Abstract
A series of analytic relations for the main characteristics of a FEL amplifier with a circular electron beam, a circular waveguide and a helical undulator are obtained. An analytic solution of the self-consistent field equations at the given conditions at the input into the interaction region is obtained with the Laplace transform technique. The case is considered when the unmodulated electron beam and the radiation from the driving generator is fed into the amplifier input. An asymptotic formula for the gain taking into account the effect of the space charge and the energy spread of the particles in the beam is derived. The results of the calculation results with the analytic formulae are compared with the resu;ts obtained by direct integration on a computer of the self-consistent field equations.
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