The Deadly Arithmetic of Nuclear Proliferation

How hard is it to build a bomb? Mr. Biden might want to pay attention.
John Wohlstetter
The American Spectator
October 1, 2012
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THE SEPTEMBER 11 ATTACKS brought to global public consciousness the fear that rogue nations might use nuclear weapons or transfer them to terrorist groups, or that terrorists might themselves make a nuclear bomb. The first fear has far more foundation than does the second. The good news is that it is very hard to make bombs; the bad news is that it is not impossible.

The magnitude of the nuclear threat posed by a terrorist state or a terrorist group sponsored by such a state can be shown via certain metrics—call them metrics of mass destruction. But let’s begin with baseline concepts.

In the parlance of proliferation, there are three significant nouns that the adjective “nuclear” commonly modifies: “weapon,” “device,” and “capability.” A nuclear weapon is compact and light enough to fit into a missile warhead, or the business end of a bomb or artillery shell.

A nuclear device is the kind of bomb we have been worrying about since 9/11: one too large to be delivered by traditional military means, but which can be put into a van, truck, or shipping container.

And a nuclear capability is the wherewithal to make either of the above.

Uranium Enrichment Math

AT FIRST GLANCE IT SEEMS a huge leap for a potential proliferator state to get from low-enriched, commercial uranium Fuel for a power reactor all the way up to highly enriched, weapons-grade uranium fuel for a bomb. But simple arithmetic gives a counter-intutive result: commercial-grade fuel is perilously close to weapons-grade fuel.

Recall that significantly less than 1 percent of mined uranium is fissile U-235; the less desirable, non-fissile isotope U-238 makes up 139 out of every 140 uranium atoms. In order to run a reactor or build a nuclear weapon, the ratio of U-235 to U-238 must be much higher.

Commercial-grade fuel is at minimum 3.5 percent enriched—it has one atom of U-235 for every 27 of U-238. The next important step is 20 percent enriched fuel—one atom of U-235 for every four of U-238—that can run a medical research reactor. Weapons-grade uranium is about 90 percent enriched.

The key is that the process is not linear. To illustrate, start with raw uranium, which contains one atom of U-235 for every 139 of U-238. Enriching to 3.5 percent requires removing 112 of the U-238 atoms. At this stage you have done 80 percent of the isotopic separation needed to build a full weaponsgrade bomb of the kind in the U.S. arsenal.

Moving from 3.5 percent to 20 percent enriched requires removing only an additional 23 of the U-238 atoms. At this stage, you have done 97 percent of the isotopic separation work needed to make a full weapons- grade nuclear bomb.

One conservative estimate for Iran in early 2012, made by scholar Maseh Zarif of the American Enterprise Institute, showed how enrichment times accelerate:

• Start with 14,000 kilograms (15 tons) of natural unenriched uranium ore.

• It takes 331 days to enrich that to 1,400 kilograms of 3.5 percent commercial-grade fuel.

• It takes 37 days to enrich the commercial fuel to make 116 kilograms of 20 percent medical research-grade fuel.

• It takes only 8 days to enrich the medical-grade fuel to make 15 kilograms (33 pounds) of 90 percent weapons-grade fuel.

Other expert calculations assume a faster progression through the three stages, but in round figures one can apply two rules of thumb: 10-10-10 for the three stages of material shrinkage listed above; and 11-1-1 for the three time periods: 11 months for commercial reactor fuel, then one month more for medical reactor fuel, then one week for weapons-grade uranium.

To these rules we can add one more number each, to complete the sequences. Adding a final 10 to the 10-10-10 sequence captures the difference between the minimum amount of fuel needed for a crude uranium bomb a terrorist can use (roughly 60 kilograms—the amount used in the Hiroshima bomb), and a conservative estimate of the minimum amount needed for a highly sophisticated plutonium bomb that a first-rank nuclear state can use to optimize its nuclear arsenal (roughly 6 kilograms—some estimate the number even lower). Adding another 1 to the second sequence tells us that once all needed components are in place, it takes about one day to build an operational weapon. (Final assembly of the Nagasaki bomb took one day.)

Enrichment is by far the hardest part of the total work needed to assemble a nuclear device. But a country does not need to intend a weapons program initially. For example, India’s decision to seek nuclear weapons was driven by its high-altitude 1962 border conflict with China, its serial wars with Pakistan, and a series of Chinese tests: of an A-bomb in 1964, an H-bomb in 1966, and a nuclear-capable ballistic missile later that year. By 1966, India was, courtesy of its 10 years of commercial nuclear activity, close to having fuel for a weapon. It detonated its first device in 1974.

As the late historian Roberta Wohlstetter (full disclosure: my aunt) explains in her landmark 1976 study, The Buddha Smiles

The Indian case…illustrates…that a government can, without overtly proclaiming that it is going to make bombs (and while it says and possibly even means the opposite), undertake a succession of programs that progressively reduce the amount of time needed to make nuclear explosives, when and if it decides on that course.

Thankfully, putting together the vast, industrial-scale infrastructure needed to enrich uranium via these methods is extremely difficult; no terrorist is going to do this in a garage or on the back lawn with presently available methods.

One of the main sources of concern, however, lies in the ability of a state enriching uranium to rapidly assemble a bomb, which—as noted above—need not be a full-scale weapon, but merely a rudimentary device to fit inside a shipping container or a road vehicle. Thus, when the Obama administration uses as the measure of Iran’s weapons status whether it can assemble a modern weapon, the Obama calculus ignores the crude device that can be assembled far more easily and faster—and transferred to Hezbollah.

Plutonium, Fission, and Fusion

SO MUCH FOR URANIUM, the fuel of choice for proliferators. But what about plutonium? Plutonium accumulates in the spent fuel collected from nuclear reactors. The U-238 in a nuclear reactor will capture a neutron and, instead of fissioning, become an extremely unstable atom with a combined total of 239 neutrons and protons. In a series of transmutations (changes in chemical composition), this U-239 naturally becomes fissile Pu-239, the most common modern fuel for nuclear weapons.

How a reactor is designed and run determines how readily and conveniently it creates Pu-239. The reactor the Iraqis built in the late 1970s was to run on weapons-grade fuel and was made to maximize plutonium production; Israel understood this perfectly well, and hence destroyed it in 1981—before it was fueled, to avoid scattering radioactive material for miles upon bombing it. Proliferation expert Henry Sokolski writes that a light-water reactor rated at a tenth the size of a commercial plant can be run so as to produce dozens of pounds of plutonium in a year. This is more than enough to fuel several nuclear bombs.

Weapons-grade plutonium makes for a more efficient bomb fuel than weapons-grade uranium, and thus offers more explosive power per pound. The actual amount of plutonium converted into energy inside the core of the Nagasaki bomb was about one gram, or one-third the weight of a penny. Einstein’s E = mc2 equation explains this. The released mass (m) converted into kinetic, thermal, and radiant energy is infinitesimally small—less than a thousandth of the mass that fissioned, as most of what fissioned careens around in search of other nuclei to split. But the “c2” represents, in kilometers per second, the square of the speed of light in a vacuum. Applying this huge multiplier to every atom whose nucleus is split in a detonation yields a vast release of energy (E) in various forms.

A crude uranium bomb is relatively easy to build. The Hiroshima bomb used uranium enriched to 80 percent U-235. Within the bomb, half the uranium was fired—by a miniature version of a World War II warship’s naval gun—into the other half, causing a supercritical mass to form and detonate in microseconds (millionths of a second). The Manhattan Project scientists were so certain a guntrigger design would work that they did not even test it—uranium was in short supply and they needed it to create plutonium for the Trinity test and then the Nagasaki bomb.

But Pu-239 is much harder to make into a nuclear bomb. It must be placed in a special configuration, far more complex than that for a uranium bomb. A plutonium detonation occurs in nanoseconds (billionths of a second), a thousand times faster than a uranium detonation. To make sure as much of the plutonium as possible fissioned, the Trinity and Nagasaki bombs were “implosion” devices. A complicated arrangement of 32 symmetrically spaced conventional explosives surrounded those bombs’ plutonium cores. Thirty-two lenses converted the shock waves from convex to concave, to compress the plutonium core extremely rapidly and evenly. A timing discrepancy among the implosion lenses of 10 microseconds—10 one-millionths of a second—reduces symmetry and can create a dud; a timing discrepancy of just one microsecond is enough to create a partial dud. In essence, plutonium bombs require superspeed, supersymmetry, and supersmall compression.

For a nuclear weapons state seeking to arm missiles, plutonium is the fuel of choice, because it provides more yield per pound, and thus is more suitable for small warheads. It is very unlikely that terrorists would be able to build a plutonium fission device on their own, due to the extreme sophistication involved.

And it is even harder to master the deep subtleties of a hydrogen bomb. This requires a conventional explosive to trigger an atomic bomb, whose radiated thermal energy then compresses the plutonium core so rapidly and compactly as to fuse hydrogen atoms and generate a thermonuclear explosion.

Bombmaker’s Bonus: A Nuclear Jalopy Will Do

NOW THE BAD—VERY BAD—NEWS: You do not need a full U.S. weapons-grade fuel to build a bomb. Less than 20 percent-enriched uranium suffices. In 1962 the United States tested a uranium bomb at its Nevada underground test site, and obtained a nuclear explosion with fuel enriched somewhat short of 20 percent (the exact figure remains classified). It was, in the parlance, suboptimal. Such a bomb would cause less devastation and kill fewer people than a fully enriched bomb.

Also, a weapon fueled with highly enriched uranium but of crude design may “predetonate,” thus greatly reducing its explosive yield. Supercritical chain reactions in uranium typically at least double with each fission. Think of the parable about the king who offers a peasant serial doublings of wheat stalks for each square on a chessboard—one stalk of wheat on square one, two on square two, four on square three, etc. Before reaching 64 doublings the kingdom goes broke; the final squares are never covered, as there is no wheat left with which to do so. The difference in the nuclear case is that doublings go past the 64th square. Exponential progressions look like the famed “hockey stick” curve, which rockets upward at an ever-increasing rate.

In an 84-doubling sequence not uncommon in a fission weapon, after 70 doublings, only 1 percent of the energy will have been released. After 80 doublings, only 5 percent will have been released, and after 83 doublings, only 50 percent. North Korea’s early tests fell far short of the Hiroshima bomb in yield, due to pre-detonation. A primitive weapon releases far less energy than a well-engineered one.

But a low-enriched or crudely designed bomb could still could inflict vast damage. Consider the consequences wrought by conventional explosives: The 1,336-pound truck bomb that exploded in a garage of the World Trade Center in 1993, had it been more carefully placed a few yards away, would have toppled one tower into the other, killing many tens of thousands. The much bigger 1995 Oklahoma City bomb, which destroyed a large federal building and killed 168 people, used two and a half tons of conventional explosives. A nuclear bomb that unleashes just 1 percent of the 14 kilotons of energy released at Hiroshima would be the equivalent of 140 tons of TNT—200 times the explosive energy of the 1993 World Trade Center bomb.

A “puny” A-bomb (like that detonated in North Korea’s 2006 plutonium test, for example) could easily be equivalent to a few hundred tons of high explosives. Such a primitive device would embarrass any self-respecting bomb designer, but elegance is not a terrorist’s criterion. Terrorists may find a nuclear jalopy more useful to their purposes than the search for a nuclear Ferrari.

A Growing Threat

ONCE ONE REALIZES THE IMPLICATIONS of the metrics presented, and contemplates nuclear weapons falling into the hands of Islamists, it becomes clear that the nuclear threat to civilization is growing:

• Commercial nuclear power puts a country near a weapons capability.

• Going from commercial to weapon status takes far less time than going from non-nuclear to commercial.

• A crude design can rapidly be assembled, with no need to be tested.

So American policymakers—and the population as well—should understand that nuclear capability can be acquired by hostile powers leveraging off a commercial program, upon intent formed on the spur of the moment, and with a path to rapidly attain weapon status once all necessary materials are in place. Which makes denying access to critical materials the front line of defense against proliferation by America’s enemies.