Determination of Neutron Emission from Spent Fuel for Safeguards Verification

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Facoltà di Ingegneria Civile ed Industriale Corso di laurea magistrale in Ingegneria Energetica e Nucleare

Determination of neutron emission from spent fuel for safeguards verification

Relatore: Prof. Romolo Remetti Candidato: Mario Cometto

Correlatore: Alessandro Borella (SCK∙CEN) N° matricola: 1349062

Riccardo Rossa (SCK∙CEN)

Anno Accademico 20014-2015

A nonno Mario

Table of Contents

List of figures ...... iv

List of tables ...... viii

Introduction ...... 3

Structure of the thesis ...... 4 Overview of the work done at SCK-CEN ...... 5 1 Nuclear Safeguards and Non-Proliferation ...... 9

1.1 Historical background ...... 9 1.2 The Non-Proliferation treaty (NPT) ...... 14 1.3 Safeguards verification ...... 15 1.4 NDA Techniques ...... 17 1.5 Techniques for spent fuel ...... 19 1.5.1 Measurement principles ...... 19 2 Computational tools used for the simulations ...... 21

2.1 Introduction ...... 21 2.2 Origen ARP ...... 22 2.3 Cross section libraries in SCALE ...... 24 2.4 GUI (Graphical User Interface) ...... 25 2.5 Validation of the code ...... 28 2.6 Cygwin ...... 29 3 ARP Simulations model ...... 30

3.1 General input options ...... 30 3.1.1 Express window ...... 30 3.1.2 Neutron energy spectra ...... 30 3.1.3 Gamma energy spectra ...... 30 3.1.4 Cases window ...... 30 CT part 1 ...... 31 CT part 2 ...... 31 CT part 3 ...... 31

CT part 4 ...... 31 3.1.5 Irradiation output options ...... 31 3.1.6 Decay output options ...... 31 3.1.7 Other option selected ...... 31 3.2 LEU simulations options ...... 32 3.3 MOX simulations options ...... 32 4 Structure of the library ...... 34

4.1 LEU simulations ...... 34 4.2 MOX simulations ...... 35 4.3 Plutonium sensitivity simulation ...... 36 5 Study on the actinides production ...... 37

5.1 Introduction ...... 37 5.2 Transmutation mechanism ...... 38 5.3 Isotopes properties ...... 39 5.3.1 Uranium isotopes ...... 39 5.3.2 Neptunium isotopes ...... 39 5.3.3 Plutonium isotopes ...... 40 5.3.4 Americium isotopes ...... 40 5.3.5 Curium isotopes ...... 41 5.4 Curium isotopes production ...... 41 5.4.1 Curium-242 ...... 42 5.4.2 Curium-244 ...... 43 5.4.3 Verification of the theoretical assumptions ...... 44 6 Main results from the fuel library ...... 48

6.1 LEU simulations ...... 48 6.1.1 Neutron emission as a function of the burnup ...... 48 6.1.2 Neutron emission as a function of the cooling time ...... 50 6.1.3 Isotopic contribution ...... 52 6.1.4 Influence of the initial enrichment to the total neutron emission ...... 54 6.2 MOX simulations: ...... 62 6.2.1 Neutron emission as a function of the burnup ...... 62 6.2.2 Neutron emission as a function of the cooling time ...... 64

6.2.3 Isotopic contribution ...... 66 6.2.4 Influence of the plutonium content on the total neutron emission ...... 68 6.2.5 Isotope concentration at the discharge ...... 73 6.3 Comparison between MOX and LEU fuel assemblies: ...... 75 6.3.1 Neutron emission as a function of the burnup ...... 75 6.3.2 Isotopic contribution for different fuel compositions...... 77 7 Conclusions ...... 83

8 References ...... 85

Annex A ...... 88

Annex B ...... 89

Annex C ...... 90

Annex D ...... 91

Annex E ...... 94

Annex F ...... 95

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List of figures

Figure 1: Overview of the NDA methods ...... 18

Figure 2: ORIGEN-ARP UO2 Express window...... 26

Figure 3: ORIGEN-ARP MOX Express window...... 26 Figure 4: Primary transmutation mechanism for U-235 and U-238 leading to the production of Cm isotopes. The figure shows selected decay mechanisms that contribute the transmutation chain...... 38 Figure 5: Concentration of different isotopes as a function of the cooling time for a MOX fuel composition with 8% of plutonium...... 42 Figure 6: Concentration of different isotopes as a function of the cooling time for a MOX fuel composition with 8% of plutonium...... 43 Figure 7: Concentration of different isotopes as a function of the cooling time for a MOX fuel composition with 8% of plutonium, with variable average power...... 44 Figure 8: Concentration of different isotopes as a function of the cooling time for a MOX fuel composition with 8% of plutonium, with variable average power...... 45 Figure 9: Comparison between the results of different simulations...... 45 Figure 10: Comparison between the results of different simulations...... 46 Figure 11: Neutron emission as a function of the burnup for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and cooling time of 30 days...... 48 Figure 12: Neutron emission as a function of the burnup for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and cooling time of 10 years...... 49 Figure 13: Neutron emission as a function of the burnup for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and cooling time of 1000 years...... 49 Figure 14: Neutron emission as a function of the cooling time for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and burnup of 10 GWd/tU...... 50 Figure 15: Neutron emission as a function of the cooling time for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and burnup of 35 GWd/tU...... 51 Figure 16: Neutron emission as a function of the cooling time for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and burnup of 60 GWd/tU...... 51 Figure 17: Contribution of the single isotopes to the total neutron emission as a function of the cooling time for a 17x17 PWR fuel assembly with initial enrichment of 2.5% and burnup of 10

GWd/tU. The considered isotopes are indicated...... 53 Figure 18: Contribution of the single isotopes to the total neutron emission as a function of the cooling time for a 17x17 PWR fuel assembly with initial enrichment of 2.5% and burnup of 10 GWd/tU. The considered isotopes are indicated...... 53 Figure 19: Contribution of the single isotopes to the total neutron emission as a function of the cooling time for a 17x17 PWR fuel assembly with initial enrichment of 2.5% and burnup of 10 GWd/tU. The considered isotopes are indicated...... 53

Figure 20: Ratio of the total neutron emission for different enrichment as a function of the burnup with cooling time of 30 days...... 54 Figure 21: Ratio of the total neutron emission for different enrichment as a function of the burnup with cooling time of 10 years...... 55 Figure 22: Ratio of the total neutron emission for different enrichment as a function of the burnup with cooling time of 1000 years...... 55 Figure 23: Ratio of the total neutron emission for different enrichment as a function of the cooling time with burnup of 10 GWd/tU...... 56 Figure 24: Ratio of the total neutron emission for different enrichment as a function of the cooling time with burnup of 35 GWd/tU...... 56 Figure 25: Ratio of the total neutron emission for different enrichment as a function of the cooling time with burnup of 60 GWd/tU...... 57 Figure 26: Ratio between the total neutron emissions of two 17x17 PWR assemblies. The ratio is plotted as a function both of cooling time and burnup...... 58 Figure 27: Ratio between the total neutron emission of two 17x17 PWR assemblies, one with initial enrichment of 2.5% and the other with initial enrichment of 4.5%. The ratio is plotted as a function of the cooling time, for 4 different values of burnup...... 58 Figure 28: Total neutron emission with different initial enrichment- role of selected isotopes

(BU: 5 GWd/tU)...... 59 Figure 29: Total neutron emission with different initial enrichment- role of selected isotopes

(BU: 10 GWd/tU)...... 59 Figure 30: Total neutron emission with different initial enrichment- role of selected isotopes

(BU: 35 GWd/tU)...... 60 Figure 31: Total neutron emission with different initial enrichment- role of selected isotopes

(BU: 70 GWd/tU)...... 60 Figure 32: Ratio between the total neutron emission of the isotope 244Cm for different initial enrichment. The ratio is plotted as a function of the cooling time for selected burnup values. 61 Figure 33: Neutron emission as a function of the burnup for a 17x17 PWR MOX spent fuel assembly with an initial content of plutonium of 8% and cooling time of 30 days...... 62 Figure 34: Neutron emission as a function of the burnup for a 17x17 PWR MOX spent fuel assembly with an initial content of plutonium of 8% and cooling time of 10 years...... 63 Figure 35: Neutron emission as a function of the burnup for a 17x17 PWR MOX spent fuel assembly with an initial content of plutonium of 8% and cooling time of 1000 years...... 63 Figure 36: Neutron emission as a function of the cooling time for a 17x17 PWR MOX spent fuel assembly with an initial content of plutonium of 8% and burnup of 10 GWd/tU...... 64 Figure 37: Neutron emission as a function of the cooling time for a 17x17 PWR MOX spent fuel assembly with an initial content of plutonium of 8% and burnup of 35 GWd/tU...... 65 Figure 38: Neutron emission as a function of the cooling time for a 17x17 PWR MOX spent fuel assembly with initial content of plutonium of 8% and burnup of 60 GWd/tU...... 65 Figure 39: Contribution of the single isotopes to the total neutron emission as a function of the cooling time for a 17x17 PWR MOX fuel assembly with initial content of plutonium of 8% and burnup of 10 GWd/tU. The considered isotopes are indicated...... 66

Figure 40: Contribution of the single isotopes to the total neutron emission as a function of the cooling time for a 17x17 PWR MOX fuel assembly with initial content of plutonium of 8% and burnup of 35 GWd/tU. The considered isotopes are indicated...... 67 Figure 41: Contribution of the single isotopes to the total neutron emission as a function of the cooling time for a 17x17 PWR MOX fuel assembly with initial content of plutonium of 8% and burnup of 60 GWd/tU. The considered isotopes are indicated...... 67 Figure 42: Ratio of the total neutron emission for different Pu content as a function of the cooling time for a 17x17 PWR MOX fuel assembly with burnup of 5 GWd/tU...... 69 Figure 43: Ratio of the total neutron emission for different Pu content as a function of the cooling time for a 17x17 PWR MOX fuel assembly with burnup of 10 GWd/tU...... 69 Figure 44: Ratio of the total neutron emission for different Pu content as a function of the cooling time for a 17x17 PWR MOX fuel assembly with burnup of 35 GWd/tU...... 70 Figure 45: Ratio of the total neutron emission for different Pu content as a function of the cooling time for a 17x17 PWR MOX fuel assembly with burnup of 60 GWd/tU...... 70 Figure 46: Ratio of the total neutron emission for different Pu content as a function of the burnup for a 17x17 PWR MOX fuel assembly with cooling time of 30 days...... 71 Figure 47: Ratio of the total neutron emission for different Pu content as a function of the burnup for a 17x17 PWR MOX fuel assembly with cooling time of 10 years...... 72 Figure 48: Ratio of the total neutron emission for different Pu content as a function of the burnup for a 17x17 PWR MOX fuel assembly with cooling time of 106 years...... 72 Figure 49: Trend of the neutron flux during the irradiation time for different Pu content with a burnup of 5 GWd/tU...... 74 Figure 50: Concentration of 242Cm at the discharge as a function of the Pu content for different burnup values...... 74 Figure 51: Concentration of 244Cm at the discharge as a function of the Pu content for different burnup values...... 74 Figure 52: Concentration of 246Cm at the discharge as a function of the Pu content for different burnup values...... 75 Figure 53: Comparison between the total NE as a function of the burnup between two different 17x17 PWR fuel assemblies with cooling time of 30 days. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 76 Figure 54: Comparison between the total NE as a function of the burnup between two different 17x17 PWR fuel assemblies with cooling time of 10 years. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 76 Figure 55: Comparison between the total NE as a function of the burnup between two different 17x17 PWR fuel assemblies with cooling time of 1000 years. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 77 Figure 56: Comparison between the single isotopes contribution to the total NE as a function of the cooling time between two different 17x17 PWR fuel assemblies with burnup of 10

GWd/tU. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 78 Figure 57: Comparison between the single isotopes contribution to the total NE as a function of the cooling time between two different 17x17 PWR fuel assemblies with burnup of 10

GWd/tU. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 78

Figure 58: Comparison between the single isotopes contribution to the total NE as a function of the cooling time between two different 17x17 PWR fuel assemblies with burnup of 35

GWd/tU. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 79 Figure 59: Comparison between the single isotopes contribution to the total NE as a function of the cooling time between two different 17x17 PWR fuel assemblies with burnup of 35

GWd/tU. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 79 Figure 60: Comparison between the single isotopes contribution to the total NE as a function of the cooling time between two different 17x17 PWR fuel assemblies with burnup of 60

GWd/tU. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 80 Figure 61: Comparison between the single isotopes contribution to the total NE as a function of the cooling time between two different 17x17 PWR fuel assemblies with burnup of 60

GWd/tU. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 80 Figure 62: Ratio between the neutron emission due to single isotopes for two different 17x17 PWR fuel assemblies. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 81 Figure 63: Comparison between the 242Cm concentration during the IT for two different 17x17 PWR fuel assemblies. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 82 Figure 64: Comparison between the 244Cm concentration during the IT for two different 17x17 PWR fuel assemblies. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%...... 82

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List of tables

Table 1: Spent fuel measurement system...... 20 Table 2: Organizations, computer codes and cross-section libraries involved in the benchmark ...... 28 Table 3: Overview of the cooling time structure...... 31 Table 4: Initial enrichment cases overview...... 32 Table 5: LEU burnup cases overview...... 32 Table 6: Pu content cases overview...... 33 Table 7: MOX burnup cases overview...... 33 Table 8: Overview of the LEU fuel filenames library...... 34 Table 9: Overview of the MOX fuel filenames library...... 35 Table 10: Overview of the plutonium sensitivity filenames library...... 36 Table 11 Ratio between the total neutron emission due to the considered isotopes and the total neutron emission, as a function of the Burnup and of the Cooling time ( IE 2,5 %)...... 88 Table 12: Ratio between the total neutron emission due to the 242Cm and the total neutron emission, as a function of the burnup and of the cooling time ( IE 2,5 %)...... 89 Table 13: Ratio between the total neutron emission due to the 244Cm and the total neutron emission, as a function of the burnup and of the cooling time ( IE 2,5 %)...... 90 Table 14: Ratio between the total neutron emission of single isotopes for different initial enrichments as a function of the cooling time and of the burnup. Some values are not reported in the table because some nuclides have decayed for long cooling times...... 93 Table 15 Nuclides table; data are taken from the nuclear library "ENDF/B-7.1 except the ones marked with * that are taken from the library TENDL-2013...... 94

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This Master Thesis summarizes the work done during my three months internship at the Belgian nuclear research center SCK•CEN under the supervision of Alessandro Borella and Riccardo Rossa and completed, in the last two months, in Rome with Prof. Romolo Remetti.

Introduction

Nuclear material accountancy and verification of the spent fuel elements (SFE) are two important aspects of the safeguards inspection. The final aim of these inspections, according to the worldwide policy of non-proliferation of the nuclear weapons, is to detect if the nuclear facility under examination is being used to produce also fissile material suited for nuclear weapons or not. In particular the inspectors has to verify, according to the neutron emission, if the plutonium in the SPF is a Reactor-Grade (RG) Pu or Weapons-Grade (WG) Pu.

Safeguards inspectors, in order to verify operator declared data, rely on the measurement of the radiation emission of the SFE (neutron, gamma, Cherenkov etc.). Considering the difficulty in handling the spent fuel, difficulty due to the high decay heat and primarily to the very high radioactive emission, different non-destructive assays (NDA) have been developed in order to allow these measurements.

With the purpose of creating a reference spent fuel composition that can be used to investigate and improve NDA methods, Rossa et al. {11, 22} started the definition of a spent fuel library through the simulations performed with the ORIGEN-ARP and ALEPH2.2 codes. Rossa et al. {1, 2}, considered the PWR 17x17 fuel geometry and the cases of low enriched uranium (LEU) fuel with initial enrichment in 235U between 3.5 and 5%, discharge burnup between 5 and 70 GWd/tU and cooling time up to 3 million years.

1 Rossa R. et al., "Development of the reference spent fuel library using ORIGEN-ARP and ALEPH2.2", Restricted contract report SCK∙CEN-R-5511 2 Rossa R. et al., "Development of the reference spent fuel library of 17x17 PWR fuel assemblies", ESARDA BULLETIN, No 50, December 2013

The aim of this work is to expand the existing LEU library, extending the initial enrichment range in order to represent the most of the enrichments currently worldwide used, and to develop a spent fuel library for mixed oxide (MOX) fuel assemblies.

Structure of the thesis

In the first chapter of this thesis a little introduction to the Safeguards and Non- proliferation topics is given to the reader. The second chapter contains the description of the different computational tools utilized to perform the simulation and the data analysis, in particular the burnup code ORIGEN-ARP. In order to better understand the results a brief explanation of the actinides production is done in chapter three. The description of the simulations models and an overview of the structure of the fuel library are presented in the fourth and in the fifth sections. The main results obtained from the simulations are shown and commented in the last chapter, which is followed by the final conclusions reported at the end of the document.

Overview of the work done at SCK-CEN

In the first part of the work LEU fuel simulations have been carried out to study the sensitivity of the total neutron emission to different parameters such as burnup (BU), cooling time (CT), and initial enrichment (IE). Fourteen different burnup values (from 5 to 70 GWd/tU), thirty different cooling time steps (from the discharge up to 3 million years) and three different initial enrichments (2, 2.5 and 3 %) were considered, for a final amount of 1260 case studies.

The data analysis focused first on fuel with 2.5% initial enrichment in order to evaluate the influence of burnup and cooling time on the total neutron emission and on the fuel composition. Both (α,n) reactions and spontaneous fissions were considered in the analysis of the total neutron emission, as well as the contribution of few selected nuclides. To better understand the role of these nuclides on the neutron emission, three tables were created: the first table shows the ratio between the sum of the neutron emission of these nuclides and the total neutron emission (Annex A), the second and the third tables report the percentage of the total neutron emission due to 242Cm and 244Cm respectively (Annex B and C).

After the burnup and the cooling time, the sensitivity to the initial enrichment is evaluated. The total neutron emissions of three compositions (with 2.0%, 2.5% and 3.0% IE) are compared with the total neutron emission of a reference case (LEU fuel with IE of 4.5%). This comparison has been done in order to create continuity between this work and the one made by Rossa e al. {1, 2}. The ratio is plotted as a function of cooling time and burnup. Moreover the ratio between the total neutron emission of single nuclides for different initial enrichment (2.5% and 4.5%) is calculated. The ratio is plotted as a function of the cooling time for selected burnup values.

In the second part of the work similar data analysis is applied to a PWR 17x17 MOX fuel composition. Starting from a reference composition, and keeping constant the plutonium isotopic vector, four different fuel compositions are considered. Each composition is characterized by a different percentage of plutonium on the total fuel

5 mass (i.e. 4, 6, 8 and 10%3). For the MOX fuel simulations we considered only 12 different burnup values (from 5 to 60 GWd/tU) because of the range of applicability of ORIGEN-ARP; as in the previous section, 30 cooling time steps are considered in the calculations.

To better understand the isotopes production chains and in particular the influence of the plutonium concentration on the fuel isotopic composition at the discharge, and therefore on the total neutron emission, we created an isotopes table (Annex E) in which the following parameters are reported for several nuclides: half-life, branching ratio, (n, γ) thermal cross section and total resonance integral.

The data analysis of the MOX cases is focused on the production of the isotopes during the irradiation time; we considered the isotopic concentration as a function of the irradiation time for different Pu content and the corresponding neutron flux. Moreover, the concentration of the single isotopes at the discharge is plotted against the Pu content for different burnup values.

By taking the fuel with 8% Pu concentration as reference composition, we carried out simulations with different power level histories in order to investigate the isotopes chain production. These simulations were also used to verify some assumptions on the production of several nuclides.

A comparison between two different fuel compositions in terms of neutron emission is the object of the third part of the work. We confronted two different fuel assemblies respectively one with MOX composition and one with LEU composition, in order to compare their neutron emission. In particular we considered compositions with roughly the same absolute content of fissile material.

The two compositions were:

- MOX with 6% of Plutonium (38.5 kg of fissile material, namely 239Pu and 241Pu); - LEU with initial enrichment of 4% (40 kg of fissile material, namely 235U).

3 All the percentages in the report are weight percent.

The total neutron emissions of the two compositions are plotted against the burnup and the cooling time. Then the contribution of single isotopes is considered: for each isotope, the ratio between the neutron emission in the MOX case and the one in the case of LEU fuel is calculated and plotted.

All the previous simulations with the MOX fuel were done keeping constant the plutonium isotopic vector. In the fourth part of the work we analyzed the influence of the different plutonium isotopes on the total neutron emission. Adopting the composition with 8% of plutonium as reference, we did five sets of simulations one per each plutonium isotopes. First we calculated the mass content of each of these isotopes in the reference composition, and then per every set we did two groups of simulations (with the same structure of the previous MOX simulations): 1. Keeping constant the mass of the other isotopes we added the 5% of the mass of isotope considered in the set. 2. Keeping constant the mass of the other isotopes we subtracted the 5% of the mass of isotope considered in the set. After all addictions/subtractions, the percentage composition of the plutonium isotopes vector and the percentage of plutonium in the total heavy metal have been recalculated.

The work and the analysis performed for my master thesis deal with the detection of neutron radiation from spent fuel. This topic is part of a wider subject: Nuclear Safeguards and Non-Proliferation. This subject is very broad and involves historical, economical, political, technical and scientific issues. In this chapter, starting from a historical point of view, a little presentation of this topic will be done.

1 Nuclear Safeguards and Non-Proliferation

1.1 Historical background The history of Nuclear Safeguards and Non-Proliferation is strictly linked with the one of the nuclear energy and its use, both civilian and military. From this point of view the first important date is the 1911. In fact in this year, after centuries of physical and philosophical speculations, Ernest Rutherford, during one of his experiments, formulated the theory that the atom was supposed to consist of a central cluster of charged particles, surrounded by an equal quantity of particles with opposite electric charge uniformly distributed throughout a sphere. During the following years, several scientists, among them Niels Bohr, Albert Einstein, Otto Hahn and Robert Oppenheimer, devoted their studies to this new branch of physics.

A turning point for the exploitation of nuclear energy happened in 1939 when the German chemists Otto Hahn and Fritz Strassmann described, in an article appeared on the 6th of January on the magazine Die Naturwissenschaften, the discovery of the nuclear fission reaction.

Soon new discoveries were done: Leo Szilard, Hungarian-American physicist, established that in the reaction between a neutron and an atom of 235U, two neutrons are released; a couple of week later the Otto Frisch and Lise Meitner demonstrated that energy is released during a fission reaction.

Given the outbreak of World War II in the same years of the discovery of nuclear fission and considering the tremendous energy that can liberated by each fission event, the knowledge of the new process lead to an arm race. The political leader of the United States, Great Britain, Germany and Soviet Union started program for the development nuclear weapons aware of the fact that the outcome of the war would depended also on which of the competing powers won that race4. The first important step was to discover the locations of the uranium reserves. For this reason both United Kingdom and United States started secret surveys in order to discover and gain control over these. The United States, in a report of the 1944, ranked eleven states according to their estimated production potential. In particular Belgian Congo was classified as “excellent”, United States, Canada, Russia, Portugal, Madagascar and Czechoslovakia as “Good” while Bulgaria and Sweden as “Poor”. In the following year, through the Combined Development Trust Agreement, United States and Great Britain came to control more than the 97% of the world’s uranium production5, while the Soviet Union was presumed to have only small quantities at its disposal6.

The destructive power of the nuclear energy was manifested on August 6 1945 when “Little Boy”, an atomic bomb based on the fission of uranium, was dropped over Hiroshima, Japan, killing 66000 people and injuring other 690007. After three days a bomb based on the fission of plutonium, "Fat Man", was dropped on Nagasaki killing other 80000 people.

In November 1945 United States, Great Britain and Canada presented the “Three Nation Agreed Declaration on Atomic Energy”, in which they suggest that the United Nations (UN), established on the 24 of October 1945, should have the power to control the use of nuclear power in order to promote its peaceful use:

4 Gunnar Skogmar, De nya malmfalten. Det svenka uranet och inledningen till efterkrigstidens neutralitet-spolitik. Research program Sweden during the Cold War, Working Paper 3, Stockholm 1997. 5David Holloway, Stalin and the Bomb: The Soviet Union and Atomic Energy, 1939-1956. New Haven: Yale University Press, 1994, p. 174. 6 Skogmar p. 28 et passim. 7 The Manhattan Engineer District (June 29, 1945). "The Atomic Bombings of Hiroshima and Nagasaki". Project Gutenberg Ebook. docstoc.com. p. 3.

 We recognize that the application of recent scientific discoveries to the methods and practice of war has placed at the disposal of mankind means of destruction hitherto unknown, against which there can be no adequate military defence, and in the employment of which no single nation can in fact have a monopoly.  We desire to emphasize that the responsibility for devising means to ensure that the new discoveries shall be used for the benefit of mankind, instead of as a means of destruction, rests not on our nations alone, but upon the whole civilized world...  We are aware that the only complete protection for the civilized world from the destructive use of scientific knowledge lies in the prevention of war. No system of safeguards that can be devised will of itself provide an effective guarantee against production of atomic weapons by a nation bent on aggression…  We believe that the fruits of scientific research should be made available to all nations, and that freedom of investigation and free interchange of ideas are essential to the progress of knowledge...8

In December James F. Byrnes, U.S. Secretary of State, and Ernest Bevin, British Foreign Secretary proposed to the Soviet Union, to create a new supranational authority. The Soviets accepted and the United Nation Atomic Energy Commission (UNAEC) was formed on January 24, 1946. The central aims of the mandate were taken directly from the Three Nation Agreed Declaration:

 For extending between all nations the exchange of basic scientific information for peaceful ends.  For control of atomic energy to the extent necessary to ensure its use only for peaceful purposes.

8 United States Department of State, “Agreed Declaration by the President of the United States, the Prime Minister of the United Kingdom and the Prime Minister of Canada,” in Department of State Bulletin Vol. XIII, No. 334 (Washington, DC: U. S. Government Printing Office, 1945), 781.

 For the elimination from national armaments of atomic weapons and of all other major weapons adaptable to mass destruction.  For effective safeguards by way of inspection and other means to protect complying states against the hazards of violations and evasions.9

However, despite the peaceful activities proposed by the organization, after four years and 200 sessions, the UNAEC was abolished because of the failure of the negotiations between the member states5.

During the same year, on August 29 the Soviet Union, with great surprise for Americans, detonated its first atomic bomb. Not so long time after also Great Britain performed its first nuclear test on 3 October 1952.

The change of the world scenario brought first to the creation of the United Nations Disarmament Commission (UNDC), January 1952, and later, December 1953, to the launch of the “Atoms for Peace” program.

The aim of this program was to promote the civilian use of the atomic power through an international cooperation.

The natural development of this program was the creation, in the 1955, of a new international organization the International Atomic Energy Agency (IAEA), formally created in 1957. Originally the organization was composed by: United States, Great Britain, France, Canada, Australia, Belgium and Portugal. Soon other countries entered in the organization (for example Brazil and India).

On February 1956 the IAEA (now formed by twelve nations) presented a proposal for regulations. The text had two main purposes:

9 United States Department of State, “Agreed Declaration by the President of the United States, the Prime Minister of the United Kingdom and the Prime Minister of Canada,” in Department of State Bulletin Vol. XIII, No. 334 (Washington, DC: U. S. Government Printing Office, 1945), 782.

1. To promote and spread the civilian utilization of nuclear technology and know-how; 2. To prevent and avoid, through strict control, the proliferation of nuclear weapons.

These two resolutions were transposed in the five objectives of the final IAEA statute:

 Take any action needed to promote research on, development of, and practical applications of nuclear energy for peaceful purposes (Article III.A.1);  Provide materials, services, equipment and facilities for such research and development, and for practical applications of atomic energy “with due consideration for the needs of the under-developed areas of the world” (Article III.A.2);  Foster the exchange of scientific and technical information (Article III.A.3);  Establish and apply safeguards to ensure that any nuclear assistance or supplies with which the IAEA was associated should not be used to further any military purposes—and apply such safeguards, if so requested, to any bilateral or multilateral arrangement (Article III.A.5);  Establish or adopt nuclear safety standards (Article III.A.6). 10

In 1958 Ireland suggested the creation of a treaty aimed at preventing “the wider dissemination of nuclear weapons”. The negotiations on the Irish proposal started in December 1961. On 14, February 1967, the treaty of Tlalelolco (known as The Treaty for the prohibition of Nuclear Weapons in Latin America) was signed by the Latin American states. Finally, in 1968 a worldwide treaty was signed: The Non-proliferation Treaty.

10 Fischer, David. History of the International Atomic Energy Agency: The First Forty Years (Vienna: International Atomic Energy Agency, 1997), 86.

1.2 The Non-Proliferation treaty (NPT) The Treaty on the Non-Proliferation of Nuclear Weapons is an international agreement that aims three different purposes:

1. To prevent the dissemination of nuclear weapons; 2. To promote nuclear disarmament; 3. To promote the peaceful use of nuclear energy.11

Undersigned on July 1, 1968 by USA, UK and Soviet Union and 50 other countries, the treaty entered into force in March 5 1970. In the 1992 was joined by France and China. The North Korea entered in the 1985 but then, suspected of building nuclear weapons, left in 2003. Today 189 countries adhere to the treaty.

The treaty acknowledges five states as Nuclear Weapons State (NWS), USA, UK, Soviet Union, France, and China, since they possessed nuclear weapons before the signing of the treaty. On the other hand the treaty defines the other members as Non-Nuclear Weapon States (NNWS). Moreover, three states (Belarus, Kazakhstan and Ukraine) that acceded to the treaty as NNWS had nuclear weapons in their territories because they were part of the Soviet Union, and they were obliged to relocate the nuclear weapons in the Russian Federation. The states of India, Pakistan, and Israel never ratified the NPT; moreover India and Pakistan tested nuclear weapons in the past, while Israel always kept a policy of ambiguity over its nuclear program.

The complete text of the treaty, composed by a preamble and eleven articles, is reported in annex F, while a summary of the key points is reported below:

 Nuclear weapon states (NWS) must not to transfer nuclear weapons or other nuclear explosive devices to any non-nuclear weapon states and must not to assist, encourage, or induce any of the latter to manufacture or otherwise acquire them. (Art. I);

11 http://www.un.org/disarmament/WMD/Nuclear/NPT.shtml

 NNWS should not manufacture, acquire and receive nuclear weapons or other nuclear explosive devices. (Art. II);

 NNWS must place all nuclear materials in all peaceful nuclear activities under IAEA safeguards. (Art. III);

 All Parties are obligated to facilitate and participate in the exchange of equipment, materials, and scientific and technological information for the peaceful uses of nuclear energy. (Art. IV, V);

 All Parties must pursue negotiations in good faith on effective measures relating to the cessation of the nuclear arms race and to nuclear disarmament, and on a treaty on general and complete disarmament under strict and effective international control. (Art. VI, VII).

Despite the fact that since the signature of the treaty the number of the states capable of manufacturing nuclear weapons has increased, the NPT has contributed decisively to limit the spread of nuclear weapons.12

A list with all the signatory states is given in Annex G.

1.3 Safeguards verification According to the third article of the NPT,

“1. Each non-nuclear-weapon State Party to the Treaty undertakes to accept safeguards, as set forth in an agreement to be negotiated and concluded with the International Atomic Energy Agency in accordance with the Statute of the International Atomic Energy Agency and the Agency’s safeguards system, for the exclusive purpose of verification of the fulfilment of its obligations assumed under this Treaty with a view to preventing diversion of nuclear energy from peaceful uses to nuclear weapons or other nuclear explosive devices. Procedures for the safeguards required by this Article shall be followed with respect to source or special fissionable material whether it is being produced, processed or used in any principal nuclear facility or is outside any such facility. The safeguards required by this Article shall be applied on all source or

12 http://www.uspid.dsi.unimi.it/doc/TNP/node1.html

special fissionable material in all peaceful nuclear activities within the territory of such State, under its jurisdiction, or carried out under its control anywhere.” ; and to the article III.A.5 of the Statute of the IAEA13 ,

“The Agency is authorized:

…

5) To establish and administer safeguards designed to ensure that special fissionable and other materials, services, equipment, facilities, and information made available by the Agency or at its request or under its supervision or control are not used in such a way as to further any military purpose; and to apply safeguards, at the request of the parties, to any bilateral or multilateral arrangement, or at the request of a State, to any of that State's activities in the field of atomic energy.”

Therefore the International Atomic Energy Agency has the duty to guarantee to the international community that all the states that have signed safeguards agreements are fulfilling their obligations using nuclear material only for peaceful use and not diverging from it. That means that the Agency must be able to detect any diversion from the peaceful nuclear use. Every State, according to the agreements, has to provide to the IAEA a report in which all the activities pertaining nuclear material under safeguards are indicated (detailing quantities, types and location of nuclear material inventories, inventory changes etc.). Meanwhile the Agency has to perform independent verifications in order to confirm the correctness of the reports and their completeness.

The basis for safeguards verifications is the nuclear material accountancy, which is performed to verify the correctness of the accounting information provided by the state’s accounting system and, eventually, to detect missing items (gross defects)14. Moreover Containment and surveillance (C/S) techniques, like optical surveillance and

13 https://www.iaea.org/about/statute 14 IAEA, “Safeguards Techniques and Equipment: 2011 edition”, International Nuclear Verifications Series No. 1 (Rev.2).

16 sealing, are applied to complement nuclear material accountancy. The use of C/S measures is aimed at verifying information on movement of nuclear or other material, equipment and samples, or preservation of the integrity of safeguards relevant data. In many instances C/S measures cover the periods when the inspector is absent, thus ensuring the continuity of knowledge for the IAEA and contributing to cost effectiveness15. Additional methods used for safeguards verifications are, for instance, non-destructive assays (NDA). They are used to measure the inventory of nuclear material and to detect partial defects from the declaration. Focusing on spent fuel verifications, Cherenkov radiation, y-ray spectrometry and neutron counting are used in the field 16.

1.4 NDA Techniques Non-Destructive Assays (NDA) are all those techniques which do not alter the physical or chemical state of the nuclear material subjected to analysis. They measure radiation, spontaneous or induced from nuclear material. In particular the radiations used in the NDA techniques are y-rays, x-rays and neutrons since α and β particles do not penetrate sufficiently in bulk material to be useful for assays17.

The advantages of this kind of measurements, compared to destructive methods, are that those are not intrusive, are safer for the operators, since reduce their exposure, and are normally cheaper and faster than the chemical assay18. On the other side the accuracy of the results obtained with NDA techniques is generally lower than the one of the destructive assays.

The IAEA uses more than 100 different NDA systems to verify, check and monitor nuclear materials, figure 1 shows an overview of the NDA methods in use.

15 http://nsspi.tamu.edu/nsep/reference-modules/technical-safeguards-terminology/containment,- surveillance,-and-monitoring/containmentsurveillance-measurues 16 IAEA, “Safeguards Techniques and Equipment: 2011 edition”, International Nuclear Verifications Series No. 1 (Rev.2). 17 James Doyle, Nuclear Safeguards, Security and Non Proliferation: achieving security with technology and policy, Elsevier, April 8 2004. 18 ESARDA, Nuclear Safeguards and Non-Proliferation, Course Syllabus.

Figure 1: Overview of the NDA methods

1.5 Techniques for spent fuel One of the tasks of the safeguards inspectors is to verify data of the fuel declared by the operator in order to give assurance of their completeness and correctness and so to find eventual diversion. In particular the verifications have to guarantee that the mass data and the isotopic composition are consistent with the declaration and that no material is missing or has been replaced by dummies19.

1.5.1 Measurement principles The NDA methods used for the verification of the spent nuclear fuel are based on the detection of the radiation emitted from the fuel. A first important classification can be done considering the type of radiation detected by the measurement system. According to this classification we define primary radiation the one emitted directly from the material, while secondary radiation refer to radiation emitted because of the interaction of primary radiation with other materials.

NDA techniques can also be differentiated based on the type of radiation detected. Therefore, the main families according to this criterion are y-rays, neutron, and Cherenkov detector. Moreover, calorimetric measurements are also performed for specific applications. A list of spent fuel measurement systems is given in Table 1 21.

19 Matti Tarvainen et al., NDA techniques for spent fuel verification and radiation monitoring, finish support programme to the IAEA safeguards, August 1997.

Table 1: Spent fuel measurement system.

2 Computational tools used for the simulations

2.1 Introduction The study of the neutron emission from spent fuel requires the complete characterization of the fuel in terms of isotopic composition as a function of the irradiation and cooling time after discharge. This characterization is obtained solving the system of equations formed by the Boltzmann equation and by the Bateman equations, together with the proper boundary conditions. The Boltzmann and Bateman equations are chosen for the system because the first one describes the neutron balance, while the second one the time dependence of the atomic densities. The analytic solution of this system of equations is very complex, and sometimes even impossible to solve, so it is normally tackled by the coupling of burn-up codes and neutron transport codes, and by applying the appropriate simplifications. With this approach, first the neutron transport code, starting from the composition of the fresh fuel and according to the reactor operating conditions, calculates the reaction rates in the fuel and derives the effective cross section values. Then the burn-up code uses these cross section values to solve the Bateman equations and to determine the variation of the fuel nuclides compositions as a function of time. The cross sections are recalculated after appropriate time steps in order to consider the changes in the nuclide concentration due to the fuel burn-up. This iterative process is repeated several times in order to have a more precise characterization of the fuel composition. It is evident that a codes system like the one described above can be very accurate but on the other hand requires significant computation resources and long time for the calculation. Origen-ARP (ORIGEN, 2009) is a burn-up code that is able to perform the same simulations of the traditional burn-up codes systems reducing the computation time but keeping the same accuracy in the solution.

2.2 Origen ARP ORIGEN-ARP is a part of the SCALE package and it is developed since the mid-1990s by the Oak Ridge National Laboratory (ORNL). The main feature of this code is that through a set of pre-compiled average cross sections the code is able to run complete spent fuel burn-up simulations faster than other simulation codes.

The ORIGEN-ARP code contains different analytic modules:

 ARP (Automatic Rapid Processing): module that interpolates the pre-generated cross section libraries in order to create a problem-dependent cross section for the ORIGEN-S code;  ORIGEN-S: isotope depletion and decay code;  OPUS: module that produces an output file that can be used to make a variety of plots from the ORIGEN-S output files;  PlotOPUS: graphics-plotting program that can use directly the output data produced by OPUS and generate Windows metafile (WMF), JPEG bitmap (JPG) or Windows bitmap (BMP) files for saving the plot images.

The resolution scheme of ORIGEN-ARP code is based on a set of precompiled cross section values. These values were calculated in advance with a reactor physic transport code for different fuel assemblies and reactor types.

The module ORIGEN-S first solves the Bateman equations and calculates the material concentration. Then, starting from the set of pre-compiled cross-sections the module ARP interpolates, according to the input parameters selected by the user, updated cross section values for the next iteration with ORIGEN-S. The presence of the precompiled cross section library eliminates the great part of the time required for the traditional simulations, since it removes the need to perform reactor physics calculation.

The interpolation of the cross section values depends on the parameter specified by

22 the user in the input file. In particular for the uranium-based fuel the dominant parameters are initial enrichment, burnup, and water density, while for the mixed oxide fuel (MOX) the interpolation parameters are plutonium content, plutonium isotopic vector, and water density.

2.3 Cross section libraries in SCALE The main feature of the ORIGEN-ARP analytical sequence is the presence of a set of pre-compiled cross section libraries which leads to a reduction of the total computational time.

These libraries have been generated with a reactor physics transport code and include a wide range of commercial power reactor and fuel assembly designs:

 BWR o GE 7x7, 8x8, 9x9, 10x10, 10x10-8, o ABB 8x8 o ATRIUM-9 and ATRIUM-10 o SVEA-64 and SVEA-100  PWR o Siemens 14x14 o Westinghouse CE 14x14 and 16x16 o Westinghouse 14x14, 15x15, 17x17, 17x17 OFA  CANDU reactor fuel (28- and 37-element bundle designs)  Magnox graphite reactor fuel  AGR fuel  VVER 400 flat enrichment (1.6% - 3.6%) and profiled enrichment (average 3.82%, 4.25%, 4.38% )  VVER 1000  MOX BWR 8x8-2, 9x9-1, 9x9-9,10x10-9  MOX PWR 14x14, 15x15, 16x16, 17x17,18x18

The cross sections in the libraries were generated with different codes: for the LEU reactor, BWR and PWR, the two-dimension depletion analysis module TRITON (SCALE5.1) has been used, for the MOX, Magnox and AGR fuel the one-dimension depletion analysis module SAS2 (SCALE 5) has been used, while for the CANDU reactor the WIMS lattice code has been chosen.

In addition to the previous cases, with ORIGEN-ARP the user has the possibility to generate cross section libraries for other reactor configurations not included in the SCALE package. The complete procedure to perform this operation is contained in {20}20.

2.4 GUI (Graphical User Interface)

Another important feature of this code is the Windows Graphical User Interface (GUI) called OrigenArp. This interface is a Windows-based program that allows the user to setting up easily an input file for ORIGEN-S, ARP and the other modules implemented in ORIGEN-ARP. It is a user-friendly interface that through a set of windows, menus and toolbars guides the user in the compilation of an input file.

Two different input forms are included:

 Origen Express  Detailed Input

The “Origen Express” allows the creation of the input with the minimum amount of data required for this kind of simulation, and has a different format in the case of UO2 or MOX fuel. This form is utilized when the characteristic of the spent fuel assembly under investigation are not completely known.

Figure 2 and 3 show the express form for, respectively, a UO2 and a MOX fuel type.

When all the parameters are inserted and saved, the user can directly run the input file. Alternatively more details can be added by pushing the “Detailed input” button.

The user can have access to the “Detailed form” from the “Express form”, to modify the

20 I. Gauld, S.Bowman, J.Horwedek. "Origen-ARP: automatic rapid processing for spent fuel depletion, decay and source term analysis." ORNL/TM-2005/39. January 2009

25 express input file, or directly from a new file. In the first case the input form will contain data extrapolated from the express input, while in the second case the input file will be empty.

Figure 2: ORIGEN-ARP UO2 Express window.

Figure 3: ORIGEN-ARP MOX Express window.

In the detailed input five different menus are present:

 Compositions: in this menu the user can select the fuel type, the initial enrichment and the amount of fuel loaded (from which the code calculates the uranium isotopic vector) and to add other materials to better characterize the fuel;  Neutron Groups: here the user can choose the energy groups structure for the neutron-decay source spectra. The code has a list of pre-loaded groups that the user can modify. Moreover is it possible to input other structures;  Gamma Groups: like for neutrons, it is possible to choose the proper energy groups structure for the gamma-decay source spectra or otherwise to import a desired one;  Case Data: in this menu the user can describe the irradiation and decay histories at which the fuel will be subjected. The menu is divided in two forms: Irradiation Case and Decay Case. In the Irradiation Case the time of irradiation and the power level are defined. It is also possible to define the print options. In the Decay Case the user specifies the time steps for the decay time: the time steps must respect the “rule-of-three” for which each time step cannot exceed three times the previous step (this rule is set to keep the accuracy in the solution). It is also possible to set the fuel matrix for the (alpha,n) neutron source, the one for the bremsstrahlung photons, the cut-off for the (alpha,n) reactions and the gamma library for the calculation of the gamma spectra.

2.5 Validation of the code The necessary validation of the ORIGEN-ARP code has been done both for the LWR spent fuel {21}21and the MOX fuel {22}22. In particular a comparison between ARP results, SASH2 calculations and measured values have been done for the PWR and BWR spent fuel nuclides concentrations. The calculations and the measures have been done considering these fuel assemblies:

 PWR: the 14 × 14 Calvert Cliffs, the 14 × 14 Obrigheim, and the 15 × 15 H. B. Robinson.  BWR: the 6 × 6 Gundremmingen, the 6 × 6 JPDR, and the 7 × 7 Cooper.

For the MOX fuel the validation has been done comparing the results from ORIGEN- ARP with a numerical benchmark and with available radiochemical assays experiments.

The numerical benchmark has been developed by the OECD/NEA/NSC (Organization For Economic Cooperation and Development / Nuclear Energy Agency / Nuclear Science Committee) Criticality Working Party, Burn-up Credit Working Group to address the calculation of irradiated MOX fuel composition. The results for this benchmark have been provided by several organizations using different computer code (as shown in table 2). Organization Computer Code Cross-section library BNFL WIMS8A JEF2.2 PSI BOXER/ETOBOX JEF ½ (maybe it’s 1.2) GRS KENOREST-99 JEF2.2 CEA APPOLO2/PEPIN2 JEF2.2 ORNL SCALE/SAS2D ENDF/B-V NUPEC CASLIB ENDF/B-IV JAERI MVP-BURN JENDL-3.2 DTLR MONK8A JEF2.2

Table 2: Organizations, computer codes and cross-section libraries involved in the benchmark

21L.C Leal, O.W. Hermann, S.M. Bowman, and C.V. Parks, ARP: Automatic Rapid Process for the Generation of Problem-Dependent SAS2H/ORIGEN-S Cross-Section Libraries, ORNL/TM-13584, Lockhedd Martin Energy Research Corporation, Oak Ridge National Laboratory, April 1998. 22I.C. Gauld, MOX Cross-Section Libraries for ORIGEN-ARP, ORNL/TM-2003/2, UT-Battelle, LLC, Oak Ridge National Laboratory, July 2003.

The ORIGEN-ARP code was benchmarked with the other simulations code for several fuel assembly cases, and the comparison shows that data from ORIGEN-ARP are in good agreement with the results computed by the other codes {21}.

Within the international program ARIANE (Actinides Research In A Nuclear Element) developed by Belgonucleaire to provide experimental data for code validations, experimental measurement of spent MOX fuel have been performed. This enabled to have an experimental comparison for ORIGEN-ARP also for this fuel type. The measurements used for the comparison have been obtained from assemblies from the Beznau PWR power plant in Switzerland. Moreover other comparisons have been done considering MOX samples analyzed at the Paul Scherrer Institute (Switzerland) and at the SCK-CEN laboratory (Mol, Belgium). Again the results from ORIGEN-ARP show a good agreement with the experimental data{21}.

2.6 Cygwin An important tool used for the data analysis is Cygwin. Cygwin is a software that allows the user to simulate in Microsoft Windows the Unix environment. In our work it has been used to extract from the ORIGEN output files the relevant data for the analysis. In particular we used the following scripts:

- step01: it converts the files from .out to .out_bis extension; - get_all_totals_01: this script extracts from the output file the data related to the total neutron emission and its composition in terms of spontaneous fissions, (α, n) reactions and delayed neutron emission. - get_all_NE_isotopes_01: this script extracts from the output file the total neutron emission of single selected nuclides.

The extracted data have been analyzed using Microsoft Excel 2010 and plotted with the graphing software Origin 9.1.

3 ARP Simulations model

One of the main features of ORIGEN-ARP is the graphical user interface (GUI) that allows to define in a very precise and accurate way the model of the simulation. In this section, following the GUI structure, the input options adopted for the simulations are listed.

3.1 General input options In order to make the results of all the simulations comparable, all the models have the same general structure described by the following parameters:

3.1.1 Express window

- Fuel type: w17x17 (mox17x17 in the case of MOX fuel); - All results are normalized to 1 ton of fuel (uranium in the case of LEU, heavy metal (U+Pu) in the case of MOX);

- Average power: 40 MW/tU; - Moderator density: 0.723 g/cm3 (default values).

3.1.2 Neutron energy spectra

- Group structure: 238GrpENDF5.

3.1.3 Gamma energy spectra

- Group structure: 74 GrpFOUR (this group structure is not present in the default options, but must be defined by the user).

3.1.4 Cases window

This window allows the user to define the irradiation history of the fuel assembly. The characterization is done describing “irradiation cases" and "decay cases". For our simulations, according to model adopted by Rossa et al. {1, 2}, we consider irradiation cycles of maximum 360 days with 30 days of cooling time between to complete cycles. Fixed the value of the burnup, the duration of the last irradiation cycle is defined consequently.

After the last irradiation cycle, thirty cooling times divided in four parts, as shown in the next table, are set.

I II III IV V VI VII

Discharge 1 day 3 days 10 days 30 days 100 days 300 days CT part 1

VIII IX X XI XII XIII XIV XV XVI

1 year 2 years 3 years 4 years 5 years 6 years 7 years 8 years 9 years CT part 2

XVII XVIII XIX XX XXI XXII XXIII XXIV

10 years 20 years 30 years 50 years 100 years 300 years 1000 years 3000 years CT part 3

XXV XXVI XXVII XXVIII XXIX XXX

104 years 3*104 years 105 years 3*105 years 106 years 3*106 years CT part 4

Table 3: Overview of the cooling time structure.

3.1.5 Irradiation output options

- Output precision: 6 digits; - Output tables: nuclides; - Tables cutoff: 0; - Output units: grams.

Light elements, Fission products and Actinides are selected to be shown in the output file

3.1.6 Decay output options

- Output precision: 6 digits; - tables: nuclides; - Tables cutoff: 0; - Results in: grams; - Edit by: Light elements, Fission products, Actinides.

3.1.7 Other option selected

- The fuel matrix for the (α,n) evaluation is the UO2; - Bremsstrahlung radiation is not considered in the model.

3.2 LEU simulations options

In the LEU simulations we consider three different values of initial enrichment:

I II III

IE 2.0 % 2.5 % 3.0 %

Table 4: Initial enrichment cases overview.

The uranium isotopic vector used is the one elaborated from the code for each value of initial enrichment inlaid. A concentration of 134500 g/ton of oxygen is added in the composition table in order to simulate UO2 fuel. In this group of simulations, 14 values of burnup are considered:

I II III IV V VI VII VIII IX X XI XII XIII XIV

BU (GWd/t ) U 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Table 5: LEU burnup cases overview. 3.3 MOX simulations options

In the case of MOX fuel simulations, the code requires the definition of the abundances of the uranium and plutonium isotopes. We use the composition proposed in {4} that considers the following heavy metal isotopic composition:

Plutonium:

- 238Pu 2.5% - 239Pu 54.7% - 240Pu 26.2% - 241Pu 9.5% - 242Pu 7.2%

Uranium:

- 234U 0.00119% - 235U 0.25% - 238U 99.7488%

In the simulation these isotopic vectors are kept constant all the time, while 4 different values of the total plutonium content in the heavy metal, HM, are considered:

I II III IV

% Pu/HM 4% 6% 8% 10%

Table 6: Pu content cases overview.

Due to the intrinsic limitations of ORIGEN-ARP, according to the available cross section libraries, in these simulations only 12 values of BU are considered:

I II III IV V VI VII VIII IX X XI XII

BU (GWd/t ) U 5 10 15 20 25 30 35 40 45 50 55 60

Table 7: MOX burnup cases overview.

In this group of simulations, in order to better understand the production mechanism of the different isotopes, two specific simulations have been carried out.

In particular, considering the composition with 8% of Pu and keeping the general structure adopted for the other simulations, the fuel undergoes a complete irradiation cycle (360 days). In the first simulation the average power is constant (40 MW/tU) during the whole cycle, while in the second one it follows the following scheme:

- From the charge up to 108 days: 40 MW/tU;

- From 108 to 288 days: 10 MW/tU;

- From 288 to 360 days (discharge): 40 MW/tU.

4 Structure of the library

The purpose of this work is to extend the existing reference library of spent fuel. To make the results consultation simpler the output file names of the simulations are organized according to the following conventions.

4.1 LEU simulations

The generic output file name for this group of simulations has the following structure:

L0XXXYYY - L stands for LEU (0 is not used) - XXX are the three digits for the initial enrichment (e.g. 2.5% → L0250YYY)

- YYY are the three digits for the discharge burnup (e.g. 35 GWd/tU → L0XXX350)

In the next table all the cases considered in this section are summarized.

IE (%)

BU (GWd/tU) 2.0 2.5 3

5 L0200050 L0250050 L0300050 10 L0200100 L0250100 L0300100 15 L0200150 L0250150 L0300150 20 L0200200 L0250200 L0300200 25 L0200250 L0250250 L0300250 30 L0200300 L0250300 L0300300 35 L0200350 L0250350 L0300350 40 L0200400 L0250400 L0300400 45 L0200450 L0250450 L0300450 50 L0200500 L0250500 L0300500 55 L0200550 L0250550 L0300550 60 L0200600 L0250600 L0300600 65 L0200650 L0250650 L0300650 70 L0200700 L0250700 L0300700

Table 8: Overview of the LEU fuel filenames library.

4.2 MOX simulations

The generic output file name for this group of simulations has the following structure:

M0XXXYYY - M stands for MOX (0 is not used) - XXX are the three digits for the percentage of plutonium in the heavy metal (e.g. 6% → M0060YYY)

- YYY are the three digits for the discharge burnup (e.g. 35 GWd/tU → M0XXX350)

Pu/HM(%)

4 6 8 10 BU (GWd/tU) 5 M0040050 M0060050 M0080050 M0100050 10 M0040100 M0060100 M0080100 M0100100 15 M0040150 M0060150 M0080150 M0100150 20 M0040200 M0060200 M0080200 M0100200 25 M0040250 M0060250 M0080250 M0100250 30 M0040300 M0060300 M0080300 M0100300 35 M0040350 M0060350 M0080350 M0100350 40 M0040400 M0060400 M0080400 M0100400 45 M0040450 M0060450 M0080450 M0100450 50 M0040500 M0060500 M0080500 M0100500 55 M0040550 M0060550 M0080550 M0100550 60 M0040600 M0060600 M0080600 M0100600

Table 9: Overview of the MOX fuel filenames library.

4.3 Plutonium sensitivity simulation

The generic output file name for this group of simulations has the following structure:

M0080XXXZ05YYY

- M stands for MOX (0 is not used) - 080 are the three digits for the percentage of plutonium in the heavy metal of the reference case (8%) - XXX are the three digits for the considered plutonium isotope (e.g. 242Pu→ M0080242) - Z is the digit that indicates if the mass of the isotope have been added (P) or subtracted (M) (e.g. addition of 5% of 242Pu→ M0080242P05) - 05 indicates that we added/subtracted the 5% of the mass of the considered isotope.

- YYY are the three digits for the discharge burnup (e.g. 35 GWd/tU → M0080242P05350).

238 239 240 241 242 isotope Pu Pu Pu Pu Pu

BU (GWd/tU) P M P M P M P M P M

M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 5 P05050 M05050 P05050 M05050 P05050 M05050 P05050 M05050 P05050 M05050 M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 10 P05100 M05100 P05100 M05100 P05100 M05100 P05100 M05100 P05100 M05100 M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 15 P05150 M05150 P05150 M05150 P05150 M05150 P05150 M05150 P05150 M05150 M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 20 P05200 M05200 P05200 M05200 P05200 M05200 P05200 M05200 P05200 M05200 M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 25 P05250 M05250 P05250 M05250 P05250 M05250 P05250 M05250 P05250 M05250 M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 30 P05300 M05300 P05300 M05300 P05300 M05300 P05300 M05300 P05300 M05300 M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 35 P05350 M05350 P05350 M05350 P05350 M05350 P05350 M05350 P05350 M05350 M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 40 P05400 M05400 P05400 M05400 P05400 M05400 P05400 M05400 P05400 M05400 M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 45 P05450 M05450 P05450 M05450 P05450 M05450 P05450 M05450 P05450 M05450 M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 50 P05500 M05500 P05500 M05500 P05500 M05500 P05500 M05500 P05500 M05500 M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 55 P05550 M05550 P05550 M05550 P05550 M05550 P05550 M05550 P05550 M05550 M0080238 M0080238 M0080239 M0080239 M0080240 M0080240 M0080241 M0080241 M0080242 M0080242 60 P05600 M05600 P05600 M05600 P05600 M05600 P05600 M05600 P05600 M05600

Table 10: Overview of the plutonium sensitivity filenames library.

5 Study on the actinides production

5.1 Introduction The results obtained from the simulations carried out with ORIGEN-ARP are shown and analysed in this chapter. The data analysis is focused on the influence of the different parameters (burn-up, cooling time etc.) on the total neutron emission, and considering also the contribution of the single isotopes.

In this chapter the production mechanisms of the actinides (the major contributors to the total neutron emission) and their sensitivity to the irradiation parameters are investigated in order to better explain the results.

In order to achieve these objectives, a theoretical study is first presented, supported by a group of simulations performed to verify the theoretical assumptions. Moreover an isotopes table, reported in Annex E, has been developed. The table lists for a wide group of isotopes (from 234U to 252Cf) the corresponding half-life, branching ratio, (n,γ) thermal cross section and the total resonance integral.

In the first part of the chapter the features of different isotopes are described, and then the production chains of the 242Cm and 244Cm are accurately studied.

The information about the isotopes are taken from the chapter “Actinide isotope production, depletion, and decay” of {23}23.

23 Bosler, G.E.; Phillips, J.R.; Wilson, W.B.; LaBauve, R.J.; England, T.R.; Los Alamos National Lab., NM (USA) “Production of Actinide Isotopes in simulated PWR fuel and their influence on Inherent Neutron Emission”

5.2 Transmutation mechanism The build-up of isotopes is mainly determined by the fission and capture reactions of the isotopes contained in nuclear fuel as a result of fuel irradiation. Figure 4 shows the principal transmutation chains that from the uranium isotopes lead to the production of the curium isotopes. The half-life is also reported for each isotope.

The arrows that link the different isotopes represent the different decay modes, following this legend:

 Neutron capture  β-decay  -decay

Figure 4: Primary transmutation mechanism for U-235 and U-238 leading to the production of Cm isotopes. The figure shows selected decay mechanisms that contribute the transmutation chain.

5.3 Isotopes properties

5.3.1 Uranium isotopes

234 235 In the fresh UO2 fuel four uranium isotopes are present in different percentages: U, U, 236U and 238U. The total percentage in weight of 234U and 236U is less than 0.1 %. The actual percentages of the isotopes in the fresh fuel depend on the initial enrichment of the fuel, that for the commercial light water reactors vary from 2.0% and 4.5%.

During the irradiation the 234, 235 and 238 isotopes are “burned” while the 236 isotope is produced through neutron capture from the 235 isotope, as shown in figure 1.

234U: Uranium-234 concentration decreases during the irradiation, through (n,γ) 235 5 capture to form U. Considering its long life (t1/2: 2.45·10 years) its concentration is not affected by reactor shutdown or fuel discharge from the reactor. During the cooling time the 238Pu decays through α emission and produces additional 234U.

235U: The 235 isotope during the irradiation absorbs neutrons and either undergoes fission or forms uranium-236. 235U has a half-life of 7.04·108 years.

236U: This isotope has a half-life of 2.34·107 years. During the reactor operation it is consumed by neutron captures forming 237U, while it is produced in the same way from the 235U. The thermal absorption cross-section of 235U is larger than the one of 236U (99 b and 5 b, respectively), therefore the 236U concentration increases with the irradiation time

238U: 238U is the isotope with the highest concentration in the LWR fuel. The depletion of this isotope is due to two different reactions, either fissions due to fast neutrons or production of 239U by thermal neutrons capture. Considering its long half-life, 4.47·109 years, its concentration is unaffected by reactor shutdown.

5.3.2 Neptunium isotopes

The neptunium isotopes are the precursors of the plutonium isotopes. Except for the 237 isotope that has a long half-life (2.14 ·106 years), the other isotopes quickly undergo beta decay forming different plutonium isotopes.

5.3.3 Plutonium isotopes

The plutonium isotopes, in particular 238, 239, 240 and 242, are important neutron emitters, as will be shown in the following chapter. Moreover the 239Pu and the 241Pu are fissile materials. The neutrons emitted could be produced by spontaneous fission, from 238Pu, 240Pu and 242Pu, or by (α,n) reactions due to the α particles emitted by 238Pu, 239Pu and 240Pu.

238Pu: This isotope is produced mainly by β-decay of 238Np, and a little percentage of its build-up is due to the α-decay of 242Cm. Its concentration increases during the irradiation time and increases with the increase of the burnup. Since its production depends principally from decays it is produced also during the shutdown and the cooling time.

239Pu: This is one of the two fissile isotopes of plutonium. During the irradiation it is formed from decay of 239Np and minimally from neutron capture of 238Pu. For high burnup, when part of the 235U has been depleted, it represents a significant contribution to the total neutron fissions in a reactor core.

240Pu: 240Pu has a half-life of 6.55·103 years. It is formed primarily from (n,γ) reaction from 239Pu, a little amount is produced from beta decay of 240Np. It forms 241Pu by neutron capture.

242Pu: It is produced from neutron capture in the 241Pu. Another source for this isotope is the electron capture in the 242Am. Considering its long half-life (3.76·105 years), it remains constant during reactor shutdown.

5.3.4 Americium isotopes

From a radiological point of view the americium isotopes are not relevant {23}, but they are important in this study since they are the precursors of the curium isotopes. Only the 241Am can have a relevant role in the neutron emission since it is an α-emitter.

241Am: this isotope is produced from beta decay of the 241Pu (half-life 14.7 years) both during the irradiation and the cooling time. Capturing neutron it forms 242Am but it can also undergo α-decay.

5.3.5 Curium isotopes

The curium isotopes, particularly 242 and 244, are very important in the characterization of spent fuel, both in LEU and MOX fuel. In fact they are, up to 100 years of cooling time, the major neutron emitters (as will be analysed in the following chapters). For high burnup also the isotopes 246 and 248 gain importance as neutron sources.

242Cm: It is formed by the beta decay of 242Am. As shown in the annex E, it is consumed through alpha decay (≈ 100%) or spontaneous fission (6.2·10-6%) but it can also absorb a neutron to form 243Cm. It has a half-life of 162.8 days, so a significant amount is depleted during the reactor shutdown.

244Cm: it is produced from the beta decay of 244Am and from the 243Am neutron captures in fuel with high burnup. It is depleted through three different ways: α- decay (principally), neutron capture and spontaneous fission.

5.4 Curium isotopes production

Considering the importance of the curium isotopes for the neutron emission in spent nuclear fuel, it is important to know the mechanisms which lead to the production of these isotopes during the irradiation time. We concentrated our analysis on the two main isotopes: 242Cm and 244Cm. First of all we hypothesized the theoretical chain of reactions and then through simulations performed with ORIGEN-ARP we verified these assumptions.

5.4.1 Curium-242

For the isotope 242Cm we considered this series of nuclear reactions:

242mAm β- 241Pu 241Am n,γ 242Cm β- 242Am

The 241Pu (half-life: 14.4 years) is depleted through β-decay in 241Am. 241Am in turn absorbs neutrons to form 242Am (probability of 88%) and 242mAm (probability of 12%). The latter decays through isomeric transition in 242Am. The 242Cm is finally formed by β-decay from the 242Am (half-life: 16.0 hours). Figure 5 reports the concentration of the considered isotopes as a function of the irradiation time for a MOX fuel composition with 8% of Pu. For this simulation 360 days of irradiation and an average power of 40 MW/tu have been considered. In the figure the decays of the

Isotope concentration as a function of the IT ( %Pu: 8 IT:360 days) 105

104 Pu241

103  pu241 (40) am241(40) 2 10 am242m (40) Am241 (n,γ) am242 (40) cm242 (40) 101

 0  10 Cm242 IT

Am242m -1

Isotopes Concentration (grams) Concentration Isotopes 10 Am242

10-2 0 36 72 108 144 180 216 252 288 324 360 Irradiation Time (days)

Figure 5: Concentration of different isotopes as a function of the cooling time for a MOX fuel composition with 8% of plutonium. 42

different isotopes are indicated.

5.4.2 Curium-244

For the production of the 244Cm isotope we considered the following decays and reactions:

- β n,γ

I. 243Pu 243Am 244Am 244Cm

II. 242Cm 243Cm 244Cm

The plutonium-243 (half-life: 4.956 hours) undergoes β-decay and produces americium-243 243 244 (half-life: 7380 years). The Am forms Am by absorbing a neutron (σth: 80 barns). In turn the 244Am (half-life: 101 hours) undergoes beta decay to form 244Cm. 244 243 The Cm can also be produced from neutron capture of Cm (σth: 131 barns), which is 242 generated from the neutron capture in Cm (σth: 19 barns). This “path” is promoted by high neutron fluxes (e.g. high burnup and low fissile content). In figure 6 the concentration of these isotopes in a MOX fuel composition with 8% Pu is shown. The concentrations are plotted as a function of the irradiation time. The irradiation time and the average power have the same values of the ones chosen for the simulation shown in figure 5.

Isotope concentration as a function of the IT ( %Pu: 8 IT:360 days) 103

Am243

102 Cm244 (n,γ)  Cm242 pu243(40) 101 am243 (40) (n,γ) am244 (40)  cm242 (40) (n,γ) cm243 (40) 0 Pu243 10 cm244 (40)

10-1 Am244 Isotopes Concentration (grams) Concentration Isotopes

Cm243 10-2 0 36 72 108 144 180 216 252 288 324 360 Irradiation Time (days)

Figure 6: Concentration of different isotopes as a function of the cooling time for a MOX fuel composition with 8% of plutonium.

5.4.3 Verification of the theoretical assumptions

In order to verify the correctness of the two isotopes production chains shown in the previous paragraph, two different simulations have been performed for each chain.

The simulations considered a MOX fuel composition with 8% of plutonium content subjected to an irradiation time of 360 days. For the first simulation the average power has been maintained constant and equal to 40 MW/tu during all the irradiation time. The results of this simulation are shown in figures 5 and 6 for, respectively, the 242Cm-chain and the 244Cm- chain. In the second simulation the average power followed the following scheme:

- From the fresh fuel loading up to 108 days: 40 MW/tu;

- From 108 to 288 days: 10 MW/tu

- From 288 to 360 days (discharge): 40 MW/tu.

The results of this simulation are reported in figures 7 and 8, respectively, the 242Cm-chain and the 244Cm-chain.

Isotope concentration as a function of the IT ( %Pu: 8 IT:360 days) 105

Pu241 104

103  Am241 pu241 am241 2 10 am242m (n,γ) am242 cm242 1 10 Cm242 Am242m

0 10  IT -1 Am242

Isotopes Concentration (grams) Concentration Isotopes 10

10-2 0 36 72 108 144 180 216 252 288 324 360 Irradiation Time (days)

Figure 7: Concentration of different isotopes as a function of the cooling time for a MOX fuel composition with 8% of plutonium, with variable average power.

Isotope concentration as a function of the IT ( %Pu: 8 IT:360 days) 103

Am243

102

Cm244 pu243 am243 101 Cm242 am244 cm242 cm243 0 10 Pu243 cm244

10-1

Am244 Cm243 Isotopes Concentration (grams) Concentration Isotopes

10-2 0 36 72 108 144 180 216 252 288 324 360 Irradiation Time (days) 1

Figure 8: Concentration of different isotopes as a function of the cooling time for a MOX fuel composition with 8% of plutonium, with variable average power.

In order to have an immediate comparison between the two simulations, their results are plotted together in figure 9 and 10 for the 242Cm and 244Cm, respectively. In these two graphs the dotted lines refer to the simulation with a constant average power while the solid lines to the simulation with a variable average power.

Isotope concentration as a function of the IT ( %Pu: 8 IT:360 days) 105

Pu241 104

103 pu241 am241 am242m 102 Am241 am242 cm242 pu241 (40) 101 am241(40) am242m (40) am242 (40) Cm242 100 cm242 (40)

Am242m -1

Isotopes Concentration (grams) Concentration Isotopes 10 Am242

10-2 0 36 72 108 144 180 216 252 288 324 360 Irradiation Time (days)

Figure 9: Comparison between the results of different simulations.

Looking at figure 9 it is clear that the variation of the average power, resulting in the variation of neutron flux, influences the concentration of the isotopes in different ways.

The trend confirms the hypothesis postulated on the 242Cm production chain since the 241Pu present in the fresh fuel is not influenced by the variation of the power. Consequently the 241Am, produced from the beta decay of 241Pu, remains almost constant in the two simulations.

On the contrary, the concentration of the 242Am undergoes a strong decrease with the decrease of the average power confirming its production from neutron absorption in the 241Am. The decrease of the 242Am is due to the fact that its production decrease due to the lower power level, but its decay continues regardless of the power.

The variation in the concentration of the 242Cm is indirectly influenced by the variation of the neutron flux. The decrease of concentration of the 242Am involves, as precursor, a less marked decrease in the concentration of the 242Cm due to the power level change. In addition the concentration of the 242Am decreases immediately with the power, but as soon as the power returns to the original value the concentration equals the one of the simulation with a constant power. This is due to the very low half-life, 16 hours, of the 242Am which prevents the build-up as in the case of 242Cm.

Isotope concentration as a function of the IT ( %Pu: 8 IT:360 days) 103

Am243 102 pu243 am243 Cm244 am244

1 cm242 10 Cm242 cm243 cm244 pu243(40) am243 (40) 0 Pu243 am244 (40) 10 cm242 (40) cm243 (40) cm244 (40)

-1

10 Am244 Cm243 Isotopes Concentration (grams) Concentration Isotopes

10-2 0 36 72 108 144 180 216 252 288 324 360 Irradiation Time (days)

Figure 10: Comparison between the results of different simulations.

As in figure 9, figure 10 confirms the Curium-244 production chain theorized in the previous paragraph. All the isotopes produced by neutron capture (243Pu, 244Am and 243Cm) undergo a strong reduction in their concentration due to the reduction of the power level. On the other hand the other isotopes, produced by beta decay, undergo a reduction that is more evident for low-Z nuclides.

6 Main results from the fuel library

6.1 LEU simulations

6.1.1 Neutron emission as a function of the burnup

In Figures 11, 12 and 13 the total neutron emission as a function of the burnup for different cooling times is shown. Moreover, the contribution to the total neutron emission of the spontaneous fissions and of the (α,n) reactions are represented. All the data have been calculated for the composition with 2.5% of initial enrichment. The results have the same trend also with the other initial enrichment values considered in the work. As we can see, the total neutron emission grows with the burnup. The main contribution to the total neutron emission is due to the spontaneous fissions both for short and long cooling times. Figure 12 shows that at 10 years of cooling time and low burnup values, there is an increase in the contribution to the total neutron emission from (α,n) reactions.

Neutron emission (IE: 2.5% CT: 30 days ) 1011

1010

109

108

107

Neutron emission (n/s/tU) emission Neutron Total 6 10 alpha, n SF 105 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Burnup (Gwd/tU)

Figure 11: Neutron emission as a function of the burnup for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and cooling time of 30 days.

Neutron emission (IE: 2.5% CT: 10 years ) 1010

109

108

107

106

Neutron emission (n/s/tU) emission Neutron Total 5 10 alpha, n SF 104 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Burnup (Gwd/tU)

Figure 12: Neutron emission as a function of the burnup for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and cooling time of 10 years.

Neutron emission (IE: 2.5% CT: 1000 years ) 109

108

107

106

5 Neutron emission (n/s/tU) emission Neutron 10 Total alpha, n SF 104 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Burnup (Gwd/tU)

Figure 13: Neutron emission as a function of the burnup for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and cooling time of 1000 years.

6.1.2 Neutron emission as a function of the cooling time

In the Figures 14, 15 and 16, the total neutron emission is plotted against the cooling time, considering an initial enrichment of 2.5% and different burnup values. In the graphs the total neutron emission is reported as well as the contribution of the spontaneous fissions and of the (α,n) reactions. In general the total neutron emission decrease with the increase of the cooling time And the neutron emission consist mainly of spontaneous fissions. The (α,n) reactions are lower than the spontaneous fission for almost all the burnup values and cooling times. Figure 14 shows that with a cooling time around 100 years the contribution of the (α,n) reactions is greater than the one of the spontaneous fissions, and we observed the same trend with a burnup of 5 and 15 GWd/tu. In order to investigate this fact in the next section the contributions of single nuclides to the total neutron emission are evaluated.

Neutron emission (IE: 2.5% BU: 10 GWd/tU) 1x107 Total alpha, n SF 1x106

1x105 Neutron Emission Neutron 1x104

1x103 1x10-2 1x10-1 1x100 1x101 1x102 1x103 1x104 1x105 1x106 Cooling Time

Figure 14: Neutron emission as a function of the cooling time for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and burnup of 10 GWd/tU.

Neutron emission (IE: 2.5% BU: 35 GWd/tu) 1x1010 Total 1x109 alpha, n SF 1x108

1x107

1x106

Neutron Emission Neutron 1x105

1x104

1x103 1x10-2 1x10-1 1x100 1x101 1x102 1x103 1x104 1x105 1x106 Cooling Time

Figure 15: Neutron emission as a function of the cooling time for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and burnup of 35 GWd/tU.

Neutron emission (IE: 2.5% BU: 60 GWd/tU)

1x1010 Total alpha, n 1x109 SF

1x108

1x107

1x106 Neutron Emission Neutron 1x105

1x104

1x103 1x10-2 1x10-1 1x100 1x101 1x102 1x103 1x104 1x105 1x106 Cooling Time

Figure 16: Neutron emission as a function of the cooling time for a 17x17 PWR spent fuel assembly with initial enrichment of 2.5% and burnup of 60 GWd/tU.

6.1.3 Isotopic contribution In order to investigate the trend of the total neutron emission with the cooling time, we plotted the percentage contribution of single nuclides to the total neutron emission as a function of the cooling time for the burnup values considered in the previous paragraph. We can see that only few nuclides contribute to the total neutron emission, while other nuclides gain importance only at very high cooling time (when the total neutron emission is very low compared with the one at the discharge). In particular up to 100 years of cooling time the main contribution is due to the curium isotopes 242 and 244 that alone cover almost the 90% of the total. Then after their decay (half-life of 162.8 days and 18.1 years respectively), the dominant role on the neutron emission is taken by the plutonium isotopes. Between 30 and 3000 years (with a peak around 100 years) there is a strong contribution from 241Am (due to the decay of 241Pu, half-life of 14.4 years). This contribution, very relevant at low burnup (i.e. 5, 10 and 15 GWd/tu) explains the trend of the Figure 14. Increasing the burnup the contribution of the curium isotopes became more and more important. As we can see in 244 Figure 18, with a burnup of 35 GWd/tu the contribution of Cm reaches the 98-99% of the total. Moreover the contribution of two other isotopes, 246Cm and 248Cm, absent at low burnup, increases with the increase of the burnup.

Isotopic Contribution (IE: 2.5% BU: 10 Gwd/tU) 100

80 u238 cm242 cm242 pu240 cm244 pu242 cm246 60 cm248 cm244 u238 pu238 40 pu239 am241 pu240

Fraction of the total the of Fraction pu241 20 pu242 others am241 others 0 10-2 10-1 100 101 102 103 104 105 106 Cooling time

Figure 17: Contribution of the single isotopes to the total neutron emission as a function of the cooling time for a 17x17 PWR fuel assembly with initial enrichment of 2.5% and burnup of 10 GWd/tU. The considered isotopes are indicated.

Isotopic Contribution (IE: 2.5% BU: 35 Gwd/tU) 100

pu242 80 cm242 cm244 cm244 cm246 60 cm248 u238 pu238 pu240 40 pu239 cm242 pu240

Fraction of the total the of Fraction pu241 20 pu242 u238 am241 am241 others 0 10-2 10-1 100 101 102 103 104 105 106 Cooling time

Figure 18: Contribution of the single isotopes to the total neutron emission as a function of the cooling time for a 17x17 PWR fuel assembly with initial enrichment of 2.5% and burnup of 10 GWd/tU. The considered isotopes are indicated.

Isotopic Contribution (IE: 2.5% BU: 60 Gwd/tU) 100

cm244 cm246 pu242 80 cm242 cm244 cm246 60 cm248 u238 pu238 40 pu239 pu240

Fraction of the total the of Fraction pu241 20 pu242 cm242 am241 am241 others 0 10-2 10-1 100 101 102 103 104 105 106 Cooling time

Figure 19: Contribution of the single isotopes to the total neutron emission as a function of the cooling time for a 17x17 PWR fuel assembly with initial enrichment of 2.5% and burnup of 10 GWd/tU. The considered isotopes are indicated.

6.1.4 Influence of the initial enrichment to the total neutron emission

As next step in the analysis we considered the ratio between the neutron emission due to two different initial enrichments as a function of the cooling time and of the burnup. The ratios have been made between the initial enrichments values considered in this work (2.0%, 2.5% and 3.0%) and the initial enrichment 4.5% that has been studied by Rossa et al. {1, 2}. We did this in order to make the two works comparable. In Figures 20, 21 and 22 three different cooling times have been chosen: 30 days, 10 years and 1000 years. In Figures 23, 24 and 25 we considered three different burnup: 10, 35 and

60 GWd/tu. The graphs show that the neutron emission increases as the initial enrichment decreases, with a peak that moves from low to high burnup values with the increase of the cooling time. By comparing the variation of the neutron emission due to the initial enrichment with the one due to the variation of the cooling time and of the burnup, is evident that the IE has less influence on the neutron emission than the two other variables.

Comparison of the NE with different IE ( CT: 30 days) 5.0

4.5 2.0/4.5 2.5/4.5 4.0 3.0/4.5 3.5

3.0

2.5

2.0

1.5

Ratio beetwen different IE different beetwen Ratio 1.0

0.5

0.0 10 20 30 40 50 60 70 Burnup (GWd/tU)

Figure 20: Ratio of the total neutron emission for different enrichment as a function of the burnup with cooling time of 30 days.

Comparison of the NE with different IE ( CT: 10 years) 6.0 5.5 2.0/4.5 5.0 2.5/4.5 3.0/4.5 4.5 4.0 3.5 3.0 2.5 2.0

1.5 Ratio between different IE different between Ratio 1.0 0.5 0.0 10 20 30 40 50 60 70 Burnup (GWd/tU)

Figure 21: Ratio of the total neutron emission for different enrichment as a function of the burnup with cooling time of 10 years.

Comparison of the NE with different IE ( CT: 1000 years) 5.0

4.5 2.0/4.5 2.5/4.5 4.0 3.0/4.5 3.5

3.0

2.5

2.0

1.5

Ratio between different IE different between Ratio 1.0

0.5

0.0 10 20 30 40 50 60 70 Burnup (GWd/tU)

Figure 22: Ratio of the total neutron emission for different enrichment as a function of the burnup with cooling time of 1000 years.

Comparison of the NE with different IE ( BU: 10 GWd/tU) 6.0

5.5 2.0/4.5 5.0 2.5/4.5 4.5 3.0/4.5 4.0 3.5 3.0 2.5 2.0

1.5 Ratio between different IE different between Ratio 1.0 0.5 0.0 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (Years)

Figure 23: Ratio of the total neutron emission for different enrichment as a function of the cooling time with burnup of 10 GWd/tU.

Comparison of the NE with different IE BU: 35 GWd/tU) 5.0

4.5 2.0/4.5 4.0 2.5/4.5 3.0/4.5 3.5

3.0

2.5

2.0

1.5

Ratio between different IE different between Ratio 1.0

0.5

0.0 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (Years)

Figure 24: Ratio of the total neutron emission for different enrichment as a function of the cooling time with burnup of 35 GWd/tU.

Comparison of the NE with different IE ( BU: 60 GWd/tU) 6.0

5.5 2.0/4.5 5.0 2.5/4.5 4.5 3.0/4.5 4.0 3.5 3.0 2.5 2.0

1.5 Ratio between different IE different between Ratio 1.0 0.5 0.0 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (Years)

Figure 25: Ratio of the total neutron emission for different enrichment as a function of the cooling time with burnup of 60 GWd/tU.

In order to investigate the origin of the peaks observed in Figures 20, 21 and 22 we focused on ratio 2.5%/4.5%. Figure 26 shows this ratio as a function both of cooling time and burnup. In Figure 27 four curves taken from Figure 26 are reported, and the movement of the peaks to long cooling times for high burnup is clearly visible. The shape of these curves is further explained in Figures 28, 29 and 30. In each picture the ratio between the single isotope contribution with the IE 2.5% and the total neutron emission with IE of 4.5% is plotted against the cooling time. The peaks shown in Figure 27 are clearly linked with the neutron 244 246 emission of the Cm for the burnup of 10 GWd/tu and with the one of Cm in the case of

70 GWd/tu.

Figure 26: Ratio between the total neutron emissions of two 17x17 PWR assemblies. The ratio is plotted as a function both of cooling time and burnup.

Comparison of the total neutron emission with different IE 3.5 BU 5 BU 10 3.0 BU 35 BU 70

2.5

2.0 ratio 2.5/4.5 ratio

1.5

1.0

10-2 10-1 100 101 102 103 104 105 106 Cooling Time

Figure 27: Ratio between the total neutron emission of two 17x17 PWR assemblies, one with initial enrichment of 2.5% and the other with initial enrichment of 4.5%. The ratio is plotted as a function of the cooling time, for 4 different values of burnup.

Comparison of the total neutron emission with different IE ( BU: 5 GWd/tU)

Total 2 cm242 Total cm244 cm246 cm248 u238 cm242 pu238 pu240 1 pu239

Ratio 2.5%/4.5% Ratio u238 pu240

am241 pu241 pu242 am241

0 10-2 10-1 100 101 102 103 104 105 106 Cooling Time

Figure 28: Total neutron emission with different initial enrichment- role of selected isotopes (BU: 5 GWd/tU).

Comparison of the total neutron emission with different IE ( BU: 10 GWd/tU) 3

Total cm242 cm244 cm242 2 cm246 cm248 Total u238 cm244 pu238 pu240 pu242 pu239 1

Ratio 2.5%/4.5% Ratio pu240 pu241 pu242 am241

0 10-2 10-1 100 101 102 103 104 105 106 Cooling Time

Figure 29: Total neutron emission with different initial enrichment- role of selected isotopes (BU: 10 GWd/tU).

Comparison of the total neutron emission with different IE ( BU: 35 GWd/tU)

total

3 cm244 Total cm242 cm244 cm246 cm248 2 u238 pu242 pu238 pu239

pu240 Ratio 2.5%/4.5% Ratio 1 cm242 pu241 pu242 am241

0 10-2 10-1 100 101 102 103 104 105 106 Cooling Time

Figure 30: Total neutron emission with different initial enrichment- role of selected isotopes (BU: 35 GWd/tU).

Comparison of the total neutron emission with different IE ( BU: 70 GWd/tU) 3

Total Total cm246 cm242 cm244 2 cm246 cm248 cm244 u238 pu238 pu242 pu239 1

Ratio 2.5%/4.5% Ratio pu240 cm248 pu241 pu242 am241

0 10-2 10-1 100 101 102 103 104 105 106 Cooling Time

Figure 31: Total neutron emission with different initial enrichment- role of selected isotopes (BU: 70 GWd/tU). At the end of this section a comparison between the neutron emission due to single isotopes for different initial enrichments (2.5 and 4.5 %) has been made. In Figure 31 we can see the 244 ratio in case of Cm: it is very high at low burnup (5 and 10 GWd/tU) and then decreases

60 with the burnup. The same trend is found for the other isotopes as shown in the Annex D where the ratios for the other isotopes are reported.

Comparison of the 244Cm NE with different IE 7.0

6.5

6.0

5.5

5.0 BU 5 4.5 BU 10 4.0 BU 35 BU 70 3.5

3.0 Ratio NE IE 2.5%/4.5% IE NE Ratio 2.5

2.0

1.5 10-2 10-1 100 101 102 103 104 Cooling Time

Figure 32: Ratio between the total neutron emission of the isotope 244Cm for different initial enrichment. The ratio is plotted as a function of the cooling time for selected burnup values.

6.2 MOX simulations:

6.2.1 Neutron emission as a function of the burnup

As shown in Figures 33, 34 and 35, the total neutron emission of a 17x17 PWR MOX spent fuel assembly increases with increasing of the burnup for every cooling time. Moreover the main contribution to the total neutron emission is due to the spontaneous fissions (SF) that are almost always one order of magnitude greater than the contribution of the (α,n) reactions. The influence of the cooling time on the two contributions will be evaluated in the next section.

Neutron Emission ( Pu/HM: 8% CT: 30 days ) 1011

1010

109

10 Total Neutron Emission (n/s/tU) Emission Neutron alpha, n SF

107 5 10 15 20 25 30 35 40 45 50 55 60 Burnup (GWd/tU)

Figure 33: Neutron emission as a function of the burnup for a 17x17 PWR MOX spent fuel assembly with an initial content of plutonium of 8% and cooling time of 30 days.

Neutron Emission ( Pu/HM: 8% CT: 10 years ) 1011 Total alpha, n SF 1010

109

108 Neutron Emission (n/s/tU) Emission Neutron

107 5 10 15 20 25 30 35 40 45 50 55 60 Burnup (GWd/tU)

Figure 34: Neutron emission as a function of the burnup for a 17x17 PWR MOX spent fuel assembly with an initial content of plutonium of 8% and cooling time of 10 years.

Neutron Emission ( Pu/HM: 8% CT: 1000 years ) 109

108

107

Total Neutron Emission (n/s/tU) Emission Neutron alpha, n SF

106 5 10 15 20 25 30 35 40 45 50 55 60 Burnup (GWd/tU)

Figure 35: Neutron emission as a function of the burnup for a 17x17 PWR MOX spent fuel assembly with an initial content of plutonium of 8% and cooling time of 1000 years.

6.2.2 Neutron emission as a function of the cooling time

In figures 36, 37 and 38 the total neutron emission has been plotted as a function of the cooling time for three different burnup values (10, 35 and 60 GWd/tU). As we can see the neutron emission decreases with the cooling time, for every burnup value. The figures report also the contribution to the total neutron emission of spontaneous fissions and (α,n) reactions. In general the main contribution is due to spontaneous fissions but for low burnup levels (5, 10 and 15 GWd/tU) and for a cooling time around 100 years the two contributions become similar. Also for higher burnup there is an increase in the (α,n) reactions but its relevance is less than in the previous cases. The trend of the neutron emission with the cooling time and the origin of the increase of the (α,n) reactions are analyzed in the next section.

Neutron Emission ( Pu/HM: 8% BU: 10 GWd/tU) 1010 Total 109 alpha, n SF

108

107

106 Neutron Emission (n/s/tU) Emission Neutron 105

104 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (years)

Figure 36: Neutron emission as a function of the cooling time for a 17x17 PWR MOX spent fuel assembly with an initial content of plutonium of 8% and burnup of 10 GWd/tU.

Neutron Emission ( Pu/HM: 8% BU: 35 GWd/tU) 1012

1011 Total alpha, n 1010 SF

109

108

107

106 Neutron Emission (n/s/tU) Emission Neutron

105

104 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (years)

Figure 37: Neutron emission as a function of the cooling time for a 17x17 PWR MOX spent fuel assembly with an initial content of plutonium of 8% and burnup of 35 GWd/tU.

Neutron Emission ( Pu/HM: 8% BU: 60 GWd/tU) 1012

1011 Total alpha, n 1010 SF

109

108

107

106 Neutron Emission (n/s/tU) Emission Neutron

105

104 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (years)

Figure 38: Neutron emission as a function of the cooling time for a 17x17 PWR MOX spent fuel assembly with initial content of plutonium of 8% and burnup of 60 GWd/tU.

6.2.3 Isotopic contribution

Figures 39, 40 and 41 aim at clarifying the trend of the neutron emission seen before by plotting the contribution of single nuclides against the cooling time for the three burnup values considered in the previous section. In particular the increase of the (α,n) reactions observed in Figure 36 could be explained looking at Figure 39: around 100 years there is an increase of the neutron emission of the 241Am (α-emitter build up by the decay of the 241Pu). The plots show that up to 100 years the main contribution to the neutron emission is due to the 242Cm and, in particular, to the 244Cm (with importance increasing with the burnup). Then, for low burnup levels, the main role is taken by the plutonium isotopes 240 and 242. With the increase of the burnup, Figures 40 and 41, 246Cm gains significant importance between 100 and 10000 years of cooling time.

Isotopic contribution (Pu/HM: 8% BU: 10 GWd/tU) 1.0 pu242

0.8 cm244 cm242 cm244 cm246 pu240 0.6 cm248 u238 pu238 pu239 0.4 pu240 pu241 cm242 pu242 Fraction of the total the of Fraction am241 0.2 others

0.0 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (years)

Figure 39: Contribution of the single isotopes to the total neutron emission as a function of the cooling time for a 17x17 PWR MOX fuel assembly with initial content of plutonium of 8% and burnup of 10 GWd/tU. The considered isotopes are indicated.

Isotopic contribution (Pu/HM: 8% BU: 35 GWd/tU) 1.0

pu242 cm244 0.8 cm242 cm244 cm246 0.6 cm248 u238 pu238 pu239 cm246 0.4 pu240 pu241

pu242 Fraction of the total the of Fraction cm242 pu240 am241 0.2 others

0.0 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (years)

Isotopic contribution (Pu/HM: 8% BU: 60 GWd/tU) 1.0 pu242 cm244 cm246 0.8 cm242 cm244 cm246 0.6 cm248 u238 pu238 pu239 0.4 pu240 pu241 pu242 Fraction of the total the of Fraction am241 cm242 0.2 others cm248

0.0 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (years)

Figure 41: Contribution of the single isotopes to the total neutron emission as a function of the cooling time for a 17x17 PWR MOX fuel assembly with initial content of plutonium of 8% and burnup of 60 GWd/tU. The considered isotopes are indicated.

6.2.4 Influence of the plutonium content on the total neutron emission

The dependence of the total neutron emission from the plutonium content varies widely with the cooling time and the burnup. Figure 42 reports the ratio between the total neutron emissions of two 17x17 PWR MOX fuel assemblies with a different content of Pu as a function of the cooling time for a burnup of 5

GWd/tu. The plot shows that by increasing/decreasing the plutonium content there is a relative increase/decrease of the total neutron emission for every cooling time with an increase from 100 years.

In figure 43, in which the same ratio is plotted for a burnup value of 10 GWd/tU, the increase of the plutonium content causes a decrease of the neutron emission around 10 years of cooling time.

In figure 44, with 35 GWd/tU, around 1000 years there is an inverse proportionality between the plutonium content and the neutron emission and the fuel with 4% of plutonium becomes the main emitter. Looking at Figure 40 it is clear that this trend depends on the higher concentration of the 246Cm in the configuration with 4% of plutonium.

With a burnup value of 60 GWd/tU the same increment around 1000 years is more evident, and also the neutron emission due to the fuel configuration with 6% of plutonium overcomes the neutron emission of the 8% configuration.

Comparison of NE with different %PU (BU 5 GWd/tU) 1.8

10/8 1.6 6/8 4/8 1.4 10/8 1.2

1.0

0.8 6/8

0.6

Ratio between different % Pu/HM % different between Ratio 4/8

0.4 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (Years)

Figure 42: Ratio of the total neutron emission for different Pu content as a function of the cooling time for a 17x17 PWR MOX fuel assembly with burnup of 5 GWd/tU.

Comparison of NE with different %PU (BU 10 GWd/tU) 1.8

1.6 10/8 6/8 4/8 1.4 10/8 1.2

1.0

0.8 6/8

0.6

Ratio between different % Pu/HM % different between Ratio 4/8

0.4 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (Years)

Figure 43: Ratio of the total neutron emission for different Pu content as a function of the cooling time for a 17x17 PWR MOX fuel assembly with burnup of 10 GWd/tU.

Comparison of NE with different %PU (BU 35 GWd/tU) 1.8

1.6 10/8 6/8 4/8 1.4

10/8 1.2 4/8

1.0

6/8 0.8

0.6 Ratio between different % Pu/HM % different between Ratio

0.4 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (Years)

Figure 44: Ratio of the total neutron emission for different Pu content as a function of the cooling time for a 17x17 PWR MOX fuel assembly with burnup of 35 GWd/tU.

Comparison of NE with different %PU (BU 60 GWd/tU) 1.8

4/8 1.6 10/8 6/8 4/8 1.4

6/8 1.2

1.0 10/8 0.8

0.6 Ratio between different % Pu/HM % different between Ratio

0.4 10-2 10-1 100 101 102 103 104 105 106 Cooling Time (Years)

Figure 45: Ratio of the total neutron emission for different Pu content as a function of the cooling time for a 17x17 PWR MOX fuel assembly with burnup of 60 GWd/tU.

In Figures 46, 47 and 48 the same ratio of the previous pictures is plotted against the burnup for three different cooling times. In general there is a relative increase of the total neutron emission with burnup that is proportional to the reduction of the plutonium content. For high cooling times (Figure 48), the configuration with the higher plutonium content (10 %) is the main neutron emitter for every burnup value because, according to Figures 39, 40, and 41, the plutonium isotopes are the main contributors to the neutron emission for those cooling times. In order to better understand the trends shown in the previous plots, in the next section the isotope concentrations at the discharge for different plutonium contents are analyzed.

Comparison of the NE with different % Pu (CT: 30 days ) 1.10

1.05

10/8 1.00

6/8 0.95 4/8

0.90 10/8

Ratio between different % Pu/HM % different between Ratio 6/8 4/8 0.85 5 10 15 20 25 30 35 40 45 50 55 60 Burnup (GWd/tU)

Figure 46: Ratio of the total neutron emission for different Pu content as a function of the burnup for a 17x17 PWR MOX fuel assembly with cooling time of 30 days.

Comparison of the NE with different % Pu (CT: 10 years ) 1.10

1.05 4/8

6/8 1.00

10/8

0.95

0.90 10/8

Ratio between different % Pu/HM % different between Ratio 6/8 4/8 0.85 5 10 15 20 25 30 35 40 45 50 55 60 Burnup (GWd/tU)

Figure 47: Ratio of the total neutron emission for different Pu content as a function of the burnup for a 17x17 PWR MOX fuel assembly with cooling time of 10 years.

Comparison of the NE with different % Pu (CT: 1000000 years ) 1.40 1.35 1.30 1.25 10/8 1.20 1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 6/8 0.75 0.70 0.65 4/8 0.60 10/8 0.55

Ratio between different % Pu/HM % different between Ratio 6/8 0.50 0.45 4/8 0.40 5 10 15 20 25 30 35 40 45 50 55 60 Burnup (GWd/tU)

Figure 48: Ratio of the total neutron emission for different Pu content as a function of the burnup for a 17x17 PWR MOX fuel assembly with cooling time of 106 years.

6.2.5 Isotope concentration at the discharge

The decrease in the plutonium content, and therefore also of the fissile isotopes 239Pu and 241Pu, implies an increase of the neutron flux in order to achieve the same burnup level. This trend is shown in Figure 49.

The increase of the neutron flux causes a variation in the isotopes concentration at the discharge because promotes (n,γ) captures that results in a major production of 244Cm and 246Cm to the detriment of the 242Cm. The influence of the neutron flux on the isotopes production increases with the increase of the burnup. The trends shown in Figures 50, 51 and 52, clarify that for low burnup, i.e. 5 and

10 GWd/tU, the variation of the plutonium content doesn’t influence the production of the curium isotopes. 242 Increasing the burnup (35 GWd/tU) the concentration of the Cm decrease with the decrease of the plutonium content, while the production of the 246Cm is tripled passing from 10% to 4% of plutonium. The 244Cm undergoes a small increment. 242 With a burnup of 60 GWd/tU these effects are more evident: the Cm concentration is 246 halved, while the Cm concentration increases from 15 to 36 grams/tHM.

2.5x1013

2.0x1013

/s) 2

1.5x1013

1.0x1013

Neutron Flux (n/m Flux Neutron %P: 10 %Pu: 8 5.0x1012 %Pu: 6 %Pu:4

0.0 0 20 40 60 80 100 120 Irradiation Time (days)

Figure 49: Trend of the neutron flux during the irradiation time for different Pu content with a burnup of 5 GWd/tU.

242Cm concentration at the discharge with different BU 200

180 )

HM 160 BU 60

140

120 BU 5 BU 35 BU 10 100 BU 35 BU 60 80

IsotopicConcentration (grams/t BU 10 20 BU 5 0 10 8 6 4 % Pu/HM

Figure 50: Concentration of 242Cm at the discharge as a function of the Pu content for different burnup values.

244Cm concentration at the discharge with different BU 1800

BU 60

1600

) HM 1400

1200 BU 5 BU 10 1000 BU 35 BU 60 800 BU 35

600

400

IsotopicConcentration (grams/t 200 BU 10 BU 5 0 10 8 6 4 % Pu/HM

Figure 51: Concentration of 244Cm at the discharge as a function of the Pu content for different burnup values.

246Cm concentration at the discharge with different BU 38 36 34

) 32 HM 30 28 26 BU 60 24 22 BU 5 BU 10 20 BU 35 18 BU 60 16 14 12 10 8 6

IsotopicConcentration (grams/t BU 35 4 2 BU 10 0 10 8 6 4 % Pu/HM

Figure 52: Concentration of 246Cm at the discharge as a function of the Pu content for different burnup values.

6.3 Comparison between MOX and LEU fuel assemblies:

In this section a comparison between the neutron emissions of two different fuel compositions has been made. The two fuel compositions are: a MOX fuel with 6% of plutonium and LEU fuel with initial enrichment of 4%. We chose these two compositions because they have almost the same fissile content (38.5 and 40 kg respectively).

6.3.1 Neutron emission as a function of the burnup

First we compared the neutron emission as a function of the burnup, considering three different cooling times (the same chosen for the previous analysis). As we can see, the neutron emission with the MOX fuel composition is always higher than the one of the LEU fuel and the difference increases with the burnup. This fact will be investigated in the next section.

NE for different fuel compositions (CT: 30 days) 1011

1010

109

108

107

106 Neutron Emissions (n/s/tU) Emissions Neutron 5 10 LEU MOX 104 5 10 15 20 25 30 35 40 45 50 55 60 Burnup (GWd/tU)

Figure 53: Comparison between the total NE as a function of the burnup between two different 17x17 PWR fuel assemblies with cooling time of 30 days. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%.

NE for different fuel compositions (CT: 10 years) 1011

1010

109

108

107

Neutron Emissions (n/s/tU) Emissions Neutron 106 LEU MOX 105 5 10 15 20 25 30 35 40 45 50 55 60 Burnup (GWd/tU)

Figure 54: Comparison between the total NE as a function of the burnup between two different 17x17 PWR fuel assemblies with cooling time of 10 years. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%.

NE for different fuel compositions (CT: 1000 years) 109

108

107

106

Neutron Emissions (n/s/tU) Emissions Neutron 10 LEU MOX 104 5 10 15 20 25 30 35 40 45 50 55 60 Burnup (GWd/tU)

Figure 55: Comparison between the total NE as a function of the burnup between two different 17x17 PWR fuel assemblies with cooling time of 1000 years. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%.

6.3.2 Isotopic contribution for different fuel compositions

In order to investigate the differences between the two neutron emissions, the single isotopic contributions have been analyzed. We plotted in Figures 56, 57, 58, 59, 60 and 61 the isotopic contributions to the total neutron emission as a function of the cooling time for three different burnup (10, 35 and 60 GWd/tU). The contribution of the 242Cm is always higher in case of LEU fuel than in the MOX one. On the contrary the curium isotopes 244 and 246 have more importance in the case of MOX fuel. The differences decrease with increasing burnup. Considering the plutonium isotopes, the 240 contribution is more significant for the LEU composition while, on the contrary, the 242 has a greater influence in the case of MOX fuel. Again the different contributes are almost equal at high burnup.

Isotope contribution for different fuel compositions (BU: 10 GWd/tU) 1.0 Cm242 LEU 244 Cm Cm242 MOX Cm244 LEU 0.8 Cm244 MOX Cm246 LEU Cm246 MOX

0.6 242 Cm

0.4 Isotope Contribution Isotope 0.2

246 Cm 0.0 10-2 10-1 100 101 102 103 104 105 106 Cooling Time

Figure 56: Comparison between the single isotopes contribution to the total NE as a function of the cooling time between two different 17x17 PWR fuel assemblies with burnup of 10 GWd/tU. The compositions are: (i) MOX fuel with %Pu=6.0% (ii) LEU fuel with IE=4.0%.

Isotope contribution for different fuel compositions (BU: 10 GWd/tU) 1.0 U238 LEU U238 MOX 242 Pu240 LEU Pu 0.8 Pu240 MOX Pu242 LEU Pu242 MOX

0.6

0.4 240 Pu 238

U Isotope Contribution Isotope 0.2