Nonlinear Dynamics of Radiation in Multiple-Beam Vacuum Electronic Devices

The article is devoted to overview of different types of vacuum electronic devices with two or more charged particle beams. There are travelling wave and backward wave tubes, free electron lasers and masers, volume free electron lasers. Two different cases take place in such situation: multiple-beam instability in such devices and multiple-stream instability. In the first case some charged particle beams moves in the system with different velocities. In the second one there are beams with almost equal velocities (streams). Two systems of equations for volume free electron laser with two electron beams are proposed. Some numerical results of VFEL numerical simulation are given and discussed.