Abstract
The nonlinear propagation of ion acoustic shock waves (IASWs) are studied in an unmagnetized plasma consisting of nonthermal electrons, nonthermal positrons, and singly charged adiabatically hot positive ions, whose dynamics is governed by the two dimensional nonplanar Kadomstev-Petviashvili-Burgers (KPB) equation. The shock solution of the KPB equations is obtained numerically. The effects of several parameters and ion kinematic viscosities on the properties of ion acoustic shock waves are discussed in planar and nonplanar geometry. It is shown that the ion acoustic shock wave propagating in cylindrical/spherical geometry with transverse perturbation will be deformed as time goes on. Also, it is seen that the strength and the steepness of the IASWs increases with increasing β, the nonthermal parameter.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ablowitz, M.J., Clarkson, P.A.: Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, Cambridge (1991)
Akbari-Moghanjoughi, M.: Phys. Plasmas 17, 082315 (2010)
Akhtar, N., Hussain, S.: Phys. Plasmas 18, 072103 (2011)
Ali, S., Shukla, P.K.: Phys. Plasmas 13, 022313 (2006)
Ali, S., Moslem, W.M., Shukla, P.K., Schlickeiser, R.: Phys. Plasmas 14, 082307 (2007)
Alinejad, H.: Astrophys. Space Sci. 327, 131 (2010)
Andersen, H.K., D’Angelo, N., Michelsen, P., Nielsen, P.: Phys. Rev. Lett. 19, 149 (1967)
Asbridge, J.R., Bame, S.J., Strong, I.B.: J. Geophys. Res. 73, 5777 (1968)
Begelman, M.C., Blandford, R.D., Rees, M.J.: Rev. Mod. Phys. 56, 255 (1984)
Berezhiani, V.I., Tskhakaya, D.D., Shukla, P.K.: Phys. Rev. A 46, 6608 (1992)
Boström, R.: IEEE Trans. Plasma Sci. 20, 756 (1992)
Burns, M.L.: In: Burns, M.L., Harding, A.K., Ramaty, R. (eds.) Positron-Electron Pairs of Astrophysics. American Institute of Physics, Melville (1983)
Cairns, R.A., Mamun, A.A., Bingham, R., Boström, R., Dendy, R.O., Nairn, C.M.C., Shukla, P.K.: Geophys. Res. Lett. 22, 2709 (1995)
Das, A., Bandyopadahyay, A., Das, K.P.: Phys. Plasmas 16, 073703 (2009)
Doumaz, D.B., Djebli, M.: Phys. Plasmas 17, 074501 (2010)
Dovner, P.O., Eriksson, A.I., Bostrom, R., Holback, B.: Geophys. Res. Lett. 21, 1827 (1994)
El-Awady, E.I., El-Tantawy, S.A., Moslem, W.M., Shukla, P.K.: Phys. Lett. A 374, 3216 (2010)
Feldman, W.C., Anderson, R.C., Bame, S.J., Gary, S.P., Gosling, J.T., McComas, D.J., Thomsen, M.F., Paschmann, G., Hoppe, M.M.: J. Geophys. Res. 88, 96 (1983)
Gill, R.G.: Nucl. Fusion 33, 1613 (1993)
Greaves, R.G., Tinkle, M.D., Surko, C.M.: Phys. Plasmas 1, 1439 (1994)
Greaves, R.G., Surko, C.M.: Phys. Rev. Lett. 75, 3846 (1995)
Noaman-ul-Haq, M., Saeed, R., Shah, A.: Appl. Phys. 108, 043301 (2010)
Helander, P., Ward, D.J.: Phys. Rev. Lett. 90, 135004 (2003)
Hirota, R.: Phys. Rev. Lett. 27, 1192 (1971)
Jehan, N., Mirza, A.M., Salahuddin, M.: Phys. Plasmas 18, 052307 (2011)
Jukui, X., He, L.: Phys. Plasmas 10, 339 (2003)
Liang, E.P., Wilks, S.C., Tabak, M.: Phys. Rev. Lett. 81, 4887 (1998)
Mahmood, S., Akhtar, N.: Euro. Phys. J. D 49, 217 (2008)
Malfliet, W.: Am. J. Phys. 60, 650 (1992)
Malfliet, W.: J. Comput. Appl. Math. 164, 529 (2004)
Mamun, A.A.: Phys. Review E 55, 1852 (1997)
Mamun, A.A., Shukla, P.K.: Phys. Lett. A 290, 173 (2001)
Mamun, A.A., Cairns, R.A., Shukla, P.K.: Phys. Plasmas 3, 2610 (1996)
Masood, W., Rizvi, H.: Phys. Plasmas 17, 052314 (2010)
Michel, F.C.: Rev. Mod. Phys. 54, 1 (1982)
Michel, F.C.: Theory of Neutron Star Magnetosphere. Chicago University Press, Chicago (1991)
Mille, H.R., Witta, P.: Active Galactic Nuclei, p. 202. Springer, Berlin (1987)
Misner, W., Thorne, K., Wheeler, J.A.: Gravitation, p. 763. Freeman, San Francisco (1973)
Miura, M.R.: Backlund Transformation. Springer, Berlin (1978)
Moslem, W.M., Sabry, R., Shukla, P.K.: Phys. Plasmas 17, 032305 (2010a)
Moslem, W.M., Abdelsalam, U.M., Sabry, R., El-Shamy, E.F., El-Labany, S.K.: J. Plasma Phys. 76, 453 (2010b)
Mushtaq, A., Shah, H.A.: Phys. Plasmas 12, 072306 (2005)
Nejoh, Y.N.: Phys. Plasmas 3, 1447 (1996)
Pakzad, H.R.: Phys. Lett. A 373, 847 (2009)
Pakzad, H.R.: Astrophys. Space Sci. 331, 169 (2011)
Piran, T.: Phys. Rep. 314, 575 (1999)
Popel, S.I., Vladimirov, S.V., Shukla, P.K.: Phys. Plasmas 2, 716 (1995)
Rees, M.J.: Nature 229, 312 (1971)
Rees, M.J.: In: Gibbsons, G.W., Hawking, S.W., Siklas, S. (eds.) The Very Early Universe. Cambridge University Press, Cambridge (1983)
Saeed, R., Shah, A.: Phys. Plasmas 17, 032308 (2010)
Salahuddin, M., Saleem, H., Siddiq, M.: Phys. Rev. E 66, 0346407 (2002)
Sabry, R., Moslem, W.M., Shukla, P.K.: Eur. Phys. J. D 51, 233 (2009)
Shah, A., Saeed, R., Noaman-ul-Haq, M.: Phys. Plasmas 17, 072307 (2010)
Shukla, P.K., Mamun, A.A.: Introduction to Dusty Plasma Physics. IoP, Bristol (2002)
Shukla, P.K., Mendonca, J.T., Bingham, R.: Phys. Scr. T 113, 133 (2004)
Surko, C.M., Lemvethal, M., Crane, W.S., Passner, A., Wyocki, F.J., Murphy, T.J., Strachan, J., Rowan, W.L.: Rev. Sci. Instrum. 57, 1862 (1986)
Tandberg-Hansen, E., Emshie, A.G.: The Physics of Solar Flares, p. 124. Cambridge University Press, Cambridge (1988)
Tang, R., Xue, J.-K.: Phys. Plasmas 11, 3939 (2004)
Tinkle, M.D., Greaves, R.G., Surko, C.M., Spencer, R.L., Mason, G.W.: Phys. Rev. Lett. 72, 352 (1994)
Verheest, F., Hellberg, M.A., Gary, G.J., Mace, R.L.: Astrophys. Space Sci. 239, 125 (1995)
Verheest, F.: Waves in Dusty Space Plasmas. Kluwer Academic, Dordrecht (2000)
Verheest, F.: Phys. Plasmas 16, 013704 (2009)
Verheest, F., Pillay, S.R.: Phys. Plasmas 15, 013703 (2008)
Washimi, H., Taniuti, T.: Phys. Rev. Lett. 17, 996 (1966)
Xue, J.-K.: Phys. Lett. A 314, 479 (2003a)
Xue, J.-K.: Phys. Plasmas 10, 3430 (2003b)
Xue, J.-K.: Phys. Plasmas 12, 012314 (2005)
Yoshino, R., Tokuda, S., Kawano, Y.: Nucl. Fusion 39, 151 (1999)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chatterjee, P., Ghosh, D.K. & Sahu, B. Planar and nonplanar ion acoustic shock waves with nonthermal electrons and positrons. Astrophys Space Sci 339, 261–267 (2012). https://doi.org/10.1007/s10509-012-1011-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-012-1011-z