A study of imaging the Fukushima Daiichi reactors with cosmic-ray muons to assess the damage to the reactors is presented. Muon scattering imaging has high sensitivity for detecting uranium fuel and debris even through thick concrete walls and a reactor pressure vessel. Technical demonstrations using a reactor mockup, detector radiation test at Fukushima Daiichi, and simulation studies have been carried out. These studies establish feasibility for the reactor imaging. A few months of measurement will reveal the spatial distribution of the reactor fuel. The muon scattering technique would be the best and probably the only way for Fukushima Daiichi to make this determination in the near future.
The 9.0-magnitude earthquake followed by the vast tsunami on March 11, 2011, caused a nuclear crisis at Fukushima Daiichi.1 Damage of the reactor cores has attracted worldwide attention to the issue of the fundamental safety of atomic energy.2 A cold shutdown was announced by the Japanese government in December, 2011, and a new phase of cleanup and decommissioning was started. However, it is hard to plan the dismantling of the reactors without any realistic estimate of the extent of the damage to the cores, and knowledge of the location of the melted fuel.3,4 In the case of Three Mile Island, it took more than 3 years before a camera could be put into the reactor, and about 10 years before the actual damage to the reactor could be assessed.5 Since access to the reactor buildings is very limited due to high radiation fields, imaging the reactor cores from outside the buildings will be a valuable step, and can reduce the time required to dismantle the reactors significantly, resulting in cost savings and lower total worker radiation dose.
One technique for imaging the cores without access is muon imaging, which utilizes naturally occurring cosmic-ray muons to image large-scale objects. Cosmic-ray muons which have a sea-level flux of 104 m−2 min−16 are the results of hadronic showers high in the atmosphere. Since 1950s, imaging objects by measuring transmitted muons with a muon telescope has been applied to study mine overburden,7 an Egyptian pyramid,8 a temple gate,9 volcanoes,10–13 a blast furnace14 and caverns.15 By measuring the attenuation of the muon flux, two-dimensional density maps are obtained. An approximation of muon attenuation in matter is given by:
Here, N is the number of muons, λ the attenuation length, dN/dE the value of the muon energy spectrum at low energy, and −dE/dx the mean energy loss rate. Since the attenuation arises by muon stop in material due to the energy loss, the transmission method is most sensitive to low atomic number (Z) materials where the specific energy loss is largest and the Coulomb scattering is smallest. In practical applications, muon transmission imaging often suffers from poor position resolution due to the continuous scattering along the muon path, and from low signal-to-noise ratio caused by low statistics because of small detection area (typically ∼2 m2).16,17 Also, the muon flux incident on the object is of critical importance to determine the attenuation for transmission method, which is sometimes not easy to estimate.
A more sensitive technique, muon scattering radiography, was invented at Los Alamos National Laboratory,18–21 and has been used by some other groups.22–24 The scattering method uses two muon trackers to measure incoming and outgoing tracks of individual muons, where the region of interest is contained within the acceptance of the tracker pair. Combining the incoming and outgoing tracks provides better spatial resolution when compared to the transmission method where only the information from the scattered outgoing tracks is available. The multiple Coulomb scattering25 is a stochastic process and the Gaussian width of the angle is given by:26
where βc and p are the velocity and momentum of the incident muon, and x and X0 are the thickness and radiation length of the scattering medium. The radiation lengths for water, concrete, steel and uranium are 39.3, 11.6, 1.76 and 0.317 cm6. The muon momentum can be estimated by the muon scattering within the detector.27 A method for calculating most probable muon trajectory and providing higher precision in density inferences has been presented.28 Techniques used to reconstruct matter distributions are: the point of closest approach;20,27 maximum-likelihood / expectation-maximization;29 Bayesian estimation.30 The scattering method has high sensitivity to high-Z materials such as uranium, and is very useful for detecting them in a background of low-Z material. This method has been applied to scan trailers and shipping containers for special nuclear material.31,32 It is also a promising technique for International Atomic Energy Agency's nuclear safeguards and non-proliferation.33,34 To image Fukushima Daiichi reactors, a new analysis, displacement method, has been developed, which is described in the latter section.
A week after the Great East Japan Earthquake, we began to study applying the muon scattering technique to Fukushima Daiichi to assess damage of the reactor cores. Several groups in Japan and the US have suggested imaging the reactors with muon transmission method and compact detectors (∼1 m2). However, since uranium fuel and water give similar energy losses for muons, the fuel is difficult to distinguish from the overburden of water, concrete and steel with the transmission method. The energy loss of a muon through matter is given by:
The muon energy loss rate in uranium dioxide and water are 1.15 and 1.98 MeV cm2 g−1 for minimally ionizing particles respectively.35 In a fuel rod, uranium dioxide pellets are packaged in a zircaloy tube, and the density of uranium fuel averaged over the active volume of the assembly is about 2.6 g/cm3.36 Even with the whole assembly, an intact core attenuates the muon flux ∼2% more than water does, which makes distinguishing the reactor core from water in the presence of the overburden difficult using the transmission radiography. In contrast, the fuel gives a distinct signal in scattering radiography, producing an image contrast of ∼30% even through the same overburden. Also, the muon scattering and flux attenuation can be combined to distinguish materials.37 Compared to conventional transmission radiography, scattering radiography improves the spatial resolution and the image contrast by an order of magnitude for imaging reactor cores.38
In the summer of 2011, a reactor mockup was imaged using Muon Mini Tracker (MMT) at Los Alamos (altitude of 2,231 m). The MMT consists of two muon trackers each having effective detection area of 1.2 × 1.2 m2 and consisting of 6-x and 6-y planes of sealed drift tubes. In the demonstration, cosmic-ray muons passing through a physical arrangement of material similar to a reactor were measured. The reactor mockup consisted of two layers of concrete shielding blocks with a thickness of 2.74-m each, and a lead assembly in between; one tracker was installed at 2.5-m height, and another tracker was installed on the ground level at the other side. Several arrangements of lead were studied to test specific features of the reactor imaging technique. One of the results is shown in Figure 1 where lead with a conical void similar in shape to the melted core of the Three Mile Island reactor was imaged through the concrete walls. It took 3 weeks to accumulate 8 × 104 muon events. The analysis was based on point of closest approach, where the track pairs were projected to the mid-plane of the target, and the scattered angle was plotted at the intersection. Even with event rate of an order of magnitude smaller than what we expect at Fukushima Daiichi with proposed Fukushima Muon Tracker (FMT), we successfully imaged the lead cores.
Left – Lead reactor core with conic void. Right – Observed core where average scattering angles of muons are plotted. The void in the core is clearly imaged through two 2.74-m concrete walls. The lead core of 0.7-m thickness gives an equivalent radiation length to the uranium fuel in Unit 1, and gives a similar scattering angle. Hot spots at the corners are artifacts caused by edge effect of MMT.
Left – Lead reactor core with conic void. Right – Observed core where average scattering angles of muons are plotted. The void in the core is clearly imaged through two 2.74-m concrete walls. The lead core of 0.7-m thickness gives an equivalent radiation length to the uranium fuel in Unit 1, and gives a similar scattering angle. Hot spots at the corners are artifacts caused by edge effect of MMT.
A proposed plan for Fukushima Daiichi Unit 2 is shown in Figure 2. The plan includes installation of several muon trackers on the operation floor of turbine building (FMT-1) and in front of the reactor building (FMT-2). With this geometry, muons from the east can image the bottom region of RPV while muons from the west can image the original core region. The bottom of the reactor containment vessel can be imaged by installing FMT-2 below the ground level. Specifications of FMT-1 and 2 are shown in Table I. They consist of gas-filled ionization drift-tube detectors made of aluminum,39,40 and have spatial and angular resolutions of 0.4 mm and 2 mrad (full width at half maximum) with tracking efficiency of close to 100%. The FMT system can measure muon scattering and flux attenuation simultaneously. Muon trackers of the similar sizes have been manufactured in the past with sealed drift tubes,41,42 and the technique is mature. Advantages of the drift tube compared to other muon detectors are: less γ-ray sensitivity when compared to solid state detectors e.g. plastic scintillators; adequate spatial resolution; mechanical robustness; operational independence of tubes resulting in negligible inefficiencies of the muon tracker in case of failures; relatively low cost. Drift-tube pulses are amplified, discriminated and digitized at the detectors in field-programmable gate-array (FPGA) time-to-digital converters (TDCs). The data are transferred to data-acquisition computers on the Fukushima Daiichi site through a dedicated Ethernet link, converted into muon tracks for online analysis, and then further analyzed in detail. The system is triggerless in the sense that tracks are built after the data have been digitized. The position calibration will be carried out in situ using the muon track data (auto calibration).
Muon imaging setup for Fukushima Daiichi Unit 2. FMT-2 is installed inside a concrete radiation shield in front of the reactor building. Typical muon scattering angles are a few degrees.
Muon imaging setup for Fukushima Daiichi Unit 2. FMT-2 is installed inside a concrete radiation shield in front of the reactor building. Typical muon scattering angles are a few degrees.
Specifications of FMT-1 and 2. Measurement time scales inversely with the product of total area of FMT-1 and 2 at the lowest-order approximation. However, there is a strong angular dependence of muon flux (∝ cos2θz, where θz is the zenith angle).43,44
| FMT-1 | FMT-2 | |
|---|---|---|
| Detection area | 3.0 × 3.0 m2 | 5.5 × 5.5 m2 |
| Detector size | 3.3 × 3.3 × 0.6 m3 | 5.8 × 5.8 × 0.6 m3 |
| Drift tube | 5-cm diameter, 12 layers (xx-yy…) | |
| Modules to be installed | 3–15 | 2–4 |
| FMT-1 | FMT-2 | |
|---|---|---|
| Detection area | 3.0 × 3.0 m2 | 5.5 × 5.5 m2 |
| Detector size | 3.3 × 3.3 × 0.6 m3 | 5.8 × 5.8 × 0.6 m3 |
| Drift tube | 5-cm diameter, 12 layers (xx-yy…) | |
| Modules to be installed | 3–15 | 2–4 |
A major engineering challenge at Fukushima Daiichi is operation of the FMT in a high radiation environment. The site has radiation level of up to a few mSv/h near the reactor buildings of Units 1 - 3, which mostly consists of γ rays from 134Cs and 137Cs. The γ rays trigger drift tubes through Compton scattering which mostly takes place at their aluminum walls. Though most γ-ray events can be discriminated by taking time coincidences between multiple drift-tube layers, average background rate of each drift tube must be kept below 20 kHz so as not to exceed the bandwidth of the Ethernet. On May 25, 2012, background rate in the 0.3-m long drift tubes was measured at Fukushima Daiichi in collaboration with Tokyo Electric Power Company (TEPCO) to estimate the shield requirement for the FMT-2. The radiation levels of the locations were 0.6, 0.7 and 1.2 mSv/h on the ground. The measured background rates were 950 kHz per 1 mSv/h (normalized to the 5.5-m length of the FMT-2 detector). Assuming the radiation level at the installation point to be 1 mSv/h, a concrete shield of 40- to 50-cm thickness will be needed to reduce the γ-ray levels by a factor of 50.45 The radiation levels on the operation floor of turbine building are below 0.02 mSv/h at most locations in the case of Unit 2 (December 10, 2012), which allows FMT-1 to be operated without any radiation shield.
Simulation studies were performed with a geometry based on Fukushima Daiichi Unit 2 to test the feasibility of the proposed plan. Modeling studies on Unit 1 are described in the previous paper.38 GEANT4 framework46 was used and a cosmic-ray generator was implemented, which reproduces the correct energy spectrum of muons for different zenith angles in good agreement with known measurements.47 The reactor model included all the major structures of Unit 2 as shown in Figure 2. The core in the simulation had an average density of 4.3 g/cm3 over the volume and consisted of uranium dioxide (60.5%), zirconium (22%), stainless steel (2%) and water (15.5%);36 the debris has density of 8.2 g/cm3 and consisted of uranium (70%), zirconium (14%), oxygen (13%) and stainless steel (3%), which is similar to nuclear debris found at the Three Mile Island accident.48 For the image reconstruction, we have devised a new method that uses the displacement between the projection of the incoming trajectory to the exit detector from the measurement point as illustrated in Figure 3. When a muon goes through an object, it tends to be scattered more at the latter part of the trajectory because the scattering width scales inversely with the muon energy.49 For the low energy part of the transmitted muon spectrum, most of the muon scattering can take place in the reactor core and in the concrete after the core. Since the contribution from each scatterer scales with the distance to the exit detector (Li = diθi), the latter part of the trajectory is less weighted.
Concept of image reconstruction with the displacement method. The incoming and outgoing tracks are projected to a plane at the center of the core, the intersection points are combined with weights chosen to optimize the position resolution, and a three-dimensional histogram of x, y, and the displacement length (L) is created. The largest weight (>80%) is placed on the incoming muon because it has higher energy and is scattered less in the intervening material between the detector and the core.
Concept of image reconstruction with the displacement method. The incoming and outgoing tracks are projected to a plane at the center of the core, the intersection points are combined with weights chosen to optimize the position resolution, and a three-dimensional histogram of x, y, and the displacement length (L) is created. The largest weight (>80%) is placed on the incoming muon because it has higher energy and is scattered less in the intervening material between the detector and the core.
The simulation results for Unit 2 with various core conditions (0 to 100% melted) analyzed with the displacement method are shown in Figure 4 where the reactor cores with conic voids were imaged through concrete walls and the steel RPV. The results correspond to 90 days of measurement with dimensions of 15 × 9 m2 and 5.5 × 22 m2 for FMT-1 and 2 respectively. A displacement threshold was selected to discriminate background from the water and concrete walls. Though detector resolutions are not included in the simulations, the scattered angle from the core is more than an order of magnitude larger than the detector resolution, thus they have little effect. In all cases, muon scattering is observed to provide detailed information about the reactor core allowing for quantitative assessment of the intact fraction. In addition, spherical debris of 20-, 30- and 40-cm radii can be distinguished. Figure 5 shows the image development with time (10 to 150 days) for the 50%-melted core with two debris of 20-cm radius. The estimated event rates are 12k and 70k per day for muons that pass through both FMT-1 and 2 from the east and west sides, respectively.
Results of the GEANT4 simulations for Unit 2 with the geometry shown in Figure 2. The simulations were run with intact core (left), 10%-, 30%-, 50%-, 70%-melted core and no core (right). Two spherical debris of 10-cm (under 10%-melted core), 20-cm, 30-cm and 40-cm (under 70%-melted core) radii were placed in the lower region of RPV.
Results of the GEANT4 simulations for Unit 2 with the geometry shown in Figure 2. The simulations were run with intact core (left), 10%-, 30%-, 50%-, 70%-melted core and no core (right). Two spherical debris of 10-cm (under 10%-melted core), 20-cm, 30-cm and 40-cm (under 70%-melted core) radii were placed in the lower region of RPV.
GEANT4 simulations for 50%-melted core of Unit 2 with various measurement time spans. The simulation results correspond to measurement spans of 10 (left), 20, 30, 60, 120 and 150 days (right).
GEANT4 simulations for 50%-melted core of Unit 2 with various measurement time spans. The simulation results correspond to measurement spans of 10 (left), 20, 30, 60, 120 and 150 days (right).
As a conclusion, feasibility of assessing the damage of the Fukushima Daiichi reactors with muon scattering imaging is shown. Muons are strongly deflected by high-Z materials such as uranium, which enables the scattering technique to spot them in a reactor. A few months of measurement will reveal the distribution of the reactor-core fuel materials, and can guide planning and execution of reactor dismantlement, potentially reducing overall project span by many years.
The authors wish to thank Y. Otsuka, D. Yamada and TEPCO for suggestions and providing information. We acknowledge J.D. Bacon, L.J. Barber, M.I. Brockwell, K. Chung, M.C. Everhart, K. Nagamine, S.C. Scott, D.S. Seely, D. Tupa for help and discussions. We thank C.J. Fendel for his generous support. This work has been sponsored by the Laboratory Directed Research and Development Program of Los Alamos National Laboratory, and CC2 LLC.
