Zhirong Huang and Kwang-Je Kim
Argonne National Laboratory, Argonne, Illinois 60439, USA
We discuss the results of a recent investigation[1] of linear and nonlinear harmonic generation in high-gain free-electron lasers employing a planar undulator. For the processes of coherent amplification and self-amplified spontaneous emission, the three-dimensional evolution of harmonic radiation is analyzed using the coupled Maxwell-Klimontovich equations that take into account nonlinear harmonic interactions. Although the linear harmonic generation is always negligible compared to the amplification of the fundamental radiation, strong bunching caused by the fundamental radiation can give rise to significant nonlinear harmonic generation. As a result, gain length, transverse profile, and temporal structure of the first few harmonics are eventually governed by those of the fundamental. Transversely coherent third-harmonic radiation power is found to approach one percent of the fundamental power level for current high-gain FEL projects.
[1] Z. Huang and K.-J. Kim, submitted to Physical Review E, 2000.
