Analysis of the stability of a uniform liquid fuel layer inside a spherical-shell cryogenic inertial confinement fusion target

The effects of thickness perturbations on the stability of a uniformly thick liquid layer of a ternary deuterium--tritium mixture inside a spherical-shell cryogenic inertial confinement fusion target are investigated. Initially, the surface tension gradient required at the liquid--vapor interface to keep the liquid fuel layer uniform is calculated directly by balancing the forces acting on the interface. This method is much faster than the trial-and-error method previously employed. Once the value of the surface tension coefficient is known for each cell, the transient, incompressible Navier--Stokes equations, along with the continuity equation, are solved using the volume-of-fluid algorithm for given perturbations. The solution gives the transient behavior of the liquid fuel layer for varying liquid layer thicknesses and different perturbation amplitudes and wavelengths