Self-similar compression flows in spherical geometry: numerical calculations and implementations

During the previous APS-SCCM meeting(2007) we exhibited a set of theoretical solutions for the implosion of a sphere initiated by a strong shock. We assumed that: 1. The sphere contains a perfect gas with a polytropic coefficient $\gamma $=5/3. 2. The shock follows the equation: r$_{s}$/r$_{0}$=(-t/t$_{foc})^{\alpha }$ where $\alpha $ is a positive constant and where --t$_{foc}<$t$<$0 The well known G.Guderley solution corresponds to $\alpha =\alpha _{ref}$= 0.6883 and we showed that one other self-similar solution exists for each value of $\alpha $ between 0 and $\alpha _{ref }$. In this paper, we continue this work by solving numerically two particular problems with shock parameter $\alpha $=1/2 and $\alpha $=2/3. The theoretical solutions are obtained with a very good accuracy. For example, the relative gap on the focalization time is less than 1/10000. Then, we use one of these implosions ($\alpha $=2/3) to generate thermonuclear neutrons in DT gas. These neutrons are obtained very early, before the focalization of the initial shock.