Focusing the Cherenkov radiation using dielectric concentrator: simulations and comparison with theory

We proceed with investigation of specific dielectric target that effectively concentrates Cherenkov radiation from a charged particle bunch into a small vicinity of the focus point located at the symmetry axis of the target. The case of "non-ideal concentration" where the charge velocity differs from the designed one was considered theoretically in our previous paper. In particular, we have noted that geometrical rays form caustics in this case, and areas of radiation concentration are shifted with respect to the designed focus point. Since the direction of this shift relates to the sign of the charge velocity deviation, this effect can be used for diagnostics of bunch velocity. Here we perform numerical simulations in COMSOL using frequency domain solver and compare simulated results with theoretical ones. In particular, we show that simulated focus area is indeed shifted with change in charge velocity and the position of this area correlate very well with analytical predictions.