On the Nonconservation of Noise Parameters in Multivelocity Beams

Macroscopic equations for conservation of charge, momentum, and energy, as derived from the Boltzmann equation, are applied to an electron stream having a velocity spread. For small velocity spreads, these equations are simple to treat. The noise parameters, S and Π, which determine the minimum noise figure of a beam-type microwave tube, lose their invariance in the presence of velocity spread; they become functions of position. The changes of S and Π are such as to lower the minimum noise figure. These results are in agreement with a detailed numerical solution of the Boltzmann equation as previously reported by others.