The electron beam with virtual cathode in a two-section drift tube

An analysis based on the law of conservation of the z component of field and particle momentum in a thin annular magnetized monoenergetic electron beam in a two-section drift tube composed of tube segments with different radii (R ₁<R ₂) allowed the critical injected beam current to be determined for which a virtual cathode, formed in the wider tube at the joint section, starts traveling through the narrower tube toward the beam injection region. A region behind the traveling virtual cathode features a “squeezed” single-flux state of the beam (corresponding to the “slow” left branch of the current characteristic, high charge density, but low relativistic factor). When the injected current decreases below a critical transition level (I _in<I _Tr), the virtual cathode returns to the initial position and restores the double-flux electron beam. This current is smaller than (I _lim1+I _lim2)/2, and, depending on R ₂, varies from the limiting transport current for the narrower section (I _lim1) up to I _F/2, where I _F is the Fedosov current for this tube section.