Beam extension in longitudinally heterogeneous systems

Investigation of initial perturbation evolution of beam particles in beam-plasma system with inhomogeneous dielectrical permittivity along their propagation is interesting for description of many problems. Medium parameters along direction of beam extension in beam-plasma systems are not constant very often. If beam is expansion its density and compensate charge particle density are reducing in process of transporting, under beam focusing - they are increasing. In this article was discussed influence of changing both as plasma density, BS compensate charge particle density along propagation direction on evolution of instability oscillations. It was show that in some cases solution can be find in analytic form. Some examples of beam-plasma system were observed. Evolution of beam-plasma instability of compensates charge particles beam transporting in free space and in different parts of divide setup of isotopes electromagnetic separator was observed by computer simulation.