Where Be9 is being produced

Anna asked:

Could we graph the 9Be and 9Be/Al as a function of r/r0, where r and r0 is a) l outer radius of the cold fuel and then b)the outer radius of the hotspot; r-0 being the initial value.

Be9 production doesn't really have a radial profile in the same sense as e.g. the pressure or the temperature, because it is only produced at the location of the outer ablator material.  This ablator radius does shift with time, however, so I assume what she wanted was the rate of Be9 production plotted at the radius where it was produced.  Since the plots are multivalued (the ablator moves in and then out later on), I've color coded the passage of time, to clarify what is going on.

Here is a plot of the instantaneous rate of Be9 production versus the radius at which it was produced:

The radius is normalized by the initial Hot Spot radius (R0=0.012 cm) at the beginning of the simulation.  The pink is the inward traveling shell, and you can see Be9 production shut off dramatically as the shell turns around (and the dots tend to yellow).

Here is a plot of the ratio of the rates:

If the control were perfect, we'd expect the pink portion on the inward journey to be perfectly flat, and we see that it is indeed approximately flat, though not perfectly so.

It's also fun to look at the evolution of the integrated signal.  Here's the Be9 by itself:

Which as we expect, is monatonic until the production shuts off.  Here is the integrated ration of Be9/Al:

Here you clearly see the shutting off at the innermost radius, and you also get a feeling for how the overall rates die off very shortly after the ablator turns around (i.e. the burn stops and there are no more 14 neutrons incident on the outward moving shell).

Normalizing by the initial ablator radius (R0=0.02 cm) gives the exact same plots of course save the x axis, but these were part of what you asked for, so here they are (Note: The initial ablator radius is not the same as the initial size of the capsule, because our simulation does not start until the shock crosses the hotspot radius, well into the implosion process):

You'll notice this was not a particularly powerful implosion, the initial velocity I used in this simulation was 2.9e7 cm/sec (with a total yield of 2.47848e-03 (MJ) and 4.43250e+15 reactions).  I also tried a much higher implosion velocity of 3.5e7 cm/sec (yield of 7.93379e-03 (MJ) and 1.41888e+16 reactions) but it didn't really collapse much smaller to be honest.   But anyway here are the plots, in case you're interested (I have even higher implosion velocities to test, but they may be unrealistic??):

The points appear sparser than in the earlier plots because the time step decreased drastically during the simulation, and I had to thin the data by a factor of 10 to get it to plot in a reasonable time.

That's it for now, let me know if you've got any questions.