“Reprocessing LWR waste” is very complex (most people think of PUREX reprocessing), and very controversial, and only reduces the waste a few percent. Geologic storage is very complex, and there is concern we can’t store anything for 100,000 years and know it is going to remain stored safely.
When you realize there are many different types of nuclear reactors, not just the Light Water Reactor we’ve been using, you can see other approaches for dealing with LWR waste. There are far simpler methods.
Separating uranium from the nuclear waste is a simple chemical process, fluoride volatility, already used in enriching light water reactor fuel. After shredding the fuel rods and dissolving them in acid, fluorination makes uranium a gas (molten UF4 becomes gaseous UF6) easily separated from molten waste.
Similarly, we can remove plutonium from LWR waste; melt it, use known chemical processes. (No, that would not be weapons grade, far too many other isotopes to be used in a weapon.)
Those two steps reduce the waste from Light Water Reactors to almost completely fission products, a few percent of the original waste.
Virtually all of the fission products have half lives so short they are safe in under 10 years (83%); 2 require 350 years (17%). We know how to store each of these elements for 350 years. No geological storage (million years) is needed.
(There are some long-term fission products created, but neutron bombardment has them decay to short-term radioactive elements. That happens inside the reactor, where there are always neutrons bombarding the fuel.)
The small remaining amounts of isotopes found in LWR waste with longer half lives, aren’t very radioactive, a function of long half lives. These can a) can be separated and bombarded with neutrons (either in a MSR or a special neutron source) so they are transmuted to elements that have very short half lives; or b) are fissile, e.g. plutonium, should be put in a MSR as fuel, they will eventually fission.
Uranium is not highly radioactive. There are small amounts of uranium in most of the earth’s crust and all the oceans. (It is useful in nuclear reactors because it is fissile, not because it is very radioactive.) By itself it is easy to store safely. For example, this is how we’re storing depleted uranium (lower in U235 than natural uranium): “Depleted uranium can be disposed of as low-level radioactive waste if it is converted to chemically stable uranium oxide compounds, such as triuranium octoxide (U3O8) or uranium dioxide (UO2), which are similar to the chemical form of natural uranium.” and “[these oxides] are generally suitable for near-surface disposal as low-level radioactive waste. Uranium exists in the oxide form in nature, but at significantly diluted concentrations. The specific radioactivity (radioactivity per mass of uranium oxide) of the depleted uranium oxides is less than natural uranium because of the reduction of U234, U235, and the majority of daughter products which are removed during the enrichment process. The majority of these daughter products return to natural levels over the course of several million years.” http://www.nrc.gov/materials/fuel-cycle-fac/ur-deconversion/faq-depleted-ur-decon.html
Instead of storing (geologic time frames), use the uranium in a Molten Salt Reactor (thermal-spectrum MSR can use low-enriched uranium, or fast-spectrum MSR can use un-enriched or depleted uranium) or in some other types of reactor. Eliminate the uranium by fission.
People in the LFTR community are developing the specifications and regulations for storing the fission products, including what elements in what amounts would best be stored in which storage method. Some can be stored in glass, or something else to keep them in place, in a metal container. Some will chemically bind with something, to keep them in place in storage. Keeping the fission products each separated, or only with the few fission products that store well in the same way, makes the storage much simpler. Again, most of the fission products have half-lives under 1 year, so need to be stored less than 10 years.
Stopping the radiation is a simple “matter”. “Alpha rays could be stopped by thin sheets of paper or aluminium, whereas beta rays could penetrate several millimetres of aluminium.” [http://en.wikipedia.org/wiki/Beta_decay] Gamma rays are very high energy photons (light), stopped by a few meters of packed dirt, or concrete, or more dense materials like lead or depleted uranium.
The big concern about radiation in nuclear waste is that it might move over time, not that we can’t stop the radiation where it is today. But we don’t have to store the isotopes with short half-lives for long time periods, and these are the highly radioactive isotopes, and we don’t have to store them with long half-life isotopes. We clearly can store these safely for much longer than needed.
All the “no solution for the nuclear waste problem” conversation is by people who don’t know there are other types of nuclear reactor than the Light Water Reactor we’ve been using.
Why aren’t we using Molten Salt Reactors, or other types of reactors the Atomic Energy Commission and nuclear physicists and nuclear engineers recommended since the early 1960s? The fossil fuel companies convinced US Congress to pick LWR, the one type of nuclear reactor safe enough to use yet expensive enough to never destroy the fossil fuel industry; and Congress likes living in those nice cozy lobbyist pockets.