Transient response of a microwave beam amplifier

A model of a beam amplifier consisting of a chain of lightly-coupled cavities has been studied for initial time response with the aid of a computer. The beam flows through the center-holes of 20 cavities stacked together and coupled so the pass band width would be 5 per cent in an infinitely long chain. The intermediate cavities are externally loaded for stability. The electronic transit angle for each cavity is 3π/4,
\omega_{q}/\omega = 0.1
, and the beam-circuit coupling coefficient C
B
is small. Computations have been made of the steady-state input resistance, gain and bandwidth around the 3π/4 "cold" circuit phase shift frequency, as well as of the transient response for t ≥ 0. Results show 1) at the 3π/4 frequency the voltage in the output cavity overshoots the steady-state value, and reaches its first peak at a time almost exactly equal to the amplifier length divided by the group velocity; 2) at a frequency nearer to cutoff, for which the group velocity is smaller, the voltage does not overshoot, but approaches the steady-state value asymptotically, such that at a time equal to the amplifier length divided by the group velocity the voltage has about 80 per cent of its steady-state value.