Small Signal Bi-Period Harmonic Undulator Free Electron Laser

Abstract

In this paper, we discuss the spectral property of radiation of an electron moving in a biperiod harmonic undulator field with a phase between the primary undulator field and the harmonic field component. We derive the expression for the photons per second per mrad 2 per 0.1% BW of the radiation. A small signal gain analysis also is discussed highlighting this feature of the radiation. A bi-period index parameter, i.e., Λ is introduced in the calculation. According to the value of the index parameter, the scheme can operate as one period or bi-period undulator. It is shown that when Λ = π, the device operates at the fundamental and the third harmonic. However, when Λ = π/2, it is possible to eliminate the third harmonic.