A 1.2 × 1.2 m2 muon tracker was moved from Los Alamos to the Toshiba facility at Kawasaki, Japan, where it was used to take ∼4 weeks of data radiographing the Toshiba Critical Assembly Reactor with cosmic ray muons. In this paper, we describe the analysis procedure, show results of this experiment, and compare the results to Monte Carlo predictions. The results validate the concept of using cosmic rays to image the damaged cores of the Fukushima Daiichi reactors.

Cosmic ray muon radiograph has been proposed as a method for obtaining information about the location of the fissile material in the melted cores of the Fukushima Daiichi reactors. In a recent paper,1 the simulation code GEANT42 was used to track cosmic rays through a model of a boiling water reactor similar to Fukushima Daiichi Reactor No. 1. The model of the reactor included all major structures, the reactor building, containment vessel, and the pressure vessel. Calculations were performed for an intact core, a core with a 1 m diameter of material removed from the core and placed in the bottom of the pressure vessel, and with no core. The goal of the work was to compare images obtained using the stopping of cosmic rays with images made using the scattering of transmitted cosmic rays.

Although muons of sufficient energy can be transmitted through thick objects, they continuously interact with the electrons and nuclei in the matter. These interactions consist of the Coulomb and the weak interaction between the muons and the electrons and nuclei. To a good approximation, these can be treated separately and each can be used for radiography.3 In the context of radiography, the weak interaction can be ignored.

The Coulomb interaction between muons and the much lighter electrons results in continuous energy loss4 and eventual stopping of the muons as they move through matter. In contrast, the Coulomb interaction between muons and atomic nuclei results in deflections of the muon trajectory, but negligible energy changes. Because the integral of the Coulomb cross section is infinite, the solution to the problem of charged particle transport in matter is non-trivial. The number of collisions is large, and this process results in a continuous increase of the angular divergence of the beam described by Coulomb multiple scattering.5 

The stopping rate, dNdx, of cosmic rays in material can be related to the energy spectrum, dN(E=0)dE, as

dNdx=dNdEdEdxdEdx=KZA1β2[12ln(2mec2β2γ2TmaxI2)β2δ(βγ)2],
(1)

where Z and A are the atomic number and mass, β = v/c where v is the muon velocity and c is the velocity of light and γ=11β2, me is the electron mass, I is the mean ionization potential, and δ is a function described in Ref. 6. The low energy part of the spectrum depends upon altitude, azimuth, and overburden and is best determined experimentally.

The multiple scattering is described by

dNdθ=12πθ02eθ22θ02dΩθ0=14.1pβLX01X0=KA{Z[Lradf(Z)]2+ZLrad},
(2)

where dN/dθ is the polar angular (θ) distribution of muons of momentum p (in MeV/c) that pass through a distance L of material. K and Lrad, L′rad, and f(Z) are described in Ref. 6. The Z2 dependence of radiation length (RL), X0, leads to a high sensitivity of Coulomb multiple scattering to high-Z materials.

The conclusions of Ref. 1 are: the large Z-dependence of multiple scattering radiography makes it far better suited for reactor radiography when compared to stopping radiography; and that several weeks of exposure provide enough information to provide clear images of the core with <1% mass sensitivity. These conclusions are apparent from the radiographs shown in Ref. 1, where scattering and transmission radiography are compared.

The simulations assumed 50 m2 of detector on opposite sides of the reactor. The residual radiation on the site is still ∼1 mSv/h in the locations where the detectors were placed in the simulation. Shielding is necessary to mitigate the detector backgrounds from γ-rays. The engineering and construction problems were partially addressed in further Monte Carlo studies where the detector locations and sizes were adjusted to fit in practical locations.7 In addition, a new reconstruction technique that increases the sensitivity for commercial reactor geometries, where the scattering of outgoing muons in the shielding and concrete build walls reduces the sensitivity of scattering radiography, displacement radiography, was described.

Finally, muon radiography of a small research reactor at the University of New Mexico, an AGN-201M, was demonstrated using the Los Alamos Mini Muon Tracker (MMT).8 The University of New Mexico Research Reactor consists of 10.9 kg of polyethylene loaded with about 3.3 kg of enriched uranium. Moderator and shielding consisting of graphite, lead, water, and concrete surround the core. Even though the density of uranium in the core is only about 0.3 g/cm3, the combination of simulation and data demonstrated sufficient sensitivity to detect the uranium through the 10 cm thick lead reflector and water and concrete shielding surrounding the core. However, the sensitivity was not high. Here, we present the results of a similar experiment aimed at measuring of the Toshiba Nuclear Critical Assembly (NCA) reactor where the core, although only ∼1/3 scale, is more similar to a commercial power reactor.

This experiment used the MMT detectors mounted outside of the reactor water vessel. A 0.5 cm thick steel plate and a 1 cm thick aluminum plate covered the front of the lower detector and some 28 × 20 × 12 cm3 steel blocks were placed in front and behind 20 × 20 × 20 concrete blocks in front of the upper detector to test the ability of muon tomography to view through overburden. The core was loaded with a configuration of 1.5 m long, 1 cm diameter UO2 ceramic fuel rods, on 1.5 cm centers, configured in a 40 cm diameter cylinder with a 20 cm void at its center. In addition, 3 × 3 assemblies of rods were placed to the sides in front and behind the cylinder as shown in Figure 1.

FIG. 1.

Layout and some slices from the three dimension tomograph showing the major features in the NCA image.

FIG. 1.

Layout and some slices from the three dimension tomograph showing the major features in the NCA image.

Close modal

This geometry provided multiple objects to image: the center cylinder, the smaller fuel rod bundles to the sides, and the steel blocks near the upper detectors. In order to accomplish this, we have used the tomographic muon imaging techniques described in Refs. 9 and 10.

Approximately 4 weeks of data were taken in the configuration shown in Figure 1. In the previous work, it has been shown the lowest variance can be obtained from multiple scattering tomography by using a multi-energy group fit to the angular-distribution data to form an image of radiation lengths.10 We have used that method here and have calibrated it using the known path lengths through the NCA reactor. Areal densities were taken normal to the reactor axis.

The images of RLs at a plane at the center of the reactor core generated as a function of exposure time are shown in Figure 2. The reactor core is visible after only 4 h of exposure. After 1 day, the void at the center can be observed. The image continues to improve through the entire 4-week experiment.

FIG. 2.

Time development of the radiographic signal.

FIG. 2.

Time development of the radiographic signal.

Close modal

Images focused at different image planes along a line connecting the detector centers are shown in Figure 3. The core is best focused in the image at 200 cm in the detector coordinate system. At 180 cm, the bundle of 9 fuel rods closest to the lower detector is clear, and at 220 cm the fuel bundle closest to the upper detector is clear. Around 250 cm, the flange on the top of the water tank can be seen as the bottom of an oval. At 310 cm, the steel bricks mounted in front of the upper detectors are in focus. The major features are shown in the drawing in Figure 1.

FIG. 3.

Slices through the tomography in 10 cm steps along a line connecting the detector centers.

FIG. 3.

Slices through the tomography in 10 cm steps along a line connecting the detector centers.

Close modal

The images have units of radiation lengths (ρAX0). In the case of an axially symmetric core, radiation length volume density can be obtained by performing an Abel inversion. Here, we use a regularized Abel technique previously described in Ref. 8. The results are shown as images and in the line plots in Figure 4.

FIG. 4.

(Top) images of the radiation length weighted areal (left) and volume (right) densities. (Bottom) Line plots of the areal and volume density average over the region marked by the white lines. Data points are the experimental values and solid lines are a model fitted to the areal density data.

FIG. 4.

(Top) images of the radiation length weighted areal (left) and volume (right) densities. (Bottom) Line plots of the areal and volume density average over the region marked by the white lines. Data points are the experimental values and solid lines are a model fitted to the areal density data.

Close modal

GEANT2 Monte Carlo simulations of this geometry have been performed. These did not include the details of the detector or the building, so the calibration of the multi-group model was redone for the Monte Carlo data set, and the images were formed using the same reconstruction software. The cosmic ray generator was the same as was used in the previous work.1,7,8 The z values are offset by 200 cm because of different coordinate systems. The major features observed in the experimental data are also observed in the Monte Carlo reconstructions (Fig. 5).

FIG. 5.

Slices through the tomography in 10 cm steps along a line connecting the detector centers. These can be compared to Figure 3.

FIG. 5.

Slices through the tomography in 10 cm steps along a line connecting the detector centers. These can be compared to Figure 3.

Close modal

The grey scales are the same in both sets of images. Qualitatively, the contrast from the objects is the same. The major quantitative difference is a difference on the background dark levels between the two reconstructions. A comparison of the Monte Carlo results and the data is shown in Figure 6, both as horizontal density plot and images. The offsets have been adjusted to be the same. The quantitative agreement is within 3% in measured density. Similar agreement is obtained for the other slices in z.

FIG. 6.

Comparison of reconstructed densities between the GEANT2 Monte Carlo simulation and the data for a slice through the center of the core. (Top) images with the projected region marked by the green lines. (Bottom) plots of areal density vs. horizontal position for the Monte Carlo results (blue) and the data (red).

FIG. 6.

Comparison of reconstructed densities between the GEANT2 Monte Carlo simulation and the data for a slice through the center of the core. (Top) images with the projected region marked by the green lines. (Bottom) plots of areal density vs. horizontal position for the Monte Carlo results (blue) and the data (red).

Close modal

We have presented an analysis of muon radiography of the Toshiba NCA reactor. Data were taken for 4 weeks using the Los Alamos Mini Muon Tracker. All of the features designed into the scene are observed in the three dimensional reconstruction of the data. In addition, the data demonstrate that absolute densities can be obtained from cosmic muon radiography. Monte Carlo simulations and the data agree to within 3%.

This work has been supported by the Tokyo Electric Power Company and by Toshiba Corporation, Power Systems Company.

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