Better Shell Density Profile

Inspection of this plot from the Sanz et al. paper shows that our simplified model of a constant density in the cold fuel as a function of radius is not what simulations of the acceleration phase would predict.

Indeed, their theoretical model is a quadratic function plus a cut off.  For this reason, I put a new shell density model into the code, and ran it.   Here is the $\rho_0(x)$ that I used.

The new density model affected the pressure model in only one of the possible configurations, namely, before the shock and the outer boundary cross, in the region between the shock and the outer boundary.  Currently the pressure model is isobaric behind the shock.  The approximation I made was that in the cold un-shocked region, between the shock position and the outer boundary defining the edge of the ablator shell, the material is isothermal and the shape of the pressure profile is affected by the changing density.  Unfortunately, for all the models I ran, the shock has crossed the outer boundary at peak burn time, therefore the profile plots were all qualitatively similar.  The only difference was that the shock had propagated further by peak burn time in the new model.  The initial conditions look similar to those used in the Sanz paper, here are examples of the initial mass and pressure profiles:

But in order to see the effects of this on other quantities like RIF production, which depend on the pressure, I'll have to find a simulation for which the shock has not yet crossed the outer boundary by the time of peak burn.  Possibly even more of a fizzler than this.   I'll try and get back to this soon. 

For the moment, however, I am going to go back to the velocity diagnostic, and re-run the simulation turning on the radiation losses and the feedback from reactions.  We shall see if we are getting the blow-up behavior seen in the garnier paper.