Abstract
A nonlinear propagation of modified ion-acoustic (mIA) shock waves in a relativistic degenerate plasma (containing inertial viscous positive and negative ion fluids, relativistic electron fluids, and negatively charged immobile heavy ions) has been investigated theoretically. The modified Burgers (mB) and further modified Burgers (FmB) equations have been derived by adopting reductive perturbation technique. The solutions of both mB and FmB equations have been numerically analyzed to characterize the basic features of mIA shock waves. The basic properties (speed, amplitude, width, etc.) of these electrostatic shock waves are found to be significantly modified by the effects of negatively charged static heavy ions and the plasma particle number densities. It is found that the properties of these shock waves obtained from this analysis are significantly different from those obtained from the analysis of standard Burgers equation. The implications of our results in space and interstellar compact objects like non-rotating white dwarfs, neutron stars, etc. are briefly discussed.
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References
Akhter, T., Hossain, M.M., Mamun, A.A.: Commun. Theor. Phys. 59, 745 (2013)
Ali, S., Shukla, P.K.: Eur. Phys. J. D 41, 319 (2007)
Bacal, M., Hamilton, G.W.: Phys. Rev. Lett. 42, 1538 (1979)
Bohm, D.: Phys. Rev. 92, 626 (1953)
Bohm, D., Pines, D.: Phys. Rev. 92, 609 (1953)
Brodin, G., Marklund, M.: New J. Phys. 9, 227 (2007)
Chaizy, P.H., Reme, H., Sauvaud, J.A., D’Uston, C., Lin, R.P., Larson, D.E., Mitchell, D.L., Anderson, K.A., Carlson, C.W., Korth, A., Mendis, D.A.: Nature 349, 393 (1991)
Chandrasekhar, S.: Philos. Mag. 11, 592 (1931a)
Chandrasekhar, S.: Astrophys. J. 74, 81 (1931b)
Chandrasekhar, S.: Mon. Not. R. Astron. Soc. 170, 405 (1935)
Chatterjee, P., Ghosh, D.K., Sahu, B.: Astrophys. Space Sci. 339, 261 (2012)
Crouseilles, N., Hervieux, P.A., Manfredi, G.: Phys. Rev. B 78, 155412 (2008)
El-Taibany, W.F., Mamun, A.A.: Phys. Rev. E 85, 026406 (2012)
El-Taibanya, W.F., Wadatib, M.: Phys. Plasmas 14, 042302 (2007)
Gardner, C.L.: J. Appl. Math. 54, 409 (1994)
Gervino, G., Lavagno, A., Pigato, D.: Cent. Eur. J. Phys. 10, 594 (2012)
Glenzer, S.H., Redmer, R.: Rev. Mod. Phys. 81, 1625 (2009)
Glenzer, S.H., Landen, O.L., Neumayer, P., Lee, R.W., Widmann, K., Pollaine, S.W., Wallace, R.J., Gregori, G., Holl, A., Bornath, T., Thiele, R., Schwarz, V., Kraeft, W.D., Redmer, R.: Phys. Rev. Lett. 98, 065002 (2007)
Gottscho, R.A., Gaebe, C.E.: IEEE Trans. Plasma Sci. 14, 92 (1986)
Harding, A.K., Lai, D.: Rep. Prog. Phys. 69, 2631 (2006)
Hasan, M., Hossain, M.M., Mamun, A.A.: Astrophys. Space Sci. 345, 113 (2013)
Hossen, M.R.: Nonlinear Excitations in Degenerate Quantum Plasmas. Lap-Lambert Academic Publishing, Germany (1939). ISBN-10: 3659597392
Hossen, M.R., Mamun, A.A.: J. Korean Phys. Soc. 65, 2045 (2014a)
Hossen, M.R., Mamun, A.A.: Braz. J. Phys. 44, 673 (2014b)
Hossen, M.R., Ema, S.A., Mamun, A.A.: Braz. J. Phys. 62, 888 (2014a)
Hossen, M.A., Hossen, M.R., Mamun, A.A.: J. Korean Phys. Soc. 65, 1883 (2014b)
Hossen, M.A., Hossen, M.R., Nahar, L., Mamun, A.A.: Braz. J. Phys. 44, 703 (2014c)
Hossen, M.R., Nahar, L., Mamun, A.A.: Phys. Scr. 89, 105603 (2014d)
Hossen, M.R., Nahar, L., Mamun, A.A.: J. Astrophys. 2014, 653065 (2014e)
Hossen, M.R., Nahar, L., Mamun, A.A.: J. Korean Phys. Soc. 65, 1863 (2014f)
Hossen, M.R., Nahar, L., Mamun, A.A.: Braz. J. Phys. 44, 638 (2014g)
Hossen, M.R., Nahar, L., Sultana, S., Mamun, A.A.: Astrophys. Space Sci. 353, 123 (2014h)
Hossen, M.R., Nahar, L., Sultana, S., Mamun, A.A.: High Energy Density Phys. 13, 13 (2014i)
Hultqvist, B., Ieroset, M., Paschmann, G., Treumann, R.: Magnetospheric Plasma Sources and Losses. Kluwer Academic, Dordrecht (1999)
Jacquinot, J., McVey, B.D., Scharer, J.E.: Phys. Rev. Lett. 39, 88 (1977)
Klimontovich, Y.L., Silin, V.P.: Dokl. Akad. Nauk 82, 36 (1952)
Lee, H.: J. Korean Phys. Soc. 43, 6 (2003)
Mamun, A.A., Shukla, P.K.: Phys. Lett. A 324, 4238 (2010a)
Mamun, A.A., Shukla, P.K.: Phys. Plasmas 17, 104504 (2010b)
Mamun, A.A., Zobaer, M.S.: Phys. Plasmas 21, 022101 (2014)
Mamun, A.A., Cairns, R.A., Shukla, P.K.: Phys. Lett. A 373, 2355 (2009)
Mandal, P.K., Ghorui, M.K., Saha, A., Chatterjee, P.: Astrophys. Space Sci. (2014). doi:10.1007/s10509-014-2144-z
Manfredi, G.: Fields Inst. Commun. 46, 263 (2005)
Manfredi, G., Haas, F.: Phys. Rev. B 64, 075316 (2001)
Mannan, A., Mamun, A.A.: Astrophys. Space Sci. 340, 109 (2012)
Marklund, M., Brodin, G.: Phys. Rev. Lett. 98, 025001 (2007)
Markovich, P.A., Ringhofer, C.A., Schmeiser, C.: Semiconductor Equations. Springer, Vienna (1990)
Masood, W., Eliasson, B.: Phys. Plasmas 18, 034503 (2011)
Massey, H.: Negative Ions. Cambridge University Press, Cambridge (1976)
Mendis, D.A., Rosenberg, M.: Annu. Rev. Astron. Astrophys. 32, 419 (1994)
Mendonça, J.T., Serbeto, A.: Phys. Rev. E 83, 026406 (2011)
Moslem, W.M., Shukla, P.K., Ali, S., Schlickeiser, R.: Phys. Plasmas 14, 042107 (2007)
Plastino, A.R., Plastino, A.: Phys. Lett. A 174, 384 (1993)
Roy, N., Tasnim, S., Mamun, A.A.: Phys. Plasmas 19, 033705 (2012)
Saha, A., Chatterjee, P.: Astrophys. Space Sci. 350, 631 (2014a)
Saha, A., Chatterjee, P.: J. Plasma Phys. 80, 553 (2014b)
Saha, A., Pal, N., Chatterjee, P.: Phys. Plasmas 21, 102101 (2014)
Samanta, U.K., Saha, A., Pal, N., Chatterjee, P.: Phys. Plasmas 20, 052111 (2013)
Serbeto, A., Mendonça, J.T., Tsui, K.H., Bonifacio, R.: Phys. Plasmas 15, 013110 (2008)
Shapiro, S.L., Teukolsky, S.A.: Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects. Wiley, New York (1983)
Shemansky, D.E., Hall, D.T.: J. Geophys. Res. 97, 4143 (1992)
Shukla, P.K.: Nature 75, 056318 (2007)
Shukla, P.K.: Nat. Phys. 5, 92 (2009)
Shukla, P.K., Eliasson, B.: Phys. Rev. Lett. 96, 245001 (2006)
Shukla, P.K., Eliasson, B.: Phys. Usp. 53, 51 (2010)
Stasiewics, K.: Phys. Rev. Lett. 12, 125004 (2004)
Stockman, M.I.: Phys. Today 64, 39 (2011)
Tasnim, S., Islam, S., Mamun, A.A.: Phys. Plasmas 19, 033706 (2012)
Yasmin, S., Asaduzzaman, M., Mamun, A.A.: J. Plasma Phys. 79, 545 (2013)
Zel’dovich, Ya.B., Raizer, Yu.P.: Physics of Shock Waves and High Temperature Hydrodynamic Phenomena. Academic, New York (1967)
Zobaer, M.S., Roy, N., Mamun, A.A.: J. Mod. Phys. 3, 755 (2012)
Zobaer, M.S., Roy, N., Mamun, A.A.: Astrophys. Space Sci. 343, 675 (2013)
Acknowledgement
One of the authors (M.R. Hossen) gratefully acknowledge “National Science and Technology, Bangladesh” for an M.S. research fellowship.
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Hossen, M.R., Hossen, M.A., Sultana, S. et al. Modeling of modified ion-acoustic shock waves in a relativistic electron degenerate multi-ion plasma for higher order nonlinearity. Astrophys Space Sci 357, 34 (2015). https://doi.org/10.1007/s10509-015-2278-7
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DOI: https://doi.org/10.1007/s10509-015-2278-7