The effect of tolerances in conical flow Pierce guns II—The perturbed flow in the magnetic field

The first-order perturbations to a beam initially in nonrippling Brillouin flow, which results from several common manufacturing errors in conical flow Pierce guns, are calculated. The manufacturing errors are changes in cathode-anode spacing, changes in cathode curvature, tilt, and transverse displacement of the cathode-focus electrode assembly, and tilt and transverse misalignment of the whole gun to the magnetic field. Errors in cathode-to-focus electrode spacing are not discussed. The tolerances which destroy the rotational symmetry of the gun are shown to cause the smooth beam to perform a helical motion; the tolerances which preserve the symmetry are shown to produce an undulating beam. Using the results of Part I of this paper [1], the magnitudes of individual gun tolerances are related to the effects they produce in the magnetic field. A method of setting limits to the individual gun tolerances is presented and illustrated by calculating tolerances for a gun used in an X-band traveling-wave tube. The calculated tolerances are found to have values which may readily be achieved by careful engineering.