The characteristics of noise propagation through a multi‐velocity region with linearly increasing dc potential have been calculated using the density‐function formulation of Siegman, Watkins, and Hsieh. [J. Appl. Phys.28, 1138 (1957)]. This type of noise transducer approximates that found experimentally in electron guns which have produced noise figures of 3 db and less atSband. It is shown that arbitrarily low values of beam noisiness can be obtained by reducing the slope of the potential profile and that adjustment of this parameter provides the practical possibility of attaining very low noise figures in slow space‐charge wave amplifiers as frequency is increased. The calculated results are compared with experimental data atSband andXband.