Three-dimensional analysis of harmonic generation in high-gain free-electron lasers

In a high-gain free-electron laser (FEL) employing a planar undulator, stro ng bunching at the fundamental wavelength can drive substantial bunching an d power levels at the harmonic frequencies. In this paper we investigate th e three-dimensional evolution of harmonic radiation based on the coupled Ma xwell-Klimoniovich equations that take into account nonlinear harmonic inte ractions. Each harmonic field is a sum of a linear amplification term and a term driven by nonlinear harmonic interactions. After a certain stage of e xponential growth, the dominant nonlinear term is determined by interaction s of the lower nonlinear harmonics and the fundamental radiation. As a resu lt, the gain length, transverse profile, and temporal structure of the firs t few harmonics are eventually governed by those of the fundamental. Transv ersely coherent third-harmonic radiation power is found to approach 1% of t he fundamental power level for current high-gain FEL projects.