The current of an annular electron beam with virtual cathode in a drift tube

Abstract

An analysis based on the laws of conservation of energy and the z components of the field and particle momentum shows that a thin magnetized annular electron beam in a homogeneous drift tube behind a virtual cathode under stationary conditions occurs in a “squeezed” state corresponding to a slow left-hand branch of the current characteristic with a relativistic factor in the interval 1≤γ≤Γ1/3. The beam current I 1 behind the virtual cathode in a homogeneous drift tube can vary from zero up to a limiting value I lim, while the injection currents (I 2) and the current of electrons reflected from the virtual cathode (I 3) for every stationary state are single-valued functions of I 1 and fall within the intervals I F/2≤I 2≤I lim and 0≤I 3≤I F/2, respectively, where I F is the Fedosov current.