Undulator central cone on harmonic 7
The following image presents the angular pattern of the radiation produced by a 6 GeV filament and mono-energetic electron beam electron beam passing through a 20 periods undulator (K=1.35, Period= 46 mm) and observed at a distance of 27 m from the source at a photon energy of 27 keV corresponding to the 7 th harmonic on axis. The small and bright central cone is the 7th harmonic emission while the rings corresponds to harmonics 8,9 and 10 (The calculation was not done for the higher harmonics. These parameters corresponds to the Machine diagnostic undulator (ID6) which is permanently imaged in the ESRF Control Room.
The next image corresponds to the same electron beam, undulator and observation parameters as in the previous image except for the convolution with the electron emittances of ESRF namely 4 nm (0.04 nm) in the horizontal (vertical) plane. The horizontal (vertical) beta functions in the undulator are 35 m (2.5 m). The central cone of the 7th harmonics has expended into an ellipsoidal bright spot with typical dimensions of 1 x 0.5 mm FWHM. Energy spread is not taken into account but, it is expected to give a small change to the image. The undulator field errors are neglected (correction by spectrum shimming). Clearly the 7-th harmonic of the radiation dominates all other harmonics which are either absent (1-6) or appears as a background (8-10). Between 1992 and 1994, the measurement of the size of the cone of this harmonics was the primary emittance diagnostic of the electron beam at ESRF. Since then it has been replaced by two independent pinhole camera set-up observing the photon beam from bending magnets. (see E. Tarazona, P. Elleaume, Emittance Measurements at the ESRF, Rev. Sci. Instrum. Vol. 66, No. 2, 1995 p 1974. ).
The FWHM horizontal (vertical) divergence of the radiation of the 7th harmonic is 26 (12) micro-rad. It is clear from this image that , at least, the 7th harmonics of the undulator can be efficiently used for experiments requiring both a small beam spot and small divergence. A sample having a dimension of a few tenth of a millimeter can be placed in the cone of the 7th harmonics without any additional focusing of the photon beam.
