On the enhancement of coherent emission by energy-phase correlation in a bunched electron beam

Abstract

The coherence effect [1,2] describes emission of radiation from a group of sources whose emission phases are such that the fields of individual sources may be added constructively. While the power of usual incoherent radiation grows in proportion to the number of sources, that of the coherent radiation grows in proportion to its square. A collection of free electrons in a short bunch is an example of such a group of sources. Recent advances in rf accelerator technology have provided us with intense electron bunches that are short enough for inducing coherent effects in the THz frequency range [3, 4]. Coherent THz radiation utilizing those bunches has been demonstrated through various emission processes, such as synchrotron radiation [5], transition radiation [6], and undulator radiation [7]. Recently, Doria et al. proposed that an appropriate energy-phase correlation may enhance the output power of coherent undulator radiation significantly [8,9]. Their claim is that the proposed correlation induces constructive interference of the individual radiation fields emitted by each electron when the electron distribution satisfies the phase-matching condition. This condition is derived from the mode amplitude at the undulator exit [8]: