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.