Stepped electric-field profiles in transit-time tubes

In its classical embodiment-a circular cylindrical cavity driven by a rectilinear electron beam-the simplest of the transit-time microwave tubes, the monotron, has its conversion efficiency limited to 20.0%. However, we demonstrate here that on considering a stepped electric-field axial profile described by a tanh(z) function, the monotron efficiency can attain the theoretical maximum value of 57.0%, almost three times as high as that obtained from the conventional uniform field distribution. This is accomplished by using two cavities electromagnetically coupled by an annular slit crossed by an electron stream. From a one-dimensional analysis, a two-cavity monotron is developed to operate in the TM₀₁₀ mode at 4.0 GHz when self-excited by a 20-keV, 10-A hollow electron beam. The device operation is examined through a 2.5-dimensional particle-in-cell (PIC) simulation giving a 47.5% conversion efficiency. Departure from the theoretically predicted efficiency is explained by beam-thickness effects.