Study of instability of sapphire tubes growth by Stepanov method

The paper considers the experimentally observed instability of capillary shaping during the growth of thick-walled sapphire tubes by the Stepanov method. The explanation of this phenomenon is based on the theoretical model of radiative-conductive heat transfer in a crystal. An algorithm is developed for the asymptotic expansion of the problem based on the presence of two small parameters. It is shown that the spatial density of the radiation is inhomogeneous along the cross section of the tube and is maximum near its inner walls. This leads to their overheating and the meniscus separation from the inner edges of the shaper.