considerations ([@Robinson92c]).

The influence of plasma inhomogeneity on Langmuir waves and beam electrons has been studied from various points of view. An account of plasma inhomogeneities may explain why accelerated beam electrons appear in the experiments with quasilinear relaxation of an electron beam ([@Ryutov69]). Relativistic dynamics of an electron beam with random inhomogeneities, as applied to laboratory plasmas, was considered in ([@Hishikawa76]). It has been shown ([@Muschietti85]) that the solar corona density fluctuations may be extremely effective in quenching the beam-plasma instability. Moreover, the isotropic plasma inhomogeneities may lead to efficient isotropisation of plasma waves ([@Goldman82]) whereas those alongated along the direction of ambient magnetic field have little influence on the beam stability. Therefore, the growth rate of beam-plasma instability was postulated to be very high in the regions of low amplitude density fluctuations ([@Melrose86]; [@Melrose87]). Isotropic density fluctuations of ambient plasma density were also employed to explain low level of Langmuir waves in microbursts ([@Gopalswamy93]).

In this paper the dynamics of a spatially limited electron cloud is considered in a plasma with small scale density fluctuations. In the treatment presented here, quasilinear relaxation is a dominant process and density inhomogeneities are too weak to suppress the instability. Indeed, observations 