Mathematical model of fuel layer degradation when the laser target is heated by thermal radiation in the reactor working chamber

Abstract

We propose a mathematical model of the changes occurring in the geometrical properties of the deuterium-tritium layer on the laser target in the process of its insertion into the reactor working chamber. The model is a parabolic equation of general form in spherical coordinates with nonlinear boundary conditions on a moving boundary. We show that under physically justified assumptions this problem may be regarded as a Stefan problem for a singularly perturbed parabolic equation. The first terms of the solution series are written out. Numerical calculations of the fuel layer degradation time are presented for a real target.