On small-signal amplification of a TM circular cylindrical wave-guide mode in a gyro-TWT

A self-consistent kinetic-theory based method of analysing the small-signal amplification of a transverse magnetic (TM) mode of a circular cylindrical waveguide linearly interacting with an annular beam of gyrating electrons in a gyro-travelling wave tube (TWT) configuration is presented. When the cyclotron-resonance condition is enforced over the entire frequency range by allowing the gyro-radius and the relativistic factor to be frequency-dependent for a constant value of the axial electron speed chosen to coincide with the reciprocal of the TM-mode phase speed at a particular frequency, the initial growth rate of the interacting TM wave is seen to exhibits a shallow minimum close to, but shifted to the right of, that frequency. The growth-rate curve, however, exhibits two maxima on either side of the minimum, a sharp but large maximum to the left and a broad but a smaller maximum to the right. A gyro-TWT designed by choosing the amplifier parameters (none of them varying any longer with frequency) in such a way as to place the broad maximum of the growth-rate curve at the design frequency is shown to be capable of operation over a wide band of frequencies around the design frequency coupled with a decent value of small-signal gain and negligible frequency distortion.