Virtual cathode formation in annular electron beam in an external magnetic field

The conditions of virtual cathode (VC) formation in an annular electron beam in the presence of an external focusing magnetic field have been studied by means of numerical simulation within the framework of a two-dimensional model. The dependences of a critical beam current (at which the VC is formed) on the magnetic field and of the optimum field (at which the critical current is minimal) on the beam geometry are determined. The optimum magnetic field depends on the Brillouin field value.