Comparison of plasma frequency reduction factors simulated via 1D time domain lagrangian code and expressions in the literature

In this work, we present a comparison between plasma reduction factors for the case of a pencil e-beam inside a hollow metallic pipe. The values under comparison were obtained via analytic expressions given in the literature and the result of a 1D large signal time domain code. The main distinctive feature of this analysis is the additional consideration of dc space charge forces, since the actual electrostatic force among particles is computed, instead of making the assumption of a neutralizer background. In this way, the propagation of space charge waves can be simulated and the reduced plasma wavelength can be obtained. Simulated results were compared to three others obtained via formulae in the literature. A discrepancy of 1.6~5.4% for a klystron example and 0.7~2.2% for a TWT example, between analytic and simulated results were observed.