Abstract
A study is made of the propagation of ion acoustic waves in a collisionless unmagnetized dusty plasma containing degenerate ion and electron gases at nonzero temperatures. In linear theory, a dispersion relation for isothermal ion acoustic waves is derived and an exact expression for the linear ion acoustic velocity is obtained. The dependence of the linear ion acoustic velocity on the dust density in a plasma is calculated. An analysis of the dispersion relation reveals parameter ranges in which the problem has soliton solutions. In nonlinear theory, an exact solution to the basic equations is found and examined. The analysis is carried out by Bernoulli’s pseudopotential method. The ranges of the phase velocities of periodic ion acoustic waves and the velocities of solitons are determined. It is shown that these ranges do not overlap and that the soliton velocity cannot be lower than the linear ion acoustic velocity. The profiles of the physical quantities in a periodic wave and in a soliton are evaluated, as well as the dependence of the critical velocity of solitons on the dust density in a plasma.
Similar content being viewed by others
References
P. K. Shukla and S. Ali, Phys. Plasmas 12, 114502 (2005).
S. Ali and P. K. Shukla, Phys. Plasmas 13, 022313 (2006).
W. M. Moslem, P. K. Shukla, S. Ali, and R. Schlickeiser, Phys. Plasmas 14, 042107 (2007).
W. F. El-Taibany and M. Wadati, Phys. Plasmas 14, 042302 (2007).
A. Mushtaq, Phys. Plasmas 14, 113701 (2007).
S. Ali, W. M. Moslem, I. Kourakis, and P. K. Shukla, New J. Phys. 10, 023007 (2008).
S. A. Khan, W. Masood, and M. Siddiq, Phys. Plasmas 16, 013701 (2009).
M. Sadiq, S. Ali, and R. Sabry, Phys. Plasmas 16, 013706 (2009).
B. Sahu and R. Roychoudhury, Phys. Plasmas 14, 012304 (2007).
S. A. Khan and A. Mushtaq, Phys. Plasmas 14, 083703 (2007).
W. Masood, A. Mushtaq, and S. A. Khan, Phys. Plasmas 14, 123702 (2007).
A. P. Misra, S. Samanta, and A. R. Chowdhury, J. Plasma Phys. 74, 197 (2007).
S. Mahmood, Phys. Plasmas 15, 014502 (2008).
M. Tribeche, S. Ghebache, K. Aoutou, and T. H. Zerguini, Phys. Plasmas 15, 033702 (2008).
H. Ur-Rehman, S. A. Khan, W. Masood, and M. Siddiq, Phys. Plasmas 15, 124501 (2008).
S. A. Khan, S. Mahmood, and A. M. Mirza, Phys. Lett. A 372, 148 (2008).
Y.-Y. Wang and J.-F. Zhang, Phys. Lett. A 372, 6509 (2008).
W. Masood, M. Siddiq, Sh. Nargis, and A. M. Mirza, Phys. Plasmas 16, 013705 (2009).
M. Salimullah, I. Zeba, Ch. Uzma, et al., Phys. Lett. A 372, 2291 (2008).
P. K. Shukla, J. Plasma Phys. 74, 107 (2007).
S. Ali and P. K. Shukla, Eur. Phys. J. D 41, 319 (2007).
P. K. Shukla and L. Stenflo, Phys. Lett. A 355, 378 (2006).
W. Masood, M. Salimullah, and H. A. Shah, Phys. Lett. A 372, 6757 (2008).
Sh. Bagchi, K. R. Chowdhury, A. P. Mishra, and A. R. Chowdhury, Int. J. Theor. Phys. 48, 1132 (2009).
M. Salimullah, M. Jamil, H. A. Shah, and G. Murtaza, Phys. Plasmas 16, 014502 (2009).
L. Stenflo, P. K. Shukla, and M. Marklund, Europhys. Lett. 74, 844 (2006).
P. K. Shukla, Phys. Lett. A 352, 242 (2006).
A. P. Misra and C. Bhowmik, Phys. Plasmas 16, 012103 (2009).
S. Ali and P. K. Shukla, Phys. Plasmas 13, 102112 (2006).
S. Ali and P. K. Shukla, Phys. Lett. A 372, 4827 (2008).
M. V. Kuzelev and A. A. Rukhadze, Usp. Fiz. Nauk 169, 687 (1999) [Phys. Usp. 42, 603 (1999)].
G. Manfredi and F. Haas, Phys. Rev. B 64, 075316 (2001).
A. E. Dubinov, Prikl. Mekh. Tekh. Fiz. 48, 3 (2007).
A. E. Dubinov and A. A. Dubinova, Fiz. Plazmy 33, 935 (2007) [Plasma Phys. Rep. 33, 859 (2007)].
A. E. Dubinov, Fiz. Plazmy 33, 239 (2007) [Plasma Phys. Rep. 33, 210 (2007)].
A. E. Dubinov and M. A. Sazonkin, Zh. Tekh. Fiz. 78(9), 29 (2008) [Tech. Phys. 53, 1129 (2008)].
A. E. Dubinov and M. A. Sazonkin, Fiz. Plazmy 35, 18 (2009) [Plasma Phys. Rep. 35, 14 (2009)].
B. M. Mladek, G. Kahl, and M. Neumann, J. Chem. Phys. 124, 064503 (2006).
A. E. Dubinov and A. A. Dubinova, Fiz. Plazmy 34, 442 (2008) [Plasma Phys. Rep. 34, 403 (2008)].
F. Haas and M. Lazar, Phys. Rev. E 77, 046404 (2008).
B. Eliasson and P. K. Shukla, Phys. Scr. 78, 025503 (2008).
A. E. Dubinov, A. A. Dubinova, and M. A. Sazonkin, Radiotekh. Élektron. 55, 968 (2010) [J. Comm. Technol. Electron. 55, 907 (2010)].
G. N. Pykhteev and I. N. Meleshko, Properties and Calculation of Polylogarithms (Izd. BGU, Minsk, 1976) [in Russian].
A. A. Dubinova, Zh. Tekh. Fiz. 79(2), 48 (2009) [Tech. Phys. 54, 210 (2009)].
V. F. Zaitsev and A. D. Polyanin, Handbook of Ordinary Differential Equations (Nauka, Moscow, 2001) [in Russian].
Author information
Authors and Affiliations
Additional information
Original Russian Text © A.E. Dubinov, D.Yu. Kolotkov, M.A. Sazonkin, 2011, published in Fizika Plazmy, 2011, Vol. 37, No. 1, pp. 68–78.
Rights and permissions
About this article
Cite this article
Dubinov, A.E., Kolotkov, D.Y. & Sazonkin, M.A. Nonlinear ion acoustic waves in a quantum degenerate warm plasma with dust grains. Plasma Phys. Rep. 37, 64–74 (2011). https://doi.org/10.1134/S1063780X10121037
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063780X10121037