A new one-dimensional analysis of the collective interaction in a free-electron
laser with combined helical wiggler and uniform axial magnetic fields is
presented. Maxwell's curl relations and the cold-fluid equations are employed, with
the appropriate form of solution for right and left circularly polarized electromagnetic
waves and space-charge waves. A set of three linear homogeneous algebraic
equations for the electric field amplitudes of the three propagating waves is derived.
This set may be employed to obtain the general dispersion relation in the
form of a tenth-degree polynomial equation. With the left circular wave assumed
to be nonresonant, the dispersion relation reduces to a seventh-degree polynomial
equation corresponding to four space-charge modes and three right circular modes.
The results of a numerical study of the spatial growth rate and radiation frequency
are presented.
A design for the generation of temporally-coherent radiation pulses in the VUV and beyond by a self-seeding high-gain free electron laser amplifier