Spatial echo in a relativistic plasma

Summary form only given, as follows. It was already known that the interference of the microoscillations of the distribution function modulated by the fields of two or several sources separated by a certain spatial distance lead to a pulse focusing of the particles over space and that this focusing could be accompanied by the appearance of macroscopic signal: spatial echo. In present report it is shown the possibility of spatial echo oscillation in the relativistic electron beam plasmas due to nonlinear interaction of eigen beam oscillations. The expression for echo field of second order due to nonlinear interaction of perturbations propagating parallel and perpendicular to beam one obtained. The amplitudes and forms of these echo signals are essentially different. We thus have the opportunity to diagnostic of relativistic electron beam plasmas.