Electron synchrotron radiation in the far infrared

Recent installations at a number of synchrotron light facilities have extended the use of the synchrotron radiation spectrum into the far infrared. At these low frequencies, it is not self-evident that the high-frequency, far-field expressions used normally to describe the synchrotron spectrum are valid. In this paper this question is examined. The near-field distance of the synchrotron source, analogous to the Rayleigh distance of conventional sources, is derived. It is shown that at wavelengths from cm to ${\mathrm{mm}}^{\mathrm{-}1}$ this distance is of the order of 1 m, which is sufficient to influence the siting of an initial aperture. The effect of the finite length of the curved sections of the electron orbit is investigated and it is shown that structure on the ±10-dB level is introduced into the spectrum at these wavelengths. Finally, the temporal and spatial coherence of the field is examined. It is demonstrated that no coherent radiation is to be expected from the synchrotron at these wavelengths, but that at mm wavelengths the field will be spatially coherent over apertures of order 100 mrad.