Abstract
The dispersion relations of transverse and longitudinal modes in a free-electron laser with helical and axial magnetic fields are derived exactly for the one-dimensional case. The modes with positive and negative helicity are distinguished clearly. An analytically solvable expression for the growth rate of the modes, in resonance with the beam, is obtained. The dependence of the growth rate on system parameters is studied for broad ranges of values and comments on optimization are made.
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