  We propose a setup for measuring visible and near-visible internal
Smith-Purcell radiation and Cherenkov Diffraction Radiation, based on silica
and silicon, and perform quantitative numerical analysis of its radiation
efficiency. We calculate the total radiated energy per electron and the
spectral distribution of different radiation orders, taking into account
material dispersion and absorption. For an optimized silica grating of 200
micrometer length, the total radiated energy reaches 2~eV per electron for 2
MeV electrons. Above the Cherenkov threshold, in most cases the energy of
Cherenkov diffraction radiation is several times higher than the energy of
internal Smith-Purcell radiation, but for some geometries and frequency ranges
first or second order radiation may dominate over Cherenkov radiation (zeroth
order). Radiation up to the 4th order is detected in the simulation. The
spectrum of Cherenkov radiation is highly resonant, with local minima for
frequencies where maxima of the other radiation orders occur. The spectrum of
Cherenkov radiation takes a frequency comb-like shape for a uniform layer of Si
on SiO2 substrate, due to a Fabry-Perot effect occurring for the evanescent
field of the moving electron. The proposed setup could become a prototype of a
non-invasive particle beam monitor for both conventional and laser particle
accelerators.
