Amplification on relativistic electron beams in combined helical and axial magnetic fields

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Abstract
A free-electron laser with the guide magnetic field operating as an amplifier is analyzed. A simple dispersion relation, similar in form with or without the guide field, is derived. The study of the solutions of the dispersion relation indicates that the guide allows us to (a) enhance the spatial instability in the amplifier, and (b) significantly extend the frequency range of the instability to lower and higher frequencies. This improved operation of the amplifier with the guide field may be achieved at lower values of the pump helical magnetic field. An expression for the power gain in the amplifier as a function of its length is derived and applied in numerical examples to demonstrate the effects of the guide field.