Cosmic-Ray Muons Might Help Thwart Transport of Concealed Fissile Material

The great majority of cosmic-ray particles reaching Earth’s surface are positive and negative muons. At sea level, the muon flux is about 10⁴/m² per minute. These muons are mostly decay products of short-lived π mesons created by cosmic-ray protons hitting the upper atmosphere. Because muons are 200 times heavier than electrons and impervious to the strong nuclear force, they are far more penetrating than electrons, neutrons, x rays, or even gamma rays. With a typical energy of 3 GeV, a cosmic-ray muon will pass through 15 m of water or 2.5 m of steel.

Christopher Morris and colleagues at Los Alamos National Laboratory are proposing to exploit this ubiquitous, penetrating flux for a new kind of radiographic surveillance. In a recent issue of Nature, ¹ they reported experimental and computer simulations that suggest the feasibility of locating small quantities of fissile material concealed in ordinary cargoes at US border crossings and seaports. With relatively inexpensive and well-tried particle-physics tracking chambers installed in drive-through facilities at border checkpoints, they argue, one could spot a 10-cm cube of a high-Z material like uranium or its lead shielding, hidden in a truckload of sheep, or even steel, in just one minute of observation.

Weapons-grade nuclear materials are, of course, radioactive. But attempts to detect that telltale radioactivity can, like x-ray imaging, be thwarted by lead shielding. The Los Alamos group proposes to distinguish high-Z metals from common metals such as iron, copper, and aluminum (all with Z less than 30) by measuring the Z-dependent multiple Coulomb scattering of muons traversing the material in question. Unlike non-tomographic x-ray imaging, this new radiography is intrinsically three-dimensional. And, of course, it requires no radiation source.

In the late 1960s, a group of particle physicists led by Luis Alvarez exploited the penetrating power of cosmic-ray muons to look for hidden chambers in the pyramid of Chephren in Egypt. Alvarez and company measured the directional dependence of the fraction of muons lost by absorption in traversing tens of meters of stone. They found no hidden chambers. ²

In a sufficient thickness of material, muons are gradually brought to rest by losing energy as they excite or ionize the atoms they’re passing through. But if one is looking for a subcritical mass of weapons-grade material no bigger than an orange, muon absorption alone won’t do. Only about 10% of cosmic-ray muons would be stopped by 5 cm of uranium. So, with a flux of only one muon per square centimeter per minute, collecting adequate statistics to reliably discern a 10% loss of cosmic-ray muons stopped by an object a few cm across would take much too long.

Furthermore, muon absorption, like ordinary x-ray imaging, only provides two-dimensional shadow projections. One doesn’t know where along its path a missing muon came to rest.

Multiple Coulomb scattering

One can do better by measuring multiple Coulomb scattering. A muon passing through a thickness of material too thin to stop it will, nonetheless, suffer repeated Coulomb scattering, mostly off nuclei, through very small angles. The muon’s net direction change θ after many such scatters will have a random, roughly Gaussian distribution about zero. The root-mean-square width θ₀ of that random distribution is proportional to $\sqrt{l/l_0}/p,$ , where p is the muon’s momentum, l is its path length, and l ₀ is the “radiation length” of the material.

The radiation length—the characteristic distance for bremsstrahlung energy loss by a high-energy electron—is a sensitive function of the material’s Z. And that Z dependence is the crux of the new muon radiography. For a 3-GeV muon traversing 10 cm of iron (Z = 26), the rms cumulative scattering angle θ₀ is 15 milliradians. But for tungsten (Z = 74), it’s 38 mrad. In 10 cm of water, θ₀ is only 3 mrad.

Even 38 mrad is barely 2 degrees. To measure such small deflections, the Los Alamos group proposes using planar drift chambers of the kind used for decades in high-energy physics experiments. Each chamber consists of a plane of parallel anode wires running in one direction and, just below it, a second plane whose wires run in the orthogonal direction. Together, the two adjacent wire planes record the place at which a muon traverses the chamber. Each anode wire, held at about 2 kV, is surrounded by a grounded, gas-filled aluminum tube 25 mm in diameter. A muon passing through a particular tube ionizes the gas, leaving behind free electrons that drift toward the tube’s wire and eventually produce an avalanche pulse on it. The distance of the muon’s closest approach to the wire is measured to within about 0.4 mm by the electrons’ drift time in the gas before they produce the pulse.

A pair of drift chambers 1 m apart can measure, with an accuracy of about 0.2 mrad, the direction of an undeflected muon passing through both. Figure 1 shows the proposed arrangement for truck surveillance. The two drift chambers above the truck measure the direction of each incident muon, and the two immediately below it measure the change θ in that direction due to scattering by materials inside the truck. The larger the θ, the more accurately one can localize the material in which the deflection took place by extrapolating the incoming and outgoing tracks to an approximate intersection point.

In addition to those four indispensable drift chambers, two additional chambers at the very bottom and two steel plates constitute a proposed refinement. Even without knowing an individual muon’s momentum, one can statistically relate the observed θ to the scattering material’s Z by averaging over the known energy spectrum of cosmic-ray muons. But some knowledge of the muon’s momentum sharpens that relation. The bottom two drift chambers would provide a rough measure of each muon’s momentum by measuring its multiple Coulomb scattering in known thicknesses of steel.

An experimental demonstration

To test this scheme, the Los Alamos group performed a small-scale experiment. They used a stack of four 60 × 60-cm drift chambers spaced 27 cm apart to image a 10-kg tungsten cylinder, 11 cm in diameter, standing between the two middle chambers. In that experiment there was no momentum measurement. The resulting radiograph, after about an hour of collecting cosmic-ray muons, is shown in figure 2. On either side of the very bright spot that indicates the tungsten cylinder are fainter lines indicating two steel support rails.

How does one turn the muon scattering data into a 3D image like figure 2 that highlights the location of high-Z material? First Morris and company divided the 60 × 60 × 27-cm region under scrutiny into 1-cm cubes (“voxels”). Next, for every scattered muon, they assigned the scattering locality to one or more voxels by finding the point of closest approach between the incoming and outgoing tracks and smearing that point with an appropriate uncertainty estimate. Then they assigned to each voxel in the volume a display brightness determined by the rms θ of all scattering events localized to that voxel. The observed distribution of deflection angles for all muons scattering in the tungsten, shown in figure 3, agrees very well with a Monte Carlo simulation of the experiment.

“This is still a rather primitive reconstruction algorithm,” says Morris. “Larry Schultz, our graduate student, is developing a more sophisticated maximum-likelihood program.” For one thing, the present algorithm doesn’t take account of the small fraction of muons actually stopped by the tungsten. Nor does it take full advantage of the tomographic possibilities inherent in the fact that muons arrive from all directions on the sky. Because the deflections are so small, the scattering locale along any one muon’s trajectory has a large uncertainty. But knowing that many muons with very different incident directions appear to scatter in roughly the same region should help define that scattering region more sharply.

The exposure times necessary to create images at least as good as figure 2 should become significantly shorter with the use of more efficient drift chambers optimized for the task. The group’s estimate that it wouldn’t take more than a minute of cosmic-ray exposure to spot a 10-cm cube of uranium in a truckload of organic or metallic freight is based on a computer simulation of three such uranium blocks hidden among 69 sheep inside a steel cargo container. “You could even do it with a load of iron instead of sheep,” says Morris, “as long as it doesn’t exceed the standard weight limit on iron cargoes.”

The Los Alamos group estimates that the cost of drift chambers and related electronics for a border surveillance station like that in figure 1 would be about $1.5 million. Assuming such a station could analyze a vehicle in just one minute, they estimate that 500 such stations could handle the entire traffic of passenger cars and trucks entering the US.

Because the cosmic-ray flux is so much less than the punishing fluxes encountered in accelerator experiments, the surveillance drift chambers should last for many years. “On the other hand,” the group warned in a recent submission to the US Department of Homeland Security, they would have to be largely maintenance-free. “The large, inexpensive [sic], skilled work force required to maintain a high-energy-physics detector will not be available at border crossings.”