Predicting the Equilibrium Deuterium-Tritium Fuel Layer Thickness Profile in an Indirect-Drive Hohlraum Capsule

A numerical procedure for calculating the equilibrium thickness distribution of a thin layer of deuterium and tritium on the inner surface of an indirect drive target sphere (∼ 2.0 mm in diameter) is described. Starting with an assumed uniform thickness layer and with specified thermal boundary conditions, the temperature distribution throughout the capsule and hohlraum (including natural convection in the hohlraum gas) is calculated. Results are used to make a first estimate of the final non-uniform thickness distribution of the layer. This thickness distribution is then used to make a second calculation of the temperature distribution with the same boundary conditions. Legendre polynomial coefficients are evaluated for the two temperature distributions and the two thickness profiles. Final equilibrium Legendre coefficients are determined by linear extrapolation. From these coefficients, the equilibrium layer thickness can be computed