Chaotic dynamics of an asymmetric circular billiard with ray splitting

Abstract

The ray evolution in a composite asymmetric circular billiard with ray refraction at the inner phase interface is studied. A quantitative criterion has been derived for the exponential angular widening of an arbitrary ray bundle as a necessary condition of the ray chaos. The possible reconstructions in the phase portrait of the mentioned billiard family in the phase space at changes in the controlling parameter (asymmetry) have been analyzed qualitatively. Lacunar features have been revealed and explained in the phase dynamics associated with the geometric thinning of the acceptable ray paths and with the total internal reflection of the rays from the billiard inner boundary. The results obtained are of importance in description of the light collection phenomena in composite detectors made of several different scintillation materials.