I. Introduction
Compared with the traditional cylindrical electron beam, the sheet electron beam could provide a much higher beam current by enlarging its cross-sectional area while remaining a relatively similar or even smaller space charge intensity [1], [2]. In recent years, sheet electron beam devices, including traveling wave tubes (TWTs) [3], klystrons [4], backward wave oscillators [5], and extended interaction oscillators [6] are widely studied as they are capable of generating much higher output power in comparison to vacuum electron devices based on a cylindrical beam.