MODULATIONAL INSTABILITY OF THREE DIMENSIONAL WAVES IN A PLASMA WITH VORTEX ELECTRON DISTRIBUTION

Abstract

In the present work, employing the three dimensional equations of a plasma composed of a cold electron uid, hot electrons obeying a trapped /vortex-like distribution, and stationary ions, we study the amplitude modulation of an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the eld equations with fractional power type of nonlinearity, we obtained the three dimensional form of the modied nonlinear Schrodinger equation as the evolution equation of the same order of nonlinearity. The modulational instability of the homogeneous harmonic solution is investigated and the criteria for the instability is discussed as a function of the obliqueness angle.The numerical calculations show that the critical value of the wave number of the envelop wave increases with the wave number k of the carrier wave and the obliqueness angle.

Keywords

• Modied nonlinear Schrodinger equation,modulational instability,solitary waves.

References

1. Fried, B. D. and Gould, R. W., (1961), Longitudinal Ion Oscillation in a Hot Plasma, Phys. Fluids, 4, pp. 139-147.
2. Watanabe, K. and Taniuti, T., (1977), Electron-Acoustic mode in Plasma of Two-Temperature Electrons, J. Phys. Soc. Japan, 43, pp. 1819-1820.
3. Dubouloz, N., Pottelette, N., Malignre, M., and Truemann, R. A., (1972), Generation of Broadband Electrostatic Noise by Electron-Acoustic Solitons, Geophys. Res. Lett. 18, pp. 155-158.
4. Abbasi, H., Tsintsadze, N. L. and Tskhakaya, D. D., (1999), Influence of Particle Trapping on the Prop- agation of Ion-Cyclotron Waves, Phys. Plasma, 6, pp. 2373-2379.
5. Schamel, H., (1972), Stationary Solitary, Snoidal and Sinusoidal Ion-Acoustic Waves, Plasma Phys. 14, pp. 905-924.
6. Schamel, H., (1973), A Modified Korteweg-De vries Equation for Ion-Acoustic Waves due to Resonant Electrons, J. Plasma Phys., 9, pp. 377-387.
7. Washimi, H. and Taniuti, T., (1966), Propagation of Ion-Acoustic Solitary Waves of Small Amplitude, Phys. Rev. Lett., 17, pp. 996-998.
8. Mamun, A. A. and Shukla, P. K., (2002), Electron-Acoustic Solitary Waves via Vortex Electron Distribu- tion, J. Geophysical Res., 107, A7.10.1029/2001JA009131.

9. Taniuti, T., (1974), Reductive Perturbation Method and Far Fields of Wave Equations, Suppl. of Progress in Theoretical Phys., 55, pp. 1-35.
10. Demiray, H., (2018), Higher Order Perturbation Expansion for Ion-Acoustic Solitary Waves with Q- Nonextensive Nonthermal Distribution, TWMS J. Appl. and Engr. Mathematics, V.8, pp. 438-447.
11. Demiray, H., (2012), Contribution of Higher Order Terms to the Nonlinear Shallow Water Waves, TWMS J. Appl.and Engr. Mathematics, V.2, pp. 210-218.
12. Johnson, R. S., (1997), A modern Introduction to the Mathematical Theory of Water Waves, Cambridge University Press, Cambridge.
13. Dullin, H. R., Gottwald, Holm D. D., (2001), An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion, Phys. Rev. Lett. 87, pp. 4501-4504.
14. Kliakhandler, I., Trulsen K., (2000), On Weakly Nonlinear Modulation of Waves in Deep Water, Phys. Fluids, 12, pp. 2432-2437.
15. Hue, J. K., (2005), Modulation of Multidimensional Waves in a Dusty Plasma, Physics of Plasmas, 12, 062313.
16. Jukui, X., (2003) Modulational Instability of Ion Acoustic Waves in a Plasma Consisting of Warm Ions and Non-Thermal Electrons, Chaos, Solitons and Fractals, 18, pp. 849-853.
17. Demiray, H., (2016), Modulation of Electron-Acoustic Waves in a Plasma with Kappa Distribution, Physics of Plasmas, 23, 032109.
18. El-Labany, S. K., El-Taibany, W. F. and Zedan, N. A., (2017), Modulated Ion-Acoustic Waves in a Plasma with Cairns-Gurevich Distribution, Physics of Plasmas, 24, 112118.
19. Demiray, H., (2015), Modulation of Electron-Acoustic Waves in a Plasma with Vortex-Electron Distribu- tion, Int. J. Nonlinear Sci. Numerical Simul., 16, pp. 61-66.
20. Ravindran, R., Prasad, P. A., (1979), Mathematical Theory of Nonlinear Waves in a Fluid-Filled Vis- coelastic Tube, Acta Mech., 31, pp. 253-280.
21. Demiray, H., (2001), Modulation of Nonlinear Waves in a Viscous Fluid Contained in an Elastic Tube, Int. J. Nonlinear Mech., 36, pp. 649-661.
22. Antar, N., Demiray, H., (1999), Weakly Nonlinear Waves in a Pre-stressed Thin Elastic Tube Containing a Viscous Fluid, Int. J. Engr. Sci., 37, pp. 1859-1876.