The Iran Nuclear Program and the Boiling Frog Syndrome

The framework is out for the Iran nuke deal, and the shrieking has begun.  However, based on a little arithmetic that I'm kicking myself for not having done about four years ago, the deal may--now--be the best we can do.

From the framework, it is asserted that Iran currently has 19,000 centrifuges deployed and 10 tonnes (metric tonnes, each equal to 1000 kg) of low-enriched uranium (LEU).  I knew about the 19,000 centrifuges, but the 10 tonnes of LEU took me be surprise.  And it's the cause of the self-kicking.

It turns out it's a lot harder to take natural uranium (NU), which is about 0.7% U-235 and enrich it to 3.7% LEU than it is to take 3.7% LEU and enrich it to 90% highly-enriched uranium (HEU).  Here's a handy blurb on how it's done, but the key graph, reproduced below, is the second one:

This takes a little explaining.

First, we're dealing with a standard metric of how much energy it takes to separate a given amount of feed stock uranium of a particular assay to a product stock of a particular enriched assay, called a separative work unit (SWU).  Reading the definition will make your head hurt, but the SWU is very handy, because it tells you how much spinning of centrifuges has to happen to get to a certain level of enrichment.  And if you know how many SWUs a year a particular centrifuge can produce, you can figure out what the enrichment capacity is.

The IR-1 centrifuges that make up most of Iran's separation capacity did about 0.7-0.9 SWUs per centrifuge per year by the end of 2011, and I'd guess that performance has improved somewhat in the intervening three years.  It's gonna be a little less than 1 SWU/year-centrifuge.  I'm going to call it 0.9 SWU/year-centrifuge but remember that that number is an educated guess.

But back to the graph above.  This is the enrichment curve for 1 tonne of NU feedstock.  The horizontal axis is the enrichment level that that uranium has reached, and the vertical axis tells you how many SWUs you have to apply to get there.  Labeled along the curve are some key milestones for typical LEU (4%, although we're going to eyeball that back to 3.7% in a moment, because that's what the agreement implies), and the amount of enriched product stock you get out of that original 1 tonne of feed.  The rest of the stock is assumed to be "tails", or "depleted", meaning that it's had most of the U-235 removed from it (somewhere about 0.2% U-235).

Note that it takes about 800 SWUs to turn the 1 tonne of NU feedstock into 133 kg of 3.7% LEU, but it only takes another 500 SWUs to turn that 133 kg of LEU into 5.6 kg of 90% HEU, fully capable of going boom.

That sounds weird. Why does it take fewer SWUs to make the stock much more enriched?  The answer lies with the amount of material you're enriching.  You go from 1 tonne of NU to 133 kg of LEU, and then to only 5.6 kg of HEU.  The SWUs are work amount on feedstock.  If you consider the LEU to be the feedstock for HEU, rather than NU, then the fewer kilograms to work on means less work for more and more enrichment.

So, to get 1 kg of HEU from NU, you need to put in 232 SWU/kg.
But to get 1 kg of HEU from 3.7% LEU, you only need to put in 89 SWU/kg.  Call it 100 SWU/kg.

Another thing to note:  Enriching from NU to LEU reduces the amount of product by a factor of 7.5.  Enriching NU to HEU reduces the amount of product by a factor of 179.  But enriching LEU to HEU only reduces the amount of product by a factor of about 24, which we will round off to 25 for ease of use.

So how much 90% HEU do we need for a bomb?

The Little Boy bomb dropped on Hiroshima was a "gun-type fission weapon", and it required 64 kg of 80% HEU.  Using conventional cannon technology, it fired a hollow cylinder of HEU over a thinner cylinder of HEU that fit just inside the hollow, to create a critical mass in the world's nastiest game of ring-toss.  It had a yield of about 15 kilotons.

The Fat Man Nagasaki bomb used plutonium in an "implosion" configuration.  In this, shaped charges went off to liquefy, then compress, a solid sphere of plutonium.  Harder to do, but it requires less material, and it generates a better yield.  Fat Man yielded 21 kilotons using 6.2 kg of Pu-239.

Turns out that you can build implosion weapons out of HEU as well, and the state of the art requires a lot less material.  This paper examines three different implosion technologies for both HEU and Pu bombs, labelled "low-tech" (equivalent to Fat Man technology), "medium-tech", and "high-tech".  The "medium-tech" scenario, of which I'd think we'd have to assume a country like Iran was capable, requires only 9 kg of 90% HEU to produce a 20 kiloton bomb, equivalent to what was used on Nagasaki.

Now let's go back to our 10 tonnes of Iranian LEU, and 19,000 centrifuges:

• 10,000 kg of 3.7% LEU / 25 LEU-to-HEU factor = 400 kg of 90% HEU.
• 19,000 centrifuges * 0.9 SWU/yr-cfuge = 17,000 SWU/yr.
• 17,000 SWU/yr / 100 SWU/kg = 170 kg/yr of HEU.
• That's 14 kg/month of HEU.
• So, assuming Iran has a bomb design ready to go (a conservative bet), it could enrich its whole stock of 10 tonnes of LEU and produce 1.5 Nagasaki-sized bombs a month, for two and a half years, ending up with 44 bombs.

Holy shit.

Iran can break out whenever it wants.  It can have 3 bombs, one to test and two to deploy, in two months, give or take some machining and assembly time.  If the IAEA comes to inspect once a month, one trumped-up excuse to force it to skip a visit is all the wiggle room they need.

Based on that, a deal that limits Iran to about 5000 centrifuges and 300 kg of LEU on-hand sounds fuckin' awesome.

But even with the deal, the "one year break out" is silly:

• 300 kg of LEU / 25 LEU-to-HEU factor = 12 kg of 90% HEU
• 5000 centrifuges * 0.9 SWU/yr-cfuge = 4500 SWU/yr.
• 4500 SWU/yr / 100 SWU/kg = 45 kg/yr of HEU.
• That's 3.75 kg/month of HEU.
• We can't use the same 3-bomb criterion for a break-out, because there isn't enough LEU to support 3 bombs' worth of HEU.  But a 1-bomb break out would take 2.4 months.

That doesn't sound like "more than a year" to me.  You can argue whether one untested bomb constitutes a break-out, of course.  But consider the following two game propositions:

1. If I respond to a breakout, I run a risk that the one bomb will be successfully used against me.  Upside: better foreign policy leverage = medium.  Downside * probability of downside: Huge times kinda small = medium.  Downside-to-upside ratio: 1.
2. If I don't respond to a breakout, there is no risk that the bomb will be successfully used against me.  Upside:  Maybe the horse will sing = small.  Downside * probability of downside: foreign policy hemmed in * medium probability = medium.  Downside-to-upside ratio:  less than 1.

But I digress from the main point by pointing out that even the fuckin' awesome deal isn't so fuckin' awesome.  And the main point is this:

How for fuck's sake did we allow this to happen?

Let's go back to the IR-1 centrifuge performance blurb.  There we learn (fig. 1) that Iran had only 7000 centrifuges in May, 2009, and this NYT article states that Iran had about 1 tonne of LEU in February of 2009.

Let's run the numbers:

• 1000 kg of LEU / 25 LEU-to-HEU factor = 40 kg of 90% HEU
• 7000 centrifuges * 0.6 SWU/yr-cfuge (based performance estimates cited above--yaaaay Stuxnet!) = 4200 SWU/yr.
• 4200 SWU/yr / 100 SWU/kg= 42 kg/yr of HEU.
• That's 3.5 kg/month.
• Using the 3-bomb breakout criterion, that's a 7.7 month breakout time.

So, being charitable, the Obama Administration's "deal" pretty much undoes the damage they allowed to happen on their watch.

So how did we get to 10 tonnes and 19,000 centrifuges?

Well, I have to admit that I feel pretty stupid for not running these numbers back then.  There's no magic here.  But the real answer appears that the administration was... really vague, in a happy-talk kinda way, without ever actually lying its ass off:

If Tehran has no hidden fuel-production facilities, to create a bomb it would have to convert its existing stockpile of low-enriched uranium into bomb-grade material. International inspectors, who visit Natanz regularly, would presumably raise alarms. Iran would also have to produce or buy a working weapons design, complete with triggering devices, and make it small enough to fit in one of its missiles.

The official American estimate is that Iran could produce a nuclear weapon between 2010 and 2015, probably later rather than sooner. Meir Dagan, the director of the Mossad, Israel’s main spy agency, told the Israeli Parliament in June that unless action was taken, Iran would have its first bomb by 2014, according to an account in the Israeli newspaper Haaretz that Israeli officials have confirmed.

It's hard not to come to the conclusion that things were pretty bad when Obama took office, and now they're not only bad in a "Waaaahhh, Iran's going to destabilize the region" kind of way; now it's more like "Oh shit oh god, Iran could have a strategic nuclear capability in about two years".

I've been pretty sure that Obama and Clinton's booting of the Status of Forces Agreement for Iraq was the single worst foreign policy blunder of the administration--until now.  This situation's gone from a grease fire in the kitchen at the beginning of Obama's tenure to a five-alarm fire.

Make no mistake:  the deal, if it actually gets done, is not only pretty good, it is now existentially necessary.  But it should never have come to this.  Like the frog that sits in the pot of water and slowly boils to death, we just assumed that the constant accumulation of stockpile and capacity would never make a qualitative difference.