Helically distorted relativistic electron beam equilibria for free electron laser applications

The purpose of this paper is to develop a self-consistent kinetic description of helically distorted relativistic electron beam equilibria for free electron laser applications. In particular, radially confined equilibria are considered for a helically distorted electron beam propagating in the combined transverse wiggler and uniform axial guide fields described by B0 = B0êz +δB = B0êz −δB cos k0zêx −δB sin k0zêy , where B0 = const, δB = const, and λ0 = 2π/k0 = const is the axial wavelength of the wiggler field. It is assumed that the beam density and current are sufficiently small that the equilibrium self fields can be neglected in comparison with B0. In this context, it is found that there are three useful (and exact) invariants (C⊥,Ch,Cz) associated with single-particle motion in the equilibrium field B0êz+δB . These invariants are used to construct radially confined Vlasov equilibria fob(C⊥,Ch,Cz) for an intense relativistic electron beam propagating primarily in the z direction. Examples of both solid and hollow beam equilibria are considered, and it is shown that the transverse wiggler field can have a large modulational influence on the beam envelope, depending on the size of δB/B0.