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

has been cited by the following article:

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

  AUTHORS: Khaled H. El-Shorbagy, Abdelrahman S. Al-Fhaid, Mohamed A. Al-Ghamdi

  KEYWORDS: Separation Method, Beam-Plasma Interaction, Warm Plasma Waveguide

  JOURNAL NAME: Journal of Modern Physics, Vol.2 No.10, October 19, 2011

  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.