be the case for a homogeneous plasma ([@Melnik00]; [@Melnik00a]). The second process is the influence of plasma inhomogeneity on the Langmuir waves. Depending on the sign of the density gradient, the Langmuir wave spectrum takes on a different form.

Consider the time evolution of the electron distribution function and the spectral energy density of Langmuir waves at two close points $x=15.2d$ and $x=15.47d$ (see fig. \[fig3\]). The first point is chosen in the region with increasing density and the second in the region where the density decreases with distance. The first particles arrive to these points at approximately $t\sim
1.9$s. The arriving electrons form a plateau in the electron distribution function and generate a high level of plasma waves for the time of quasilinear relaxation $\tau \approx  0.01$ s.

![The electron distribution function $f(v,x,t)$ and the spectral energy density of Langmuir waves $W(v,x,t)$ at $x=15.2d$ and at $x=15.47d$. Numerical solution of kinetic equations for a plasma with sine-like density fluctuations (\[sin\]) $n'=100$cm$^{-3}$, $v_0=1.0\times 10^{10}$cm s$^{-1}$.[]{data-label="fig3"}](ms1121f3a.eps "fig:"){width="90mm"} ![The electron distribution function $f(v,x,t)$ and the spectral energy density of Langmuir waves $W(v,x,t)$ at $x=15.2d$ and at $x=15.47d$. Numerical solution of kinetic equations for a plasma with sine-like density fluctuations (\[sin\]) $n'=100$cm$^{-3}$, $v_0=1.0\times 