Abstract
The paper presents the analysis of the angular distributions of the incoherent Smith-Purcell radiation (SPR) generated by a charged particle passing over a periodic conducting structure (grating). The calculations were carried out for a grating which consists of conducting strips separated by vacuum gaps and a lamellar grating with the use of three models of this radiation: van den Berg`s model, the surface current model, and the resonant diffraction radiation model. The two last models predict sufficiently close results for different geometries, while the results obtained with van den Berg`s model predict primarily the SPR intensity which is by a few orders of magnitude lower for the electron energy $\ensuremath{\approx}6\text{ }\text{ }\mathrm{MeV}$. The authors propose simple criteria to verify the SPR models by comparing the SPR yields between the volume (with the thickness comparable with a grating period) and flat (with the thickness which is much less than that of a period) gratings; by comparing the azimuth dependencies of the SPR intensities from the flat gratings; by comparing the dependencies of the SPR intensity on the Lorentz factor of a particle.
Highlights
In [1,2,3,4], the authors proposed using the coherent SmithPurcell radiation (SPR) of relativistic electrons to determine the length of short electron bunches
As one can see from the above expressions, the main difference in the predicted SPR intensity between the current model and the one of van den Berg is due to behavior of the radiation factor jRn j2
Similar dependencies for a lamellar grating are presented in Fig. 7: a solid line shows the intensity according to the surface current model (b=d 1=8), dotted and dashdotted lines demonstrate the intensities according to van den Berg‘s model (b=d 1=8 and b=d 0:001)
Summary
In [1,2,3,4], the authors proposed using the coherent SmithPurcell radiation (SPR) of relativistic electrons to determine the length of short electron bunches (with the length less than 1 mm). The authors of [4] came to the conclusion that the power of coherent SPR of electrons with the energy equal to 2.3 MeV agrees satisfactorily with that predicted by the surface current model. In one of the first experiments studying the SPR with the electron energy Ee 3:6 MeV [21], the authors obtained a good agreement with the calculation according to the current model, while the experimental results in [8] for. One should point out that in experiment [19] the measured intensity of the SPR in the optical range for the electrons with energy 855 MeV satisfactorily agrees with van den Berg‘s model and is by 6 orders of magnitude lower than the theoretical estimation of the surface current model. In this work the authors compare the calculated SPR characteristics of different models for characteristic grating types and it is shown that rejection of one or the other model may be achieved by using rather simple relative measurements
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