Plasma frequency reduction in electron streams by helices and drift tubes

G. M. Branch has emphasized the point that “the principal factor in the reduction of plasma frequencies in electron beams in either cylindrical drift tubes or in helices is due to the finite diameter of the beam.” This point is made by showing that the plasma frequency reduction factor, p , is much more dependent on yb (the ratio of stream circumference to slow wavelength) than on 1) b/a (stream-to-boundary radius), and 2) whether the boundary is a drift tube or a helix.