The one-dimensional relaxation of a spatially bounded electron stream in non-uniform background plasma is simulated. The corresponding system of quasi-linear equations is \begin{equation}\frac{\partial f}{\partial t}+V\frac{\partial f}{\partial x}=\frac \partial {\partial V}\left( D\frac{\partial f}{\partial V}\right),\, \frac{\partial W}{\partial t}=2\gamma W,\, \gamma =\frac \pi 2\frac{\omega _p}{n_p}V^2\frac{\partial f}{\partial V},\, D=\frac{8\pi ^2e^2}{m^2}\frac WV. \end{equation} Here $f$ - the electron distribution function, $D$ - diffusion coefficient, and $\gamma$ and $W$ - are the growth rate and spectral energy density of plasma waves respectively, $n$ - background plasma density, $\omega_p$ - plasma frequency. Initial conditions (the electron distribution function at $t = 0$): \begin{equation}f(x,V,t=0)=An_{b}\exp \left(-\frac{(V-V_b)^2}{2V_{Tb}^2}\right)\exp \left(-\left(\frac xd\right)^2\right)\end{equation}To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html