Simplified small signal gain calculations in free electron lasers

A method proposed recently⁽¹⁾ is used for the evaluation of the small signal gain in various free electron laser configurations. The theory is applied to (a) the wiggler-free free electron laser with a uniform axial guide magnetic field and arbitrary direction of propagation of the amplified radiation and (b) the free electron laser with the axially modulated guide field (lowbitron⁽²⁾). It is demonstrated that the new approach simplifies the gain calculation significantly in comparison with the traditional method.