No, I don't think there's much point getting fancy. Most of the radiation from a p-¹¹B Polywell is high-energy photons, and with high-energy photons lead is pretty much it. Photons are essentially stopped by mass, though lead is a bit better at it than other substances.
Tungsten shields are smaller, but they're more expensive, and it looks like they're probably heavier, even for the high-energy gammas - take a look at that chart you posted, and remember that tungsten is about 70% denser than lead.
Actually, try normalizing the attenuation coefficient on density and plotting its inverse against photon energy. Tungsten looks to be completely failing to gain any ground on lead. A tungsten shield is smaller but heavier, if this trend continues as it looks to...
Boron isn't necessarily helpful for a reactor with a neutronicity of 1e-8 and a gamma emission rate of 1e-4; if you've got a foot of lead in the way anyhow, you might as well not bother.
The only reason to complicate the shield that I can see is the cooling requirement - most of the bremsstrahlung will come out in the first few mm, meaning the vacuum vessel itself will probably take a good chunk of the load...
On the other hand, if there were some way to deflect gammas so as to pass through the shield more longitudinally, thus magnifying the effect of a given shield thickness... but that would be pretty tough even with just X-rays...
EDIT: I had forgotten that there's a neutron-producing p-¹¹B reaction that's suppressed if the high-energy tail is depleted. So maybe the gammas work similarly after all. If so, then neutrons and bremsstrahlung could be the only major components, and they require roughly comparable amounts of shielding, but of different types. The water/boron/lead shield sounds about right to me; most of the X-ray power would be dissipated in the water layer, which is easy to cool, opening the possibility of a solid layer of lead past the boron-10. IMO... and I'm not a nuclear engineer...
In other words,
Skipjack wrote:Hmm, ok, so do we have any relyable numbers on the amount of shielding that is now actually needed?
...no. Not yet. For D-D, sure, but no one cares about D-D...