Thursday, November 1, 2012

19 January 2012 – Going nuclear: Models vs. History

“I’m sure that in 1985 plutonium is available in every corner drugstore, but in 1955 it’s a little hard to come by!” - Dr. Emmet L. Brown


With Iran’s accelerating nuclear activities (and the periodic unfortunate demise of certain of its scientists) consuming all of our attention, a question of an historical bent seems pertinent:  Just how long does it take to build an atomic bomb?

It’s not an idle query, because there are no hard and fast rules.  Every historical case is unique.  The US Manhattan Project, for example, was launched in 1942 and achieved its first nuclear detonation on 16 July 1945, a delay of only three years.  While a great deal of the elementary physics of nuclear explosives had already been set out (including, in some cases, by scientists who later participated in the Project), the fact that two separate viable bomb designs (gun-type, used in the Little Boy weapon dropped on Hiroshima, and implosion-type, used in the Fat Man design that was tested at Alamogordo and subsequently dropped on Nagasaki), and more importantly two separate production processes for weapons-grade fissile material (highly enriched uranium for the gun-type weapons, and plutonium for the implosion weapons) were arrived at in only three years was a feat of defence-focussed R&D that wouldn’t be repeated until the Apollo Program.

(A note on weapon design.  Gun-type weapons function by slamming two sub-critical masses of fissile material together from opposite ends of a tube.  The speed of assembly is limited by the expansion of the combustion products for the propellant used, and runs at several hundred metres per second. Conventional propellant can create velocities of 500-800 metres per second. In an implosion type weapon, a sphere of fissile material is compressed by the controlled explosion of an outer shell of HE.  HE explodes at a speed of 7000-9000 metres per second, depending on the explosive compound (TNT is at the low end, with an explosive velocity of 6900 m/s, while Octol, which is a mix of 75% HMX and 25% TNT, is at the high end, around 8900 m/s.  Speed of assembly for an implosion type weapon is therefore in the range of tens of thousands of metres per second.  Why this is important will be explained later.)

The US experience therefore serves as the benchmark.  All subsequent nuclear weapons programs benefitted from the success of the Manhattan Project, if only from the knowledge that building a nuclear explosive was possible (something that the Manhattan Project scientists couldn’t confirm empirically until the Trinity test).  More direct assistance was available in some cases; the Soviet atomic program, for example, benefitted from espionage by communist agents in the employ of the US government, while Pakistan’s bomb designs were provided by China.  Still, for the sake of historical comparison, it’s worth tracking the progress of nuclear weapons development by other states, if only to demonstrate the extent to which they differ. 

Progress rates of nuclear weapon programs*
Program Start
Fission wpn test
Fusion wpn test
∆to fission
∆to fusion

With the exception of a few outliers, though, the timelines don’t really differ all that much.  In fact, with only two exceptions the average time from program start to achieving a fission explosion seems to vary from 3 to 7 years, with the mode being 6.5 years; while the average time from program start to achieving a fusion (as opposed to simply a boosted fission) explosion seems to vary from 9 to 12 years, with the mode being 11 years.
Of course, those of us looking backward benefit from the existence of historical data points.  And of course there’s no guarantee that the next country to “go nuclear” will necessarily follow historical patterns; every case is different.  Some countries developed nuclear weapons under wartime pressures, while others did not; some had outside assistance, while others went it alone; and one - the US - pursued the project without knowing whether a nuclear weapon was even possible (or, on the other end of the scale, whether it would overperform, and end up setting the atmosphere on fire or destroying the world).  It’s important not to underestimate the value of knowing that something can be done before you set out to try and do it yourself.   It’s also important to bear in mind that at least one of the above countries - Pakistan - likely possessed a nuclear weapon long before testing it.
All of which brings me to the subject of this discussion, which was the attempt by the US Government 46 years ago to try and guesstimate how long it would take for the “next” country to develop a nuclear weapon. 
In May of 1964, the Lawrence Radiation Laboratory at the University of California Livermore (now known as Lawrence Livermore Labs) launched a highly classified, very small project.  Dubbed the “Nth Country Experiment”, the project brought together three post-graduate students, none of whom had any expertise in or specialized knowledge of nuclear weapons, and tasked them to design a workable nuclear explosive device.  The three participants were:

·         David A. Dobson, 27, Ph.D. (Physics, Berkley, 1964) - experimental atomic physics

·         David N. Pipkorn, 28, Ph.D. (Physics, University of Illinois, 1964) - experimental solid state physics

·         Robert W. Seldon, 28, Ph.D. (Physics, University of Wisconsin, 1964) - low temperature physics

Note that all were newly-graduated doctoral candidates.  The experiment was designed to simulate the challenges facing a putative “Nth Country”, one that had access to qualified academic personnel, but no outside assistance.  They were to work entirely from unclassified sources.  The trio were given a single point of contact at LRL - a physicist, A.J. Hudgins - and had to go through him for all information requests.  All communications were conducted in writing to minimize the chance of accidentally passing any helpful information to the team.  Hudgins, using the resources of the weapons designers at LRL and other Department of Energy facilities, took the questions, and - simulating the testing process that would be available to a real team of weapon designers - staffed them out to expert groups to develop answers.  In this way, the trio could propose design and fabrication features for a weapon, and subsequently receive “test data” (derived either from actual previous US nuclear weapon tests, or from simulations of how the proposed material designs might work) to help guide them in their work.
Based on what they were able to learn from unclassified sources (not a great deal, compared to what is available today), they made a number of interesting assumptions about how they should proceed.  I use the word “interesting” because they departed somewhat from their fields and took into consideration economic and political issues in addition to questions of pure physics.  For example, they dismissed U-233 as a fissile material because the cost of building a thorium breeder reactor to produce the element was deemed “prohibitive”.  They established that it would cost about the same to produce U-235 or Pu-239; but when they questioned “Nth Country Treasury Department”, they were informed that the country had the resources to produce one or the other, but not both.  Interestingly, they weighted Pu-239 higher, because it is isolated from uranium reactor waste (whereas U-235 is produced by enriching natural uranium).  This meant that building plutonium-fuelled bombs had economic advantages because it required the “Nth Country” to invest in nuclear reactor technology rather than simply in uranium enrichment technology.
The two other considerations they looked at were physics, and weapon design.  From a physics standpoint, plutonium has both a lower critical mass (meaning less fissile material would be required per bomb) and higher compressibility, which makes it easier than U-235 to use in an implosion type weapon. But plutonium cannot be produced without Pu-240 contamination, which has a high neutron background and a high spontaneous fission rate, making it impossible to use in gun-type weapons, because given their slow assembly speed, the high neutron flux would initiate fission before the core was assembled, causing a premature explosion and a poor yield (a “fizzle”).  U-235, on the other hand, has a low neutron background and a low spontaneous fission rate, meaning that it could be used in a gun-type weapon, which is by far the easier type of design to develop.
According to the trio,

So there was a certain amount of scientific hubris involved in the selection process - which I suppose means that the trio were behaving like normal scientists.  In any event, by December 1964, the three ersatz weaponeers had settled on a plutonium-based implosion type weapon.
The trio attacked the problem in three phases.  Phase I was achieving an understanding of the basic concepts and design considerations required to begin the design process.  Phase II extended the basic physics of the design problem through quantitative neutronics calculations looking at compression characteristics of the materials in question, the design of converging explosive lenses, and the development or selection of detonators and a neutron initiator (an “initiator” provides an initial burst of neutrons to kick-start a fission chain reaction).  The second phase also looked at optimizing the mass of the plutonium core, and establishing the required thickness of the tamper (a metallic layer outside the core that serves both as a solid mass to provide the compressive impulse when struck by the explosive shock wave, and as a neutron reflector to intensify the building neutron flux in the compressed core).  Phase III of the project extended Phase II into final calculations of the implosion physics and the “iterative fission expansion” (i.e., the production of sufficient neutrons at the correct rate to sustain and multiply the fission reaction).  Once these calculations were complete, the bomb design would be “proved” to the maximum theoretical extent possible short of an actual build-and-test.
The trio submitted their design in September 1966.  The final report was submitted in December of that year and was assessed by experienced weapon designers at LRL and elsewhere.  Each of the elements of the design - the core, the tamper, the initiator, the explosives, the detonators, and all of the physics calculations - was individually critiqued.  The final report, which was published in March of 1967, was classified SECRET (ATOMIC WEAPON CATEGORY SIGMA 1), and the version which was released 30 years later in 1995 is so heavily redacted that it does not show whether, in the opinion of the assessors, the design would have worked or not.  The physicists who critiqued the design disagreed with some of the numbers and calculations in the trio’s report, and opined that the designers offered very little firm information about the criticality of the proposed system; they state that “confidence in the expected yield is unwarranted.”  This was not a crushing comment; the US nuclear testing program experienced many extreme variances between expected and actual yields, ranging from numerous complete “fizzles” that achieved no criticality, to the infamous Castle Bravo test shot on 1 March1954, which was expected to produce a yield of 4-6 Mt, but which actually produced a yield of 15 Mt, completely obliterating Bikini Atoll and resulting in a 280-mile fallout plume that contaminated the Marshall Islands and the crew of a Japanese fishing vessel. Sometimes you don't know what you don't know until you "go empirical", and find out the hard way.
One of the interesting things about the report of the Nth Country Experiment is that while the redactors severed anything that might assist an actual Nth Country in building a bomb, they left in a good many very interesting observations made by the project trio and by the experts that assessed their work.  The trio, for example, rejected a priori any comparison between their work and the work at Los Alamos by the Manhattan Project scientists, noting that that prior group contained “some of the world’s outstanding physicists”, and acknowledging the “motivational climate in which they worked.”  The trio, by contrast “had the advantage of knowing that a bomb could be built”.  They also acknowledged the importance of having access to a library containing “a large quantity of literature on shock waves, explosives, nuclear physics and reactor technology” that had been published since 1945.  They noted that the project rules slowed them down somewhat; they spent “a good deal of time preparing requests which presented enough information about our understanding of what was being requested so that a suitable reply could be obtained”; such procedures would not necessarily obtain if a real Nth Country was racing to build a bomb.  There were no artificial firewalls or stovepipes between the physicists, engineers and technicians working at Los Alamos.
They also noted that they could have designed a U-235-based gun type bomb, and that had they done so, they would have been able to submit a working design much earlier.  They also made two very interesting observations about thermonuclear weapons, stating first that while they believed that their implosion weapon would be credible without a test, they could see no way of designing a thermonuclear weapon without testing.  In that context, they made the following observation:

That report was submitted on 14 December 1966.  Exactly six months later, on 17 June 1967, China tested its first thermonuclear weapon, a 3.3 Mt radiation implosion (Teller-Ulam) style device, at Lop Nor.  Obviously the trio knew what they were talking about.
The assessment team also made a number of very interesting observations about the assumptions made by the trio in designing their approach to the experiment:
In other words, an Nth Country might be less interested in long-term economic benefits and challenging scientific problems than getting their hands on a workable bomb NOW.  Such a country might opt for uranium enrichment and a simple, reliable gun-type weapon over building a plutonium production complex and designing a complicated implosion type weapon.
It would certainly explain why, for example, a country with immense oil and gas reserves might be building an enormous uranium enrichment complex (<cough> IRAN <cough>). Hint: it's not for nuclear power plants.
Would a new bomb project work out the same way today?  A lot of things are different from 1966.  There’s a lot more information out there about nuclear weapons design, it’s a lot easier to find thanks to the Innerwebz; and it’s an AWFUL lot easier to do the kinds of calculations necessary to design explosives, cores and shock waves.  One of the anecdotes recounted by Robert Seldon during an interview for the final report details just how much computing technology changed from 1945 to 1965:

An average laptop today has orders of magnitude more computing power than the LRL mainframe did in 1965, and that mainframe was orders of magnitude more powerful than "a room full of girls with desk-calculators".  What took months of data manipulation for the Trinity scientists and weeks of programming for the Nth Country trio would take at most hours for a modern computing setup. Maybe seconds.
So what’s the point of all of this?  Well, I find it interesting that the Nth Country trio managed to get from nothing to what was likely a workable bomb design in about two and a half years of desultory effort (only one of the members was full-time; the others were part-time), all while working from unclassified sources.  That matches pretty closely to the low end of the “delta to fission” timeline that history demonstrates seems to be the average to get to a working bomb.  If you factor in having to build a reactor and produce and refine plutonium from the reactor waste (which admittedly would probably be done concurrently to the bomb design effort), you might add another year or two to that, still falling comfortably into the mid-range of the average time it takes for a country to go from nothing to its first fission test.  So here we have a case where the output of an experimental model seems to line up fairly well with historical experience.
Suppose we apply that model and experience to Iran...what do we get?  Well, it’s a little hard to nail down the beginning of Iran’s nuclear weapons program, as they’ve had a reactor program for quite some time.  The existence of concealed uranium enrichment facilities was revealed in 2002, launching the ongoing IAEA investigation process and leading to seven successive UNSC resolutions demanding cessation of enrichment and imposing sanctions.  Iran has since “doubled down”, building more enrichment capacity and declaring itself a “nuclear state” in 2010.  The point is that we are at the very least well past the decade mark in Iran’s quest for nuclear weapons.  Only North Korea took longer to go from “mission” to “fission” - and Iran isn’t North Korea.  We won’t be able to put Iran on the chart until they actually detonate a nuclear weapon - but if history and the Nth Country Experiment are any guide, statistically speaking there’s a pretty solid chance that they’ve already got one.
But as I said above - “of course there’s no guarantee that the next country to 'go nuclear' will necessarily follow historical patterns; every case is different.”  Some countries - like South Africa, Brazil, and Argentina - stop short of testing.  Others might be stopped short of testing.  I hate to say “we’ll have to wait and see what happens”, but everything, in one way or another, is an experiment, whether it’s leaving 3 guys alone in a room for a couple of years and waiting to see what they come up with...or leaving a bunch of folks like Khomeini and Ahmadinejad alone in a resource-rich country for three decades, and waiting to see what they come up with.
Some experiments go well.  Some don’t.  I guess we’ll have to wait and see how this one goes.
While we're waiting, if you'd like to read the (expurgated) summary report of the Nth Country Experiment, it's available here:


A) I left Israel off the list because the alleged start date for their nuclear weapon program is unconfirmed, and there has been no confirmed test.  Although if that data were entered, it would be a start date in the “late 1950s” with a first weapon built in the “late 1960s”, and a possible test (in conjunction with South Africa) in 1979.  This would give a “delta to fission” of about 20 years.  Deployment-before-testing is historically unusual, but not surprising in an undeclared nuclear power that likely received outside assistance with, and therefore had high confidence in, its bomb design.  Pakistan almost certainly fits this mould as well; it received bomb design assistance from China, and almost certainly had a deployed nuclear weapon long before conducting its first test in 1998 in response to India’s wave of nuclear tests.