Comment on “Quantum effects in spontaneous emission by a relativistic, undulating electron beam” by Robb G. R. M. and Bonifacio R.

Abstract

In a recent letter, Robb and Bonifacio [1] claimed that a previously neglected quantum effect results in noticeable changes in the evolution of the energy distribution associated with spontaneous emission in long undulators. They revisited theoretical models used to describe the emission of radiation by relativistic electrons as a continuous diffusive process, and claimed that a drift-diffusion approach can only be used when the parameter =Nw ω/(γmc ) is much smaller than unity, whereNw is the number of undulator periods, is the reduced Planck constant, ω is the photon frequency, γ the relativistic Lorentz factor, m the electron rest mass and c the speed of light. In that work it is argued that when 1, a drift-diffusion equation is no more sufficient to describe the evolution of the distribution of electron momenta, which “occurs as discrete momentum groups according to a Poisson distribution”. However, these results are based on a one-dimensional model of the spontaneous radiation emission. Such model does not account for the angular distribution of the radiation, but only for the emission on axis, which is characterized by an overall relative bandwidth ∼ 1/Nw. In contrast to this, the electron recoil related with the quantized nature of photons depends on the entire angular