R., Merlino, R.L.: Phys. Plasmas 14, 123701 (2007)
Tribeche, M., Merriche, A.: Phys. Plasmas 18, 034502 (2011)
Tribeche, M., Zerguini, T.H.: Phys. Plasmas 11, 4115 (2004)
Tribeche, M., Hamdi, R., Zerguini, T.H.: Phys. Plasmas 7, 4013 (2000)
Tsallis, C.: J. Stat. Phys. 52, 479 (1988)
Wang, Z.X., Liu, Y., Liu, J.Y., Wang, X.: Phys. Plasmas 12, 014505 (2005)
Williams, J.D., Thomas, E. Jr., Marcus, L.: Phys. Plasmas 15, 043704 (2008)
Acknowledgements
The authors are grateful to the referees for comments and constructive suggestions.
S.S. Kausik and C.S. Wong are being supported by University of Malaya Research Grants RG204-11AFR and RP008-13AFR to participate in this work.
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Roy, K., Chatterjee, P., Kausik, S.S. et al. Shock waves in a dusty plasma having q-nonextensive electron velocity distribution. Astrophys Space Sci 350, 599–605 (2014). https://doi.org/10.1007/s10509-014-1783-4
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DOI: https://doi.org/10.1007/s10509-014-1783-4