Focusing of brillouin electron beams by use of long-period magnetic fields

This paper presents theoretical and experimental results on the focusing of Brillouin electron beams by use of long-period magnetic fields. This type of focusing was evolved to overcome limitations on continuous and average powers, efficiency, and operating frequency in state-of-the-art microwave tubes employing short-period sinusoidal focusing fields. The theoretical analysis presents the derivation of the optimum field shape for focusing through a single field reversal, and shows that optimum focusing is achieved when the magnetic flux density is peaked immediately before and after the change of polarity. New theoretical results are presented on the use of long-period focusing fields consisting of optimally peaked reversals separated by constant-field regions. The most important of these results is the high degree of stability possessed by such fields and virtual elimination of stop-bands usually produced by periodic systems. The theory presented is in good agreement with numerical solutions obtained by use of a digital computer. Experimental results obtained on long-period magnet assemblies employing three and seven reversals show beam-transmission efficiencies of 98 percent at perveances comparable to those focused by the optimum state-of-the-art short-period magnets.