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In this paper, the transport of intense sheet electron beams in a uniform solenoidal magnetic field in high-power vacuum electronic devices is theoretically examined with the 3-D beam optics code MICHELLE. It is shown that a solenoidal magnetic field can be an effective transport mechanism for sheet electron beams, provided the beam tunnel is matched to the beam shape, and vice versa. The advantage of solenoidal magnetic field transport relative to periodic magnetic transport resides in the feasibility of transporting higher current density beams due to the higher average field strength achievable in practice and the lower susceptibility to field errors from mechanical misalignments. In addition, a solenoidally transported electron beam is not susceptible to voltage cutoff as in a periodic magnetic focusing system; hence, device efficiency is potentially higher.