One solution to it from mid-1990s was sealed reactors that are refueled by sending them back to manufacturer, fitting on single railway car. Combined with being rather hard to extract the material due to coolant used (liquid metal solidifying when shut down or leaking) and various anti-proliferation poisons used, it makes a pretty good solution.
Keep in mind, most of the reactors we are used to are basically 1960s designs. Part of the appeal of building new reactors is that they are so much more efficient that they can actually burn up more of the spent fuel than they themselves create.
Some of the designs are not made to be refueled. In those the fuel gets loaded in at the factory and sealed up. Though in that case they are loaded up with quite a large amount of fuel (like a couple tons of plutonium for a ~30y lifespan)
In such designs you really would only need high security at the factory as stealing fuel from a reactor that is not meant to be opened (you would have to cut into it) and that is on without someone noticing is really really hard.
edit: Would also like to add that such designs are not actively being pursued anymore. The tradeoffs just are not worth it. We know how to securely transport fuel around so that is not that big of an issue really.
Your article also mentions the solution to the fuel problem: Not throwing away almost all the energy, but instead using breeder reactors to extract it.
Although I agree that modern nuclear reactors are extremely safe, I'd hardly say that the problem is 'solved'. They still don't use the fuel efficiently comparatively to what could be done with eg. breeder reactors, and the solution to the waste problem is still 'bury them'. Separating the nuclear waste by isotopes is a very complex and costly process, and even once it's done it doesn't necessarily follow that what is obtained can be used as fuel or for medicine. It depends on the reactor you use, or the kind of medical imaging you need to do.
Research is still ongoing in nuclear (fission) technology.
The big problem with recycling spent nuclear fuel is that the required reprocessing is much worse in terms of safety than the nuclear power plants themselves. Lots of lovely, toxic, highly radioactive solutions which are practically iching to go prompt critical and ruin everyone's day. I think the only reprocessing program which managed not to be a safety train wreck is France's, and I half-suspect they might have just been better at covering up because it's so unusual (and in keeping with other aspects of their nuclear program).
Add “reprocess nuclear fuel rods”. Even once expended and removed from reactors there’s a lot of life left in fuel rods and reprocessing reduces the amount of waste that has to be stored long term.
They've given up on fast reactors. Reprocessing with thermal reactors doesn't actually solve the problem, as MOX fuel cannot then be further reprocessed and used in thermal reactors again. You still end up with all the fission products, and now the higher actinides from spent MOX, to deal with.
Having said that, dry casks are a perfectly cromulent way to deal with spent fuel.
Is that not only an issue when a plant is permanently decommissioned? That seems like a fairly easy problem to solve as well: Bury it like you would any other nuclear waste that can't be reprocessed; or melt the steel down and use it in a new reactor.
Yucca mountain is the wrong solution. We can reprocess nuclear fuel waste easily already, reducing this issue by quite a lot. As a policy issue the United States does not, so you end up with much more “spent fuel” than necessary.
Radioactive byproducts (steel and such) are a bigger issue, but hopefully you only see a lot of that when you are actively decommissioning a plant.
It's not that hard conceptually to deal with. Ideally you reprocess it into more fuel. Worst case you store it on-site in casks, or bury it somewhere geologically stable.
Follow the link in the Wikipedia page to the article on reprocessing. It solves both of the issues you raise: it greatly extends the time the fuel lasts, and it greatly shortens the time that the remaining waste is dangerous. The only reason this was even an issue in the US (it isn't in other nuclear-using countries) is that the Carter administration banned reprocessing because of misplaced concerns about proliferation. In March 1999 the Clinton administration finally reversed that position (probably because it was obvious by then that reprocessing didn't increase proliferation risk--every other nuclear-using country has reprocessed its fuel from the beginning and there have been no incidents). So we can just take all the stuff that was supposed to be stored in Yucca Mountain for 10,000 years and reprocess it instead. Problem solved.
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