Time-Dependent Nonplanar Dust-Ion-Acoustic Gardner Double Layers

Farah Deeba, A. A. Mamun

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DOI: 10.4236/oja.2011.13009                

Abstract

A theoretical investigation has been made on the nonplanar (cylindrical and spherical) dust-ion-acoustic (DIA) double layers (DLs) in a dusty plasma system, containing inertial ions, Boltzmann electrons, and negatively charged stationary dust. In this investigation, in order to analyze the time dependent nonplanar DIA DLs, we have used the modified Gardner equation, which has been obtained by employing the reductive perturbation method. It has been found that the behaviors of DIA DLs have been significantly modified by the time period and the nonplanar geometry. The nonplanar DIA DLs has been found to be similar with planar DIA DLs only at large time scale and the cylindrical DIA DLs have been found to be smaller than the spherical DLs, but larger than the planar DLs.

Keywords

Dust-Ion-Acoustic, Double Layers, Nonplanar

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	P. K. Shukla and V. P. Silin, “Dust Ion-Acoustic Wave,” Physica Scripta, Vol. 45, No. 5, 1992, p. 508. doi:10.1088/0031-8949/45/5/015
[2]	A. Barkan, N. D'Angelo and R. L. Merlino, “Experiments on Ion-Acustic Waves in Dusty Plasmas,” Planetary and Space Science, Vol. 44, No. 1, 1996, pp. 239-242. doi:10.1016/0032-0633(95)00109-3
[3]	P. K. Shukla and M. Rosenberg, “Boundary Effects on Dust-Ion-Acoustic and Dust-Acoustic Waves in Collisio- nal Dusty Plasmas,” Physics of Plasmas, Vol. 6, No. 3, 1999, pp. 1038-1040. doi:10.1063/1.873345
[4]	P. K. Shukla and A. A. Mamun, “Introduction to Dusty Plasma Physics,” Institute of Physics Publishing Ltd., Bris- tol, 2002. doi:10.1887/075030653X
[5]	R. L. Merlino and J. Goree, “Dusty plasmas in the labo- ratory, Industry, and Space,” Physics Today, Vol. 57, No. 7, 2004, pp. 32-39. doi:10.1063/1.1784300
[6]	V. E. Fortov, et al., “Complex (Dusty) Plasmas: Current Status, Open Issues, Perspectives,” Physics Report, Vol. 421, No. 1-2, 2005, pp. 1-103. doi:10.1016/j.physrep.2005.08.007
[7]	O. Ishihara, “Complex Plasma: Dusts in plasma,” Journal of Physics D, Vol. 40, No. 8, 2007, p. R121. doi:10.1088/0022-3727/40/8/R01
[8]	P. K. Shukla and B. Eliasson, “Colloquium: Fundamentals of Dust-Plasma Interactions,” Reviews of Modern Physics, Vol. 81, No. 1, 2009, pp. 25-44. doi:10.1103/RevModPhys.81.25
[9]	G. E. Morfill and A. V. Ivlev, “Complex plasmas: An In- terdisciplinary Research Field,” Reviews of Modern Phy- sics, Vol. 81, No. 4, 2009, pp. 1353-1404. doi:10.1103/RevModPhys.81.1353
[10]	K. E. Lonngren, “Soliton Experiments in Plasmas,” Plas- ma Physics, Vol. 25, No. 9, 1983, p. 943. doi:10.1088/0032-1028/25/9/001
[11]	Y. Nakamura and A. Sharma, “Observation of Ion-Acoustic Solitary Waves in a Dusty Plasma,” Physics of Plasmas, Vol. 8, No. 9, 2001, pp. 3921-3926. doi:10.1063/1.1387472
[12]	Y. Nakamura, H. Bailung and P. K. Shukla, “Observation of Ion-Acoustic Shocks in a Dusty Plasma,” Physical Reviews Letters, Vol. 83, No. 8, 1999, pp. 1602-1605. doi:10.1103/PhysRevLett.83.1602
[13]	Q. Z. Luo, N. D'Angelo and R. L. Merlino, “Experimental Study of Shock Formation in a Dusty Plasma,” Physics of Plasmas, Vol. 6, No. 9, 1999, pp. 3455-3458. doi:10.1063/1.873605
[14]	C. Charles, “A Review of Recent Laboratory Double La- yer Experiments,” Plasma Sources Science and Technology, Vol. 16, No. 4, 2007, pp. R1-R25. doi:10.1088/0963-0252/16/4/R01
[15]	R. Bharuthram and P. K. Shukla, “Large Amplitude Ion- Acoustic Solitons in a Dusty Plasma,” Planetary and Space Science, Vol. 40, No. 7, 1992, pp. 973-977. doi:10.1016/0032-0633(92)90137-D
[16]	S. I. Popel and M. Y. Yu, “Ion Acoustic Solitons in Impu- rity-Containing Plasmas,” Contributions to Plasma Physics, Vol. 35, No. 2, 1995, pp. 103-108. doi:10.1002/ctpp.2150350202
[17]	A. A. Mamun and P. K. Shukla, “Cylindrical and Spheri- cal Dust Ionacoustic Solitary Waves,” Physics of Plasmas, Vol. 9, No. 4, 1997, pp. 1468-1470.
[18]	P. K. Shukla and A. A. Mamun, “Solitons, Shocks and Vor- tices in Dusty Plasmas,” New Journal of Physics, Vol. 5, 2003, pp. 17.1-17.37.
[19]	S. I. Popel, et al., “Weakly Dissipative Dust-Ion-Acoustic Solitons,” Physical Review E, Vol. 67, No. 5, 2003, p. 056402(5). doi:10.1103/PhysRevE.67.056402
[20]	P. K. Shukla, “Dust Ion-Acoustic Shocks and Holes,” Physics of Plasmas, Vol. 7, No. 3, 2000, pp. 1044-1046. doi:10.1063/1.873905
[21]	S. I. Popel, A. P. Golub and T. V. Losseva, “Dust Ion- Acoustic Shock-Wave Structures: Theory and Laboratory Experiments,” JETP Lettrers, Vol. 74, No. 7, 2001, pp. 362-366. doi:10.1134/1.1427122
[22]	A. A. Mamun and P. K. Shukla, “The Role of dust Charge Fluctuations on Nonlinear Dust Ion-Acoustic Waves,” IEEE Transactions on Plasma Science, Vol. 30, No. 2, 2002, pp. 720-724. doi:10.1109/TPS.2002.1024274
[23]	A. A. Mamun, P. K. Shukla and B. Eliasson, “Arbitrary Amplitude Dust Ion-Acoustic Shock Waves in a Dusty Plasma with Positive and Negative Ions,” Physics of Plasmas, Vol. 16, No. 11, 2009, pp. 114503-114506. doi:10.1063/1.3261840
[24]	S. S. Duha and A. A. Mamun, “Dust-Ion-Acoustic Shock Waves Due to Dust Charge Fluctuation,” Physical Letters A, Vol. 373, No. 14, 2009, pp. 1287-1289. doi:10.1016/j.physleta.2009.01.059
[25]	A. A. Mamun, P. K. Shukla and B. Eliasson, “Solitary Waves and Double Layers in a Dusty Electronegative Plasma,” Physical Reviews E, Vol. 80, No. 4, 2009, p. 046406(6). doi:10.1103/PhysRevE.80.046406
[26]	H. Alinejad and A. A. Mamun, “Small Amplitude Dust Ion- Acoustic Solitary Waves and Double Layers in a Dusty Plasma with Flat-Topped Electron Distribution,” Physics of Plasmas, Vol. 17, No. 12, 2010, p. 123704(5). doi:10.1063/1.3526649
[27]	S. Ghosh and R. Bharuthram, “Ion Acoustic Solitons and Double Layers in Electronpositronion Plasmas with Dust Particulates,” Astrophysics and Space Science, Vol. 314, No. 1-3, 2008, pp. 121-127. doi:10.1007/s10509-008-9748-0
[28]	R. Roychoudhury and P. Chatterjee, “Arbitrary Amplitude Double Layers in Dusty Plasma,” Physics of Plasmas, Vol. 6, No. 1, 1999, pp. 406-408. doi:10.1063/1.873294
[29]	A. A. Mamun and P. K. Shukla, “Cylindrical and Spheri- cal Dust Ionacoustic Solitary Waves,” Physics of Plasmas, Vol. 9, No. 4, 2002, pp. 1468-1470. doi:10.1063/1.1458030
[30]	A. A. Mamun and P. K. Shukla, “Effects of Nonthermal Distribution of Electrons and Polarity of Net Dust-Charge Number Density on Nonplanar Dust-Ion-Acoustic Solitary Waves,” Physical Reviews E, Vol. 80, No. 3, 2009, pp. 037401(4). doi:10.1103/PhysRevE.80.037401
[31]	A. A. Mamun and P. K. Shukla, “Cylindrical and Spherical Dust Ion-Acoustic Shock Waves in Dusty Plasmas,” Europhysics Letters, Vol. 87, No. 2, 2009, p. 25001. doi:10.1209/0295-5075/87/25001
[32]	H. Washimi and T. Taniuti, “Propagation of Ion-Acoustic Solitary Waves of Small Amplitude,” Physical Reviews Letters, Vol. 17, No. 19, 1966, pp. 996-998. doi:10.1103/PhysRevLett.17.996
[33]	S. Maxon and J. Viecelli, “Spherical Solitons,” Physical Reviews Letters, Vol. 32, No. 1, 1974, pp. 4-6. doi:10.1103/PhysRevLett.32.4
[34]	N. C. Lee, “Small Amplitude Electron-Acoustic Double Layers and Solitons in Fully Relativistic Plasmas of Two- Temperature Electrons,” Physics of Plasmas, Vol. 16, No. 4, 2009, p. 042316(10). doi:10.1063/1.3121242