Two-frequency undulator and harmonic generation by an ultrarelativistic electron

Abstract

The spectrum of electromagnetic radiation of a relativistic electron moving in the magnetic field oscillating in two mutually transversal spatial directions with two different frequencies is analytically investigated. The spectral properties of radiation in the planar biharmonic undulator are also discussed. The technique based on the associated Bessel functions was effectively applied in our calculations. The effect of the magnetic field and the undulator parameters on the radiation of the fundamental as well as low and high harmonics was elucidated. It is demonstrated that the biharmonic undulator can be exploited to regulate the emission of certain selected harmonics and hence contribute to the development of the efficient devices with high extraction and narrow spectrum.