| Summary: | We report on experimental studies on the harmonic interaction between an optical laser and a relativistic electron beam in an undulator up to the 15th order. In this experiment, a significant energy modulation is imprinted on the beam longitudinal phase space through the electron-laser interaction when the laser frequency is the 3rd, 5th, 7th, 9th or 15th harmonic of the fundamental resonant frequency of the undulator. The experimental results are in good agreement with theory, and indicate that high harmonic interactions in undulators with large K values and small phase errors can be quite efficient. The results confirm the basic physics of harmonic interaction with a goal toward ushering forward the development of many high harmonic based applications in free-electron lasers.
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