Low-Energy State Electron Beam in a Uniform Channel

In our earlier work, we showed that a low-energy state of an electron beam exists in a nonuniform channel between two virtual cathodes in a magnetron with diffraction output, which consists of three uniform sections with increasing radius. A uniform axial magnetic field fills the interaction space. This led to magnetron operation with >90% efficiency when combined with a magnetic mirror field at the output end. In this present paper, we show that a low-energy state of an electron beam can be realized in a uniform channel in which an increasing magnetic field is used in order to create a magnetic mirror at the output end. We consider two cases, one where the injected beam current slightly exceeds the space-charge-limiting current and the other where the injected beam current greatly exceeds the space-charge-limiting current. On the time scale of relevance to planned experiments (∼30 ns), when the injected current slightly exceeds the space-charge-limiting current a stationary virtual cathode forms and when the injected current greatly exceeds the space-charge-limiting current the virtual cathode oscillates back and forth.