# Photofission tomography of nuclear waste packages

Mathieu Agelou, Frédérick Carrel, Mehdi Gmar, Frédéric Lainé, Bénédicte

Poumarède, François Tola

► To cite this version:

Mathieu Agelou, Frédérick Carrel, Mehdi Gmar, Frédéric Lainé, Bénédicte Poumarède, et al. Photofission tomography of nuclear waste packages. NSS/MIC 2007 - IEEE Nuclear Science Symposium Conference Record, Oct 2007, Honolulu, United States. pp.801-804, 10.1109/NSSMIC.2007.4436449. cea-05481925v2

HAL Id: cea-05481925

https://cea.hal.science/cea-05481925v2

Submitted on 26 Feb 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
# Photofission tomography of nuclear waste package

Mathieu Agelou, Frédérick Carrel, Mehdi Gmar, Frédéric Lainé, Bénédicte Poumarède, François Tola

CEA, LIST, Laboratoire Simulation et Validation des Systèmes, Gif-sur-Yvette, F-91191 France
(téléphone: +33 1 69 08 93 48, e-mail: mathieu.agelou@cea.fr)

## Abstract

Being able to characterize and classify nuclear waste packages is crucial for an appropriate mode of storage. The α-activity due to the presence of actinides inside the packages can be determined using non-destructive active (NDA) methods. CEA-LIST is developing one of those, based on fission induced by photons that allows us to quantify the global mass of actinides in large concrete packages and localize it by the means of a tomography using delayed particles emitted after the fission process.

## I. Introduction

CHARACTERISATION of radioactive waste packages plays a key role in the choice for their best mode of storage. Non-destructive active methods (NDA) developed in the past years at CEA represent a good means for the determination of the quantity of actinides that are present inside the wastes and consequently their management.

In CEA-LIST, one of these methods has been studied for many years: photon interrogation. It is based on the detection of delayed particles emitted by fission products, that are created by the photofission of actinides. These delayed particles are neutrons and photons. This method has three purposes: the determination of the actinide mass present inside the package, the localization of this mass by tomography and finally, the differentiation of the actinides by a spectroscopy of delayed photons. In principle, the first two purposes can be achieved by measuring either particles (or even both).

A brief presentation of the method and the experimental setup is first provided. Tomography results on both real and mock-up packages are then presented.

## II. Assessment of actinide mass by photofission

### A. Principle

The method (sketched in figure 1) is based on the detection of delayed particles (neutrons or gammas) emitted by fission products, which are created by the photofission of actinides. Provided that the time of the measurement is greater than a few minutes, the number of delayed neutrons is given by:

$$N_c \approx \epsilon_n n v_d f t_p \frac{t_c}{\tau} \quad (1)$$

where $\epsilon_n$ is the neutron detection efficiency, $n$ the total number of pulses, $v_d$ the total number of delayed neutrons emitted by photofission, $f$ the photofission rate during a pulse in the sample, $t_p$ the pulse duration, $t_c$ the counting time between two pulses and $\tau$ the period of pulses.

The photofission rate $f$ being proportional to the mass of actinide inside the waste package, so is the number of neutrons. The determination of the mass relies then on the evaluation of $\epsilon_n$ and $f$.
<figure><img src="image_2.png" /><figcaption>Fig. 1. Sketch of the principle of photon interrogation</figcaption></figure>

In principle, the same formula could be used for the number of delayed photons but at the moment, we lack some necessary data concerning the production rate of precursors of these photons. These data are currently being measured by a team in CEA (DSM/DAPNIA/SPhN) and will be released in a photonuclear activation file (PAF) which at present contains the photonuclear cross-sections for more than 600 isotopes, fission fragments distributions and delayed neutron evaluations for most actinides in the photon energy range from 0 up to 25 MeV [1].

The feasibility of the first analysis quoted in the introduction, the mass determination of the actinide embedded in the package and called global analysis, has been demonstrated a couple of years ago using delayed neutrons detected and counted after each pulse [2]. The raw number of neutrons is the sum of the net signal and background. The latter can be split into passive (spontaneous emission of neutrons by radioactive 0 elements in the package) and active background. The main active background is the neutron from the decay of <sup>17</sup>N created by (γ, p) reaction on <sup>18</sup>O, a natural isotope of oxygen.

The detection limit obtained with this method is approximately 1 gram per ton of waste package. It depends on the nature of the matrix (chemical composition and density) and on the spatial distribution of the actinide.

## B. Experimental setup

Results presented in this paper have been obtained in an irradiation facility at CEA called SAPHIR. The main device is a linear electron accelerator whose characteristics are given in the table I. The photon beam is created by bremsstrahlung on a tungsten target at the end of the linac. The package is placed on a conveyor with which we can shift and rotate it in front of the photon beam. The detection of delayed neutrons and photons is done respectively with <sup>3</sup>He counters and BGO crystals which are set around the package. The <sup>3</sup>He counters are embedded in blocks of polyethylen (to thermalize the delayed neutrons) which in turn are coated with a cadmium layer (to stop background thermal neutrons).

<table><caption>Table I. Characteristics of SAPHIR's Linac</caption><tr><td>Energy</td><td>15 – 30 MeV</td></tr><tr><td>Pulse frequency</td><td>6.25 – 400 Hz</td></tr><tr><td>Pulse duration</td><td>2.5 μs</td></tr><tr><td>Peak current</td><td>130 mA</td></tr></table>
# III. From global analysis to tomography

## A. Principle

As said before, the mass determination strongly depends on its spatial distribution inside the waste package. In order to avoid making conservative hypotheses about this distribution, which can result in an overestimation of the mass, the tomography can be used.

The general purpose of tomography is to reconstruct the spatial distribution of a parameter inside an object divided in volume elements (so-called voxels) using different “images” of this object called projections. In our case, the package is irradiated in different positions of translation and rotation. For each position, the delayed neutrons are counted by twelve 3He counters.

Tomography breaks down in two part: a direct model that represents the physical processes involved and an inverse model that gives the distribution of the parameter of interest based on the direct model. Mathematically, the direct problem can be written in a matrix equation:

$$G = HA + B$$

where $G = (g_i)_{i=1,N_m}$ is a $N_m$-vector with $N_m$ the number of measurements and $g_i$ the raw signal for one position in one counter, $A = (a_j)_{j=1,N_v}$ is a $N_v$-vector with $N_v$ the number of voxels and $a_j$ the mass of actinide in the voxel $j$, $H$ is a $N_m \times N_v$-matrix called projection matrix and $B = (b_i)_{i=1,N_m}$ is a $N_m$-vector with $b_i$ the total background noise for measurement $i$.

The direct model consists in the calculation of the projection matrix $H$. Each element $h_{i,j}$ represents the contribution of an actinide mass unit in voxel $j$ to the measurement $i$ and is calculated by a Monte Carlo simulation (MCNPX code [3]) which takes into account all physical processes of particles transport and interaction. The inverse model or reconstruction is then achieved using mathematical algorithms.

## B. Reconstruction algorithms

Given $H$ and a measurement vector $G$, the most direct way to obtain the spatial distribution of the actinide mass $A$ is to invert $H$. But most of the time, $H$ is ill-conditioned which means that inverting it will lead to an amplification of noise errors. Moreover, a small variation in the measurement will lead to a totally different reconstruction. To overcome this issue, two different families of algorithm which avoid the direct inversion of the matrix $H$ have been studied and developed: algebraic and bayesian algorithm. They are both iterative algorithms whose goal is to obtain an estimation of the mass repartition $A$.

In algebraic algorithms, at step $k$ a corrective term is added to the image $A^{(k)}$ corresponding to the back-projection of the difference between the measured projection and the calculated projection. However, the measurement vector used is $G - B$ i.e. the net signal which means that the random nature of the counts are not taken into account leading to an amplified sensitivity to the statistical noise.

As for bayesian algorithms, they estimate $A$ maximising the log-likelihood of $P(G|A)$ and considering $A$ and $B$ as Poisson distributed values. Moreover, a new feature has been added to the existing EM (Expectation-Maximization) algorithm. As it is difficult to measure the active background on a real package, it can be simulated by Monte Carlo. But uncertainties of the bremsstrahlung spectrum and on the $^{18}$O concentration in the package make the simulation difficult. The goal of this new development is to optimize this noise term by likelihood maximization.
C. Results

Our first tomography was carried out on a real 1.4-ton package composed of four compacted drums stacked in a 223- liter drum surrounded by a layer of concrete. The average density of the drums, composed of technological wastes was 0.48 g.cm⁻³ and the density of the concrete was 2.3 g.cm⁻³.

The global analysis along with the assumption that the mass is centered in the package resulted in an
estimated actinide mass of 613 ± 450 mg [4].

For the tomography, the package was virtually divided in 24 voxels of 10 × 10 × 10 cm³ and we carried
out 6 translations and 8 rotations with 6 detectors thus obtaining 288 independent measurements. The
mass of actinide clearly appeared to be centered as shown in figure 2(a). The package was then cut open
in two parts and a direct measurement of the α-activity (figure 2(b)) confirmed that the radioactive
material was concentrated in the center of the package at the predicted altitude.

<figure><img src="image_3.png" /><figcaption>(a) Tomographic reconstruction</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>(b) Measurements of α counts after the cutting of the package</figcaption></figure>

<caption>Fig. 2. Case of a real 1A-ton waste package</caption>

Afterwards, we made studies on a mock-up package representing a large concrete package (diameter = 1.05 m, height = 1.17 m and weight = 1.8 t). Holes have been drilled into it enabling to put different samples of nuclear material. The main interest is that we know the composition of the matrix and that we can obtain the active background noise experimentally. The package is divided in 49 voxels of 10×10×10 cm³ (this size is driven by the dispersion of the photon beam).

Several parameters have been optimized to obtain better detection limit and signal-to-noise ratio. First, the best electron energy spectrum was choosen. Indeed, the (γ, p) reaction on <sup>18</sup>O has a threshold at 15.9 MeV while the photofission rate is monotonically increasing over the energy range of the linac. The ideal spectrum would then be a narrow peak around 15 MeV. Unfortunately, the standard deviation of the beam energy is about 1 MeV so a compromise illustrated in figure 3 has to be found to maximize the signal-to-noise ratio.
<figure><img src="image_5.png" /><figcaption>Fig. 3. Active background and sensitivity as a function of the mean electron energy</figcaption></figure>

The other improvement comes from a better geometry of detection. In the first tomography, the detection blocks described in II-B are symmetrically distributed around the package as shown in figure 4(a). But our studies have demonstrated that a better sensitivity can be obtained if the detection blocks are placed at the rear of the package (figure 4(b)). This nonintuitive results comes from the fact that the signal-to-noise ratio is very poor in the blocks near the beam pipe. Indeed, about 85 % of the $^{18}$O background is localized in the two front blocks. Studies on simulated data have shown that the errors on the reconstruction of a complex mass distribution (a square of voxel containing 10 g of uranium surrounding a central voxel with 1 g of uranium) are cut by half with the last geometry. In the case of small masses (at the level of the detection limit i.e. 1 g), only the optimized geometry lead to the right location and quantification.

<figure><img src="image_6.png" /><figcaption>Fig. 4. MCNP geometry (top view) of the experimental setup before and after optimization</figcaption></figure>

These results based on simulated data were confirmed by real tomographies, one of them being shown in figure 5. The center of mass of the reconstructed masses is located in the right hole and the precision on the total mass is around 30 % depending on the algorithm, which is a fairly good agreement considering that we do not know precisely the electron energy spectrum and that the package is not homogeneous as in the simulation.
## D. Next step: tomography with delayed photons

Even though we do not have presently the fundamental data which would enable us to quantify the actinide mass using delayed photons, it is however theoretically possible to locate it. As the transport of photons and neutrons is very different depending on the composition of the matrix, the delayed-gamma tomography could help us give a more accurate reconstruction. For example, a matrix enriched in light nuclei will lead to a poor neutron signal whereas the photon will be largely unaffected.

The photons we are interested in for the photon tomography are high energy ones. Indeed, as a few activation products can emit photons above around 3 MeV, almost all detected gammas come from fission products. The spectra in figure 6 obtained after irradiation of the package empty or containing 50 g of uranium 238 clearly show that nuclear material can be detected with this method. Our first delayed-photon tomography is underway, using BGO crystals as photon detectors.

<figure><img src="image_7.png" /><figcaption>Fig. 6. Delayed photon spectra with and without nuclear material in the package</figcaption></figure>

## E. Conclusion

To conclude on the advantages of tomography with respect to global analysis, we can simply compare the sensitivity of both analyses for three hypotheses on the mass distribution. The results are shown in table II. In case of a diluted mass, we over-estimate the mass by a factor 7.5 using global tomography whereas the right value is always found in tomography. Tomography is then a powerful tool to locate and quantify precisely the actinide mass inside waste packages.

<table><caption>Table II. Comparison of the assessed mass for three hypotheses in global photofission and with tomography</caption><thead><tr><th></th><th>Centered mass</th><th>Diluted mass</th><th>Off-centered mass</th></tr></thead><tbody><tr><td>Global photofission (g)</td><td>25</td><td>187.5</td><td>75</td></tr><tr><td>Tomography (g)</td><td>25</td><td>25</td><td>25</td></tr></tbody></table>
# IV. Conclusion and perspectives

We have presented in this article the principle of the only NDA method which can inspect large concrete nuclear waste packages. The results obtained on tomography using delayed neutrons emitted by photon-induced fission products are very promising to control and classify them. In the near future, combination of photon and neutron tomography will give more accurate performances.

Concerning the last purpose quoted in the introduction namely the identification of the actinides inside the waste package, we are currently developing a method based on the detection of delayed photons whose energy spectrum can be regarded as a fingerprint of the irradiated sample.

## References

[1] D. Ridikas et al., Status of the photonuclear activation file: Reaction cross-sections, fission fragments and delayed neutrons, Nuclear Instruments and Methods A Volume 562, Issue 2, 23 June 2006, pp 710-713

[2] M. Gmar, F. Jeanneau, F. Lainé, H. Makil, B. Poumarède, F. Tola Assessement of actinide mass embedded in large concrete packages by photon interrogation and photofission, Applied Radiation and Isotopes, Volume 63, Issues 5-6, November-December 2005, pp 613-619.

[3] http://mcnpx.lanl.gov/

[4] M. Gmar, F. Jeanneau, F. Lainé, B. Poumarède Photofission tomography of nuclear waste package Nuclear Instruments and Methods A, Volume 562, Issue 2, 23 June 2006, pp 1089-1092.