Acceleration and deceleration model of indirect drive ICF capsules

A general zero-dimensional modelling of implosion without thermonuclear reactions is presented, for standard indirectly driven capsules. It is not substantially a new theory, but new demonstrations and improvements of existing models. The model is derived directly from the gas dynamics conservation equations written in integral form for fluid domains with variable mass, in effect the whole non-ablated capsule, the hot spot and the dense shell. The necessary approximations which involve global or mean quantities are justifed theoretically and checked by comparisons with numerical simulations. Two different sets of approximations are developed, one for each of the acceleration and the deceleration phases of the implosion. An improved—in the sense that the time variation of the hohlraum temperature is fully taken into account as it is required for high gain capsules—rocket model is proposed for the acceleration phase. With further approximations, it gives the maximum implosion velocity and the initial capsule mass corresponding to a given final capsule mass, in terms of the initial outer deuterium–tritium radius and the maximum hohlraum temperature. For the deceleration phase, the present model gives an analytical solution for the time decrease in the implosion velocity up to stagnation. Assuming the invariance of PVγ for the different media considered—a property only approximately verified—this model defines the state of these mediums in deceleration and at stagnation, in terms of the mean entropy parameters, the capsule mass, the mean implosion velocity at the end of acceleration and the initial gas mass filling the shell. A simple ODE, which can be easily integrated numerically, is derived for the hot spot mass which depends on the heat conduction wave ablating the fuel from the inside. All the numerical coefficients presently involved in the model can be calculated from the EOS, opacities and heat conduction parameters, except for the value of the supplementary energy transferred to the non-ablated capsule during deceleration which has been taken here, for simplicity, from simulations. Results obtained with this modelling are shown to be in reasonable agreement with numerical simulations for several different capsules.