Abstract
The basic properties of nonplanar (viz. cylindrical and spherical) dust-ion-acoustic (DIA) shock waves in an unmagnetized dusty plasma system [consisting of inertial ions, negatively charged immobile dust, and superthermal electrons with two distinct temperatures] are investigated by employing the reductive perturbation method. The modified Burgers equation is derived and is numerically analyzed in order to examine the basic properties of DIA shock structures. The effects of nonplanar geometry, electron superthermality, and ion kinematic viscosity on the basic features of DIA shock waves are discussed. It is found that the properties of the cylindrical and spherical DIA shock waves in dusty plasmas with two-temperature superthermal electrons significantly differ from those of one-dimensional planar shocks. The implications of our results in space plasmas [viz. star formation, supernovae explosion, solar wind, pulsar magnetosphere, Saturn’s outer magnetosphere (R ∼13−18 R S , where R S is the radius of Saturn), Saturn’s inner magnetosphere (R <9 R S , etc.)] and laboratory plasmas (viz. laser-induced implosion, capsule implosion, shock tube, etc.), where superthermal electrons with two distinct temperatures occurs, are briefly discussed.
Similar content being viewed by others
References
N. D’Angelo, Planet. Space Sci. 38, 1143 (1990)
P.K. Shukla, V.P. Silin, Phys. Scr. 45, 508 (1992)
A. Barkan, N. D’Angelo, R.L. Merlino, Planet. Space Sci. 44, 239 (1996)
Y. Nakamura, H. Bailung, P.K. Shukla, Phys. Rev. Lett. 83, 1602 (1999)
M.M. Rahman, M.S. Alam, A.A. Mamun, J. Korean Phys. Soc. 64, 1828 (2014)
Y. Nakamura, Phys. Plasmas. 9, 440 (2002)
Q.Z. Luo, N. D’Angelo, R.L. Merlino, Phys. Plasmas. 7, 3457 (1999)
A.A. Mamun, P.K. Shukla, IEEE Trans. Plasma Sci. 30, 720 (2002)
B. Eliasson, P.K. Shukla, Phys. Plasmas. 12, 024502 (2005)
S. Sultana, G. Sarri, I. Kourakis, Phys. Plasmas. 19, 012310 (2012)
H. Abbasi, H.H. Pajouth, Phys. Plasmas. 12, 024502 (2005)
N.S. Saini, I. Kourakis, M.A. Hellberg, Phys. Plasmas. 16, 062903 (2009)
V.M. Vasyliunas, J. Geophys. Res. 73, 2839 (1968)
M.P. Leubner, J. Geophys. Res. 87, 6335 (1982)
D. Summers, R.M. Thorne, Phys. Fluids B. 3, 1835 (1991)
R.L. Mace, M.A. Hellberg, Phys. Plasmas. 2, 2098 (1995)
T.K. Baluku, M.A. Hellberg, Phys. Plasmas. 15, 123705 (2008)
M.A. Hellberg, R.L. Mace, T.K. Baluku, I. Kourakis, N.S. Saini, Phys. Plasmas. 16, 094701 (2009)
T.K. Baluku, M.A. Hellberg, I. Kourakis, N.S. Saini, Phys. Plasmas. 17, 053702 (2010)
T.K. Baluku, M.A. Hellberg, Phys. Plasmas. 19, 012106 (2012)
M.S. Alam, M.J. Uddin, M.M. Masud, A.A. Mamun, Chaos. 24, 033130 (2014)
H. Alinejad, M. Tribeche, M.A. Mohammadi, Phys. Lett. A. 375, 4183 (2011)
M. Shahmansouri, H. Alinejad, Astrophys. Space Sci. 343, 257 (2013)
M.S. Alam, M.M. Masud, A.A. Mamun, Chin. Phys. B. 22, 115202 (2013)
P. Schippers, M. Blanc, N. André, I. Dandouras, G.R. Lewis, L.K. Gilbert, A.M. Persoon, N. Krupp, D.A. Gurnett, A.J. Coates, S.M. Krimigis, D.T. Young, M.K. Dougherty, J. Geophys. Res. 113, A07208 (2008)
T.K. Baluku, M.A. Hellberg, R.L. Mace, J. Geophys. Res. 116, A04227 (2011)
M.S. Alam, M.M. Masud, A.A. Mamun, Plasma Phys. Rep. 39, 1011 (2013)
M.S. Alam. Dust-ion-acoustic waves in dusty plasmas with superthermal electrons (LAP LAMBERT Academic Publishing, Germany, 2013). ISBN-10: 3659509523
M. Shahmansouri, B. Shahmansouri, D. Darabi, Indian J. Phys. 87, 711 (2013)
M.S. Alam, M.M. Masud, A.A. Mamun, Astrophys. Space Sci. 349, 245 (2014)
S. Sultana, A.A. Mamun, Astrophys. Space Sci. 349, 229 (2014)
S. Sultana, S. Islam, A.A. Mamun, Astrophys. Space Sci. 351, 581 (2014)
M.M. Rahman, M.S. Alam, A.A. Mamun, Astrophys. Space Sci. 352, 193 (2014)
J.-K. Xue, Phys. Plasmas. 10, 4893 (2003)
A.A. Mamun, P.K. Shukla, Euro. Phys. Lett. 87, 25001 (2009)
B. Sahu, M. Tribeche, Phys. Plasmas. 19, 022304 (2012)
S. Yasmin, M. Asaduzzaman, A.A. Mamun, J. Plasma Phys. 79, 545 (2013)
D.K. Ghosh, P. Chatterjee, P.K. Mandal, B. Sahu, Pramana. 81, 491 (2013)
A.A. Mamun, R.A. Cairns, Phys. Rev. E. 79, 055401 (2009)
P.K. Shukla, A.A. Mamun, Introduction to Dusty Plasma Physics. CRC Press (2010)
S.K. Kundu, D.K. Ghosh, P. Chatterjee, B. Das, Bulg. J. Phys. 38, 409 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Alam, M.S., Masud, M.M. & Mamun, A.A. Ion-Scale Electrostatic Nonplanar Shock Waves in Dusty Plasmas with Two-Temperature Superthermal Electrons. Braz J Phys 45, 95–101 (2015). https://doi.org/10.1007/s13538-014-0286-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13538-014-0286-7