This raises a very critical point. Nuclear is the only dependable energy source. Fossil fuels will run out or go out of favor. Solar and wind on the other hand will become victims of the next major volcanic eruption as ash destroys them or renders them ineffective.
Deep drilling based geothermal can fill this role too though - and does have the substantial benefit over nuclear that it leaves no surface-supply chains for resources (uranium).
Given that we're so close to being able to do it, we honestly need a Manhattan project initiative to push it through to reality (with the outcome being the machine and process to do the drilling).
An eruption significant enough to impact solar and wind generation globally will also affect other critical requirements of humanity, and the Earth's ecosystem, globally.
Which is to say: You Will Be Having Bigger Problems.
Recovery from regional meterological catastrophes is well within human capabilities.
I do think they are, but it's also (obviously) the case that if an eruption blotted out the sun and disrupted wind currents, having the ability to keep generating power would not help much because the plants and animals we eat would all die.
And what's with the weird tone? It's a super banal point that our food requires sun. I highly doubt you're "shocked" by it.
Nuclear facilities seem pretty fragile / demanding, I doubt one would survive any kind of apocalyptic event. The infrastructure supporting it will be gone.
Nuclear facilities can probably continue to operate amid persistent cloud cover and ash. Wind turbines and solar can not. Agriculture would have to shift artificially lit greenhouses.
Though as a corollary, such an event would be civilisation-ending in any regard.
It's also ... highly rare. Somewhere in the 1 in a million to 100 million year range, which is to say, not only longer than the planning horizon of most human institutions, but well outside the existence of the human species for the most part.
It's also well beyond the available supply of terrestrially-minable uranium,[1] and possibly of ocean-extracted uranium,[2] and thorium[3]. Breeders might be another option, though I've seen no substantive estimates of total fuel availability for that case either.[4]
But as an argument favouring nuclear over other energy options ... this is pretty silly, really.
About the only viable defence against such a risk would be, and I say this as someone who's markedly pessimistic on space colonisation, independent and self-sufficient habitations off-Earth: YACP.[5]
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Notes:
1. If we relied on naturally-occurring terrestrially-mined uranium for all present human energy consumption ... supplies would last fewer than two decades. This is seldom mentioned by nuclear advocates.
2. This offers a potentially much larger supply, as uranium is present as a solute in seawater, but viable industrial-scale extraction is unproven and would require filtering vast quantities of seawater.
3. Thorium is reasonably abundant, though I'm not quite sure how abundant. Thorium-based reactors are not much used, and the concept of molten-salt reactors (MSR) which gained some popularity in the past decade ... faces some very significant engineering hurdles. Managing high-temperature highly-corrosive radioactive salts is ... challenging.
4. Breeders produce plutonium. And now you have two, or more, problems.
