Excitation of a cylindrical cavity by a helical current and an axial electron beam current

The explicit expressions (in the Vainshtein and Markov forms) are derived for the excitation of a cylindrical cavity with perfectly conducting walls and with impedance end faces. Excitation of a cylindrical cavity and a cylindrical waveguide with a preset nonuniform axial electron-beam current and a helical current with a variable pitch, which is excited by a concentrated voltage source and is loaded by a preset pointlike matched load, is considered. For the helical current, the integro-differential equation is formulated. The traveling-wave tube (TWT) is simulated in the preset beam current approximation taking into account the nonuniform winding of the spiral coil, nonuniform electron beam, and losses.