The paper is concerned with the transverse velocity and position noise on electron beams. The equivalence between the actual noisy beam and a modulated filamentary beam is pointed out, and the frequency components of the equivalent filamentary beam modulation is calculated. It is shown that the transverse position noise is reduced by a factor &Ggr;2, which is identical to the space‐charge reduction factor for the longitudinal shot noise. The noise excitation is also expressed in terms of self‐power and cross‐power densities of the four normal modes on a rectilinear filamentary beam in a longitudinal magnetic field.