Consider for a moment a torus. The torus will have two radii. The large one from above (looking down on the donut) of R and the smaller one r (the cross section of the circular tube)
Imagine a object is generated by at a random point inside the plutonium solution, the object will travel in a random direction for a fixed distance d. Each time it changes direction it has probability Pcap of being captured.
What is the probability that the object will be able to bounce around inside the torus and then escape from the torus without being captured.
Secondly what is the probability that the object will fly out of the torus and then re-enter it by flying through the hole in the "donut".
This question relates to the geometric buckling of a nuclear reactor, if we assume that the capture of the neutron in the plutonium nitrate solution has a chance "Q" per capture to generate n new neutrons. Then what will the neutron flux distribution be inside the torus ?
If you will a object with a fissile solution such as plutonium nitrate this it is possible to create a homogenous nuclear reactor, for spheres, cylinders, cubes and other boxes the equations have been worked out and published years ago.