ON PROGRESSIVE WAVE SOLUTION FOR NON-PLANAR KDV EQUATION IN A PLASMA WITH q-NONEXTENSIVE ELECTRONS AND TWO OPPOSITELY CHARGED IONS

Year 2020, Volume: 10 Issue: 2, 532 - 546, 01.03.2020

H. Demiray E. R. El-zahar S. A. Shan

Abstract

In this paper, the ion-acoustic wave is investigated in a plasma with qnonextensive electrons and two oppositely charged ions with varying masses. These parameters are found to modify the linear dispersion relation and nonlinear solitary structures. The reductive perturbation method is employed to derive modified Korteweg-de Vries KdV equation. To solve the obtained governing evolution equation, the exact solution in the planar geometry is obtained and used to obtain an analytical approximate progressive wave solution for the nonplanar evolution equation. The analytical approximate solution so obtained is compared with the numerical solution of the same nonplanar evolution equation and the results are presented in 2D and 3D figures. The results revealed that both solutions are in good agreement. A parametric study is carried out to investigate the effect of different physical parameters on the nonlinear evolution solution behavior. The obtained solution allows us to study the impact of various plasma parameters on the behavior of the nonplanar ion-acoustic solitons. The suitable application of the present investigations can be found in laboratory plasmas, where oppositely charged ions and nonthermal electrons dwell.

Keywords

Nonplanar solitons, Modified KdV, Cylindrical and spherical solitons, Electronegative plasmas, Analytical approximate solutions

References

• Nakamura, Y., Ooyama, M., and Ogino, T., (1980), Observation of Spherical Ion-Acoustic Solitons, Phys. Rev. Lett. 45, pp. 1565-1569.
• Ichiki, R., Yoshimura, S., Watanabe, T., Nakamura, Y. and Kawai, Y., (2002), Experimental observa- tion of dominant propagation of the ion-acoustic slow mode in a negative ion plasma and its application, Phys. Plasmas 9, pp.4481-4887.
• Oohara, W., and Hatakeyama, R., (2003), Pair-Ion Plasma Generation using Fullerenes, Phys. Rev. Lett. 91, 205005-(1-4).
• Bacal, M., and Hamilton, G.W., (1979), H−and D−Production in Plasmas, Phys. Rev. Lett., 42, pp. 1538-1540.
• Gottscho, R. A., and Gaebe, C. E., (1986), Negative ion kinetics in RF glow discharges, IEEE Trans. Plasma Sci., 14, pp. 92-102.
• Kokura, H., Yoneda, S., Nakamura, K., Mitsuhira, N., Nakamura, M. and Sugai, H., (1999), Diagnostic of surface wave plasma for oxide etching in comparison with inductive RF plasma, Jpn. J. Appl. Phys., 38, (part1), pp. 5256-5261.
• Boufendi, L., and Bouchoule, A., (2002), Industrial developments of scientific insights in dusty plasmas, Plasma Sources Sci. Technol., 11, pp. A211- A218 .
• Portnyagin, Yu.I., Klyuev, O.F., Shidlovsky, A.A., Evdokimov, A.N., Buzdigar, T.W., Matukhin, P.G., Pasynkov, S.G., Shamshev, K.N., Sokolov, V.V., and Semkin, N.D., (1991), Simulation of cosmic man- made dust effects on space vehicle elements in rocket and laboratory experiments, Adv. Space Res., 11, pp. 89-92.
• Chaizy, P. H., Reme, H., Sauvaud, J. A., Uston, C. D., Lin, R. P., Larson, D. E., Mitchell, D. L., Anderson, K. A., Carlson, C. W., Korth, H., and Mendis, D. A., (1991), Negative ions in the coma of comet Halley. Nature, (London), 349, pp. 393-396.
• Shibayama, T., Shindo, H., and Horiike, Y., (1996), Silicon etching by alternating irradiations of negative and positive ions, Plasma Sources Sci. Technol., 5, pp. 254-259.
• Maxon, S., and Viecelli, J., (1974), Spherical solitons, J. Phys. Rev. Lett., 32, 4-6; Ibid, (1974), Cylindrical solitons, Phys. Fluids, 17, pp. 1614-1616.
• Maxon, S., (1976), Cylindrical solitons in a warm, multiion plasma, Phys. Fluids, 19, pp. 266-271.
• Panat, P.V., (1976), Improved Korteweg–deVries type equation for cylindrical and spherical solitary wave, Phys. Fluids, 19, pp. 915-916.
• Tagare, S. G. and Shukla, P. K., (1977), Nonlinear cylindrical ion-acoustic waves in a warm collisional plasma, Phys. Fluids, 20, pp. 868-869.
• Kalita, M. K., Bujarbarua, S., (1980), Spherical and cylindrical solitons in a warm and multi-electron Plasma, Phys. Lett. A., 22, pp. 1-5.
• Y. Nishida, T. Nagasawa and S. Kawamata (1978), Experimental verification of the characteristics of ion acoustic cylindrical solitons, Phys. Lett., 69, pp. 196-198.
• Chen, T. and Schott, L., (1976), Observation of diverging cylindrical solitons excited with a probe, Phys. Lett., 58A, pp. 459-461.
• Hershkowitz, N., Glanz, J. and Lonngren, K. E., (1979), Spherical ion-acoustic solitons, Plasma Physics, 9, pp. 583-588.
• Williams, J. E., Cooney, J. L., Aossey, D. W. and Lonngren, K. E., (1992), Cylindrical and spherical solitons in a positive-ion —negative-ion plasma, Phys. Rev. A 45, pp. 5897-5900.
• Das, G. C., and Singh, K. I., (1991), Cylindrical and spherical solitons at the critical density of negative ions in a generalised multicomponent plasma, Aust. J. Phys., 44, pp. 523-533.
• Sahu, B. and Roychoudhury, R., (2005), Cylindrical and spherical ion acoustic waves in a plasma with nonthermal electrons and warm ions, Phys. Plasmas, 12, 052106 pp. 1-5.
• Hershkowitz, N. and Romesser, T., (1974), Observations of ion-acoustic cylindrical solitons, Phys. Rev. Lett., 32, pp. 581-583.
• Nakamura, Y. and Ogino, T., (1982), Plasma Phys., Numerical and laboratory experiments on spher- ical ion-acoustic solitons, 24, pp. 1295-1315.
• Tsukabayashi, I., Nakamura, Y., and Ogino, T., (1981), Reflection of a cylindrical ion-acoustic soliton at a symmetric axis, Phys. Lett., 81A, pp. 507-510.
• Schippers, P., Blanc, M., Andre, N., Dandouras, I., Lewis, G. R., Gilbert, L. K., Persoon, A .M., Krupp, N., Gurnett, D. A., Coates, A. J., Krimigis, S. M., Young, D. T., and Dougherty, M. K., (2008), Multi-instrument analysis of electron populations in Saturn’s magnetosphere, J. Geophys. Res., 113, A07208 (2008).
• Tsallis, C., (1988), Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys., 52 pp. 479- 487.
• Tsallis, C., (1995), Some comments on Boltzmann-Gibbs statistical mechanics, Chaos, Solitons and Fractals 6, pp. 539-559.
• C. Tsallis, In new trends in magnetism, magnetic materials and their applications, edited by J. L. Moran-Lopez, J. M. Sanchez, Plenum, New York, p. 451 (1994).
• Silva, R. Jr., Plastino, A R., and Lima, J. A. S., (1998), A Maxwellian path to the q-nonextensive velocity distribution function, Phys. Lett. A., 249, pp. 401-408.
• Shan, S. A. and Akhtar, N., (2013), Korteweg-de Vries equation for ion acoustic soliton with negative ions in the presence of nonextensive electrons, Astrophys Space Sci., 346, pp. 367-374.
• Taniuti, T., (1974), Reductive perturbation method and far fields of wave equations, Suppl. of Progress in Theoretical Phys., 55, pp. 1-35.
• Mamun, A. A. and Shukla, P. K., (2002), Cylindrical and spherical dust ion–acoustic solitary waves, Physics Plasmas, 9, pp. 1468-1470.
• Eslami, P., Mottaghizadeh, M., and Pakzad, H. R., (2011), Nonplanar ion-acoustic solitary waves with superthermal electrons in warm plasma, Physics Plasmas, 18, 072305 (2011).
• Shan, S. A., and Rehman, A., Astrophys Space Sci., (2014), Nonplanar solitons in a warm electroneg- ative plasma with electron nonextensivity effects, 352, pp. 593-604.
• Plastino, A. R. and Plastino, A., (1993), Stellar polytropes and Tsallis’ entropy, Phys. Lett. A, 174, pp. 384-386.
• Kaniadakis, G., Lavagno, A. and Quarati, P., (1996), Generalized statistics and solar neutrinos, Phys. Lett. B, 369, pp. 308-312 (1996).
• Lavagno, A., Kaniadakis, G., Rego-Monteiro, M., Quarati, P., and Tsallis, C., (1998), Non-extensive thermostatistical approach of the peculiar velocity function of galaxy clusters, Astrophys. Lett. Com- mun., 35, pp. 449-455.
• Torres, D. F., Vucetich, H., and Plastino, A., (1997), Early universe test of nonextensive statistics, Phys. Rev. Lett., 79, pp. 1588-1590.
• El-Taibany, W.F., and Tribeche, M., (2012), Nonlinear ion-acoustic solitary waves in electronegative plasmas with electrons featuring Tsallis distribution, Phys. Plasmas, 19, 024507-(1-4).
• Ablowitz, M. J. and Clarkson, P. A., Soliton, Nonlinear evolution equations and inverse scattering (Cambridge University Press, New York, 1991).
• Yan, C., (1996), A simple transformation for nonlinear waves, Phys. Lett. A 224, pp. 77-84.
• Zayed, E. M. E., Zedan, H. A., and Gepreel, K. A., (2004), Group analysis and modified tanh-function to find the invariant solutions and soliton solution for nonlinear Euler equations, Int. J. Nonlinear Sci. Numer. Simul. 5, pp. 221-234.
• Wazwaz, A. M., (2006), The tanh method and a variable separated ODE method for solving double sine-Gordon equation, Phys. Lett. A, 350, pp. 367-370.
• Liu, S. K., Fu, Z. T., Liu, S. D. and Zhao, Q., (2001), Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Phys. Lett. A, 289, pp. 69-74.
• Fu, Z. T., Liu, S. K., Liu, S. D., and Zhao, Q., (2001), New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Phys. Lett. A, 290, pp. 72-76.
• Parkes, E. J., Duffy, B. R., and Abbott, P. C., (2002), The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations, Phys. Lett. A 295, pp. 280-286.
• Zhang, S., Tong, J.L., and Wang, W., (2008), A generalized (G/G)-expansion method for the mKdV equation with variable coefficients, Phys. Lett. A 372, pp. 2254-2257.
• S. Reyad, M. M. Selim, A. EL-Depsy, and S. K. El-Labany, (2018), Soultions of variable coefficients CKP equation for dusty plasma system with G/G - expansion method, J. Nucl. Radiat. Phys. 13, pp. 1-16.
• Selim, M.M., and Abdelsalam, U.M., (2014), Propagation of cylindrical acoustic waves in dusty plasma with positive dust, Astrophys. Space Sci.353, pp. 535-542.
• Sabry, R., Zahran, M. A., and Fan, E., (2004), A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation, Phys. Lett. A 326, pp. 93-101.
• Finlayson, B. A., The method of weighted residuals and variational principles, Academic, New York (1972).
• Fletcher, C. A. J., Weighted Residual Methods. In: Computational Techniques for Fluid Dynamics, Springer, Berlin, Heidelberg, (1998).
• Karjadi, E. A., Badiey, M., Kirby, J. T., and Bayindir, C., (2012), The effects of surface gravity waves on high-frequency acoustic propagation in shallow water, IEEE J. Oceanic Eng. 37, pp. 112-121.
• Demiray, H., and Bayındır, C., (2015), A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution, Phys. Plasmas, 22, 092105- (1-4).
• Demiray, H., and El-Zahar, E.R., (2018), Cylindrical and spherical solitary waves in an electron- acoustic plasma with vortex electron distribution, Phys. Plasmas, 25, (4), 042102.
• El-Zahar, E. R., and Demiray, H., (2019), Analytical solutions of cylindrical and spherical dust ion- acoustic solitary waves, Results in Phys., 13, 102154.
• Demiray, H., (2010), Analytical solution for nonplanar waves in a plasma with q-nonextensive non- thermal velocity distribution: Weighted residual method, Chaos, solitons and Fractals, 130, 109448.
• Sabry, R., Moslem, W. M., and Shukla, P. K., (2009), Fully nonlinear ion-acoustic solitary waves in a plasma with positive-negative ions and nonthermal electrons, Phys. Plasmas, 16, 032302.
• Massey, H., Negative Ions, 3rd ed. (Cambridge University Press, Cambridge, 1976), pp. 663.
• Chabert, P., Lichtenberg, A. J., and Lieberman, M. A., (2007), Theory of a double-layer in an ex- panding electronegative plasma, Phys. Plasmas, 14, 093502.
• Kim, S. H., and Merlino, R. L., (2006), Charging of dust grains in a plasma with negative ions, Phys. Plasmas, 13, 052118.
• Hilmi Demiray, for the photograph and biography, see TWMS Journal of Applied and Engineering Mathematics, Volume 1, No.1, 2011.