The effect of an initial velocity spread on klystron performance

The fundamental component of beam current in a klystron is calculated by integrating the contributions due to individual velocity classes. For relatively narrow velocity distributions and operation with optimum parameters, the ratio of fundamental current amplitude to that obtained for a uniform velocity beam is given by a simple ratio of Fourier transforms of the velocity distribution functions. Several examples are calculated and the results shown graphically. For tubes with long transit angles, a moderate spread in velocity may result in appreciable decrease of the fundamental component of beam current. Considerable care in the focusing of beams therefore is warranted when efficiency is an important factor in tube performance.