Effects of relativistic electrons and spatial non-uniformities of density on periodic absolute parametric instability in a plasma waveguide

The effects of relativistic electrons and spatial plasma nonuniformity of density on periodic absolute parametric instability (API) of electrostatic waves in a relativistic 1-D nonuniform magnetoactive plasma are investigated in a cylindrical geometry. We use the separation method to solve the two-fluid plasma equations, which describe the system. The method used enables us to determine the frequencies and growth rates of unstable modes and the self-consistent electric field. Plasma electrons are considered to have a relativistic velocity. Increment has found in the buildup of the oscillations, and it is shown that the spatial nonuniformity of the plasma exerts a stabilizing effect on the parametric instability. It is shown that the growth rate of the API in relativistic plasma is reduced compared to nonrelativistic plasma. Independent of the geometry of the problem (plane and cylinder), the results of the API in a relativistic plasma waveguide are still valid. The proposal approach (3separation method.) is significantly simpler that the method ordinarily employed in the theory of parametric resonance in nonuniform plasma. Therefore, it is of special interest to apply the separation method to solution of different problems involving parametric excitation of electrostatic waves in bounded nonuniform plasma. (C) 2016 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.