A Novel Efficient Computational Method for the Electron Optics System in Multibeam Klystrons With Applications to Manufacturing Sensitivities

In a multibeam klystron (MBK) electron optics system (EOS), the beamlets are significantly offset from the global magnetic central axis, in which the transverse component of the magnetic field in the center of each beamlet causes deviation of the beamlet from its local propagation axis. Therefore, it is mandatory to manipulate the magnetic focusing system to mitigate such impact within an acceptable level. This article proposes a novel theoretical analysis method that can rapidly and accurately evaluate electron beam trajectories, significantly improving the computational efficiency by at least 1 $\sim$ 2 orders of magnitude, compared with the conventional full 3-D simulation approach, thus greatly speeding up the design process of MBK. Furthermore, this method can also be applied to determine sensitivities to manufacturing errors in klystron EOS. These errors can significantly impact the electron beam's transmission characteristics, making a thorough analysis and evaluation mandatory. The effectiveness of the proposed method is demonstrated via the optimization of a 16-beam $\textit{S}$ -band high-power high-efficiency MBK and manufacturing errors analysis of $\textit{C}$ -band high-power high-efficiency single beam klystron (SBK).