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.

Sunday, January 10, 2010

Epilogue: Israeli ex-Nuclear Head Speaks

From The Times (h/t Naked Capitalism), Uzi Eilam, former director General of the Israeli Atomic Energy Commission and former Director of R&D for the Israeli Ministry of Defense spoke recently about the nuclear threat from Iran:

Eilam, who is thought to be updated by former colleagues on developments in Iran, calls his country’s official view hysterical. “The intelligence community are spreading frightening voices about Iran,” he said.


“Those who say that Iran will obtain a bomb within a year’s time, on what basis did they say so?” he asked. “Where is the evidence?”…

According to well-placed defence sources, Israel is speeding up preparations for a possible attack on Iran’s nuclear sites…

But Eilam argues “such an attack [against Iran] would be counter-productive”.

“One strike is not practical. In order to delay the Iranian programme for three to four years, one needs an armada of aircraft, which only a super-power can provide. Only America can do it.”

Hmm...where have you heard before that the Israelis lack the relevant military capabilities, and could only possibly depend on the Americans to do it?

Tuesday, January 13, 2009

Audience of One

Earlier this week, the New York Times had a very interesting report on a possible Israeli plan to raid the Iranian nuclear enrichment plant at Natanz:

President Bush deflected a secret request by Israel last year [2008] for specialized bunker-busting bombs it wanted for an attack on Iran’s main nuclear complex...

The White House denied that request outright, American officials said, and the Israelis backed off their plans, at least temporarily...But the Bush administration was particularly alarmed by an Israeli request to fly over Iraq to reach Iran’s major nuclear complex at Natanz, where the country’s only known uranium enrichment plant is located.

In my quick hits post last July, I hinted that I wanted to follow up on the combination of several news stories, namely:

  • President George W Bush has told the Israeli government that he may be prepared to approve a future military strike on Iranian nuclear facilities if negotiations with Tehran break down, according to a senior Pentagon official.
  • The official identified two "red lines" that could trigger an Israeli offensive. The first is tied to when Iran's Natanz nuclear facility produces enough highly enriched uranium to make a nuclear weapon... The second red line is connected to when Iran acquires the SA-20 air defense system it is buying from Russia.
  • Israel carried out a major military exercise earlier this month that American officials say appeared to be a rehearsal for a potential bombing attack on Iran’s nuclear facilities.
  • Cordesman said Mullen came to Israel to deliver a message – that Israel did not have a green light to attack Iran and that it would not receive U.S. support for such a move.

I never posted that follow up. It has become timely again, with this report.

I think it is indisputable that Israel simply lacks the capability to deal a significant, long-lasting setback to the Iranian nuclear program. If the U.S.'s best-case scenario from a concentrated attack is a delay of a couple of years, Israel's best-case delay is probably measured in months.
Starting from this observation, I have always believed that Israeli actions with respect to Iran--whether rhetoric, covert action, intelligence-leaking, or military--have all been intended for an audience of one. That one being George W. Bush. So the "major military exercises," I believe, have always been intended only to push Bush towards U.S. military action, rather than as an practice run for actual Israeli military action.

This concern is echoed in the NYT report:

White House officials never conclusively determined whether Israel had decided to go ahead with the strike before the United States protested, or whether Prime Minister Ehud Olmert of Israel was trying to goad the White House into more decisive action before Mr. Bush left office.

There's not a lot of doubt in my mind about this.

On the topic of Natanz, there is an interesting post up at armscontrolwonk on analysis of uranium particle ages. The technical links at the end of the article are very interesting, and also bear on the effectiveness of nuclear forensics.

Radio Silence

The last several months have seen--between a large new contract at work, two small children, and the imminent selection of a seemingly rational president--a great decrease in both time and motivation to put the time into blogging on Iran.

I wonder sometimes if the financial crisis may have played at least some minor role in helping avert disaster. There is only so much executive-crisis-management bandwidth in Washington, and I'm sure every last bit of it was consumed for September and October with the financial crisis. Whether that played a role will be for someone on the inside to make clear someday.

I've one more blog post on an interesting NYT story; after that I expect to be posting rather little. For those of you who have contributed in emails, comments, and links, thank you--I've learned a lot the past couple of years.

Thursday, August 14, 2008

The True and Lawful End of Aspiring

This administration has a long record of using a vapid and naive cover story of democratic evangelism to justify misadventures. For the most part, these misadventures seem to have been fueled by a mix of hubris and corruption. I occasionally suspect that the policies are sold to a President easily gulled by this sort of naive moralism, and that sales pitch then doubles easily for an MSM too uninvested in the truth to care and a populace too busy trying to cover the mortgage to spend time caring.

So for the purposes of this post I wanted to lay out what I think ought to be a non-vapid role of moral considerations in various sorts of foreign policies. To do so, I'm going to make a number of assumptions: that a "right" side exists, that it can be unambiguously identified, that the highest foreign policy goal is to serve the forces of Sweetness And Light (henceforth SAL), and that the amount of SAL at stake in any one conflict can be accurately quantified in units commensurate with resources. These assumptions are not only debatable but probably mostly counterfactual. But taking them we can make some progress on how to think about what one ought to do. Countering assumptions can then be folded into that framework afterwards.

The first observation is that the moral obligation, in such a framework, is not to fix all the world's wrongs and struggle for SAL in every instance, but instead, to maximize the impact of your resources upon the extent of SAL.

The second observation is that it's OK--even necesssary--to take the long view. If you can expand the reach of SAL by 1.5% a year, then after half a century, you will have doubled the world's SAL. That would be a real contribution to humanity, and that it took half a century would not be a substantive criticism. A President might well make his policy goal to end his term with the world 6% better off than when he started it, and be satisfied he was contributing to real progress. Or, as one president put it, heed the

call to bear the burden of a long twilight struggle, year in and year out, "rejoicing in hope, patient in tribulation"—a struggle against the common enemies of man: tyranny, poverty, disease, and war itself.

Put something--even a small thing--in the win column, every year, year after year, and you'll look back after fifty years and be amazed at what's happened. You don't have to win it all in a blaze of glory. In fact, you just can't win that way.

Some years, of course, you won't make the 1.5%. You might have to average 1.7 for a while to make that up. You might make a big mistake, and have to average 2.5 for a decade or so to make up for it.

Taking that long view, one wants to approach every SAL opportunity asking: will I increase SAL by an amount commensurate with my long-term resources, or will I deplete those resources to an extent that it will limit my ability to increase SAL in the future, by more than I could possibly get out of this opportunity?

You do not do the world a favor by fecklessly chasing every single tiny thing and expending vast resources for tiny gains. That comes at the expense of much greater gains that become sacrificed.

So, one can view the twilight struggle as a series of opportunities: at each one, resources are staked, with some probability SAL increases; with some probability, there is a loss and SAL decreases by the amount of your lost resources. How do you maximize the growth of SAL, given a finite resource base, a set of given likelihoods and outcomes, and a desire to make sure that you never face ruin?

This is, as it turns out, just a math problem. The result is the Kelly formula. When the expected value of the stake is positive, you stake a fraction of your resources according to:


where b is relative amount of SAL to be increased in good versus decreased in bad outcomes, p is the likelihood of a good SAL outcome, and q is the likelihood of a bad outcome (i.e. 1-p).

However, when the expected payout is negative (i.e. bp-q is negative), you do nothing. This can occur--in fact, often does occur--when there is, in fact, a possible positive outcome b for SAL. Which is to say--just because there is a chance that you might improve SAL, is no reason to go around staking resources--let alone large resources--on an event.

Let me put it another way. If an Administration is arguing that one side is all SAL and the other side the Prince of Evil, that our foreign policy is to support people who are SAL, and that by intervening we might be able to improve the SAL of the world--even if you uncritically accept all of those assertions, that is still not a case for any particular action one way or another.

If all of those assertions are themselves questionable, well, the decision is even further from resolution.

Two footnotes:

1. The Kelly formula is widely misused and misdescribed in gambling circles. My own rule is: don't believe anything you read about it, unless it's in TeX.
2. "Power to do good is the true and lawful end of aspiring." Francis Bacon.

Filed Under: Requests I Never Imagined Making

Dear Members of the Cheney Administration:

Over the past few days it has become abundantly clear that you've come to the end of your Iraq fix and simply must have another war of some sort. I imagine this is rooted in some horrific combination of psychological insecurities and dark twisted fantasies. There being no Piggies or Simons among you, I'd really have no qualms about putting the lot of you all on an island to let you work this out among yourselves, but that doesn't seem like an option. So I have a request instead.

If you're trying to decide between war with Russia and Iran, please attack Iran.

Yours truly,

Andrew D. Foland

Saturday, July 12, 2008

Quick Hits

There's been a boatload of news of late. Doubtless readers are acutely aware, but I like to (try) to keep a record. Also, a few of the items are interesting to look at together, rather than one-by-one as they dribble in. I think 1,4,8, and 9 are particularly interesting to put together.

So below I link the big stories, and a money quote...

  • BREAKING Amber Light 7/13/08 (Times)

President George W Bush has told the Israeli government that he may be prepared to approve a future military strike on Iranian nuclear facilities if negotiations with Tehran break down, according to a senior Pentagon official.

Despite the opposition of his own generals and widespread scepticism that America is ready to risk the military, political and economic consequences of an airborne strike on Iran, the president has given an “amber light” to an Israeli plan to attack Iran’s main nuclear sites with long-range bombing sorties, the official told The Sunday Times.

In other words, some members of the Democratic leadership—Congress has been under Democratic control since the 2006 elections—were willing, in secret, to go along with the Administration in expanding covert activities directed at Iran, while the Party’s presumptive candidate for President, Barack Obama, has said that he favors direct talks and diplomacy.

For what it's worth, I think it's charming that Hersh feels he needs to remind his readers that Congress has been under Democratic control for the past two years.

demands that the President initiate an international effort to immediately and dramatically increase the economic, political, and diplomatic pressure on Iran to verifiably suspend its nuclear enrichment activities by, inter alia, prohibiting the export to Iran of all refined petroleum products; imposing stringent inspection requirements on all persons, vehicles, ships, planes, trains, and cargo entering or departing Iran;

The official identified two "red lines" that could trigger an Israeli offensive. The first is tied to when Iran's Natanz nuclear facility produces enough highly enriched uranium to make a nuclear weapon... The second red line is connected to when Iran acquires the SA-20 air defense system it is buying from Russia.

[T]he difference between acquiring knowledge and having a bomb is at least five to ten years away. And that´s why I said the intelligence, the British, intelligence, the American intelligence, is saying that Iran is still years, five to ten years away from developing a weapon.

But the designs in Switzerland included ones for smaller, more sophisticated nuclear weapons than the one found in Libya. These would have been ideal for two of Khan’s other major customers, Iran and North Korea. They both faced struggles in building a nuclear warhead small enough to fit atop their ballistic missiles, and these designs were for a warhead that would fit.

  • Operation Merlin (2000) (EW)

If this does pertain to Iran, then the event that precipitated Doe's troubles with the CIA was his report, in 2000, that Iran wasn't pursuing a nuclear program, at precisely the same time as the CIA was having a Russian plant nuclear blueprints with Iran.

  • Israeli exercises (~6/1/08) (NYT)

Israel carried out a major military exercise earlier this month that American officials say appeared to be a rehearsal for a potential bombing attack on Iran’s nuclear facilities.

  • Admiral Mullen Waves Israel Off (7/1/08) (Haaretz, ACW)

Cordesman said Mullen came to Israel to deliver a message – that Israel did not have a green light to attack Iran and that it would not receive U.S. support for such a move.

According to Cordesman, Mullen was expressing the official opinion of the U.S. administration, including that of President George W. Bush and the National Security Council.

Iran has test fired a long-range Shahab-3 missile following warnings from Tehran that it would retaliate against any strike against its nuclear facilities by Israel or the United States.

Monday, July 07, 2008

Славься, страна!

Suppose I were a ruthless, pragmatic, possibly even cynical Russian leader. (Any similarity, express or implied, to persons living or dead, is of course purely coincidental.) Looking at the possible consequences of American military action in Iran I see: American bogged down in a ruinous war, a pariah to her former European allies, and a potential doubling of the value of newfound Russian oil wealth.

What's not to like?

Sunday, July 06, 2008

The NATO Interpretation of NPT Withdrawal

Via the Project on European Nuclear Nonproliferation:

The key document on the US interpretation of Articles I and II is entitled Questions on the Draft Non-Proliferation Treaty asked by US Allies together with Answers given by the United States. (See Annex 2.) The Questions and Answers were enclosed with a letter from Secretary of State, Dean Rusk, to President Johnson. The letter and the Questions and Answers were then transmitted to the Senate on 9 July 1968, along with other relevant documents, for consideration during the Senate ratification hearings on the NPT. This interpretation was thereby made public on 9 July 1968, eight days after the NPT signing ceremony at which the first 56 nations had signed the Treaty.

They also point out:

The US is the only country which has explicitly stated that once a general war has begun, it would no longer feel bound by the NPT. It has thus created a loophole by which it could withdraw from the Treaty without the three month notice period required by NPT article X. In addition, the US approach implicitly creates a loophole for NNWS members of NATO to withdraw from their treaty obligations and receive US nuclear weapons in the event of war.

The Questions and Answers themselves can be found at PENN; here is the relevant passage from what was transmitted to the Senate:

3. Q. Does the draft treaty prohibit arrangements for the deployment of nuclear weapons owned and controlled by the United States within the territory of non-nuclear NATO members?

A. It does not deal with arrangements for deployment of nuclear weapons within allied territory as these do not involve any transfer of nuclear weapons or control over them unless and until a decision were made to go to war, at which time the treaty would no longer be controlling.

(emphasis mine)

I suspect that there is some diligent diplomat in the Iranian Foreign Ministry who has all this laid out for presentation to the UN Security Council within a few hours of any military action. I wouldn't count on a 3-month grace period before enrichment starts.

Hoist, petard, etc.

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.

How Much Uranium? (updated)

There are a number of stories in the news the last few days that hinge on issues of just how much uranium you need to build a weapon. I’ll get to addressing those items in subsequent posts. I just thought I’d lay out some general discussion first.

Critical Mass

Most people are familiar with the phrase "critical mass", as a colloquial term rather than a technical term. Recall that “fissile material” is material that can be used as the fissioning material in a weapon; for present purposes, that is mainly highly enriched uranium (HEU) though plutonium is also used in other contexts. Critical mass is, broadly speaking, the amount of fissile material that, if brought together, will result in a nuclear chain reaction and explosion.

There are a lot of different caveats and dangers hiding in that one sentence, and I want to bring out two of them:

1. Once the explosion gets underway, the hot expanding fireball tends to blow apart all that fissile material you were just trying to put together


2. How much material you need for the chain reaction depends on the exact configuration of the materials

Let's take a look at the first one. The "Little Boy" bomb over Hiroshima contained 64 kilograms of uranium. It was a gun-type assembly. It is easiest to imagine (though it's not quite exactly how it was actually designed) a "bullet" of uranium being shot into a form-fitting hollowed-out core, so that at the moment the bullet slid into and filled up the core, a sphere of uranium--of above critical mass--was formed. One can see that if each of the masses is just below critical mass, a total mass of just under twice critical mass could be acheived, allowing considerable engineering margin.

Of that 64 kg, only about 1 kg actually underwent fission. The other 63 kg of uranium were vaporized and sent spewing into the atmosphere over Hiroshima. And of that 1 kg that fissioned, only about 0.6 g--roughly the mass of a penny--was actually converted into energy. The other 999.4 g were fission products, again spewed out in the massive fireball created by a penny's worth of E=mc2.

The fraction of Uranium that actually gets fissioned (in this case, 1/64 or about 1.5%) is known as the "efficiency" of the weapon. The total energy release in a weapon is directly proportional to the efficiency. If you double the efficiency, you double the explosive power of the weapon. But higher efficiency does not lower the needed critical mass.

One way to increase the efficiency of a weapon is to surround the fissile material by a significant quantity of dense, nonfissile material, which will serve to slow down the expansion of the internal fissioning fireball--giving a few more microseconds of time for fissioning to continue before the core is blown apart.

Now let's look at the second of the issues: the amount of material you need depends on the exact confguration of the materials inside the weapon. The phrase "critical mass", in general refers to the critical mass of material needed, at standard density, in a spherical shape, bare, without being surrounded by any other materials. For pure U-235, that is 52 kg; for Pu-239, it is 10 kg.

There are various ways to decrease the "critical mass". Surrounding the material with neutron-reflecting material is one way to decrease the critical mass.

Another is to increase the density. This latter is acheived by shaped explosive charges, which are fired together all at once around the ball of fissile material. By doing this, the density increases, so the material quantity that was originally less than critical mass, is now more than critical mass, since the critical mass has been lowered. All plutonium weapons are implosion-types.

Weapons design generally has two goals: (a) how can I make a weapon critical with as little fissile material as possible, and (b) how can I make the fissioning as efficient as possible once that critical mass is assembled?

The Bottom Line: How Much HEU?

So one may ask, OK, OK, bottom line, how much fissile material do I need to build a bomb? Let's ask this question focussing on uranium, since the Iranian nuclear program is based on uranium.

The "dumbest" thing one could do is to build a gun-type device without surrounding it with reflecting material. This would require 52 kg of uranium.

The next best thing is to build a gun-type device and surround it with a very thick neutron reflector. FAS reports that enough of it might reduce the needed mass to 15 kg (, though that seems quite a low number to me—probably because it is pure U-235.

There are a few other things I can imagine one might do to shave a few more kg.

From reverse-engineering numbers in publicly available documents on Little Boy, I'd guess that the critical mass was reduced by various methods to around 25 kg.

Another route is, instead of a gun-type design, to implode uranium, increasing the density. I have yet to find any good statement on how low the critical mass can be pushed for uranium implosion devices. I'd speculate an acheivable number around 15 kg, perhaps a hair lower.

Strategic Implications

Now, let's take a moment to look at the strategic implication of good design. The main impact is not on means of delivery, but on the number of weapons a state can build with limited fissile stock. To me it seems that there is only a very short time period in the life of a nuclear power in which quality of nuclear design actually matters. (See Update for more commentary on this). When you have no material, design isn't an issue--you have no weapons. When you have plenty of material, the strategic impact of good design is relatively less; there comes a point where there's not much difference between having 100 weapons and 300; either will serve as an effective deterrent.

But when first "turning on" as a nuclear power, good design is the difference between having enough material to simply test a weapon, and enough material to test a weapon and announce you have two more ready to retaliate with if anyone tries to strike you.

A state that is considering going nuclear will likely not perform any test until it has sufficient material to make several weapons, for precisely the above reason. Good design shortens the breakout time, from the time needed to enrich 52*3 kg of U, to the time needed to enrich 15*3 kg.

Nb that the various means to decrease the critical mass of fissile material needed generally tend to increase the mass of the complete weapon. That is because reflectors, tampers, etc are generally heavier than the number of kg they save. However, because these other materials are abundant, while fissile material scarce, it is a worthwhile tradeoff. But in general, lowering the critical mass through good design does not make the weapon more easily deliverable, for instance by means of a missile. If anything, I’d speculate that for delivery purposes, high-critical-mass designs may be superior.

So a new nuclear power probably has to choose a balance between raw weapons count, and delivery capability, to maximize the deterrent it can achieve with limited fissile material.

(see update)

Finally, improved efficiency weapons, at least for the new nuclear state, does not have significant strategic implications.

How Much LEU?

Above we give a discussion of the amount of highly enriched uranium (HEU) needed to make a weapon. Iran is not currently known to possess any HEU; nor is it simple to see how it could come into possession of any while under the NPT regime.

Recall that natural uranium consists of 99.3% U-238, and 0.7% U-235. Only U-235 is usable in a (simple) weapon. Uranium in a weapon is generally above 90% U-235, though 80% is usable and considered HEU.

However, Iran is certainly enriching LEU (for argument, let us say 4% U-235). How much LEU would Iran need to stockpile, in order to eventually turn it into enough HEU material for a weapon?

In principle, the answer is simply the critical mass, multiplied by 80% divided by 4%. That gives a number somewhere between 300 and 750 kg. However, this is “the slow road”. If there is only this bare minimum amount, it will take considerable time to enrich to HEU.

By raising the tail enrichment, one can enrich to HEU with less enrichment capacity, but at the cost of needing more LEU as input. That is to say, given fixed enrichment capacity, it’s faster and easier to enrich 2000 kg of LEU to 50 kg of HEU, than it is to enrich 750 kg of LEU to 50 kg of HEU. (

For a nation with access to much LEU (as Iran does have under IAEA safeguards) and limited enrichment capacity, the fastest breakout capability is achieved by enriching as much LEU as possible, combined with “good” weapons design.

So how much LEU is needed to build a weapon? Actually “needed” is 350-700 kg. But given Iran’s limited enrichment capacity, considerably more would be desired before committing to enrich to HEU. There really is no red line in LEU quantities.

Updated: CKR rightly points out that good weapons design can have a strategic impact for a longer time than I had supposed, due to improved "weight engineering" for delivery, esp. by missile. Contrary to what I had first thought, the point is well taken, especially in light of today's ACW post about the North Korean weapon test; such designs drive down the fissile mass needed.

Update II: Figure 2 on page 16 of Cochrane & Paine has a good summary of how design quality impacts yield. A 10 kt yield would be a very reasonable one to demonstrate a deterrent capability. If I were a project manager, I would be focussed on the low-tech designs for a first weapon, just to be absolutely sure it went BANG. However, there's some evidence North Korea and Pakistan both tried to start out in the medium technology range.