In this presentation we describe the effects of plasma density fluctuations in the solar wind on the relaxation of the electron beams ejected from the Sun. The density fluctuations are supposed to be responsible for the changes in the local phase velocity of the Langmuir waves generated by the beam instability. Changes in the wave phase velocity during the wave propagation can be described in terms of probability distribution function determined by distribution of the density fluctuations. Using these
probability distributions we describe resonant wave particle interactions by a system of equations, similar to well known quasi-linear approximation, where the conventional velocity diffusion coefficient and the wave growth rate are replaced by the averaged in the velocity space. It was shown that the process of relaxation of electron beam is accompanied by transformation of significant part of the
beam kinetic energy to energy of the accelerated particles via generation and absorption of the
Langmuir waves. We discovered that for the very rapid beams with beam velocity V_b > 15 v_T, where
v_T is a thermal velocity of background plasma, the relaxation process consists of two well separated steps. On first step the major relaxation process occurs and the wave growth rate almost everywhere in the velocity space becomes close to zero or negative. At the seconde stage the system remains in the state close to state of marginal stability enough long to explain how the beam may be preserved
traveling distances over 1 AU while still being able to generate the Langmuir waves.