Evaluated Material Attractiveness of Plutonium Composition from Economic Simplified Boiling Water Reactor (ESBWR)

The potential for misuse of nuclear fuel has prompted many to make efforts to prevent a country from acquiring nuclear explosive devices (weapons). Weapon utility equated with nuclear material attractiveness when applied to protection and security. Material attractiveness evaluated using an equation first developed by Masaki Saito, namely ATTR. ESBWR is one of the reactors of the BWR reactor type that is still operating. The purpose of this study is to evaluate Material Attractiveness based on the composition of plutonium in the ESBWR reactor, during reactor operation and after reactor operation. The ATTR concept utilizes the plutonium isotope composition to evaluate the material attractiveness aspect. Parameters such as BCM, Rossi-alpha, and neutron prompt life become additional aspects in evaluating material attractiveness. In the research results, the ATTR value decreased from the beginning of reactor operation until the reactor stopped operating. At the beginning of the reactor operation, it was categorizing as a weapon-grade with an ATTR value of 0.19 and when the reactor stopped operating it was categorizing as an unusable grade with an ATTR value of 0.012. At the time of cooling time up to 1x106 (one million) cooling time, the ATTR value increases by 0.019 which was categorizing as an unusable grade. After a cooling time of 1x106 (one million) years up to 1x107 (ten million) years, the ATTR value was 0.001 which categorized as an exempt level. This states that the increasing burnup value will further reduce the ATTR value. Likewise with the Rossi-Alpha and Bare Critical Mass values. Conversely, it will decrease the value of neutron lifetime. The ATTR value after the reactor operates up to one hundred years of cooling time increases and then decreases significantly after 1x106 (one million) years due to the half-life of plutonium isotopes. Likewise, the Rossi-Alpha and Bare critical mass values. However, it is different with the neutron fast lifetime.


Introduction
The Economic Simplified Boiling Water Reactor (ESBWR) is at the forefront of advanced nuclear technology, representing a significant leap forward in the field of nuclear energy production.The ESBWR is a generation III+ boiling water reactor design developed by General Electric Hitachi.This innovative reactor design prioritizes safety, efficiency, and sustainability, making it a promising candidate for future nuclear power projects around the world [1].One of the key features of the ESBWR is its inherent safety mechanism.Unlike traditional nuclear reactors, ESBWRs rely on natural circulation, allowing the reactor to cool down passively in emergencies without external power or human intervention.This passive safety feature significantly reduces the risk of accidents and ensures reactor stability even under challenging conditions [1].
The future of nuclear technology lies in a careful balance between harnessing its vast potential for energy production and upholding strict non-proliferation measures.Emerging technologies, such as small modular reactors (SMRs) and advanced fuel cycles, offer promising avenues for sustainable energy production while minimizing the risks of nuclear proliferation.These innovations will be designing with inherent safety features and standardized designs, ensuring that nuclear power could harnessed for the betterment of society without compromising global security.In summary, ESBWRs represent a significant advance in nuclear reactor technology, offering a safer and more efficient approach to energy production.When coupled with strict non-proliferation measures, these advancements pave the way toward a future where nuclear energy could utilized responsibly, contributing to a sustainable and low-carbon energy landscape for generations to come [1].
In addition, the ESBWR incorporates advanced technologies such as the use of ceramic fuel pellets and a simplified control system, thereby optimizing its performance and efficiency.By maximizing fuel utilization and minimizing waste generation, the ESBWR contributes to a more sustainable and environmentally friendly approach to nuclear energy production.In the global landscape of nuclear technology, non-proliferation plays a key role in ensuring the responsible use and deployment of nuclear capabilities.Non-proliferation refers to the prevention of the spread of nuclear weapons and the promotion of peaceful applications of nuclear energy.International efforts, including treaties and agreements, have been making to curb the proliferation of nuclear weapons, foster international cooperation, and nuclear disarmament [2].
The concept of material attractiveness was defining as a measure of the desirability of fuel for nuclear weapons use and can also use to establish criteria for how well nuclear fuel needs to protect from theft [3][4][5].The concept of material attraction used to evaluate the level of proliferation resistance of nuclear fuel.It has progressively developed and still used to anticipate the use of nuclear fuel for explosive devices by countries, sub-nations, or groups.The criteria's level of proliferation resistance can adopt to estimate the proliferation rate of nuclear fuel composition, especially plutonium as an interesting ingredient of recycled spent fuel.For the case of plutonium, a plutonium isotope barrier based on the properties of materials with even mass numbers (Pu-238, Pu-240, and Pu-242) that include the rates of hot decay (DH) and spontaneous neutron fission (SFN), can be used to assess the intrinsic proliferation resistance [4].The concepts for evaluating material attractiveness based on scientific approaches progressively have been developing based on plutonium isotope composition.Saito has proposed the concept of material attractiveness (ATTR), although the concept of FOM function previously has been developing [6][7][8].However, this paper will focus on the application of the ATTR concept, and the reactor will have also selected for comparative evaluation of each operating reactor.Masaki Saito developed the ATTR formula [8][9] in evaluating the material attractiveness of fuel, the utilization of plutonium composition provides information that the presence of plutonium is significant in the manufacture of nuclear weapons because plutonium is a substance with properties that vary depending on the source.

Parameters and Methodology Research
The behaviour of plutonium isotopes was analysing as the main parameter during the irradiation process and after irradiation.The burnup process was conducting until it reached a value of 33 GWd/t.During the irradiation process, the effect of the fuel irradiation level on the behaviour of the fuel in the reactor core was showing.After the reactor operation stopped, the fuel removed from the reactor and evaluated for a cooling time of up to one million years.The analysis of plutonium isotope behaviour under both conditions has been analysing using the ORIGEN code for a typical LWR type [10,11].The parameters bare critical mass, neutron prompt life, and Rossi-Alpha as a material barrier refer to the technology of a nuclear fuel that can designed to prevent the misuse of nuclear technology.The material barrier evaluate the attractiveness of nuclear materials in the ESBWR reactor [12,13].The ESBWR reactor assembly design that has been developed by GE-Hitachi is shown in Figure 1.The ESBWR fuel assembly consists of fuel bundles and channels.The fuel bundles have the fuel rods and the hardware necessary to support and keep proper spacing between the fuel rods.The channels are zircaloy boxes that surround the fuel bundles to direct core coolant flow through the bundles and serve to guide the movable control rods.The fuel design which uses the GNF GE14 design, has a 10x10 array of 78 full-length fuel rods, 14 section-length rods that span approximately two-thirds of the active core, and two large central water rods.The fuel rod design includes a fully retrieved and recrystallized Zircaloy-2 cladding tube, UO2 fuel pellets, a retaining spring assembly, and lower and upper-end plugs.The fuel rods are filled with UO2 or (U, Gd)O2 fuel pellets as needed for outage margin control and power shaping [1].

Reactor Design Parameters
The ESBWR reactor core has 1028 fuel assemblies, The rod array of a fuel assembly is 10x10 square, the thermal output of the reactor is 4500 MWth, and the fuel cycle is 24 months long.In the evaluation using ORIGEN, each assembly in the reactor core is considered homogeneous.The average power density of fuel in the ESBWR reactor is 27.3 KW/kg [1].

Plutonium Isotope Vector Composition
Plutonium is one of the most feared fissile materials in the proliferation issue, especially plutonium-239 (Pu-239) are nuclear materials that have special significance in the context of non-proliferation.The detection of plutonium isotopes in nuclear samples can provide clues about nuclear activities, the IAEA uses isotope analysis methods to monitor a country's compliance with non-proliferation agreements.As one of the important approaches for the analysis of plutonium proliferation barriers, the evaluation of plutonium isotopes as vector composition (Vector composition writes down each composition of plutonium isotopes is a fraction of the total plutonium content (   ).The vector composition of plutonium isotopes is evaluated based on the following equation [14]: (1)

Analysis of material attractiveness based on ATTR concepts.
There have been various attempts to develop proliferation resistance evaluation methodologies, to ensure proliferation resistance.The concept of the evaluation function "Attractiveness (ATTR)" has been proposing by Saito, as a new function to evaluate one of the intrinsic features of proliferation resistance, the characteristics of fissile materials quantitatively based on their isotopic properties [15].The basic concept of ATTR is to assess the level of attractiveness of a material obtained from the comparison of the possibility of explosive energy from fissionable materials and technical difficulties derived from the difficulty of handling, fabrication, and others due to the serious difficulty of physical properties and the difficulty of fissionable materials [16].As has been done by Permana, S and Suzuki, M, evaluating material attractiveness based on isotopic plutonium barrier, using several parameters as analysis materials; decay heat (DH), spontaneous fission neutron (SFN), Rossi-Alpha, neutron prompt life, and bare critical mass (BCM) and the concept of material attractiveness (ATTR) for different dilute fractions of the even mass of Plutonium isotope composition to Pu-239.And the concept of the ATTR evaluation function defined by Saito is as the ratio of the potential explosive yield characteristics of fissile materials to the technical difficulty factor for proliferators to make and use nuclear explosive devices (NEDs) with these materials [8,15].The equations used areas follows [15]: This formula is related to the concept of significant quantity (SQ) to indicate the possibility of manufacturing a nuclear device based on the significant mass of fissionable material, the adopted SQ is 8 kg as the value has been publishing and adopted by the IAEA.MCNP-4C and Nuclear Data Library JENDL-3.3 adopted to evaluate the attractiveness of this material which is related to the Rossi-alpha evaluation.the Rossi-alpha, DH, and SFN values normalized to the attractiveness value of Pu-239 as the maximum attractiveness level.the index value is set to a unity that can be adjusted to reflect the uniqueness of the energy release in a particular configuration, for example when n is set to be equal to one (n=1), it can be used to characterize the energy released in a system without the effect of material density (Permana & Suzuki, 2011).Rossi-alpha used to measure the dynamic properties of atomic nuclei, one of the important characteristics in determining the potentially explosive energy strength of fissile materials and is the ratio of supercritical (  − 1) to neutron prompt lifetime ( 0 ).Rossi-alpha has been evaluating using the equation below [4,15]  ≡ Rossi-alpha measurements of fissionable assemblies used to estimate the prompt neutron decay constant, α, of a system, which can use to infer reactivity [17].Neutron prompt life itself refers to the time required by neutrons produced from a fission reaction to reach the next fissure of the fissile nucleus in a "prompt" manner after the nuclear fission reaction.If the neutron's prompt life is short in fissile material, it will indicate that the neutrons produced from nuclear fission will tend to be more active and have a higher neutron reproduction rate.This can make the material more feasible for the development of more efficient weapons.The total composition of DH and SFN (DHcomp and SFNcomp) is a material barrier adopted to increase the technical difficulty in the manufacture of nuclear technology (nuclear weapons) due to the high internal heating rate for melting and pre-initiation of high explosives.These total parameters as the main material barrier parameters evaluated and numbered with the DH 8 and SFN 8 compositions of pure Pu-238 isotopes, the pure DH and SFN values have been calculating by Kessler.Like the DH and SFN parameters, bare critical mass (BCM) has a key role in evaluating material attractiveness, where the minimum amount of fissile material required in a particular form for a sustainable fission reaction to occur independently.A mass of material that made to exceed the critical mass and fissions at an increasing rate is "supercritical" while masses insufficient to support a chain reaction termed "subcritical."If the reaction is uncontrolled, as is the case in an atomic bomb, the critical mass of fissionable material creates an explosion.If the reaction controlled, as in reactors, the critical mass could provide atomic power.In this research, BCM evaluated using the Monte Carlo method, MCNP-4C JENDL 3.3, where manually using the formula to calculate the BCM value is as follows [18][19][20].
The formula visualizes the time-independent radial distribution of the neutron density at the critical phase, assuming the neutron (n) is shaped like a sphere, the radius on the surface of the sphere can be expressed as R and the mass at the critical point is M. Plutonium density (ρ) refers to the mass of plutonium atoms contained in a certain volume.Plutonium has the most stable phase, the alpha phase, which is about 19.8 g/cc [18].There are four levels of material attractiveness for ATTR formulas as follows [21,22]: 1. ATTR>0.1:Weapon-grade level 2. 0.02<ATTR>0.1:Practically usable level 3. 0.002<ATTR<0.02:Practically unusable level 4. ATTR<0.002:Exempt The concept of ATTR with multiple levels of material attractiveness with different specifications can be categorized as the same material attractiveness perception as the weapon-grade level, which is expressed as a high level of attractiveness, a practically usable level similar to a medium level of attractiveness, and a practically unusable one similar to a low level of attractiveness [21][22][23][24].

Results and Discussion
In this section, the isotopic composition of plutonium when the reactor was operating and after the reactor decommissioned has been showing.The effect of irradiation time and decay drying time on the plutonium composition vector has been analyzing.Material Attractiveness values has been evaluating and supporting parameters such as BCM, Neutron Prompt Life, and Rossi-Alpha will be evaluating as material barriers based on plutonium isotopes.

Plutonium isotope vector composition
The plutonium isotope composition will be comparing between reactors and will also compare at the time of irradiation and after the reactor ceases operation.Reactor operation limited to a burnup of up to 33 GWd/t.The calculation results shown in Figure 2 illustrate the distribution of fuel plutonium isotope composition.Figure 2a shows the plutonium isotope composition results when the reactor is operating and Figure 2b when the reactor stops operating.The ESBWR reactor takes 1315 days to reach a burnup of 33 GWd/t.As the burnup increases, the plutonium isotope composition increases with consecutive values 1.21%, 24.92%, 12.84%, dan 4.33%, except Pu-239 which initially increases significantly but then decreases.While post-irradiation, the composition of plutonium Pu-238, Pu-239, Pu-240, Pu241, and Pu-242 affected by half-life so that only take 87.7 years (Pu-238) to run out and take 3.73 x 10 5 years (Pu-242).This is because when the reactor is operating, the highest composition of Pu-239 obtained from the transmutation process of U-238.when U-238 absorbs slow neutrons in a nuclear reactor then produces U-239, which has a relatively short half-life.then U-239 undergoes beta decay to Np-239, then will undergo beta decay to Pu-239.Pu-239 is one of the important isotopes for fission reactions in nuclear reactors and can also use as fuel in nuclear weapons.the increase in the amount of Pu-239 composition results from Cm-243 undergoing alpha decay.When the reactor stops operating, the fuel does not undergo fission reactions so both Pu-239 and other plutonium such as Pu-238, Pu-240, and Pu-241 decrease along with the half-life of each plutonium isotope.Unlike the case with Pu-242 which experienced an increase when the reactor had stopped operating.It can predict that when the reactor stops operating there is a possibility to capture neutrons without undergoing fission.If there are neutrons available, Pu-242 can capture neutrons and turn them into Pu-243 in the plutonium isotope mixture.

Analysis of material attractiveness based on the concept of attractiveness (ATTR)
The material attractiveness calculation considers the vector value of plutonium isotope composition and other material barriers such as bare critical mass, neutron prompt life, and Rossi-alpha.The material attractiveness (ATTR) value is shown in Figure 3a for the condition when the reactor is operating and (a) (b) Figure 3 ATTR.(a) when the reactor is operating (b) after the reactor deactivated Figure 3b for the condition after the reactor stops operating.Based on the categories that have been developed (Saito, 2008;2009), at the beginning of reactor operation the ATTR value is categorized as weapon-grade with an ATTR value of 0.19, this category lasts until burnup reaches 5 GWd/t or up to 183 days.Usable-grade nuclear fuel conditions occur when the reactor reaches a burnup of 5 GWd/t to 10 GWd/t.The unusable grade category occurs when the reactor reaches 15 GWd/t to 33 GWd/t.The resulting ATTR value is influenced by the value of the plutonium isotope composition produced, especially the composition of Pu-239.The ATTR concept utilizes the Pu-239 isotope in its evaluation, plutonium is the main material in nuclear weapons because it has properties that are considered likely to be able to fission fastly and strongly.When the reactor reaches a burnup value of 33 GWd/t, the reactor is then deactivated.The spent fuel is then evaluated for categorization based on the ATTR value.When the reactor is initially decommissioned until 110 5 years of cooling time, the spent fuel is categorized as unusable grade and thereafter until 110 7 cooling time is categorized as exempt.The ATTR value generated in nuclear fuel at the ESBWR reactor influenced by barrier materials such as Bare Critical Mass (BCM), Rossi-alpha, and neutron prompt life.The BCM value showed in Figure 4a when the reactor is operating and Figure 4b when the reactor stops operating up to 110 6 years of cooling time.The resulting BCM value increases both during reactor operation and when the reactor stops operating.This shows that the increasing BCM value indicates that the amount of material needed to produce weapons is also increasing [26].Figure 5 shows the neutron prompt life values for both conditions.The neutron prompt life value increases when the reactor is operating (Figure 5a).This result is one of the effects of decreasing ATTR values for reactor conditions during reactor operation.Figure 5b shows the value of neutron prompt life at the beginning of the reactor stops operating, the value of neutron prompt life has decreased, this result is in line with the ATTR value produced at the beginning of the reactor operation has increased and categorized as unusable.After one hundred years of cooling time, the neutron prompt life value has increased significantly, this result is in line with the ATTR value which has decreased significantly and categorized as exempt.Because neutron prompt life can affect the attractiveness of fissile materials, it allows sustained fission to react fastly and more efficiently used for the manufacture of more powerful nuclear weapons.A long neutron prompt life in fissile materials can provide more time to control fission reactions in nuclear reactors and allow better control of neutron production rates.This considered safer in the use of peaceful nuclear energy.Rossi-alpha value is inversely proportional to the neutron prompt life value shown in Figure 6.In mathematical equations, neutron prompt life has a value that is inversely proportional to Rossi-alpha ( ≡ 1  0 ).The decrease of Rossi-alpha indicates that the potential explosive energy strength of the fissile material at supercritical conditions decreases as the burnup and cooling time increase.This value influenced by the total isotopic composition of the plutonium produced.This value is in line with the ATTR value, decreasing with increasing burnup and categorized as unusable at the end of the cycle.At one hundred years the cooling time decreases, but after that, it increases significantly.

Conclusion
This research aims to evaluate non-proliferation aspects using the material attractiveness method (ATTR) on light-water based reactors, namely ESBWR.calculation of plutonium composition using the ORIGEN program and MCNP-4C, JENDL 3.3 used to calculate BCM and Neutron Prompt Life the results will be using to calculate the ATTR value.The composition of plutonium isotopes produced during irradiation and post-irradiation is different for the ESBWR reactor.The composition of plutonium isotopes Pu-238, Pu-240, Pu-241, and Pu-242 tends to increase, with consecutive values of 1.21%, 24.92%, 12.84%, and 4.33%.While Pu-239 decreased due to the fission process.Based on the isotope composition of Pu-240, when the reactor operates, burnup affects the increase in Pu-240 isotope composition, when the burnup of 1-2.5 GWd/t is at the super-grade level, 2.5-5 GWd/t Pu-240 weapongrade, 5-20 GWd/t Pu-240 switches conditions to the fuel-grade level, finally when the reactor reaches a burnup of 20-33 GWd/t Pu-240 becomes a reactor-grade level.This indicates that the greater the burnup effectively increases the value of Pu-240.The opposite condition when the reactor stops operating, the longer the cooling process will make Pu-240 at the super-grade level.While postirradiation, the composition of plutonium Pu-238, Pu-239, Pu-240, Pu241, and Pu-242 influenced by half-life so that only take 87.7 years (Pu-238) to run out and take 3.73 x 10 5 years (Pu-242).At the time of initial irradiation, the ATTR value for ESBWR was 0.19.The ATTR value included in the weapongrade category.Then at the end of operation the ATTR value decreased with the ESBWR ATTR value being 0.0125.The ATTR value at the end of reactor operation became categorized as un-usable grade.This shows that the attractiveness value (ATTR) decreases effectively when there is an increase in burnup from weapon-grade to un-usable grade at the end of operation.This influenced by the decline of Pu-239 as the main fissile material in the ATTR concept.In terms of ATTR analysis, these values of BCM and neutron prompt life affect the decrease in ATTR value except Rossi-alpha.The reactor stopped operating; the results showed opposite.But in contrast to neutron prompt life, it has a value inversely proportional to other barriers.

Figure 4
Bare Critical Mass (BCM) (a) when the reactor is operating (b) after the reactor deactivated.

Figure 5
Neutron Prompt Life Value (a) when the reactor is operating (b) after the reactor deactivated.

Figure 6
Rossi-Alpha Value (a) when the reactor is operating (b) after the reactor deactivated.