low levels of Langmuir turbulence are where the density gradient is positive.

![Detailed picture of the electron distribution function $f(v,x,t)$ and the spectral energy density of Langmuir waves $W(v,x,t)$ at $t=5.0$s. Numerical solution of kinetic equations with sine-like density fluctuations (\[sin\]) $n'=100$cm$^{-3}$, $v_0=1.0\times 10^{10}$cm s$^{-1}$.[]{data-label="fig5"}](ms1121f5a.eps "fig:"){width="90mm"} ![Detailed picture of the electron distribution function $f(v,x,t)$ and the spectral energy density of Langmuir waves $W(v,x,t)$ at $t=5.0$s. Numerical solution of kinetic equations with sine-like density fluctuations (\[sin\]) $n'=100$cm$^{-3}$, $v_0=1.0\times 10^{10}$cm s$^{-1}$.[]{data-label="fig5"}](ms1121f5b.eps "fig:"){width="90mm"}

The other interesting result is that while the Langmuir wave distribution is determined by the irregularities of ambient plasma the electron distribution function is a smooth function of distance (see fig. \[fig5\]). The electrons in the structure propagate as a continuous stream, being slightly perturbed by the density fluctuations. The influence of plasma inhomogeneity on electron distribution is observed in the appearance of accelerated particles with $v>v_0$ and the fact that the maximum plateau velocity is slightly decreasing with time during the course of beam-plasma passing a given point (fig. \[fig3\]). The accelerated electrons tend to accumulate at the front of the structure and the electrons decelerated concentrate at the back of the structure.

The energy distribution of waves
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