The four pillars of the waste hierarchy are really not a hierarchy but, properly used, act as a support for minimization of waste and minimization of radiotoxicity as a whole.
Prevention: It could be misinterpreted as not pursuing nuclear and forgoing its huge benefits. That is a self-defeating approach in light of the need for huge quantities of non-carbon energy and, for instance, the many medical applications of radioactivity.
However, prevention should be practiced as part of all designs of structures that are near neutron-emitting cores of reactors. On decommissioning it was realized that the deliberate omission of elements such as niobium as in the stainless steel of a reactor tank would have been a good preventative measure. Niobium becomes activated to Nb-94 with a half-life of 20,000 years, rendering the steel useless for re-use, turning it into long-term radioactive “waste”.
Reduction: Volume is only one aspect. But reduction in radioactivity can be a major factor if the other two pillars, re-use and recycling come into play. Take used CANDU fuel. At the moment its long-lived million-year radioactivity is a major concern. Being a solid, its volume cannot be reduced much.
But examined in detail, used CANDU fuel is not waste at all. Less than 1% of the material has yielded energy from the splitting of its heavy atoms, leaving a fission product residue of medium-sized atoms. Of these about 70% are non-radioactive valuable atoms immediately, while the remainder decay to stable atoms relatively quickly, requiring only safe storage during that time rather than permanent disposition. Only about half a dozen fission products have very long half-lives, with the result that their radioactivity is less than the natural uranium atoms from which they originated.
All the other atoms in used CANDU fuel are heavy, either uranium (mostly) or transuranic elements created in the reactor by neutron irradiation of uranium. Each of them, like uranium itself, can yield about 200 MeV of nuclear energy when split. This energy can all be extracted in a type of SMR, or larger reactor, called a fast-spectrum reactor. Such reactors have existed in research and commercial versions in sizes from 20 kWe to 800 MWe starting in 1951.
This has two major consequences. It extracts over 100 times more non-carbon energy from the used fuel. Second, in splitting the heavy atoms with their million-year radiotoxicity it produces stable fission products (70%) or atoms with much shorter radioactive half-lives.
The choice of such reactors fulfills the first pillar of waste minimization in that massive stockpiles of used fuel waste are avoided.
Second, the amount of material remaining, the fission products, is reduced to less than 1% of the mass of the current used fuel for every MW-h of energy produced.
It all gets done by invoking the third and fourth pillars, re-using the existing used CANDU fuel and recycling it through fast-spectrum reactors.