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The paper is concerned with investigation of the influence of an intense high frequency electric field and relativistic warm plasma waveguide on electrostatic oscillations of nonuniform bounded plasma. The stabilizing effect of a strong high frequency (pump) electrical field on beam-plasma interaction in a cylindrical relativistic warm plasma waveguide is discussed. A new mathematical technique " separation method " was applied to the two-fluid plasma model to separate the equations, which describe the system, into two parts, time and space parts. Plasma electrons are considered to have a relativistic, thermal velocity. It is shown that a high frequency electric field has no essential influence on dispersion characteristics of unstable surface waves excited in a relativistic warm plasma waveguide by a low-density electron beam. The region of instability is only slightly narrowing and the growth rate decreases by a small parameter and this result was reduced comparing to cold, nonrelativistic plasma. Also, it is found that the plasma electrons did not affect the solution of the space part of the problem.

The Effects of Relativistic Warm Plasma Waveguide and High Frequency Electrical Field on Beam-Plasma Interaction