Optimization of a high efficiency FEL amplifier

The problem of an efficiency increase of an FEL amplifier is now of great practical importance. Technique of undulator tapering in the post-saturation regime is used at the existing x-ray FELs LCLS and SACLA, and is planned for use at the European XFEL, Swiss FEL, and PAL XFEL. There are also discussions on the future of high peak and average power FELs for scientific and industrial applications. In this paper we perform detailed analysis of the tapering strategies for high power seeded FEL amplifiers. Application of similarity techniques allows us to derive universal law of the undulator tapering.