On the Nonconservation of Noise Parameters in Multivelocity Beams

Abstract
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.