Effectiveness and limitation of the periodic boundary approximation in the analysis of single-pass electron beam devices

The effectiveness and limitation of the periodic boundary condition (PBC) in the analysis of single-pass electron beam devices are discussed. A Cherenkov traveling-wave amplifier consisting of a dielectric-loaded parallel plate waveguide and a planar relativistic electron beam is picked up as an example of electron beam devices. The numerical results obtained without the PBC are compared with those obtained with the PBC. Then, errors caused by the approximation are found to be mainly attributed to two factors. One is caused by the initial condition, which is inherent to the analysis with the PBC. The other factor is the magnitude of the growth rate. The upper bound for the growth rate is given for which the analysis with the PBC is valid. The analysis with the PBC could be effective for estimating energy transfer efficiency because of its relatively small error and significantly low computational cost.