Nonlinear wave and oscillation processes in extended electron beams

An analysis is presented of nonlinear waves and oscillations in electron beams considered as confined electron plasmas. The equations of motion are written for a disk model and are solved in Euler variables; processes in thin and wide electron beams are analyzed. The nonlinear properties of a confined electron plasma are shown to be primarily determined by the radius of action of Coulomb forces, depending on the relationship of wavelength, beam radius, and the radius of the drift tube. Nonlinear 'shallow-water' equations, Korteweg-de Vries equations, and nonlinear-oscillation equations are obtained and investigated. It is shown that the formation of dense electron bunches possessing the properties of solitons is possible in thin beams. The nonlinear interaction of space-charge waves is considered.