_Warning: Mind-numbingly detailed and self-referential._

Someone requested a fuller explanation of one corner of “last week’s post on when Iran might achieve breakout capability”:http://www.totalwonkerr.net/1871/iran-when-should-we-panic, specifically the chart showing patterns of centrifuge installation at the Natanz Fuel Enrichment Plan (FEP) in Iran. So this is for anyone who didn’t quite grok the chart. It’s shown here with the original text that surrounded it:

So here, drawn from various IAEA reports, is the pace at which the Iranians have added centrifuge cascades at FEP:

!/images/66.jpg!

What we can gather from this chart is a sense of the minimum rate of centrifuge production. No one can install more than they have. So the solid black line is a floor of about 18 cascades’ worth of machines per year, or one unit. (There are 164 machines in a cascade, so this means close to 3,000 machines/year.) The dashed extension of the line shows the implication of that floor: unless centrifuge production has (for some unknown reason) slowed considerably, a backlog of machines is building up, awaiting installation.

It’s like this. We’re assuming that the Iranians are still churning out new IR-1 centrifuges somewhere, working towards the 50,000 or so that are supposed to go in the Natanz FEP, eventually. We don’t know exactly how fast the machines can be produced, but breakout capability — the subject of the blog post — is sensitive to this question, so we need to come up with a reasonable range of possibilities. Just to be pessimistic, let’s assume that, in the future, they can installed and made operational more or less as soon as they are produced.

The approach explained here is really pretty simplistic, just one part of a “rough and ready” analysis of the larger issue of breakout capability. A more sophisticated analysis is probably possible for those interested in attempting it. Presently, at least, I’m not.

Anyhow, it went like so:

First was reconstructing from IAEA reports just how many cascades (linked groups of 164 centrifuges) were present in the Natanz FEP when the IAEA actually counted them. Those are the colored bars.

_(You can find all but the most current IAEA report on Iran at the “official site”:http://www.iaea.org/NewsCenter/Focus/IaeaIran/index.shtml. ACW may post first, but ISIS rolls up “everything in one spot”:http://www.isisnucleariran.org/documents/iaea/. [I could have saved myself a little time if I’d noticed that the Wisconsin Project had already compiled most of this info in a table and “posted it here”:http://www.iranwatch.org/ourpubs/articles/iranucleartimetable.html. Sigh.] As you can see, for simplicity’s sake, I collapsed a couple of categories of information into one.)_

Second was drawing a simple inference about the lowest possible rate of production for the period (February 2007 to February 2009) from the height and spacing of the bars. This is the solid black line. You will notice that introduction of centrifuges for the period actually peaks in May 2008. So I drew the line from February 2007 to May 2008. That’s the _minimum_ cumulative level of production that would explain the observed number of centrifuges present at the Natanz FEP — assuming, of course, that there wasn’t a big stockpile of centrifuges already sitting around somewhere. Probably there wasn’t, either. What little we know suggests that production wasn’t that rapid in the past. See the bottom of page 9/top of page 10 in “GOV/2004/60”:http://www.iaea.org/Publications/Documents/Board/2004/gov2004-60.pdf.

In case the graphic has scrolled off your screen, here it is again.

!/images/66.jpg!

_You’ll notice that the line kinks at May 2007. If it had been drawn straight from the top of February 2007 to May 2008, it would have sliced through May 2007, which clearly would have violated the assumptions set out above: such a cumulative level of production would not have sufficed to explain the observed number of centrifuges present at the Natanz FEP. Thus the kink. In hindsight, I should have just made the line perfectly straight, so it would intercept the y-axis a bit above the February 2007 bar. Gimme a break, it’s a blog post._

Third was extending the line to the right, in dashed form. This illustrates another assumption: that the pace of production over the entire 25-month period has been roughly constant, _at a minimum_. This would mean that the reason new machines were not introduced to the FEP after May 2008, whatever it was, wasn’t because the machines were unavailable. This interpretation is supported by the gradual ramp-up in operations that you can see in the colors of the bars.

Fourth was eyeballing an annual rate of centrifuge production. I came up with 18 cascades’ worth, which happens to be how many there are in a “unit” (or module) of cascades inside the Natanz FEP. Peering at it again, it looks closer to 19 cascades’ worth, but 1) we’re trying to come up with a low-end estimate, so let’s round down and 2) 18 is more convenient because of its relationship to the structure of the FEP.

Either way, that’s around 3,000 machines/yr, or 250 machines/mo. Minimum. To come up with a reasonable guess at a maximum figure, I simply doubled the minimum. Thus, my working estimate was that Iran produces enough machines to stock one to two new units (or 18 to 36 cascades) per year.

Like it says, rough and ready.

Now, could that minimum figure actually be 3,000 machines/yr too high? Is it possible that the Iranians actually ran out of some key ingredient after May 2008? (Rotor juice? Ball grooves? Handles for the bellows?) Let’s not count on it. The latest report, “GOV/2009/8”:http://www.isisnucleariran.org/assets/pdf/IAEA_Report_Iran_Feb_2009.pdf, observes that

Installation work at Units A25, A27 and A28, including the installation of pipes and cables, is also continuing.

Hmm. Maybe that range should have been _one to three_ new units.

For your reference, here again is the link to “Jeff Lewis’s near-simultaneous post with a near-identical graphic”:http://www.armscontrolwonk.com/2197/nine-cascades-in-vacuum. What’s fascinating is that we independently produced these illustrations to make two different points. Seriously, “what’s the chance”:http://www.totalwonkerr.net/1855/whats-the-chance-ctd?

Hopefully that clarifies things. Yes, it’s pretty long for a footnote to a blog entry.

You’ve suffered enough. Enjoy the “musical bonus”:http://www.youtube.com/watch?v=mKH_XpNZcqI.