The energy distribution of waves $$\label{we}
  E_w(x,t)=\int_0^{\infty}Wdk=\omega_{pe}\int_0^{v_0}\frac{W(v,x,t)}{v^2}dv$$ is presented in fig. \[e\_sin\], where $E_0=mn'v_0^2/4$ is the initial beam energy. The energy distribution explicitly shows the correlation between the plasma and wave energy-density fluctuations. The regions of decreasing plasma density have higher levels of Langmuir turbulence than the corresponding regions with increasing plasma density. The energy distribution of waves appears to be modulated by the ambient plasma density fluctuations. On the other hand, the wave energy density distribution averaged over the period of density fluctuations has a spatial profile close to that in a homogeneous plasma. The maximum of wave energy together with the maximum of electron density propagate with the constant velocity $\approx 0.5v_0$.

![The energy density of plasma waves $E(x)$ at various times and the local plasma frequency $f_p(x)$ (\[sin\]) as a function of distance at various times. The bold line shows the numerical solution for homogeneous plasma. Numerical solution of kinetic equations $n'=100$cm$^{-3}$, $v_0=1.0\times 10^{10}$cm s$^{-1}$.[]{data-label="e_sin"}](ms1121f6.eps){width="90mm"}

The other physical effect that should be noted is the energy losses by the structure in the form of Langmuir waves. In figs. \[fig4\],\[e\_sin\] we see that there is a small but non-zero level of plasma waves behind the beam-plasma structure. These 