Shielding would help with protecting the general area, but wouldn’t the actual FF device itself become radioactive? I think the main concern with doing D-T runs is practical — LPP only has enough financial resources for the one FF-1 device, and if they make it too hot to handle easily, that becomes problematic for them to work on further. (I also don’t know if such residual radiation would have any impact on the actual p-B11 reaction when they would move to that fuel.)
