Calculations of Smith-Purcell radiation generated by electrons of 1–100 MeV

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Abstract
Smith-Purcell radiation is produced when a charged particle moves close to a conducting grating. Recent experiments using electrons of 3.6 MeV have demonstrated the potential use of this effect as a strong tunable radiation source in the infrared spectral range. Large intensities can be expected using high-energy electrons but apparently no detailed calculations have been published until now for this energy domain. We have calculated spectra of Smith-Purcell radiation generated by 1–100-MeV electrons using the integral method, which is of general validity for any type of grating profile, and using the modal expansion method and the improved point-matching method for lamellar and sinusoidal gratings, respectively. The calculations are restricted to perfectly conducting surfaces and to electron trajectories perpendicular to the grating rulings. Some problems related to an extension of the model to include finite electrical conductivity (as needed for calculations of Smith-Purcell radiation in the uv and x-ray spectral range) and for arbitrary tilting angles of the electron beam with respect to the grating rulings are discussed.