HF electric field effect on Buneman's instability in a relativistic plasma waveguide

The stabilizing effect of a strong HF (pump) electrical field on the Buneman instability in a plane relativistic plasma waveguide is investigated. A new mathematical technique, the separation method, is applied to the two-fluid plasma model to separate the equations, which describe the system, into two parts: temporal and space parts. The temporal (dynamical) part enables us to determine the frequencies and growth rates of unstable modes; this part within the redefinition of natural frequencies coincides with the system describing HF suppression of the Buneman instability in a uniform unbounded plasma. Natural frequencies of oscillations and spatial distribution of the amplitude of the self-consistent electrical field are determined from the solution of a boundary-value problem (space part) taking into account the specific spatial distribution of plasma density. Plasma electrons are considered to have a relativistic velocity. It is shown that the growth rate instability in the relativistic plasma has been reduced compared to the nonrelativistic plasma. Also, it is found that the relativistic plasma electrons have not affected the solution of the space part of the problem.