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Smith-Purcell radiation, generated when a beam of charged particles passes close to the surface of a diffraction grating, has been studied in the visible spectral range at wavelengths of 360 and 546 nm with the low emittance 855 MeV electron beam of the Mainz Microtron MAMI. The beam focused to a spot size of 4 microm (full width at half maximum) passed over optical diffraction gratings of echelle profiles with blaze angles of 0.8 degrees, 17.27 degrees, and 41.12 degrees and grating periods of 0.833 and 9.09 microm. Taking advantage of the specific emission characteristics of Smith-Purcell radiation a clear separation from background components, such as diffracted synchrotron radiation from upstream beam optical elements and transition radiation, was possible. The intensity scales with a modified Bessel function of the first kind as a function of the distance between electron beam and grating surface. Experimental radiation factors have been determined and compared with calculations on the basis of Van den Berg's theory [P.M. Van den Berg, J. Opt. Soc. Am. 63, 689 (1973)]. Fair agreement has been found for gratings with large blaze angles while the measurement with the shallow grating (blaze angle 0.8 degrees ) is at variance with this theory. Finally, the optimal operational parameters of a Smith-Purcell radiation source in view of already existing powerful undulator sources are discussed.

Parametric x-ray or quasi-Cherenkov radiation is produced by the passage of an electron through a crystal. A critical absorber technique has been employed to investigate its linewidth. Experiments have been performed with the 855 MeV electron beam from the Mainz Microtron MAMI. Thin absorber foils were mounted in front of a CCD camera serving as a position sensitive photon detector. Upper limits of the linewidth of 1.2 and 3.5 eV were determined for the (111) and (022) reflections of silicon at photon energies of 4966 and 8332 eV. These limits originate from geometrical line broadening effects that can be optimized to reach the ultimate limit given by the finite length of the wave train.[S0031-9007(97)04050-7] PACS numbers: 41.50. + h, 78.70.Dm Parametric x-ray radiation (PXR) is produced when charged particles traverse a crystal. This radiation can be understood as the coherent superposition of the elementary waves emitted from the atoms which are induced by the electromagnetic field of the passing particle. In an equivalent picture they can be described as the diffraction of the virtual photons associated with the moving particles or as a quasi-Cherenkov radiation in a medium with a periodic dielectricity. The most intriguing feature of PXR is the appearance of a sharp quasimonochromatic x-ray beam close to the Bragg angle. The narrow angular distribution consists of one peak above and one below the symmetry plane of the crystal. Their widths are characterized by the angle u ph ͓1͞g 2 1 ͑v p ͞v͒ 2 ͔ 1͞2 , with g the Lorentz factor of the moving particle, v the angular frequency of the emitted photon, and v p the plasma frequency of the crystal, 31 eV for Si. The theoretical description of the intensity distribution of PXR [1-5], suitably modified for self-absorption and multiple scattering effects, have been tested in a broad range of electron energies extending from 3.5 MeV [6,7] to about 1 GeV [8]. It was found to be accurate within 12%. On the other hand, very little is known about the energy width of PXR. The various theoretical descriptions of PXR predict a very narrow linewidth of less than a few meV. Actually, if it is assumed that a charged particle passes a very thick and perfect single crystal on a straight line and if self-absorption of the photons in the crystal can be neglected, simply a d function results for the line shape. Measurements of the linewidth have been performed up to now at the low beam energy of 6.8 MeV only. A variance of the linewidth of 48 eV has been determined for a 55 mm thick diamond crystal at a photon energy of 8.98 keV [9]. This rather large linewidth originates at low electron energy from the multiple scattering of electrons in the crystal.In this Letter a measurement of PXR at the Mainz Microtron MAMI with a silicon crystal at photon energies of about 5.0 and 8.3 keV is presented. For the high beam energy of MAMI of 855 MeV a line broadening by multiple scattering of the electrons in the crystal can be neglected. This fact originates from the rather surprising result ...

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