Beat frequency undulator radiation and harmonic generation

The spectrum of undulator radiation of a relativistic electron beam in a beat frequency undulator is analytically investigated and analyzed. The field configuration consists of two circularly polarized electromagnetic wave wigglers propagating collinearly in the opposite direction to the traveling relativistic electron beam. The electron motion consists of oscillations at the two wiggler frequencies and the beat frequency of the two wiggler frequencies. As a consequence there is higher harmonic emission on-axis which is absent in the case of a single-frequency circularly polarized electromagnetic wave wiggler or magnetostatic helical wiggler scheme. (paper)