The effect of tolerances in conical flow Pierce guns I—The perturbed flow within the gun

A first-order perturbation analysis of the dc effects of several important tolerances in conical flow Pierce guns is presented for the case in which the gun is part of a solenoid focused system used to produce a smooth Brillouin beam. In this, the first of two parts, the flow up to the anode of the gun is analyzed. The data presented permit calculation of the magnitude of the perturbations at the anode due to various manufacturing errors. These errors are: changes in cathode-anode spacing, changes in cathode curvature, tilt, and transverse displacement of the cathode-focus electrode assembly. The theory does not permit the analysis of cathode to focus electrode tolerances. The perturbations at the anode serve as boundary conditions for the flow beyond the gun which is calculated in the companion paper. A comparison of the magnitude of effects at the anode calculated by the theory and obtained from an experimental study shows that reasonably good agreement exists between theory and experiment.