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# Can coherent Smith–Purcell radiation be used to determine the shape of an electron bunch?

ENEA, INN-FIS, Via Enrico Fermi 45, Divisione Fisica Applicata, P.O. Box, 65 I–00044 Frascati (Roma), Italy; Particle Physics Laboratory, University of Oxford, Oxford, UK OX1 3RH; Department of Physics, University of Essex, Colchester, UK CO4 3SQ; Department of Physics & Astronomy, Dartmouth College, Hanover, NH 03755-3528, USA

Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment (Impact Factor: 1.32). 05/2002; DOI: 10.1016/S0168-9002(02)00324-8 - [Show abstract] [Hide abstract]

**ABSTRACT:**Smith-Purcell radiation (SPR), generated by an electron beam traveling above a grating, is characterized by a broad range of frequencies. The radiated wavelength depends on the angle of observation according to the SPR resonance relationship and the bandwidth is inversely proportional to the number of the grating grooves. A rigorous theoretical model of SPR from a three-dimensional bunch of relativistic electrons passing above a grating of finite length is presented by an electric-field integral equation method. The finite-length grating results are compared with the case of an infinitely long grating assumption in which periodic boundary conditions are rigorously applied and with a model based on the image-charge approximation. The SPR resonance relationship is the same in all three formalisms. Significant errors in the strength of the radiated energy are introduced by the two approximations. In particular, for gratings with less than ∼20 periods, the image-charge approximation and the infinitely long grating assumption result in an order of magnitude too high and too low radiated energy per groove, respectively, in the plane transverse to the grating groove lines. Numerical examples are calculated for an ∼18 MeV bunch traveling above different finite-length gratings with a period of 2.5 mm.Physical Review Special Topics - Accelerators and Beams 07/2005; 8(7). · 1.52 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A Smith-Purcell (SP) free electron laser (FEL), composed of a metallic diffraction flat grating, an open cylindrical mirror cavity and a relativistic sheet electron beam with moderate energy, is presented. The characteristics of this device are studied by theoretical analysis, experimental measurements and particle-in-cell (PIC) simulation method. Results indicate that the coherent radiation with an output peak power up to 50 MW at millimeter wavelengths can be generated by using relativistic electron beam of moderate energyOptoelectronics Letters 11/2006; 2(6):422-425. - [Show abstract] [Hide abstract]

**ABSTRACT:**Smith-Purcell (SP) radiation is emitted when an electron passes close to the surface of a metallic grating. The radiation becomes coherent (fluence proportional to the square of the number of electrons) when the electrons are in bunches whose dimensions are smaller than the wavelength of the radiation. This has been observed in experiments in which the electrons are prebunched by an rf linac. The enhancement of the spectral intensity is accompanied by large changes in the angular and spectral distribution of the radiation when the electrons appear in periodic bunches. This is called superradiance. Recently, superradiant SP radiation has been observed from a so-called Smith-Purcell free-electron laser (SP-FEL) in which the electrons are bunched by the lasing process. As in other slow-wave structures, the electron beam in a SP-FEL interacts with an evanescent wave for which the phase velocity matches the electron velocity and amplifies it. The frequency of this wave lies below the range of SP radiation and the wave is not radiated except from the ends of the grating. However, the bunching of the electrons by the interaction with the evanescent wave enhances the ordinary Smith-Purcell radiation and changes the angular and spectral distribution due to superradiant effects. In this article, we introduce a new method for computing the SP radiation in three dimensions, including the effects of finite grating length and superradiance due to periodic electron bunching at an arbitrary frequency. We show that the SP radiation develops spectrally and angularly narrow peaks at the harmonics of the bunching frequency. In rf linacs, where the bunches are widely spaced, several closely spaced harmonics lie under the spectral envelope of the emission from a single electron. In a SP-FEL the harmonics are widely spaced and the SP radiation appears in narrow cones at the SP angles corresponding to the harmonics of the bunching frequency. Finally, we calculate the angular spectral fluence radiated by an electron passing over a lamellar grating of finite length, examine its coherent enhancement in SP-FELs and rf linacs, and compare the results with numerical simulations and available experimental data.Review of Modern Physics 11/2005; 8. · 42.86 Impact Factor

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