of waves (where the Langmuir waves are absorbed by electrons when the plasma density increases) and regions with Langmuir waves (where plasma density is decreasing).

Pseudo-random fluctuations of density
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There is special interest in the case where the density fluctuations are random, which looks like the case for a solar coronal plasma. A pseudo-random distribution of density fluctuations can be easily built by summing $N$ sine-like perturbations with random amplitude, phase, and period $$\label{random}
  n(x)= n_0(1+ \sum \limits_{i=1}^{N}\alpha _i \mbox{sin}(x/\Delta x_i+\varphi _i))$$ where $n_0\alpha_i$, $\Delta x_i$, $\varphi _i$ are the amplitude, period and phase of a given sine-like density oscillations respectively. The values are chosen in the range to ensure the applicability of the kinetic equations. Thus, $0<\alpha_i\leq
0.001$, $d/2\leq \Delta x_i\leq d/12$, $0<\varphi _i\leq2\pi$, $N=10$ are taken for the numerical calculations. The resulting density profile can be seen in fig. \[fig7\].

The spatial distribution of waves has now more complex structure (fig. \[fig7\]). However, all the main results obtained for sine-like density fluctuations are also observed for pseudo-random density fluctuations (\[random\]). Firstly, the electron stream propagates in a plasma as a BPS. Secondly, observing the energy density profile of Langmuir waves one can see the clumps of Langmuir 