throwaway2037 13 hours ago

    > Enrichment is nonlinear

Can anyone explain the science behind this statement? To be clear: I believe it, and I have seen multiple reputable sources say that Iran can enrich to 90% within a few months. I was surprised that it is so quick.

▲ cryptonector 11 hours ago | parent | next [-]

You start with natural uranium, which has .72% U-235. Getting from that to 20% is _hard_. You need large cascades of centrifuges to do this because it's only .72%, so each stage gets you just a wee bit more enriched. You do this over and over and over again until you get to higher enrichment. Once you have HEU enriching further is very easy for the same reason that it was hard when it was unenriched: now the stuff you don't want (U-238) is much less. To get from 80% HEU to 96% is trivial using the same centrifuge cascades, and how long it takes really depends on a) how much 80% HEU you have, and b) how much 96% HEU you want. If you have 100lbs of 80% HEU then to get to 10lbs of 96% HEU might really only take weeks if not less when it might have taken years to get from .72% to 80%.

	▲	gh02t an hour ago \| parent [-]
		Yep, https://web.mit.edu/22.812j/www/enrichment.pdf is a good starting point if anybody wants to learn more about the economics/logistics of enrichment. Though, it's a notoriously confusing topic so it could take some reading. Tl;dr is that the amount of energy required to separate a mixture of gasses (U238 waste and U235 product) is roughly proportional to the logarithm of the ratio of the U238 percentage and the U235 percentage. So as your feed stream becomes more enriched in U235, it becomes much easier to do subsequent separations. This log relationship is an approximation, but arises out of the statistical mechanics of separating two mixed gasses and the resulting decrease in entropy. Edit: a key point most people I'm guessing aren't aware of: centrifuges don't really care what you feed them, whether the feed is natural or 20% or 89% enriched, they just get increasingly more efficient so that a single "pass" through them produces a greater amount of separation as the feed stock becomes more enriched. They do a fixed amount of "separative work" each pass. The same machines can be used to enrich from natural to 20% as 20%-90% (with some relatively minor caveats), and in fact it takes far fewer machines to do the 20-90 step at the same rate as natural-20.

▲ perihelions 8 hours ago | parent | prev [-]

You know how Shannon entropy works in CS, compression and stuff? Atoms work the same way: their mixing entropy is that same x*ln(x) sum which is an extremely steep function near its boundaries. That's your non-linearity. That statistical entropy corresponds to macroscopic thermodynamic properties, enthalpy and work. The starting uranium atom ratios, 0.7%/99.3%, are a very unbalanced mixture deep into that non-linearity side.

https://en.wikipedia.org/wiki/Entropy_of_mixing

(The other half of it is that, as you progressively enrich, you start to discard the "depleted" part of the mass flow, and work only with the, gradually smaller, "enriched" mass flow).