Calculation of Smith-Purcell radiation from a volume strip grating

Smith-Purcell radiation is generated by a charged particle beam passing close to the surface of a diffraction grating. Experimental investigations show a strong dependency of the emitted radiation intensity on the form of the grating profile. This influence is expressed by the radiation factor which is a measure of the grating efficiency, in close analogy to reflection coefficients of optical grating theories. The radiation factor depends on beam energy and observation geometry. Up to now calculations for radiation factors exist for lamellar, sinusoidal and échelette-type grating profiles. In this paper, calculations of Smith-Purcell radiation factors for volume strip gratings which are separated by vacuum gaps are presented. They are based on the modal expansion method and restricted to perfectly conducting grating surfaces and to electron trajectories perpendicular to the grating grooves. An infinite system of coupled linear algebraic equations for the scattered and the transmitted wave amplitudes is derived by imposing the continuity condition at the open end of the grooves, and by the boundary conditions at the remaining part of the interface. Numerical results are presented and discussed in view of using Smith-Purcell radiation for particle beam diagnostic purposes.