Separation Method in the Problem of a Beam-Plasma Interaction in a Cylindrical Warm Plasma Waveguide

ABSTRACT

The stabilization effect of a strong HF electric field on beam-plasma instability in a cylindrical warm plasma waveguide is discussed. A mathematical technique “separation method” applied to the two-fluid plasma model to separate the equations, which describe the system, into two parts, temporal and space parts. Plasma electrons are considered to have a thermal velocity. It is shown that a HF electric field has no essential influence on dispersion characteristics of unstable surface waves excited in a warm plasma waveguide by a low-density electron beam. The region of instability only slightly narrowing and the growth rate decreases by a small parameter and this result has been reduced compared to cold plasma. Also, it is found that the plasma electrons have not affected the solution of the space part of the problem.

The stabilization effect of a strong HF electric field on beam-plasma instability in a cylindrical warm plasma waveguide is discussed. A mathematical technique “separation method” applied to the two-fluid plasma model to separate the equations, which describe the system, into two parts, temporal and space parts. Plasma electrons are considered to have a thermal velocity. It is shown that a HF electric field has no essential influence on dispersion characteristics of unstable surface waves excited in a warm plasma waveguide by a low-density electron beam. The region of instability only slightly narrowing and the growth rate decreases by a small parameter and this result has been reduced compared to cold plasma. Also, it is found that the plasma electrons have not affected the solution of the space part of the problem.

Cite this paper

nullK. El-Shorbagy, A. Al-Fhaid and M. Al-Ghamdi, "Separation Method in the Problem of a Beam-Plasma Interaction in a Cylindrical Warm Plasma Waveguide,"*Journal of Modern Physics*, Vol. 2 No. 10, 2011, pp. 1104-1108. doi: 10.4236/jmp.2011.210136.

nullK. El-Shorbagy, A. Al-Fhaid and M. Al-Ghamdi, "Separation Method in the Problem of a Beam-Plasma Interaction in a Cylindrical Warm Plasma Waveguide,"

References

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[16] O. M. Gradov and L. Stenflo “On the Parametric Transparency of a Magnetized Plasma Slab,” Physics Letters A, Vol. 83, N. 6, 1981, pp. 257-258. doi:10.1016/0375-9601(81)90977-4

[17] V. V. Demchenko, Kh. H. El-Shorbagy, Sh. M. Khalil and N. G. Zaki, “The Effect of HF Electrical Field on Beam-Plasma Interaction in a Plasma Waveguide,” 15th National Radio Science Conference, Cairo, 24-26 February 1998, IEEE Catalog Number 98EX109.

[18] P. Richards, “Manual of Mathematical Physics,” Pergmon Press, New York, 2009.

[19] A. H. Nayfeh, “Perturbation Methods,” John Wiley, New York, 2006.

[20] V. A. Yakubovich and V. M. Strazhinskii, “Linear Differential Equations with Periodic Coefficients,” Wiley, New York, 2009.

[21] Kh. H. El-Shorbagy, “HF Electric Field Effect on Buneman’s Instability in a Relativistic Plasma Waveguide,” Physica Scripta, Vol. 62, No. 2-3, 2000, pp. 186-188.

[22] V. V. Demchenko, Kh. H. El-Shorbagy, Sh. M. Khalil and N. G. Zaki, “Stabilization of Buneman Instability by Intense Hfelectric Field in a Plasma Wave Guide,” XXXIII International Conference on Phenomena in Ionized Gases, Toulouse, France, 17-22 July 1997.

[23] Kh. H. El-Shorbagy, “Stabilization Effect of a Strong HF Electrical Field on Beam-Plasma Interaction in a Relativistic Plasma Waveguide,” Physics Letters A, Vol. 287, No. 1-2, 2001, pp. 120-124. doi:10.1016/S0375-9601(01)00204-3

[24] Kh. H. El-Shorbagy, “Relativistic Warm Plasma Wave- guide under the Effects of Plasma Electrons and HF Electrical Field on Buneman Instability,” Physics Letters A, Vol. 372, No. 9, 2008, pp. 1494-1497. doi:10.1016/j.physleta.2007.10.042

[25] V. V. Demchenko and K. E. Zayed, “Propagation of Potential Surface Waves in Non-Homogeneous Plasmas at the Plasma Resonance in the Transition Layer,” Physica, Vol. 59, No. 3, 1972, pp. 385-400. doi:10.1016/0031-8914(72)90195-4

[1] M. V. Nezlin, “Dynamics of Beams in Plas Mas,” Springer Verlag, Heideleberg, 1991.

[2] L. S. Bogdankevich and A. A. Rukhadze, “Stability of Relativistic Electron Beams in a Plasma and the Problem of Critical Currents,” Soviet Physics—Uspekhi, Vol. 14, N. 2, 1971, pp.163-179. doi:10.1070/PU1971v014n02ABEH004456

[3] A. F. Alexanddrov, M. V. Kuzelev and A. N. Khalilov, “Beam Instability Regimes in a Plasma,” Soviet Physics— JETP, Vol. 66, No. 5, 1987, pp 978-988.

[4] W. H. Amein and Y. A. Sayed, “Long Wavelength Oscillation in Electron Beam-Plasma Interaction,” Physica Scripta, Vol. 50, No. 2, 1994, pp. 147-149. doi:10.1088/0031-8949/50/2/010

[5] A. B. Mikhailovskii, “Theory of Plasma Instabilities,” Consultants Bureau, New York, 1974.

[6] Yu. M. Aliev and V. P. Silin, “Plasma Oscillations in a High-Frequency Electric Field,” Soviet Physics—JETP, Vol. 21, No. 3, 1965, pp. 601-607.

[7] V. P. Silin, “A Survey of Phenomena in Ionized Gases,” IAEA, Vienna, 1968.

[8] V. V. Demchenko and A. Ya. Omelchenko, “On the Problem of Parametric Resonance in a Cold Inhomogeneous Isotropic Plasma,” Radiophysics and Quantum Electronics, Vol. 19, No. 3, 1976, pp. 332-334. doi:10.1007/BF01034594

[9] H. Bohmer, E. A. Jacson and M. Rather, “Quenching of the Beam-Plasma Instability by Mode Mixing at a Density Discontinuety,” Physics Fluids, Vol. 16, No. 7, 1973, pp. 1064-1071. doi:10.1063/1.1694468

[10] W. H. Amein, V. V. Dolgopolov, A. M. Hussen and K. E. Zayed, “Beam Instability in the Case of Sharp Changes in Plasmadensity,” Physica, Vol. 79C, No. 6, 1975, pp. 628- 631.

[11] W. H. Amein, V. V. Dolgopolov, A. M. Hussen and K. E. Zayed, “Beam Instability in Inhomogeneous Bounded Plasma,” Plasma Physics, V. 17, No. 6, 1975, pp. 497- 500.

[12] P. Kaw, W. Kruer, C. Liu and K. Nishikawa, “Advances in Plasma Physics”, Wiley, New York, 1976.

[13] M. V. Kuzelev and A. A. Rukhadze,” Electrodynamics of Dense Electron Beam in Plasma,” Nauka, Mosco, 1990.

[14] M. V. Kuzelev and A. A. Rukhadze, English Completed Edition,” Plasma Free Electron Lasers,” Edition Frontier, Paris, 1995.

[15] Yu. M. Aliev and E. Ferlengi, “Parametric Excitation of Surface Oscillations of a Plasma by an External High Frequency Field,” Soviet Physics—JETP, Vol. 30, No. 5, 1970, pp. 877-879.

[16] O. M. Gradov and L. Stenflo “On the Parametric Transparency of a Magnetized Plasma Slab,” Physics Letters A, Vol. 83, N. 6, 1981, pp. 257-258. doi:10.1016/0375-9601(81)90977-4

[17] V. V. Demchenko, Kh. H. El-Shorbagy, Sh. M. Khalil and N. G. Zaki, “The Effect of HF Electrical Field on Beam-Plasma Interaction in a Plasma Waveguide,” 15th National Radio Science Conference, Cairo, 24-26 February 1998, IEEE Catalog Number 98EX109.

[18] P. Richards, “Manual of Mathematical Physics,” Pergmon Press, New York, 2009.

[19] A. H. Nayfeh, “Perturbation Methods,” John Wiley, New York, 2006.

[20] V. A. Yakubovich and V. M. Strazhinskii, “Linear Differential Equations with Periodic Coefficients,” Wiley, New York, 2009.

[21] Kh. H. El-Shorbagy, “HF Electric Field Effect on Buneman’s Instability in a Relativistic Plasma Waveguide,” Physica Scripta, Vol. 62, No. 2-3, 2000, pp. 186-188.

[22] V. V. Demchenko, Kh. H. El-Shorbagy, Sh. M. Khalil and N. G. Zaki, “Stabilization of Buneman Instability by Intense Hfelectric Field in a Plasma Wave Guide,” XXXIII International Conference on Phenomena in Ionized Gases, Toulouse, France, 17-22 July 1997.

[23] Kh. H. El-Shorbagy, “Stabilization Effect of a Strong HF Electrical Field on Beam-Plasma Interaction in a Relativistic Plasma Waveguide,” Physics Letters A, Vol. 287, No. 1-2, 2001, pp. 120-124. doi:10.1016/S0375-9601(01)00204-3

[24] Kh. H. El-Shorbagy, “Relativistic Warm Plasma Wave- guide under the Effects of Plasma Electrons and HF Electrical Field on Buneman Instability,” Physics Letters A, Vol. 372, No. 9, 2008, pp. 1494-1497. doi:10.1016/j.physleta.2007.10.042

[25] V. V. Demchenko and K. E. Zayed, “Propagation of Potential Surface Waves in Non-Homogeneous Plasmas at the Plasma Resonance in the Transition Layer,” Physica, Vol. 59, No. 3, 1972, pp. 385-400. doi:10.1016/0031-8914(72)90195-4