A guest post by R. Scott Kemp.

Friend of Wonk R. Scott Kemp is an assistant professor of nuclear science and engineering at MIT, where he directs the Laboratory for Nuclear Security and Policy. Here, he asks what sort of negotiated outcome with Iran would suffice to address the threat of nuclear breakout. The charts in this post, prepared by the University of Maryland’s Steve Fetter, could help negotiators design an agreement. Scott’s last guest post at ACW was in June 2013.

Well, this is the moment we’ve been waiting for.  Both Iran and the United States have been making positive sounds about the nuclear issue. Obama says he has made Iran a top diplomatic priority for the United States. According to diplomats who met recently with Iranian Foreign Minister Zarif, Iran will consider limits on the number of operating centrifuges and stocks of LEU. The E3+3 and Iran have a meeting scheduled for Geneva on October 15 and 16.

Now it’s time to get down to brass tacks.

While Zarif’s offer of caps is welcome, what really matters is the level of confidence that can be gained from an agreement.  To a large extent, that can only come by increasing the time it would take Iran to make a bomb, which in turn depends on the size of Iran’s nuclear program.

Why does the size of the program matter? There is a fundamental problem with safeguards at enrichment facilities: even if the IAEA could instantaneously detect an attempt to make a bomb, it would take some non-trivial length of time to respond, especially if there is to be a political response and not just a last-ditch military strike. Iran’s “breakout” time needs to be considerably longer than U.S. Central Command’s bare-minimum response time.

The problem is that Iran has already amassed a considerable enrichment capability; by some estimates, it could produce a bomb’s quantity of HEU in less than two months, even if Iran doesn’t use any of its 20%-enriched material.  Merely capping the program at the present size isn’t going to provide enough assurance to restrain the hawks back in the United States. Some rollback of the program, even if not done immediately, is really the only path to confidence and stability.

In this post, I give you the tools to decide just how much rollback is needed by enabling you to calculate the breakout time based on some retained centrifuge-enrichment capacity and the residual stocks of enriched uranium. It’s a Choose Your Own Adventure for nuclear diplomacy.

Where Does Iran Stand Today?

In adding up the numbers, I’m going to set aside the 20%-enriched uranium program and focus exclusively on the 3.5%-enriched uranium program located at FEP, the underground facility in Natanz. I make this simplification because I believe that some closure of the 20% program can be negotiated and the 20%-enriched uranium stockpile can either be converted to fuel elements or removed from the breakout calculation through one of many available technical options.

According to the last IAEA report, at Natanz as of August 24, 2013, Iran had 89 fully installed cascades of IR-1s and was working on 37 more.  Of those 89 IR-1 cascades, 54 were operating. Each IR-1 cascade contains 174 centrifuges and each IR-1 is about 0.9 SWU/year. That gives a capacity of:

IR-1 (operating):  9,396 centrifuges =  8,500 SWU/year

IR-1 (installed): 15,486 centrifuges  =  14,000 SWU/year

The IAEA also reports that Iran has six cascades of IR-2ms installed and is working on 12 more. None have been fed with uranium and we do not know for sure the exact layout of these cascades or how efficient they will be.  However, we could assume the IR-2m cascades also contain 174 machines. We could also assume, consistent with my calculations, that the IR-2m produces about 5 kg-SWU/year/centrifuge. Correcting for some cascade losses, a reasonable net performance would be around 4.7 SWU/year/installed IR-2m centrifuge.  That gives:

IR-2m (potential): 1,044 centrifuges =  4,900 SWU/year  = 5,450 IR-1 equivalents

Notice that this tiny installation of IR-2m centrifuges has more than half the potential of all the currently operating centrifuges at Natanz.  That underscores an obvious but important point: we cannot negotiate simply on the basis of numbers of centrifuges. We must base our computation on the maximum potential separative capacity installed, measured in units of SWU/year. There is some nuance to how one actually goes about accounting for and verifying this number.

In addition, Iran has “stored” separative work in the form of enriched uranium. Thus, from the breakout perspective, the residual stockpile of LEU matters because there is a direct trade-off between the number of centrifuges required and the size of the LEU stockpile available. The IAEA report indicated that Iran had a net accumulation of 5,576 kg of low-enriched uranium (not kg of UF6), which we assume has an enrichment of around 3.5%.

How Long to the Bomb?

Well, let me instead tell you how long to a notional nuclear weapon’s quantity of HEU, rather than to a fully fabricated bomb.  The below charts were produced by Steve Fetter as a result of some discussions we’ve been having.  Steve based these on the standard of one IAEA Significant Quantity (25 kg of uranium-235 contained within HEU), which is reasonable for a first-generation implosion design with manufacturing losses. Some believe Iran would need more than a single bomb; I’m of the view that a single bomb is significant—especially one based on HEU.

Centrifuge performance is based on my estimate of 0.9 SWU/IR-1/year.  We have attempted to include the effects of adjusting the tails to optimize the utilization of the LEU stockpile. However, we have ignored second-order effects such as the time required to adjust the cascades, losses from suboptimal cascade configurations or off-optimal centrifuge operation, and machine crashes associated with working on the cascades.  These problems will extend the breakout time, but the calculations below are the right place to start because they give the most efficient credible case.

These charts show the same thing under different presentations. This first chart shows the trade-off between time and centrifuges under assumptions of different LEU stockpile sizes:


This second chart lets you pick a breakout time and trade off between LEU stockpile size and centrifuge plant capacity:


What Constitutes A Workable End State?

Whatever makes you comfortable.  Policymakers will have to decide how many months of advance warning they can tolerate–or rather, how few.  From one perspective, a relatively short period is acceptable if it allows for swift and decisive military action.  I am of another view: even if military action is swift, it will only be temporarily decisive, resulting in Iran’s withdrawal from the NPT and pursuit of the bomb at a newly constructed clandestine location.  More breathing room is needed to avoid such a precarious balance, preferably closer to a year. That much time would enable reinstitution of sanctions of the harshest type and hopefully lead to a peaceful outcome before resorting to military means.