Cherenkov radiation from relativistic electrons in inclined transparent radiator

Based on the polarization currents model, a numerical calculation of the Cherenkov radiation photon yield in the wavelength range 400 $<\lambda<$ 850 nm from a silica aerogel radiator with a refractive index $n$ = 1.05 and a thickness of 1 mm, located perpendicular to the electron velocity with the Lorentz factor $\gamma$ = 50, was carried out. It was shown that the number of Cherenkov radiation photons propagating in a vacuum near a conical surface with the opening angle $\theta$ = 18.6$^\circ$ deg coincides with the theoretical estimation from the Tamm–Frank formula. The same method was used to calculate the spectral-angular characteristics of Cherenkov radiation from an inclined quartz radiator ($n$ = 1.76) of the same thickness. It was shown that for the radiator inclination angle $\psi$ = 24.25$^\circ$ deg, part of the Cherenkov cone is extracted into vacuum at an angle $\theta_{\mathrm{vac}}\approx$90$^\circ$ deg relative to the electron momentum. The number of Cherenkov radiation photons in the same spectral range reaches the value of $\Delta N\approx$5.4 photons/electron, which is 3 orders of magnitude higher than the yield of optical transition radiation, which is used to diagnose beams at modern accelerators.