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 0 fields described by B =B oz+6=Bo z-Bcosk zkxBsinkozky, where B0= const., 6B=const., and X0=27r/k 0=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 0 in comparison with . In this context, it is found that there are three useful (and exact) invariants (C±,Ch,Cz) associated with singleparticle motion in the equilibrium field B0kz+6 . These invariants are used to construct radially confined Vlasov equilibria f (C,,Cz b2 ±h2Cz) 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 6B/B 0 ' 11