Nuclear Mangos

This blog is intended to provide reliable technical analysis of nuclear issues with non-state actors and nuclear beginner states. Some technical issues have important policy implications that citizens in a democracy should be able to make informed decisions about. The motivation for the blog has been the incredible amount of lies & hyperbole on the Iran situation of early 2006. The blog title is to remind you constantly of the quality of minds in charge of our nuclear security today.

Location: MA

Until recently I was a physics professor at Harvard, where I taught the nuclear and particle physics course, among others. I've recently left that position to work as an R&D physicist in security applications. I have never done classified weapons work.

Tuesday, July 01, 2008

Enrichment: How Much Time?

Suppose Country X wishes to produce Y amount of weapons-usable highly enriched Uranium from Z amount of low-enriched Uranium. How long will it take?

(Note that for most of these designs, there's a lot more to life than simply obtaining the fissile material. More on this below.)

Recall that natural uranium is not usable for a weapon of the kind we're looking at. Instead, the isotope uranium-235 must be separated out for use. It is very difficult to separate out pure U-235, so instead material is graded by its "enrichment"--the fraction of isotope U-235 it has. Natural uranium has 0.7% U-235. "Low-enriched uranium" (LEU) is material that has about 4% U-235, and it is usable as fuel for reactors but not really as a weapon. A country that is a signatory to the Nuclear Nonproliferation Treaty has the right to produce LEU. "Highly enriched uranium" is uranium that contains a much higher fraction of U-235, high enough to be usable for a weapon. Anything more than 20% is the usual threshhold for calling a material "HEU", though weapons are very inefficient below 80% U-235, and generally use 90% HEU. In everything described below I assume the use of 90% enriched HEU.

A stockpile of LEU may be used as the input to create the HEU.

How long it takes to produce a given quantity of enriched uranium depends on the enrichment capacity of the country. Enrichment capacity is measured in "SWU-kg/yr" (separative work units). I see this very often abbreviated just to SWU but I prefer to keep track of all the units, since in principle SWU is its own separate unit.

How much enrichment capacity does Iran have? Iran has 3600 centrifuges online. The enrichment capacity per centrifuge has estimates all over the map from 1 to 5.

2-4 (Iranwatch)
5 (ISIS)
3 (Harrison, quoted via Garwin)
2-3 (Fitzpatrick)

According to a recent ISIS report by Albright et al, Iran is now enriching about 30 kg of input natural uranium to low-enriched uranium (LEU) per month. Assuming that Iran is trying to preserve as much as possible of its input uranium (which seems likely), this corresponds to about 3000 SWU-kg/yr. ISIS also reports that the cascades are running at only about 50% of full capacity. This suggests that full capacity per centrifuge is a little under 2 SWU-kg / year. The same report suggests that to date Iran has enriched about 225 kg of LEU. It also reports that a second set of cascades, another 3600, are coming online in the near future.

To make any estimate of how soon Iran could make a weapon, one must know how much enrichment capacity they are likely to have over the coming months and years. To make progress, one must take a reasonable guess. In what follows, I assume 3000 SWU-kg/yr for the rest of this year (i.e. the current enrichment capability), 4500 for 6 months after that (corresponding to bringing 3600 more on line progressively over 6 more months), 6000 for 6 months after that (running all of them near 50% capacity), and ramping to 10000 thereafter (running near 85% capacity). This seems to me like a schedule that corresponds to things going along without too many hiccups.

If Iran produces only LEU, and no weapons-grade material, the production schedule looks like this:
30 kg / month for 6 months (to 405 kg in 6 months)
45 kg / month for 6 months (to 675 kg in 12 months)
60 kg / month for 6 months (to 1035 kg in 18 months)
100 kg / month thereafter

So how much weapons-usable HEU would Country X like to produce? I lay out 5 scenarios, guided by Cochrane and Paine's estimates:

  1. 6 kg: a single implosion weapon of rather advanced design
  2. 14 kg: a single implosion weapon of fairly acheivable design (Iraq's 80's-era designs were this size)
  3. 20 kg: a single implosion weapon of conservative design
  4. 45 kg: three implosion weapons of fairly acheivable design
  5. 60 kg: one gun-type weapon of very conservative design, or three implosion weapons of conservative design
The length of time to produce the quantity of HEU depends on how much LEU is available. As more LEU available above the minimum absolutely required, the time it takes to enrich up to HEU is reduced. The most relevant number, then, is, for a given amount of LEU that has been produced, how long would it take to use it to make the quantity X? I call this the "breakout time", because enrichment up to HEU could only be done by withdrawing from the Nuclear Nonproliferation Treaty.

This is shown in the following plot, which uses FAS's SWU calculator and the enrichment capacity schedule described above (recall right now the estimate is that Iran has accumulated 225 kg of LEU):

Using the production schedule described above, the X-axis can be turned into simply "time from now". That is, depending on how long one waits from now to start HEU enrichment, and the quantity desired, one can see how long it would take to obtain the quantity of HEU once enrichment began.

This is shown in the following plot:

Drawing Some Conclusions

If you asked me, which of these we should be looking at, I'd probably say, "45 kg". A state generally does not want to test a weapon (and thereby declare itself nuclear) without having a couple of weapons ready for use. I think the record is that states generally have material for a handful of weapons (3-5) when they first test.

Remember, really to do any of this, Iran would have to (a) start a substantial weapons design program and (b) withdraw from the NPT (which takes 3 months before the IAEA safeguards come off); I think it very unlikely they would do so solely to obtain enough material for one single weapon to test and then be left without a deterrent. So I don't think 14 or 20 are really plausible numbers for an Iranian breakout plan. They might become relevant in scenarios which are not going according to plans. I don't think 6 kg is really technically in the range where new nuclear states generally start out, but it's there for completeness.

Also, notice there's no true "red line" in LEU accumulation after which one "has enough to make a weapon". It depends on how technically advanced the nation is, how much yield it is shooting for, how much material it is trying to produce, and how long it is willing to trade of LEU production within the NPT versus breakout time to produce.

So my conclusion is: sufficient material for a true Iranian "breakout" capability looks like it is ~2 years away, to enrich 45 kg of HEU. Material for a single fairly acheivable weapon design might be available 9-10 months from now (if, of course, Iran withdrew from the NPT 6-7 months from now.)

The numbers are all there if you disagree with my reasoning, interpolating between the various lines one can pretty well see how it would likely go for any number between 6 and 60 kg.

Uncertainties are significant. If enrichment capability is brought online faster than described, timelines would be shortened accordingly.

Finally, it is the conclusion of the United States Intelligence Community that Iran does not have a nuclear weapons program. Anything other than the 60 kg gun design would require substantial research and development. Even if material for relatively acheivable designs were available in 9-10 months, it is by no means clear Iran would actually be able to implement those designs in such a time frame. Everything I've ever seen suggests that the time scale for perfecting an implosion design is measured in years.


Anonymous Cheryl Rofer said...

The strategy of how many weapons one needs for what is fascinating, and I haven't seen it worked out anywhere.

You touch on it in saying that it seems foolish to enrich enough uranium merely for a test.


The Hiroshima weapon was a uranium weapon, and it was not tested because the calculations showed that it was, to use an anachronism, a slam-dunk. And indeed it worked. Most likely it was overdesigned, that is, had more uranium than was minimally needed.

The Alamogordo test was of the plutonium implosion design, which was more difficult to execute, both calculationally and operationally. So a test was prudent. This design was then used at Nagasaki.

Truman then threatened further nuclear destruction, even though there were no more bombs and no more material. It took until 1947 for the United States to have a stockpile as large as 17.

We can argue the exact reason for Japan's surrender, but the thought of more of that sort of destruction was undoubtedly an element. The Soviet Union was sufficiently impressed to steal the plans and rapidly develop its own nuclear weapons.

Maybe we should do a blog-tank to develop the strategy of a few nukes.

11:02 AM  
Blogger Andrew Foland said...

It is my understanding that the low-mass options (14, 20, etc) are implosion designs, and would probably present the same need for testing as the Los Alamos plutonium implosion design.

It seems to me that enriching ~45 gives you a successful test (proof to others you have a weapon) and two more weapons; while with 60, you have a single usable weapon, but no "proof" to the world you know how to make it go bang. If I were looking for deterrent I'd probably prefer the first (more weapons + proof), and since it is less material anyway, it dominates. The "only" issue is that it requires an active weapons program of some length. OTOH I am guessing a decent and well-funded team could put together a reasonable gun design in a couple of months at the outside.

As I recall, after Nagasaki the US was actually out of fissile material for a number of weeks.

12:08 PM  
Anonymous Anonymous said...

do you mean KG or KT? I thought these weapons used Kilo Tons of this stuff.

9:43 PM  

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