Medium Energy Hard X-ray FEL Gain

Abstract

We develop a tool for calculation to study the conditions for a hard x-ray FEL oscillator based on electron beam in the medium enegy range from 3 to 4.5GeV. We show that the approach developed by K.J. Kim, et.al. for the small signal low gain formula can be modified so that the gain can be derived wihout taking the “no focusing approximation” adopted in the approach, so that a strong focusing can be applied. We also derive the formula to allow for gain calculation of harmonic lasing. The gain in this formula can be cast in the form of a product of two factors with one of them only depends on harmonic number, undulator period and gap. Thus this factor can be used to show that it is favorable to use harmonic lasing to achieve hard x-ray FEL working in the medium energy range and in the small signal low gain regime.