Spatial echo in a relativistic plasma

Summary form only given. Interference of the microoscillations of the distribution function modulated by the fields of two sources separated by a certain spatial distance (Van Kampen waves) could lead to a phase focusing of the particles over space and that this focusing could be accompanied by the appearance of a macroscopic signal: a spatial echo. Various types of echo oscillations in unbounded and bounded plasma systems were considered by Pavlenko (1983). The non-linear wave interaction in the plasma of the relativistic electron beam (REB) are studied by Davidov et al. (1992) and Pavlenko et al. (1996). In this report the possibility of spatial echo oscillation in the REB plasmas due to nonlinear interaction of eigen beam oscillations is shown. It is shown that the nonlinear echo signal amplitude depends an the damping of space charge waves of REB, electron temperature and relativistic factor. Several practical applications of echo effects in radio wave propagation and diagnostics of the plasma of the REB are discussed.