nonlinear dynamics.

Three-dimensional electromagnetic numerical simulation is carried out of «squeezed» state of the electron beam in two-section vircator system with drift tubes of different diameters. We have studied the influence of two-section system geometric parameters on the nonlinear dynamics of electron beam. We have obtained an effective plasma frequency depending on the system parameters.

The paper deals with the retrospective consideration of course lectures on theory of oscillations in Nizhny Novgorod university and its evolution during more then 70 years.

Mathematical model of Volume Free Electron Lasers (VFEL) is described. Some aspects and origins of VFEL chaotic dynamics are examined.