Nuclear Non-Proliferation
How to prevent nuclear proliferation, where Kim Jong Il screwed up, and atomic pilgrimages to Trinity & Tinian
(Official Disclaimer: The mock-up shown here is an art project, guys)
(Go to the Using My Photos page on this site for instructions on how to obtain high-resolution versions of these images from me. I don’t charge money for my photos, but I do require a photo credit in your end-product in exchange for the use of my images.)
All of the information presented on this page is drawn from open literature sources and first-principle calculations. None of this information is restricted in any form. This information is presented to help people understand that the only way to slow down or prevent nuclear proliferation is to restrict access to the special nuclear materials U-235 and Pu-239.
If our democracy’s electorate is to have an informed understanding of this topic, and of the related issues surrounding the development of U-235 production capacity by Iran and the development of nuclear weapons by the DPRK (North Korea) it is necessary to understand the basic principles of simple nuclear bomb design. This page presents this information for this purpose of public education.
I have included some light-hearted photos on this page to inject a small bit of humor into an otherwise very serious topic.
Summary
Back in 1986, when I was finishing my undergraduate career at the University of Colorado at Boulder, I took a terrific class, “Physics of the Nuclear Arms Race.” It was taught by professors Ristinen and Petersen. For my class project I wrote a thoroughly researched paper for which I did a set of independent calculations, “Physics and Construction of a Gun-Type Fission Weapon.” I did the standard calculations for critical mass, assembly speed and tamper thickness for a U-235 device for the paper. Briefly, here is my primer on the high points of the design process. This primer culminates with a description of a full-scale mock-up that I built of a simple gun-type fission weapon. This material is presented here for the purpose of education on non-proliferation issues. There is no information that is not already available to the public in one forum or another.
I won’t post the paper that I wrote on the specifics of the gun design, but I am posting a related paper that I wrote for an excellent political science class taught by Professor Bob Lawrence of Colorado State University (now retired). In this term paper I computed the maximum number of nuclear warheads that the United States might conceivably need to have defended itself from the old Soviet Union during the Cold War. That is to say, I computed the maximum number of warheads that would ever have been needed to maintain an adequate deterrent force for the United States in the Cold War. Click here: Strategic Deterrence Requirements paper for that document, complete with Professor Lawrence’s handwritten notes and commentary.
I liked my term paper on the maximum number of nuclear warheads required for strategic deterrence because I took an analytical approach to a problem that too many people tried to work out on an emotional, political and economic basis during the Cold War. The result was that the United States and the old Soviet Union both wound up with an order of magnitude more nuclear weapons than either one of them needed to achieve deterrence.
On a related note, I wrote a nice primer on the physics of strategic reconnaissance satellites, downloadable here as Arms Verification and the Physics of Reconnaissance Satellites. Twenty years after I wrote it, I believe that it remains very informative.
(If you experience any document download problems, such as not seeing the entire document when you download it, please contact me. I have obtained the best download behavior when using the Safari browser for both PC and Mac.)
Introduction
All matter is composed of atoms. Each atom contains a core, the nucleus, and a cloud of electrons that maintains a roughly spherical shape around the core. All of the electrons are negatively charged. An equal number of positively charged particles called protons occupy the nucleus. Along with the protons in the nucleus are neutral particles called, appropriately, neutrons. The positively charged protons all want to fly away from one another. They are held together in the core by a force called the nuclear strong force which results from the exchange of particles called pions between the protons and the neutrons.
Nuclear Binding Energy: Why and How Fusion and Fission Make Energy
It is an amazing fact that this binding energy between the protons and neutrons is equivalent to mass via Einstein’s famous E=mc^2 equation. The upshot of this fact, of this equation, is that a set of, say, two protons and two neutrons, if weighed separately on a scale, will actually have a different weight than if they are all weighed together as single atomic nucleus. The aggregate of two protons and two neutrons actually weighs less than they do separately! The difference in their individual versus their aggregate masses, if multiplied by the square of the speed of light, is the amount of energy that is released if one in fact squeezes these particles together into a new atom. That process, called fusion, is what happens in stars like our sun, and this how they make heat and light. (Gravity does the squeezing, turning hydrogen atoms into the four-particle helium atoms of this example.) As stars fuse various nuclei to make energy they also make elements up to including the weight of iron. This process is called nucleosynthesis.
It happens that the most stable of all atomic nuclei is iron. If one squeezes together any two atomic nuclei that are lighter than iron to make a final nucleus that is closer to (but still less than or equal to) the weight of iron, then the fusion process yields net energy output, because the product nucleus is closer to iron and thus more stable than either of the two initial nuclei. Elements heavier than iron cannot ordinarily be made in stellar interiors because fusion does not yield energy for products that are heavier than iron.
In old stars that have exhausted their fusion fuel and which are overloaded with iron and lighter elements, and which have more than a critical amount of total mass, life ends in a catastrophic explosion called a supernova. A supernova is a thermonuclear explosion which generates, in fractions of a second, elements much heavier than iron, up to at least uranium and plutonium and even beyond. (Our sun is too small to do this. It will merely swell to the size of a red giant and then eventually fade to a white dwarf.)
The heavier-than-iron elements are less stable than iron. Just as fusion of elements that are lighter than iron to yield products that are closer to iron will yield energy, so the breakdown, or fission, of elements that are heavier than iron, resulting in products that are lighter than the original nucleus but that are heavier than (or equal to) iron nuclei will also yield energy. Just as for fusion, there is a difference between the weight of the original atom and the individual weights of the atoms into which it has fissioned. That mass difference multiplied by the square of the speed of light is the amount of energy that is liberated by the fission. It represents the release of the positively-charged-proton-against-positively-charged-proton binding energy in the atomic nucleus of the heavy original atom.
Neutron-Induced Fission Chain Reactions
As a general rule, the heavier an element is relative to iron, the more unstable it is and the more energy that will be liberated when it fissions. Some fissions occur spontaneously, but sometimes fissions are initiated by the impact of a neutron into an atomic nucleus, a bit (only a bit) like the impact of a bullet into a cookie. Moreover, most fissions yield bonus neutrons. One can envision a scenario in which a collection of unstable nuclei that are already prone to fission in fact begin to cause one another to fission in a chain reaction. The way it would work is: a heavy atomic nucleus fissions. It releases energy due to the conversion of some binding mass-energy. It also happens to release two or more neutrons, on the average. If each of those neutrons collide with neighboring atoms, then those target nuclei begin to oscillate like vibrating water drops. They assume elongated shapes that look like dumbbell weights. This is called scission. If they become sufficiently elongated, they actually snap into two or more pieces at the narrow neck of the elongation. This is the moment of fission, when more energy is released along with (on the average) two more neutrons from each of the two target nuclei. The process of fission can then run away, starting with one nucleus that fissions two more, then a total of four nuclei being fissioned by them, then eight being fissioned, then sixteen, then thirty-two, and so forth.
A thousand nuclei will fission in ten doubling generations. A million will fission in twenty generations. A billion will fission in thirty generations. In eighty generations, about two times ten to the twenty-fourth power nuclei will have fissioned. This would represent the fission of about 1 kg of material.
The fission of about this much matter, of about 80 generations-worth of a neutron chain reaction, will liberate enough energy to destroy a medium-sized city. That is an atomic bomb.
Steady-State Fission in Reactors Versus Runaway Fission in Bombs
If, on the other hand, a fission chain reaction is somehow controlled, or moderated in such a way that the rate of neutron production exactly equals the rate of neutron loss, then we have built a power-production reactor. In a reactor the chain reaction is moderated to maintain a steady state. In a weapon, in contrast, the rate of neutron production rapidly exceeds the rate of neutron loss, so that heat builds up rapidly to very high levels and the device explodes. Such neutron-induced fission chain reactions are referred to as runaway reactions.
Fission Fuels
Neutron chain reactions depend upon the ease with which nuclei will fission, the energies of the neutrons that the fissions emit, and the number of neutrons that are emitted with each fission. Nuclear weapons rely upon the sustenance of runaway fission chain chain reactions. There are two types of fuel that have suitable characteristics for runaway chain reactions: uranium-235 and plutonium-239. (The numbers 235 and 239 are the sums of protons and neutrons in each of the respective nuclei. Uranium has 92 protons and plutonium has 94 protons.)
Origins of Fission Fuels: Why Uranium Occurs Naturally but not Plutonium
Both uranium and plutonium were manufactured instantaneously via a nucleosynthesis process at the moment of a stellar supernova explosion that seems to have occurred in this part of our galaxy 4.6 billion years ago. That supernova shock wave may have somehow precipitated the collapse of the proto-solar system cloud from which our star and our planet subsequently formed.
[We know that this supernova happened just moments (geologically speaking) before our solar system formed because asteroids, which have high ratios of surface area to volume, and which therefore would not be expected to easily build up heat in their interiors, nevertheless melted internally early in the solar system’s history. The melting must have been caused by some extremely energetic, and thus highly radioactive, substance right at the time that the solar system was forming. The best candidate for this melting would be aluminum-26 (Al-26), which has since decayed to magnesium-26 that is found in meteoritic inclusions. Al-26 only lives a few million years after it forms, so the supernova that generated it had to have occurred only a few million years before the solar system formed.]
While both uranium and plutonium would have formed in that supernova explosion (as stars can otherwise only create elements as heavy as iron via ordinary, non-supernova nucleosynthesis), there is now no plutonium present in the Earth’s crust, and only a small amount of the type of uranium that sustains fission chain reactions. This situation has implications for nuclear non-proliferation, so it’s worthwhile to understand why this situation exists.
No plutonium naturally exists (now) because it only has a 10,000 to 20,000 year half-life (depending upon the variety, or isotope, that is concerned). Since a half-life is the time required for half of an element to decay into other elements, and since the Earth is 4.6 billion years old, the age of the Earth in plutonium half-lives is now (4.6 billion years/20,000 years) = 230,000 half-lives of plutonium. The fraction of plutonium that now survives is thus one-half taken to the power of 230,000, which is about as close to zero as you can get for any practical purpose.
The picture is different for uranium. This element, like plutonium, comes in several different isotopes. (Every atom of a given element has a fixed number of protons, 92 for uranium and 94 for plutonium, but the number of associated neutrons in each atomic nucleus can vary.) The nucleon number, the sum of the protons and neutrons (collectively called nucleons) in a nucleus, defines this variety as an isotope. For uranium atoms, these varieties, or isotopes, include variants that have a sum total of 238 protons plus neutrons (U-238) versus 235 protons plus neutrons (U-235). The supernova that precipitated our solar system would have manufactured both U-235 and U-238. Both of these elements will sustain fission, but only U-235, with three fewer stability-producing neutrons than U-238, will sustain the fission chain reactions of a bomb. For this purpose, U-235 is magic and U-238 is junk.
The half-life of U-238, which is useless for bombs, is, at 4.5 billion years, virtually equal to the age of the Earth. Consequently the Earth’s crust now contains half of the uranium-238 that was present at the formation of our planet. But U-235 has a half-life of only 700 million years. Thus the Earth’s age in U-235 half-lives is (4.6 billion/700 million)= 6.6 U-235 half-lives. The amount of U-235 that is now present in the Earth’s crust is therefore only one-half taken to the power of 6.6 of what is was originally. This, as luck would have it, is 1.03% of the original amount of U-235 in the Earth’s crust. By a strange quirk of fate, our planet has barely enough U-235 available in the crust to make atomic bombs. If we had evolved much earlier there would have been more U-235 floating around and making bombs would have been easier, whereas if we had evolved substantially later there might not have been enough U-235 available to make the enterprise worthwhile.
Uranium-235: The All-Natural Fission Fuel
If you scoop up a pile of natural uranium ore from the Earth’s crust and you refine it into pure uranium metal, you will find that, out of every 140 atoms of uranium, 139 of them are useless for bombs, being U-238, and one of them is useful for a bomb-making enterprise, being U-235. (If there had initially been equal quantities of U-238 and U-235 in our planet’s crust, the ratio would been closer to 1 in 100 rather than the observed 1 in 140. The supernova seems to have initially manufactured slightly less U-235 than U-238.)
Because the chemical properties of U-235 and U-238 are identical, they can only be separated from each other by painstakingly picking them apart on the basis of their one-percent mass difference ((238 - 235)/238) = (3/238) or three parts out of 238, specifically. This is very difficult and expensive and cannot be accomplished on an industrial scale required for bomb manufacturing without leaving behind easily observable, tell-tale traces such as gigantic buildings, colossal power consumption, and outgassing and venting of uranium vapors into the atmosphere, not to mention gigantic piles of uranium ore lying around.
Two major techniques are used to obtain uranium enrichment on an industrial scale: gaseous diffusion, in which the tiny mass difference is utilized to separate components of uranium hexafluoride gas (U-F6, a uranium atom joined to six fluorine atoms in a gaseous form) in many miles of plumbing and filters, and separation with cascading chains of tens of thousands of high-performance centrifuges. In World War II the US used the gaseous diffusion technique.
In recent years, nuclear proliferators who have been aided and abetted by Pakistani operatives including the physicist Abdul Qadeer Khan (called A. Q. Khan in the country where he was revered as a national hero and now lives in disgrace under house arrest) have used centrifuge processes instead. These countries have included Libya (which recently came clean and turned over its centrifuges to the US government) and Iran (which says it only wants to make natural uranium into reactor fuel). Other separation techniques (such as using lasers and electromagnetic techniques) have not been demonstrated to be feasible on an industrial scale, although they can be used in laboratories to make small amounts of U-235 for experimental purposes.
Refinement Versus Enrichment of Uranium
The process of making uranium ore into uranium metal is called refinement. Refinement is done chemically. It is not, in itself, an activity that leads to potential bomb-making. As we have seen, uranium metal is composed of 139 U-238 atoms for every U-235 atom and they cannot be separated chemically. If, however, someone decides to go beyond chemistry and begins the mechanical process of extracting the U-235 atoms from the metal, that process of enrichment can potentially lead to bomb-making. At low levels of enrichment, uranium can be used as reactor fuel. But by the time the fuel is composed of three percent U-235, about 90% of the work has been done that will be required to enrich the fuel to a purity of 95-99% U-235, which is suitable for use in a bomb. Therefore any capability for enrichment of uranium in U-235 content can potentially be applied to making bomb fuel. This is why the process of making uranium fuel for reactors is watched closely to prevent people from going all the way and making it into bomb fuel. The capability for making such fuel exists in countries such as Russia and South Africa which have agreed to protocols for preventing unauthorized production of weapons-grade U-235.
Plutonium: The Synthetic, Man-Made Fission Fuel
It was discovered in December 1940 that a new element, one with with 94 protons in its nucleus, could be made by bombarding the element that has 92 protons (namely uranium) with neutron-proton pairs called deuterons. Small amounts could be made particle-accelerator machines called cyclotrons. Element 94, eventually (and presciently) named plutonium (after the planet Pluto), did not previously exist on the Earth and had not been present in the solar system for about 4.6 billion years. For a while, all of the plutonium in the world was a tiny sample in a cigar box that belonged to its discoverer, the American physicist Glenn Seaborg. The tiny initial samples of plutonium were enough to allow physicists to determine that Pu-239, like U-235, could sustain a runaway nuclear fission chain reaction.
The concern at the time was that the Nazis would either already know this or would figure this out: that U-235 and Pu-239 could both be made into atomic bombs. Given that the Nazis might very well build such weapons, the Allies of the Second World War undertook a crash program to build countervailing atomic bombs. By 1942, with the Axis in control of Europe, much of Russia, North Africa, Southeast Asia and much of the Pacific, and with the Germans driving fast toward the oil fields of the Middle East, the race was fully on to make U-235 and Pu-239 in industrial quantities.
(The Nazis, by the way, deprived themselves of many, if not most, of the best scientific and industrial brains in Europe because of their racial-superiority tripe. Part of the pay-back for their arrogance and ignorance was that they screwed up when they tried to build a fission reactor, and as a result they didn’t get far with their atomic-bomb research. Funny how your own nastiness can eventually come back to bite you, isn’t it?)
The particle-accelerator approach to making plutonium was inadequate for industrial (kilogram) quantities. It was quickly determined that uranium that has not been enriched to weapons grade U-235 can nevertheless be used in a reactor to bombard slugs of ordinary uranium with fission neutrons. That approach was believed, correctly, to be the way to make large quantities of plutonium. The world’s first nuclear reactor was hand-built as a pile of interlaced uranium bricks and neutron-moderating bricks in an abandoned underground squash court at the University of Chicago. It demonstrated the steady-state fission chain reaction principle in spades.
The result of neutron bombardment of uranium in a reactor is to make an intermediate element that decays, in 2.3 days, to plutonium. When the bombarded slugs are pulled out of the reactor and put through a rather nasty chemical separation process, plutonium is recovered.
Large plutonium-production reactor facilities were built during WW II in an isolated area near Hanford in eastern Washington state. They were dangerous and they were tricky to run. They required vast quantities of water from the Columbia River for cooling. They initially tried to shut themselves down due to an inherent fission-residue poisoning problem, but they eventually worked very successfully. These giant machines were used to make industrial quantities of plutonium, suitable for use in bombs. The total world supply of plutonium is now about 50 tons, made one atom at a time in the Hanford reactor and many other reactors that have subsequently been built around the world.
Summary of Fission Fuel Production
The bottom line to this whole discussion is: U-235 bomb fuel has to be mined, refined and enriched from the Earth’s crust, making use of the naturally-occurring uranium stuff that came out of an ancient supernova. Pu-239, on the other hand, no longer exists in the Earth’s crust from that supernova because it is so short-lived that it has all decayed away. It must instead be synthesized in nuclear reactors (using non-weapons grade uranium as fuel). The resulting plutonium must finally undergo a chemical separation process that removes it from reactor slugs that have been irradiated. As mentioned above, the world supply of plutonium is now about 50 tons, enough to more or less destroy our civilization if completely used in explosives.
Nuclear Fuel Production Actions Currently Pursued by Iran and North Korea
Iran is currently trying to make U-235 from natural uranium using centrifuge technology that was provided by Pakistani engineers. North Korea has followed the alternative route of making plutonium-239 in a reactor and then extracting it from fuel slugs. Both countries have claimed that they have worked on these processes for the purpose of producing electricity from nuclear energy. Iran makes this claim despite its access to vast reserves of petroleum and the availability of nuclear reactor fuel via legal markets with Russia and South Africa. North Korea maintained its power-production claims for many years, even though its reactor design was especially good for making plutonium. North Korea used plutonium extracted from its reactor to fuel an atomic bomb that was exploded underground (and which essentially failed to work) in late 2006.
As of July 2007, North Korea, under intense pressure from the international community, has agreed to freeze activities at its plutonium production reactor. Iran is continuing to build centrifuge-enrichment facilities for U-235 production. Iran has claimed success with the industrial-scale effort, but no one knows how long it will take the Iranians to enrich enough U-235 fuel to make their first bomb, nor how quickly they will be able to make U-235 fuel for additional bombs, if that is indeed what they are up to. It is unclear whether Iran will submit its activities to enough international inspection protocols to ensure that they are not operating a bomb-fuel production pipeline.
It is commonly believed that Iran cannot make enough U-235 fuel for a bomb for several more years, if that action is in fact pursued by that administration. There should be enough time available to work out a deal with Iran, in which that country gets some sort of face-saving benefit concerning reactor fuel production while the international community gets a verifiable assurance put into place that no industrially significant quantities of nearly pure (weapons-grade) U-235 can ever be produced by that country.
Barring a successful diplomatic outcome (which, if properly crafted, would be to the benefit of all parties, in my personal opinion), there remains the possibility that one or more administrations might decide that the only remaining option for dealing with the issue would be military intervention. It is unlikely that the Iranians would be able to sustain the large-scale, industrial-grade enrichment activities that are required for bomb production if their facilities were attacked militarily by other countries. It is a near certainty that the Iranian facilities are not buried deeply enough to protect them from concerted airborne attacks and commando-style demolition raids. Their U-235 production pipeline is rather delicate and it won’t take much of a perturbation to shut it down (I think). The Iranians know that their system is rather fragile and must take that fact into account in their calculations of future actions. On the other hand, the contemplation of military action against Iran is likely to be a last-resort action by the international community. Diplomatically-based protocols for prevention of Iranian weapons-grade U-235 fuel production are likely to be tried rather exhaustively first. Stay tuned to see what happens.
By the way, both U-235 and Pu-239 are unbelievably hazardous and difficult materials to store, transport, handle, melt, cast, and machine into shapes, by virtue of not just their radioactivity (radioactivity being especially problematic for plutonium with its short half-life), but also because because of their extreme chemical toxicity and their recalcitrant physical characteristics.
Fission Fuel Geometry
Neutron production is a function of total fissile mass: the larger the fissioning mass you have in place, the higher the neutron production rate, in direct proportion to total mass. Neutron loss is a function of the fissile material’s surface area: the larger the mass’ surface area is, the faster the neutron loss rate. So the balance between neutron production rate and neutron loss rate is determined by the ratio of the fissile material’s mass and surface area.
The shape that gives the highest ratio of mass to surface area, and hence the highest ratio of neutron production rate to neutron loss rate, is the sphere. Moreover, the ratio of mass to surface area increases as the size of a sphere increases, in direct proportion to the sphere’s radius. There exists a critical mass at which a sphere of fissile material just balances its neutron production and loss rates. Anything above that mass and the fission chain reactions in the mass will lead to a net build-up of heat. Working weapons need to achieve final assemblies that exceed the critical mass threshold.
Critical Mass and Tampers
This critical mass limit for a bare ball of fissile material is, at 60 kg, surprisingly and clumsily large. Weapon-grade (that is, highly purified) fissile material is some of the most expensive stuff on the planet, so it is important to reduce its minimum mass if possible. The critical mass can be reduced by wrapping the surface of the sphere in a shell of material that is a good neutron reflector, the effect being to reduce the neutron loss rate in rather the same way that a wrapper of aluminum foil reduces heat loss from a roast turkey. Such a neutron reflector shell is called a tamper. Common uranium, called U-238, makes a decent tamper. An additional layer of beryllium can make a uranium tamper even more efficient. With a good tamper wrapped around a core of U-235 or Pu-239, the critical mass is only about 15-18 kg. (In a workable device the final configuration should exceed the critical mass by a substantial percentage.)
Neutron Initiators
A final trick to make the assembled device work as well as possible is to build an item that will release a flood of neutrons at the moment of final assembly. The big pulse of neutrons at the critical moment serves to kick-start the device by simultaneously initiating a large number of chain reactions. These devices, called neutron initiators, are made from pairs of elements that generate neutrons when they are mixed. Typically the initiator is crushed to mix the materials as quickly and thoroughly as possible when the assembly is fired. A good neutron initiator is critical (no pun intended) to making the device work well. Neutron initiator designs are closely guarded. No less an intellect than Neils Bohr was in charge of the development of the neutron initiators for the original American atomic bomb under Project Y, the Los Alamos Project. I think I could put one together if I had to, but it would be sub-optimal in design because I lack experience in this area.
Assembling the Critical Mass: Guns Versus Implosions
So how can the device be stored and moved around in a sub-critical configuration and then be changed into a critical assembly at a desired time and place? There are two ways. Either two sub-critical pieces can be kept separated and then brought together mechanically, or else a single sub-critical piece can be squeezed to increase its density to a critical point. Once the critical point is reached, it will take about 80 neutron-doubling generations to reach full yield (defined here as the fission of 1 kg, or 2.5 times ten to the twenty-fourth power atoms). The length of time for this many generations for the device to reach its full potential for energy production (its yield) is only about 0.8 millionths of a second (that is, 0.8 microsecond).
Either way, the assembly must done extremely fast, within a few thousandths of a second (milliseconds) at most. If the assembly goes too slowly, the neutron chain reactions will begin prematurely and the device gets too hot and expands too much before the final configuration has been reached. In that case it will tear itself apart before it reaches its full yield. This problem is called predetonation. Predetonation causes fizzle yield.
When it comes to neutron chain reactions, uranium isn’t quite as volatile as plutonium. It is possible to build a uranium weapon by smashing two small pieces of uranium together with an artillery gun barrel. One piece is kept at one end of the gun barrel while the other piece is shot down the barrel like an artillery sabot. An assembly speed of 1000 ft/sec to 3000 ft/sec is fast enough to keep the chances of predetonation pretty low, and is achievable with artillery pieces.
The problem is more difficult for plutonium. Plutonium-239 is so hot, fission-wise, that it is impossible to mechanically assemble two pieces fast enough to avoid predetonation--there’s no artillery shooting piece that’s fast enough. Instead, a sub-critical chunk of plutonium must be rapidly squeezed to a higher density, making it into a supercritical mass by virtue of having suddenly become more dense. This technique is called implosion. It is carried out with chemical explosives that are wrapped around the plutonium and which are simultaneously detonated to create an inward-moving spherically shaped shock wave. The explosives may be specially shaped, but in at least one air-to-air missile warhead design (the W-25 warhead for the unguided Genie missile) a simple wrapping of gunpowder with a large number of detonators was used. Such a simple approach reduces the device’s yield, however.
Implosions are most effectively driven if the individual high-explosive segments are set off absolutely simultaneously and quickly. The types of electronic switches that are best-designed for this purpose are controlled-export items. But bear in mind that the necessary technology was available by 1945, so it isn’t going to be all that difficult to obtain or engineer such switches in the early twenty-first century.
Tradeoffs in Fission Gun Versus Implosion Designs
Implosion is tricky; it takes a lot of practice with varying designs and a lot of practical knowledge to do it well. How tricky is it? Well, consider the historical example of 1945. In that year the United States had two completely different atomic bomb designs that it had built under Project Y. The first design was uranium-based and used a gun. (Surprisingly, it used a cylindrical rather than a spherical configuration for the fissile material--its design was sub-optimal in that regard. I’ve always wondered if this was because the uranium was difficult to machine into a sphere.) The original uranium gun design was never tested full-up. The designers were so confident that it would work, based on small-scale lab tests with small, sub-critical pieces of U-235 and firing tests of the artillery shooting mechanism using full-sized slugs of inert U-238, that the first uranium weapon, a gun device, was used directly on the Japanese city of Hiroshima. That design was never tested in advance. That shows how confident its designers were that it would work.
The second design was plutonium-based and operated on the implosion principle. The designers were worried about this design, because implosions are tricky. They decided that they needed to test it first, even though the plutonium was fabulously expensive and was in very short supply. And so it was that this design was winched to the top of a shot tower and fired in New Mexico on 16 July 1945. The second of these implosion devices was used in the second atomic-bombing of Japan, on the city of Nagasaki.
The historical example of 1945 demonstrates the confidence that can be placed in a gun design. In contrast, a certain lack of confidence exists for implosion designs until they are tested. So why not always use a gun design for a first nuclear device? Two reasons. First, as explained above, plutonium is too reactive to be used in a gun, and therefore if plutonium is the only available fuel an implosion design will have to be used (this was true of the North Korean situation in late 2006). Second, gun designs are heavier than implosion designs (some of which are very lightweight and compact, using levitated cores and the like). Third, gun designs are inherently unsafe because the possibility exists that the two pieces of fuel may come together in the event of an accident.
Gun designs are especially ill-suited to delivery with missiles, where size and weight limitations are severe. As noted above, gun designs are inherently unsafe precisely because they can go bang if they are involved in accidents. They are most suitable for applications in which size and weight are not limited and in which the reliability and robustness of the design is held at a premium. Such applications include the early air-dropped gravity bombs, as used in 1945, and in artillery projectiles, a now quaint-appearing 1950s doomsday scenario in which Army soldiers actually sit on a battlefield shooting these things at each other with atomic cannons. (I do think that it would have so ultra-cool to have fired one of those on a test range!)
Even if uranium-235 is the only fuel available, the light weight, compactness and improved safety margin of an implosion design may be the decisive factor in building an implosion device instead of a gun (as uranium may be used in either a gun or an implosion design equally well). But in that case, we are back to needing to test at least the first device to verify that the relatively tricky implosion will work properly in the bomb design.
Third World countries aspiring to join the nuclear club (for example North Korea and Iran) lack effective air forces with which to deliver atomic bombs to their likely opponent’s territories. (One of the reasons that countries such as these seek nuclear arms in the first place is a desire to use weapons of mass destruction to offset and leapfrog their existing weaknesses in conventional arms.) Their only feasible delivery methods are to either smuggle bombs into cities or else to deliver them with missiles. A smuggled bomb can be a very heavy gun device, as it can be delivered in the back of a pick-up truck. But a missile warhead will likely need to be an implosion device if it is going to be small enough and light enough to be carried across an inter-regional or intercontinental distance by the relatively small long-range missile designs that these countries are capable of building, testing and fielding.
Maximizing Yield
For a given amount of fuel, the ultimate yield of any fission design is limited by speed with which it is assembled or imploded, the effectiveness of the tamper and the neutron initiator, and then the amount of time that the super-critical assembly can hold itself together before it expands beyond a critical radius. Subsequent to the assembly/implosion, the yield doubles every 10-billionths of a second (every 10 nanoseconds) after the assembly has been completed. Let me put it this way: Half of the bomb’s yield is generated in the final 10 nanoseconds before it expands to such a size that the surface area-to-volume ratio becomes so large that the fission chain reaction ceases.
Therefore a big premium is placed on holding the assembly together within a critical radius as long as possible. Failure to hold the bomb together for a few extra tens of nanoseconds will make the difference between reaching full design yield versus obtaining a fizzle yield. The device needs to be held together for almost a microsecond (0.8 us) to achieve full yield. This is where the tamper can play a secondary role in boosting performance. The bigger and heavier the tamper, the longer it can hold the assembly together by virtue of its sheer inertia. But the tradeoff is that the design becomes heavier.
Another factor that affects yield is the symmetry of the compression of an implosion device. Small asymmetries in the implosion can reduce the yield significantly. The maximum yield that can be achieved with a fission bomb is about 250 kT, and the smallest engineered yield for a demolition-type backpack portable munition is going to be around 0.1 kT. Such designs are difficult to engineer and require resources for design and testing that Third World countries like Iran and North Korea don’t have available. Their designs will ordinarily fall into the mid-range of 10-20 kT, on the scale of the Hiroshima and Nagasaki weapons.
Analysis of the North Korean Atomic Bomb Test: Why it Failed
The Democratic People’s Republic of Korea (DPRK, North Korea) atomic bomb test of late 2006 was a bust in terms of yield. It fizzled. It most likely generated the equivalent of 700 tons (0.7 kT) of TNT when it probably should have generated twenty times more, which would have been about 15 thousand tons (15 kT) of TNT. What went wrong? If they had used plenty of fuel and had over-engineered their design they could have been practically certain of successfully building a fairly high-yield bomb. The very fact that the bomb failed implies that they were cutting it close on their design. Why would they do that?
First, let’s reconstruct the North Koreans’ situation. Initially they had to decide whether they were going to refine uranium from the Earth’s crust versus manufacturing plutonium in a reactor. They apparently decided that it would be easier to build a relatively compact nuclear reactor (which makes plutonium by bombarding uranium fuel slugs with neutrons) than to obtain weapons-pure (weapons-grade) uranium-235 which would require vast numbers of centrifuges or miles of gaseous diffusion plumbing in extremely large and expensive industrial facilities.
Having decided to obtain plutonium, they could not pursue a gun design. Instead, they were committed to building a trickier implosion design. And given that their reactor was not all that big and did not make plutonium very fast, they were not going to have much plutonium available for their program.
Being short on plutonium to begin with, they probably wanted to economize on their weapon’s size for that reason alone. Another reason to economize on fissile fuel was that they most likely wanted to test a missile-compatible warhead design immediately. This desire for an immediate warhead design would have been due to concerns about the extreme political difficulty of shooting a whole series of tests as well as the overall lack of fuel. But as discussed above, missile-compatible designs, especially for the small North Korean missiles, have to be extremely lightweight and thus need to use a minimal amount of fissile material. This warhead size and weight limitation is especially true for the DPRK’s long-range missiles.
So the DPRK engineers probably tried to build a very small and therefore very sophisticated implosion design right at the get-go, with no prior experience. That was a big mistake on their part. There’s more to a good implosion design than what you can find on a web site or in a physics textbook. Implosion devices, especially ones that push the extreme limits of what is physically achievable with a given amount of fissile fuel, need to be designed and manufactured by people like the American designer Ted Taylor who have practical experience with this sort of thing, experience based on the design, construction and testing of simpler implosion devices that are rather over-engineered (a good example being the straightforward yet totally over-engineered American Trinity-Nagasaki implosion weapon design of 1945). If the North Koreans’ strategy was to build a very sophisticated plutonium implosion warhead while lacking practical experience in this highly specialized field, then this would explain why the DPRK device fizzled.
The DPRK nuclear warhead either predetonated or else didn’t hold together long enough and with a sufficient amount of symmetry to achieve full yield. The designers probably had a good idea that the device had a high probability of fizzling, but who in their right mind in the DPRK would ever dare to question the wisdom of the Dear Leader Kim Jong Il by telling him that they couldn’t realistically prepare a sophisticated missile-compatible implosion-based warhead without a long series of politically difficult and fuel-consuming tests? It would have been equivalent to telling Kim Jong Il that all of that plutonium that he and his father, Kim Il Sung, had produced at such tremendous financial and political cost was essentially useless, as he still didn’t have enough of it, nor enough international political capital, for the realistically long test series that would be necessary to produce a working light-weight missile warhead design.
Conversely, I know that I wouldn’t have wanted to be the guy who had to tell Kim after the test failed that he had just wasted a fair amount of his precious fissile material, lost international diplomatic capital (by firing the test weapon), and damaged his prestige (due to the failure of the test). Oh, boy.
Building My Own Mock-Up of a Fission Gun
When I completed my paper I began to think about the bare minimum requirements that would need to be met to construct a bargain-basement fission device that would be guaranteed to work. I was thinking about this because I had written short story about nuclear blackmail in which a demonstration weapon is set off on a barge off the U.S. east coast along with a warning that ten more have been hidden in major U.S. cities. (There is a twist, but you’ll have to read the story in my fiction section on this web site.)
I decided that the thing would have to be a gun device, because a properly designed gun is (almost) guaranteed to work. (Remember that the first gun device ever built was never tested full-up; it was used on a city.) Therefore the fuel would have to be uranium-235. I did the math for a conservatively engineered gun and then I went shopping.
I found a sawed-off artillery gun barrel in a scrap yard and bought it. I used a CAD system to draw the plans for the spherical tamper that would hold the uranium core. I made a wooden pattern for the tamper, then made an aluminum sand casting. Inert uranium-238 would the material of choice for a real design, but I certainly wasn’t going to start handling that stuff.
I located a machinist who would cut threads into the inside of the gun barrel at one end around the outside of the barrel at the other end. I also had him cut a hole and threads into one half of the tamper. I made a precision-machined slug of tamper material that fit exactly into the gun barrel. The slug was the same thickness as the main body of the tamper. Finally I made a threaded-breech-block for the gun barrel.
When the whole thing was assembled it liked a gigantic candy sucker: It had a big spherical tamper with a gun barrel sticking out of it. The assembly would go as follows: screw the breech block into one end of the gun barrel. Then place some high explosive into the artillery barrel up against the inside of the breech block. Next slide the cylindrical tamper slug down the barrel--it’s so tightly machined that it floats down like a feather. Next, insert the one thing I don’t have: a slug of U-235, likewise machined to fit precisely into the gun barrel. Secure the slug with a shear pin. (U-235 guns are extremely dangerous designs because of the chance that the assembly can slide itself together in the event of an accident such as an airplane crash.) Finally, assemble part of the neutron initiator on the business end of the U-235 projectile.
Now comes the assembly of the uranium-235 target assembly. First the lower half of the tamper sphere is threaded onto the free end of the gun barrel. Then the target chunk of U-235 is laid into place. It is a sphere of uranium that is missing a cylindrical chunk of itself; that cylindrical chunk is inside the gun barrel. The target uranium is oriented so that, when the gun is fired, the sub-critical slug in the gun barrel will seat itself into the sub-critical target chunk inside the tamper to create a supercritical uranium mass. The second half of the neutron initiator is on its inside surface. The piece of tamper that rides behind the gun-barrel slug of uranium seats itself into place to complete the tamper shell around the uranium. The neutron initiator assembly, partly inside the cavity of the uranium sphere and partly on the business end of the gun-barrel slug, generates a flood of neutrons to kick-start the reaction and ensure a high yield.
Finally the second half of the tamper sphere is laid on top of the lower half and the entire assembly is bolted together. A second, thin wrapper of a neutron reflecting material might be wrapped around the whole tamper to further improve performance. That’s it. It’s heavy and clumsy to move, but it will generate about 10 kT yield on a good day. See the picture of the assembly above. The bigger and heavier the tamper is, the longer the assembly will hold together and the larger will be the final yield.
The Key to Non-Proliferation
So here’s the punch-line to this whole discussion: What prevents someone from making this doomsday scenario a reality? What is the key to nuclear non-proliferation?
Given that the rest of the design of a simple device is straightforward (especially if it’s a uranium gun), the answer is, the unavailability of weapons-grade fissile material is the key to nuclear non-proliferation. Preventing the production, sale or theft of weapons-grade fissile material is the only effective way of preventing nuclear proliferation.
As my exercise demonstrates, the rest of the problem beyond acquiring fissile material for would-be proliferators is not hard to solve. The only reason the North Koreans failed in their nuclear test was that they over-reached in their design. Generally, would-be proliferators can be expected to have more sense than the DPRK guys did, and thus will be more dangerous.
It is for this reason that Iran’s ongoing efforts to enrich U-235 indigenously are so ominous--once they get a sufficient quantity of sufficiently pure U-235, there are no significant barriers to their developing a complete atomic weapon. Since ninety percent of the effort of making weapons-grade U-235 is expended in making enriched reactor-grade fuel, Iran’s claim that its only goal is reactor fuel production is not comforting. If the Iranians get as far as making, say, twenty kilos of U-235 that is nearly pure, then they will have the option of using either a gun design or an implosion design for a bomb, since U-235 can be used in either type of design. They might decide to develop a gun device as a no-fail option for a public demonstration of their weapon capability, while separately developing a more sophisticated and challenging uranium implosion bomb that can be used as a missile warhead. Either way, that is not a development that will be welcomed by any other administration in the world.
To prevent countries like Iran from proliferating, it is necessary for the other governments of the world to implement both incentive and disincentive equations. Both types of equation are developed for the purpose of convincing the people who run potentially proliferating countries that the possible perceived advantages of constructing atomic weapons are more than outweighed by the disadvantages of doing so. Sometimes, the incentive side of the equation for stopping proliferation (trade credits, oil credits, construction of commercial light-water reactors that can’t be used to make plutonium, etc.) is interpreted by conservative-minded thinkers as “giving in to nuclear blackmail.” It isn’t, any more than any negotiation can be regarded as “giving in to blackmail”. The process is, in fact, called bargaining. Bargaining is more than threatening violence if you don’t get your way. It is, rather, a process in which both sides seek to come out ahead of their current positions by giving up something to the other side in return for obtaining something that they hold even more dear. For most of the world, the thing that is held most dear in this context is better national security through the prevention of nuclear proliferation.
The resulting non-proliferation deals need to include concrete, verifiable and measurable outcomes that both sides can live with. That is the process in which Iran and countries like it need to be engaged. (North Korea, in contrast, is such a weirdly degenerate case that it is hard to know where to even start with them, other than turning to China for assistance in getting them to bargain seriously.) It is long, tedious, and frustrating process, but it can work if enough determination is brought to bear by the concerted efforts of countries around the world.
Visits to Atomic Sites at Trinity and Tinian
Like the atomic scientists and engineers of the 1940s, I have had to make personal decisions about the ethical implications of working on certain projects and doing certain kinds of work. I believe that everything that I have done has needed to be done for the betterment of the general condition of humanity. I empathize with the atomic scientists of the 1940s who likewise had to make a variety of ethical decisions about the work that they did. In recognition of their situation, I have made pilgrimages to both the Trinity test site in New Mexico and the Tinian airfield in the Pacific. Someday I’ll complete the circuit by visiting Hiroshima and Nagasaki.
For information on other atomic sites, go to: http://www.atomictourist.com
Pilgrimage to the Trinity Site
In November 1987 I did some work at the north end of the White Sands Missile Range (WSMR) on North Oscura Peak. The peak is on the eastern edge of the great North American rift valley that contains the drainage of the Rio Grande. As such, the west side of the peak is a sheer cliff that drops straight into the Rio Grande Rift Valley, into the Jornada del Muerto (the Journey of the Valley of Death). The valley got its name from the Spanish old-timers who noted that one could try a short-cut through that valley on the way between El Paso and Santa Fe, but that the lack of water on that route might make it a short-cut to death rather than either of the towns.
While I and my co-worker, John Smilley, were working at the WSMR North Oscura Peak facility, we made the acquaintance of the team who operated the Stallion Range facility at the north end of the range. They had some computer problems at the facility, which John and I helped them to solve. One of the guys literally had the keys for the Ground Zero location of the Trinity test site. In return for our help with their problems, he took us out to the Trinity ground zero. We not only walked around the ground zero spot but also through the desert outside the fenced-in monument, where trinitite (desert sand fused into green glass by the heat of the bomb blast) is still to be found on the ground
The shot tower is gone, of course, but there is a basalt obelisk with a plaque that marks the site where the world’s first atomic bomb, a plutonium implosion device of the Fat Man design that was used later against Nagasaki, was tested in July 1945. (The Hiroshima bomb was a different design that was never tested before it was dropped. Being a uranium gun, they knew it couldn’t fail to work and so didn’t need to test it full-up before using it against either Germany or Japan--Japan as it turned out, Germany having surrendered in May 1945 before any atomic bombs were ready for use.)
I pondered the site and everything that it meant. I still think about it every so often. Life’s choices are never simple or easy if you are a thinking person. The event that demarcates this site in world history was the result of the paroxysm of senseless war. We, by which I mean all of humanity, must strive to not go down this road again, to never again place people into a situation where they have to make these kinds of choices.
Pilgrimage to the Tinian Airfield
In 1990, while doing some work on Guam, I took a weekend to fly north to Saipan and then to Tinian. Starting in 1944, when these islands were captured from the Japanese, they were the site of a tremendous level of activity by the U.S. Army Air Force. The islands (and pancake-flat, more northerly Tinian in particular) were used as bases for long-range B-29 bombers that flew 1500 miles to Japan and back on bombing raids. The B-29 raids on Japanese cities were mainly conducted with firebombs, the horrific nature of those raids being comparable in some ways to the later atomic bombings. When it became clear that atomic bombs would become available for military use, specially trained B-29 crews arrived on Tinian from the States. These crews used modified B-29s that were to carry extraordinarily large bombs.
I went to Tinian to find whatever was left of the B-29 base, and possibly (I hoped) find the bomb pits where Enola Gay and Bock's Car were loaded. The uranium Little Boy and plutonium Fat Man bomb designs were too large to be rolled underneath a B-29; therefore, special concrete-lined pits were constructed for the purpose of holding the atomic weapons below ground level prior to loading. The bomber aircraft would be rolled over the pit, until the bomb bay was directly above the bomb. Then, the bomb would be hoisted into the aircraft weapon bay.
Tinian, I discovered, was something of a backwater. In 1990, the islanders were debating the pluses and minuses of legalized gambling on the island, to boost the local economy by increasing Japanese tourism. I don't know if they finally did it or not.
Tinian is about the same size and shape as Manhattan. When U.S. forces occupied it during the war, they laid out a system of roads with the same general plan and orientation as on Manhattan. The main north-south road, for example, is Broadway, and it runs parallel to the other main north-south road, 8th Avenue. I inquired in the main town, San Jose (at the south end of the island), about the main wartime airfield (at the north end of the island), but nobody knew much about it. So, I drove north on Broadway. The road became less and less maintained, until, nearing the north end of the island, it degenerated into almost a trail, with forest growth on either side and overhead that was just barely wide enough for the car to pass through. The trail ran near some beautiful beaches. Then it turned back into the forest, and seemed to wind around. I began to think that I might not find the airfield, and then all of a sudden I broke out into the clear, and in front of me was an 8000-ft runway (as measured later on my car's odometer). It was grayish and weathered-looking, but very driveable (only some weedy growth crawling out onto it here and there). I drove around on the taxiways, and found four parallel runways oriented nearly east-west. I drove the car to the end of one of them, and floored it to the other end. I was imagining the takeoff run in a B-29.
Other than the runways, nothing seemed to be left of the old facilities. No buildings were to be seen. The forest had grown right up to the edges of the runways and taxiways. But then, at the northwest corner of the airfield, just off one of the taxiways, I found a little clear area, triangular-shaped, still covered by concrete. The taxiway was connected to one of the triangle's corners, and at each of the other two corners was a concrete-walled pit. Both pits were filled with dirt and were sprouting small trees that spread out over neatly tended little Japanese-looking gardens. Next to one pit was a wooden sign, with letters cut into it by a router (like signs in National Forests in the U.S.). The letters were painted yellow. They said, "Atomic Bomb Pit No. 1." Below this message was a set of Japanese characters that presumably said the same thing. Next to the other pit was the same kind of sign, labeled “Atomic Bomb Pit No. 2.” Beautifully kept little gardens, and no clue as to who came out into the jungle to tend these little plots.
Slightly spooky.
How to Get There
To get to Tinian first go to Guam, then get a commuter flight north to Saipan, then hop south a few miles to Tinian on another commuter flight. Rental cars are available at Tinian airport.
To get to the runway and bomb pits, drive north from the Tinian airport (or from San Jose) on Broadway. Stay on the road, even as it degenerates inside the forest. You'll eventually pop out on the runway/taxiway complex. Drive to the taxiway at the northwest corner of the northernmost runway. That's where the bomb pits are located.
As interpolated from a USGS topo map, the bomb-loading pits are located at 145 deg 37' 53" east longitude, 15 deg 04' 58" north latitude.
U-235 mock-up using an artillery barrel & spherical tamper.
Frank in chain maille ponders the mock-up at one of his annual Weird Science parties
Young Frank with his mock-up in his college dorm room in 1987.
Simulated U-235 critical mass sized to work inside a thick neutron tamper.
Tinian B-29 runway in 1990.
Tinian atomic bomb loading Pit 1 (Hiroshima), now filled.
Tinian atomic bomb loading Pit 2 (Nagasaki), now filled.
Frank’s sister & niece with a neutron tamper hemisphere.
Kiska the cat guarding simulated U-235 critical mass.
