Self-consistent numerical model for analyzing thermal layering of liquid mixtures of hydrogen isotopes inside a spherical inertial confinement fusion target

A self-consistent numerical model has been developed to describe the thermally induced behavior of a liquid layer of hydrogen isotopes inside a spherical inertial confinement fusion (ICF) target and to calculate the far-field temperature gradient which will sustain a uniform liquid layer. This method is much faster than the trial-and-error method previously employed. The governing equations are the equations of continuity, momentum, energy, mass diffusion--convection, and conservation of the individual isotopic species. Ordinary and thermal diffusion equations for the diffusion of fluxes of the species are included. These coupled equations are solved by a finite-difference method using upwind schemes, variable mesh, and rigorous boundary conditions. The solution methodology unique to the present problem is discussed in detail. In particular, the significance of the surface tension gradient driven flows (also called as Marangoni flows) in forming uniform liquid layers inside ICF targets is demonstrated. Using the theoretical model, the values of the externally applied thermal gradients that give rise to uniform liquid layers of hydrogen inside a cryogenic spherical-shell ICF target are calculated, and the results compared with the existing experimental data. For targets containing a mixture of hydrogen and deuterium the agreement between the theoretical predictions based on either the binary or ternary mixture model and the experimental data is shown to be excellent