Universal efficiency and gain computations for high‐gain free‐electron‐laser amplifiers

The free‐electron‐laser (FEL) equations are reduced to a set of one‐dimensional, normalized equations that allow a universal (dimensional) analysis. In universal parameters, numerical integration of the FEL equations indicates a relatively constant saturated ponderomotive wave amplitude independent of both the normalized wiggler potential amplitude and the injected signal level. The constant ponderomotive wave amplitude and an empirical fit for the universal saturation length as a function of normalized wiggler potential amplitude and gain permits unnormalized design calculations for saturated power and saturated length over a wide parameter range. Tapering is considered by deriving analytical expressions for the intrinsic efficiency and taper length. Design values for a high‐gain, high‐efficiency, tapered amplifier at 280 and 560 GHz are presented.