Equilibrium transport of sheet electron beams in solenoidal focusing fields

The transport of sheet electron beams is an important issue in the development of high-power RF generators because large amounts of current can be achieved at reduced space-charge density. In this paper we analyze equilibrium configurations for the transport of sheet electron beams in tapered solenoidal focusing fields. In particular, we use the generalized envelope equations obtained for the evolution of space-charge-dominated beams propagating through a general linear focusing channel [R. Pakter and C. Chen, Phys. Rev. E, 62, 2789 (2000)] to derive an optimal focusing field profile for sheet beam transport. Analytic solutions based on multi-time scale perturbation theory are found and compared to numerical simulations.