Smith-Purcell radiation in the highly relativistic regime

An electron moving over the surface of a diffraction grating will transfer a part of its kinetic energy to radiation via a velocity synchronous coupling with a slow space harmonic component of the field. Since the phase velocity of a slow space harmonic is less than the speed of light, the slow components decay exponentially, or evanesce, with distance above the grating and the evanescence scale is determined by the product of the relative velocity, β, the relative energy, γ, and the wavelength λ. Thus, in the relativistic regime, good electron - grating coupling can be maintained at beam heights that are greater than the emitted wavelength. In order to explore this regime a series of experiments have been carried out with moderately energetic beams and an experiment with the 70-MeV beam at the Accelerator Test Facility is in the planning stage. The work has two basic goals: the first is to explore the characteristics of the spontaneous emission produced by the beam as it moves over the grating, and the second is to evaluate the potential of grating-coupled or Smith-Purcell free electron lasers. The spontaneous emission is of direct interest. It appears on the basis of work to date that the broad spectral distribution produced by a relativistic electron beam moving over a grating is potentially an alternative source for experiments of the type now carried out on synchrotron infrared beam lines. The grating, or a system of gratings, are also a potential alternative to the magnetic undulator and thus another basic approach to free electron laser design. The presentation will include a summary of the design of the experiment which is to be carried out on the 70-MeV A.T.F. beam line and a review of the theory of Smith-Purcell radiation in the high energy limit. Gain calculations and the role of beam quality in establishing performance limits will be discussed