Calculations of beam trajectories under non-ideal conditions of PPM focusing

Deviations from ideal PPM focusing of electron beams are calculated by means of paraxial-ray equations by a simple program on a time-sharing computer. Such calculations are of interest to rapidly predict the effect of variations of operating conditions and the tolerance in designing TWT focusing systems. The objective is to eliminate cut and try adjustment of the PPM stack ("shimming"). Previously published differential equations are integrated numerically for the symmetrical cases which include variation of magnetic field level, non-ideal beam injection, and random variations from magnet to magnet. Additional terms are added to take into account asymmetrical effects.