A Photofission Delayed Γ-Ray Spectra Calculation Tool for the Conception of a Nuclear Material Characterization Facility

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A Photofission Delayed Γ-Ray Spectra Calculation Tool for the Conception of a Nuclear Material Characterization Facility EPJ Web of Conferences 170, 06001 (2018) https://doi.org/10.1051/epjconf/201817006001 ANIMMA 2017 A Photofission Delayed γ-ray Spectra Calculation Tool for the Conception of a Nuclear Material Characterization Facility D. BERNARD*, O. SEROT*, E. SIMON*, L. BOUCHER* and S. PLUMERI+ packages are made of concrete in a big cylindrical container of Abstract—The photon interrogation analysis is a non- more than 800 L. Despite of the photon attenuation through destructive technique allowing to identify and quantify fissile concrete, the photon interrogation is one of the most ambitious materials in nuclear waste packages. This paper details an ways to interrogate the waste package. The photon pulsed automatic procedure which has been developed to simulate the beam is generated by an electron convertor made of tungsten delayed γγγ-ray spectra for several actinide photofissions. This calculation tool will be helpful for the fine conception or other metal (copper, silicon,…) allowing the (collimation, shielding, noise background optimizations, etc.) and Bremsstrahlung emission. The LINAC maximum energy is for the on-line analysis of such a facility. supposed to be flexible between 15 to 25 MeV. During this irradiation phase (roughly 2 to 3 hours), the waste package is Index Terms—Photonic Interrogation, Nuclear Material axially rotating to make uniform the irradiation dose. The Characterization, Photofission Yields, Delayed γγγ, Decay Data. beam is then stopped and after a reasonable decay time (1 to 5 minutes), High Purity Germanium detectors are deployed all around the package to permit the photon spectrum acquisition I. INTRODUCTION for a large duration (around 2 to 3 hours). This photon HIS paper proposes a new tool to help the conception of a spectrum contains delayed γ-rays and X-rays emitted by the Tnew facility in order to detect and distinguish actinides in fission products decay. Its analysis then gives the quantitative a waste package. The technique used is based on the analysis information on the fissile mass present in the waste container. of delayed photons emitted after photon-burst-induced The next sections will be devoted to the developed tools to fissions. Because of the difference on fission yields, the perform the fine conception of this facility. delayed photons spectra are a signature of different actinides, if any. The first section will present the overall studied facility for the III. BATEMAN EQUATIONS photon beam inducing fissions and the delayed gamma The irradiation phase and the cooling/acquisition phase will detection set-up. The second part will be devoted to the be described sequentially. specific developed tool, called DEGAS (Delayed Gamma Spectrum), to obtain γ spectra (including fission yields and decay data libraries, Bateman depletion equations solving - A. Irradiation Phase involving numerical issues and the verification of the whole 1) Statement of the problem procedure). At the end, we will propose an automated tool to γ-induced fission of actinides leads to around 1000 select specific γ-ray lines ratios to detect a specific actinide in independent fission products for which we have to calculate the waste package. the atomic number densities , at a given time , by solving the coupled Bateman equations [1] : II. THE EXAMINATION FACILITY () This facility, under design phase, has to detect the amount of actinides and to distinguish uranium from plutonium species in nuclear waste packages. Some of these waste = − + (1) Paper submitted to ANIMMA conference for proceedings and to IEEE + () transactions in June 2017. This work was supported by the CEA/DEN and The first two terms are associated to decay probabilities ( ) ANDRA/R&D collaborative project DISN/ANDRA/CHK/A-CARAC-01-12. * and branching ratios ( ) for the disappearance and creation of CEA/DEN/DER&DTN Cadarache, F-13108 Saint-Paul-Lez-Durance, France, corresponding authors: [email protected], [email protected], the fission product (based on the specific JEFF-3.1.1/Decay [email protected], [email protected]. Data Library [2]). The last term involves the production rate + ANDRA, 1-7 rue Jean Monnet, F-92290 Châtenay-Malabry, France, by folding (with respect to the incident photon energy ) the corresponding author : [email protected]. photofission cross section ( ) of the fissile actinide times its © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). EPJ Web of Conferences 170, 06001 (2018) https://doi.org/10.1051/epjconf/201817006001 ANIMMA 2017 independent fission yield ( ) to the incident photon flux . - The photofission cross sections are taken heavy mass region (around the mass 140) and (5) The number density is calculated at the distance (location consequently a shift of the mass yield in the light mass from the ENDF/B-VII.1 library [4] (,)for major actinides of the fission event) from the center of the cylindrical waste 235,238 238,239,240,241 241 region from one fissioning nucleus to another, which ( U, Pu, Am) and from the TENDL- () = () − 242 242m package. The latter is rotating during this irradiation phase 2015 library [5] for Pu and Am: ensures the conservation of the fissioning nucleus mass Where the user’s input data stand for the distance with a period close to 2 to 3 minutes. (removing the prompt neutron multiplicity). of the fissile material from the center of the waste package, the In order to solve equation (1), we assume first the , , 0.020 10 distance between the conversion target and the package = 2⁄ 400 238 decoupling in energy, space and time of the photon incident Pu (ENDF\B7.1) 239Pu (ENDF\B7.1) surface and finally, the package radius, respectively. 350 240Pu (ENDF\B7.1) flux . In addition, since 241 0.016 Pu (ENDF\B7.1) 242Pu (TENDL-2015) the rotation period of the waste package is much lower than 300 2) Solving the Bateman equations , , = ×() ×() 1 the irradiation time, the time dependent production term is 250 0.012 For a given fissile nucleus amount, we will solve the reduced to the averaged value. By this way, equation (1) is previously described equation 2. The user has to fix a given 200 transformed into the following equation: 0.008 238 mass and the location in the waste package for this 150 Pu 239 0.1 Pu particular isotope. The boundary conditions impose that no 100 240 0.004 Pu fission product are present before the irradiation in the waste 241 BremsstrahlungSpectrum Pu 50 (%) Yield Post-neutron 242 package, . PhotofissionCross Section [mb] Pu We decide to use the DARWIN code package [8] to solve ≅ − + + × ( ) × (2) 0 0.000 6 8 101214161820 0.01 such equations, (= because) = of its robustness but also because it Where: 80 90 100 110 120 130 140 150 160 Incident Gamma Energy [MeV] contains already preprocessed nuclear data libraries. This code - stands for the energy-averaged independent 10 Fig. 2. Evaluated photofission cross sections (left axis) with incident γ- package is able to solve non homogeneous differential isotopic fission product yield for an actinide , spectrum (dashed line, right axis). equation but the source term has to be associated to neutron - its specific fission rate (relative to the mass induced production and not to photon induced reactions. One - The independent fission product yield for a given that we look for). 1 can analytically demonstrate that solving the following () fissioning nucleus at a given incident energy, homogeneous and time-iterative system (see lower case for For a given fissile isotope and by identification of equation is determined from a Monte Carlo code “homogeneous” number densities ): (1) and equation (2), the effective yield is defined as: called GEF (acronym for GEneral description of 235 , 0.1 U Fission observables) [6]. This code first calculates 238 U fission fragment yields before prompt neutron 241Am (6) Post-neutron Yield (%) Yield Post-neutron 242m (3) emission, from the concept of fission modes developed Am = − + ∑ (,) by Brosa [7]. These fission modes correspond to the 0.01 = (. ) = . (). (,) various valleys observed in the deformation potential 80 90 100 110 120 130 140 150 160 leads to the following actual number densities which solve Where: energy surface of the fissioning nucleus. When the Mass equation (2): - The incident γ-spectrum is calculated with nucleus starts its deformation from the ground state up Fig. 3. Independent effective fission (15MeV+W) mass yields obtained from to the scission point, it follows one of those valleys (7) MCNPX [3] and depends on the electron/photon the GEF code (version 2015 V2.2) [6]. conversion target and on the maximum energy of the with a given probability. The depth and width of each () = ∑ ( − . ) LINAC (see figure 1). mode are determined in order to deduce the main The average excitation energy available for a given Our developed DEGAS tool is using a MATLAB® [9] properties of the fission fragments (yield, deformation fissioning nucleus can be easily calculated: script which reads first the output file from the GEF 100 at scission, kinetic energy…). In a second step, the total simulation ( ), produces and submits a DARWIN input file excitation energy available at scission is calculated and (owing to the user specifications - -) in a second shared between the two nascent fragments. Finally, (4) Simulation 15 MeV step, and then calculates the atomic number densities at the (,) , Simulation 20 MeV thanks to a statistical treatment, the emission of prompt end of the irradiation phase: from equation (6). -1 10 Simulation 25 MeV < >= neutrons and prompt gammas are simulated to predict (,) their properties (energy spectrum, multiplicity ...). In These energies are reported in Tab. 1 for all fissioning () this way, the GEF code is able to calculate almost all nuclei investigated in the present work.
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