Theory of the free-electron laser in combined helical pump and axial guide fields

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Abstract
The linearized theory of a free-electron-laser amplifier consisting of a relativistic electron beam transported along the axis of a helical wiggler in the presence of an axial guide field is solved exactly. With suitable re-identification of parameters, the theory also applies to the case where the wiggler is replaced by a circularly polarized subluminous radio-frequency pump. The dispersion relation is derived and numerical examples of solutions are presented. These indicate (a) that the use of an axial field permits operation of a laser of given high frequency and undulatory transverse velocity of the unperturbed electron beam at lower values of the pump field, (b) that the gain can be enhanced by approaching the condition of resonance between the effective frequency of the pump and the cyclotron frequency, and (c) that the breadth in frequency of the region corresponding to spatially exponentially growing operation can be much extended.