Equilibria and waves in high-current electron beams emitted from shielded and immersed cathodes

Equilibria of high-current electron beams in an axial magnetic field are considered at the base of the approach [1]. together with results obtained earlier [2] for the two cases of shielded and immersed cathodes. Exact analytical solutions for laminar flow equilibria are used to analyze wave processes and stability properties of solid and annular beams. A general wave equation in the electrostatic approximation, which is valid in any selfconsistent equilibrium, was derived under the only assumption of constancy of full particle energy. Some solutions of an electromagnetic problem were found and properties of electrostatic and electromagnetic waves in the same equilibrium are compared.