To achieve large-scale production, Y-12 incorporated a number of modifications of the scheme sketched in figure 4.1. One was to place pairs of semi-circular-shaped vacuum tanks back-to-back and sandwich them between pairs of magnet coils, as sketched in figure 4.2; the magnet coils are indicated by the dashed circle.
Figure 4.2. Schematic illustration of two back-to-back calutron tanks and a magnet coil. From [2].
With tanks and coils in such a configuration, an efficient way to arrange them is to connect a number of them together in a closed loop and connect the coils to a common source of current; in this way a given tank will experience the fields generated by neighboring coils, which will reduce the current required. Such an arrangement came to be known as a ‘racetrack’ of tanks and coils; the one shown in figure 4.3, an ‘Alpha’ track, contained 96 tanks placed within 48 gaps between the magnet coils, which appear as rib-like structures. The structure running across the top of the photo is the ‘busbar’, a square-foot solid-silver conductor which supplied current to the coils. The vacuum tanks could be withdrawn from below for material extraction; on the floor above the tracks were located operating galleries from where employees, mostly local young female high-school graduates known as ‘calutron girls’, continuously monitored and adjusted the ion beams in each tank.
Figure 4.3. Left: A Y-12 Alpha-I racetrack; some spare vacuum tanks appear in the lower-left corner [3]. Right: ‘calutron girls’ at their operating stations. Each operator monitored two vacuum tanks, but they had no idea what was being produced [4].
The first calutrons entered operation in November, 1943, but were plagued by electrical shorts, vacuum leaks, and unstable beams. Improvements accumulated through 1944 and 1945 to the point that by mid-July, 1945, some 60 kg of bomb-grade uranium had been isolated. Every atom of U-235 in the Hiroshima Little Boy passed through Ernest Lawrence’s calutrons.
Exercise
Verify the ∼0.1 gram-per-day figure above for a U-235 ion beam of current 500 μA; assume singly-ionized molecules of 235UCl4.
4.2 U-235: the gaseous diffusion method
The second major method of uranium enrichment employed in the Manhattan project was that of gaseous diffusion, which was carried out in the Project’s K-25 building at Oak Ridge. While the basic idea of gaseous diffusion is quite straightforward, K-25 became the single most expensive facility of the Manhattan Project, and was one of the most difficult to design, engineer, and construct.
The premise of gaseous diffusion is that if a gas of mixed isotopic composition is pumped against a porous barrier containing millions of microscopic holes, atoms of lower mass will on average pass through the barrier slightly more frequently than those of greater mass, resulting in the gas which accumulates on the other side of the barrier being very slightly enriched in the lighter-isotope species. Only a small percentage enrichment can be achieved in any one such step, so the slightly-enriched gas must be pumped on to subsequent enriching stages (known as ‘cells’ or ‘tanks’), which are usually linked together in a continuous cascade as sketched in figure 4.4. The gas remaining in a cell which is slightly ‘depleted’ in the lighter isotope will still, however, contain atoms of that isotope, and can be recycled to the preceding cell in the cascade for additional processing. In the sketch, the dashed line within each cell represents the diffusion membrane; feed material enters from the left of the second cell from the bottom. In the K-25 plant, the feed point was about one-third of the way along a cascade of 2892 stages.
Figure 4.4. Schematic illustration of a diffusion cascade. Feed materials enter the cascade at the second cell from the bottom; the circles represent pumps. Gas enriched in the lighter isotope accumulates toward the top of the diagram, while that depleted in the lighter isotope accumulates toward the bottom. In the real K-25 plant, all cells were at ground level. Reproduced from [5].
The most difficult part of gaseous diffusion is manufacturing the diffusion barrier itself. Not only must it be robust and easy to manufacture, but the size of the holes needed to achieve diffusion is extremely small: no more than about a hundred-thousandth of a millimeter (100 Å). Despite the historical importance of K-25, the process for manufacturing the diffusion membrane is still considered highly-classified even though the plant has been entirely demolished. K-25 was deigned to enrich uranium to 36% U-235, with its product being sent to the Y-12 calutron complex to be enriched up to ‘bomb-grade’ uranium, which is defined as 90% U-235. Construction on the main K-25 building began in September, 1943. This immense four-floor structure was laid out in the shape of a giant letter U (figure 4.5). Each side section was 2450 feet long by 450 feet wide; the total width exceeded 1000 feet. The cascade was divided into nine sections which could be operated individually, although they were normally operated as part of an overall system.
Figure 4.5. An aerial view of the K-25 plant [6].
A detailed analysis of diffusion is quite complicated, but the essentials can be grasped by recalling a result from basic kinetic theory that was used in chapter 2: that the kinetic energy of an atom or molecule in an environment at absolute temperature T is given by
This expression tells us that the speed of a molecule is inversely proportional to the square root of its mass.
At any stage in the cascade, the number of molecules containing a given isotope will be proportional to their number density n; by working with number densities we can avoid having to specify volumes. Intuitively, it seems reasonable to assert that the number of molecules containing a given isotope that pass through the membrane in some amount of time will be proportional to their number density on the ‘feed’ side of the membrane, as well as to their speed. The latter part of this statement is based on the rationale that faster-moving molecules will have more chances of finding a hole in the membrane to pass through in a given time. Diffusion theory affirms this conclusion, which can be stated in this way: If (nlight/nheavy)1 is the ratio of the number densities in the first stage of the cascade, then the number ratio on the output side of that stage, that is, of the gas which is harvested and sent on to the second stage, can be expressed as:
where the ratio of speeds has been replaced with a ratio of masses from equation (4.7). Reiterating this logic to the next stage, and then to the one after that and so on, shows that after S successive stages the number ratio will be
In the K-25 plant, the feed gas was uranium hexafluoride, that is, molecules of 235UF6 (atomic weight 349) and 238UF6 (atomic weight 352). If the feed material is not enriched before being pumped into the first stage, the initial number-density ratio will be that of natural uranium, (n235/n238) = 0.0072/0.9928 = 7.25 × 10−3. Hence
The extent of enrichment is usually quantified by the percentage of U-235. If we define x = n235/n238, then
To reach bomb-grade U-235 (90% U-235; x = 9) requires S = 1665. Of course, the process is never as efficient as this analysis implies; not all of the material that enters each stage undergoes diffusion, and some gas inevitably diffuses back through the barrier within each cell. Figure 4.6 shows the run of U-235 percentage predicted by equation (4.11) as a function of the number of stages, assuming starting with uranium of natural isotopic composition.
Figure 4.6. U-235 enrichment as a function of number of diffusion stages. The initial number-density ratio is assumed to be that of natural uranium.
Another result from kinetic theory can be used to make an estimate of the number of membrane holes necessary to achieve a given rate of material processing. This is that if the pressure in the diffusion tank is P and the temperature is T, the rate at which molecules of mass m strike the membrane is given by
Consider uranium hexafluoride of natural-abundance uranium composition; essentially all of the uranium atoms will be U-238. Suppose that the pressure is one atmosphere (101 300 Pa), that T = 300 K, and that we wish to process 140 kg of uranium per day, which would correspond to processing (although not isolating) about 1 kg of U-235. With a molecular weight of 352, this gives a strike rate of
This corresponds to 7.1 × 1031 strikes per square meter per day, or a mass equivalent of 4.15 × 107 kg per square meter per day. Processing 140 kg then corresponds to a ‘hole area’ of 3.38 × 10−6 square meters. For holes of diameter 100 Å, this will require some 43 billion holes!
When Oak Ridge achieved full operation in the spring of 1945, uranium was first given a slight level of enrichment by the process of liquid thermal diffusion, which is not discussed in this book. This process took feed material from the natural abundance of U-235, 0.72%, up to 0.86% U-235. This product was fed to the K-25 plant to be taken to 36% U-235, which was fed to the Y-12 calutrons to be brought up to 90% U-235. By the end of the war, the K-25 gaseous process had proven itself more efficient at enriching uranium than the electromagnetic method; shutdown of calutrons began on September 4, 1945. K-25 continued to operate until it was shut down in 1985; the last remnants of the plant were demolished in early 2013. According to a 2011 report by the International Panel on Fissile Materials, the United States produced a total of some 610 metric tons (610 000 kg) of highly-enriched uranium between 1945 and 1995. Highly-enriched uranium is defined as ⩾20% U-235.
4.3 Pu-239: The Hanford reactors
Manhattan Project administrators sought to insure the success of their endeavor by pursuing production of two fissile materials, U-235 and Pu-239. To produce the latter required construction of large-scale nuclear reactors to breed plutonium by capture of moderated neutrons by U-238 nuclei according as the reactions of equations (2.8) and (2.10):
Reactor technology was an entirely novel endeavor in the 1940s. The first experimental reactor, an uncooled, graphite-moderated device, was operated for the first time on December 2, 1942, at the University of Chicago under the direction of Enrico Fermi. Reactors are rated by their power output, that is, the energy liberated per second due to fissions. Fermi’s reactor, which was code-named CP-1 (Critical Pile 1), was normally operated at a power of less than a single Watt; CP-1’s purpose was to show that a self-sustaining chain-reaction could be created and safely controlled. In November, 1943, an intermediate-scale, air-cooled, graphite-moderated reactor known as X-10 was brought into operation at Oak Ridge. X-10 operated at much higher power levels, up to 4 megawatts (MW), and was used to test fuel fabrication and handling procedures, perform radiological research, and to synthesize about 300 g of plutonium for research at Los Alamos.
While X-10 represented a million-fold leap in power from CP-1, it was by no means adequate to deliver plutonium at the pace project leaders desired; much more powerful reactors would be required. The rate of plutonium synthesis in a reactor is proportional to its power output. To get an idea of how powerful a reactor is required, we can use a formula which gives the rate of plutonium synthesis in grams per day as a function of various parameters. This is
In this expression, P is the reactor’s power output in MW, F is the fractional abundance of U-235 in the fuel, Ef is the energy liberated per fission in MeVs, is the U-238 neutron capture cross-section in barns, and is the U-235 neutron fission cross-section in barns. It is important to emphasize that these cross-sections are those for the so-called ‘thermal’, or ‘moderated’ neutrons one has in a reactor, not the fast neutrons utilized in nuclear weapons.
By putting P = 1 MW, we can evaluate the rate of plutonium production per day per megawatt of power output, and then get an idea of what power a reactor should be designed to achieve to produce a critical mass of material in a reasonable time.
For fuel of natural-abundance U-235, F = 0.0072. The cross-sections are and ; adopting Ef = 180 MeV gives
For convenience, I round this to 0.75 g day−1 MW−1. Suppose for the sake of argument we wish to produce 7.5 kg of Pu-239, which is probably a reasonable amount for a tamped bomb core (table 3.1). This would require (7500/0.75) = 10 000 MW-days of operation. If it is desired to produce this in 15 days (that is, to produce 500 g day−1) once a reactor is built and operating, then we would require a reactor of power (10 000/15) ∼ 670 MW. Manhattan Project administrators decided to build three 250-MW reactors along the banks of the Columbia River in south-central Washington, with the intent of producing 600 g of plutonium per day; General Groves wanted to deliver bombs as soon as possible for use in the war. The facility for this, the so-called Hanford Engineer Works (HEW), would come to occupy 670 square miles.
The HEW site was located in a flat, semi-arid, sparsely-populated area. Groves wanted his facilities for producing uranium and plutonium to be far apart from each other not only for security reasons, but also as insurance in the event that if one of them was destroyed by some catastrophe, the others could keep functioning. The immense flow of the Columbia provided a perfect source of water for cooling the reactors, which were also known as ‘piles’. Groves inspected the site personally in January, 1943, and approved its acquisition. As at Oak Ridge, a town had to be provided for workers and their families; this was located in Richland, Washington, and would grow to a population of over 17 000.
The three reactors were placed six miles apart, and were known as the ‘B’, ‘D’, and ‘F’ reactors after corresponding survey locations. The first one built was the B-pile; layout of the reactor building itself began in October, 1943. The three reactors were of identical design: water-cooled, graphite-moderated graphite cubes 36 feet wide by 36 feet tall by 28 feet front-to-rear, constructed out of layers of thousands of graphite bricks. The graphite cores were surrounded by shielding to protect workers; this brought their outer dimensions to 37 feet from front to rear, 46 feet from side to side, and 41 feet high. Piercing through the shielding and core were 2004 aluminum ‘process tubes’ into which could be fed slugs of natural uranium metal fuel (figure 4.7). The tubes were spaced 8 3/8 inches apart both horizontally and vertically; Fermi had determined that this was the distance a neutron would on average have to scatter through graphite to become thermalized. The fuel slugs would gradually travel through the reactor as new ones were pushed in behind them; after some days or weeks of neutron irradiation they would fall out of the rear of the reactor into a pool of water where they would be allowed to cool both thermally and radiologically before being taken away for chemical processing to extract the synthesized plutonium.
Figure 4.7. Left: B-reactor area, looking northwest, January, 1945. The Columbia River is in the background. The pile building itself is adjacent to the water tower [7]. Middle: workers laying the graphite core of B-reactor. The rear face of the reactor is toward the lower left, and the inside of the front face to the upper right. Right: front face of F-reactor, February, 1945. The middle and right photos are from Historic American Engineering Record: B Reactor (105-B) Building, HAER No WA-164. DOE/RL-2001-16. (Richland, WA: United States Department of Energy, 2001) [8].
Each pile comprised some 75 000 graphite moderating bricks, most about four inches square by four feet long; about one in five were bored lengthwise to accommodate fuel tubes. During normal operation, each tube contained 32 active fuel slugs about 1.5 inches in diameter by nine inches long. Each slug contained about eight pounds of natural uranium; the usual fuel load of about 250 tons implies over 60 000 slugs inside the pile at any time. Dummy and neutron-capturing slugs were used to help control the neutron flux, as were control rods that could be operated remotely. Essential to the safe operation of each pile was its cooling system; some 30 000 gallons of water were pumped through each pile per minute.
The first fuel was loaded into B-reactor on the afternoon of September 13, 1944, by Enrico Fermi. By the morning of the 27th, the pile was operating at 9 MW with about half of its fuel tubes loaded. At first everything seemed to be operating perfectly, but after a few hours the reactor began shutting itself down. Surprisingly, however, it spontaneously began coming back to life after a few hours of dormancy. But as soon as the power level was brought back to 9 MW, shutdown again set in.
From the pattern of the pile’s reactivity, Fermi and his colleagues deduced that the problem was likely a neutron-capturing fission
product with a half-life of several hours. The specific culprit proved to be xenon-135, which has a half-life of only 9.1 h but has a neutron capture cross-section of over three million barns. The only way to overcome the problem was to increase the amount of fuel in the reactor, which necessitated plumbing in as-yet-unused fuel tubes. This work was begun on September 30, and proceeded in stages until all tubes were ready by December 28. A power of 150 MW was achieved on the 29th, and the full design rating of 250 MW was achieved on February 4, 1945. The D and F piles started life with full fuel loads: D went critical on December 17, 1944, and F on February 25, 1945. By early May, some 1.6 kg of plutonium had been extracted and delivered to Los Alamos, and by June 1 General Groves was able to order that production be maintained at 5 kg every 10 days.
By the spring of 1945, all of Groves’ fissile-materials programs were entering mass production. At Los Alamos, scientists and engineers prepared to incorporate these materials into the world’s first nuclear weapons.
Exercise
A large commercial reactor fueled with uranium enriched to F = 0.06 produces power at a rate of 2600 MW. What will be the rate of plutonium production in this reactor? Take , , and Ef = 180 MeV per fission.
The Manhattan Project Page 6
