Phase analysis and focusing of synchrotron radiation

High accuracy calculations of synchrotron radiation (SR) emitted by a relativistic electron show that the phase of the frequency domain electric field of SR differs from the phase of radiation of a virtual point source. These differences may result in the reduction of focusing efficiency of diffraction-limited SR, if the focusing is performed by conventional optical components optimised for point sources. We show that by applying a phase correction locally, one may transform the phase of SR electric field at a desired polarisation to that of a point source. Such corrections are computed for undulator radiation (planar and helical) and bending magnet radiation (central part and edges). The focusing of the corrected SR wavefront can result in the increase of peak intensity in the focused spot up to several times compared to the focusing without correction. For non-diffraction-limited radiation, the effect of the phase corrections is reduced. Due to this reason, the use of the proposed phase corrections in existing electron storage rings is essentially of interest in the photon energy range from infrared to VUV. All numerical calculations discussed in the paper were performed by means of the computer code SRW.