On the influence of the americium isotopic vector on the cooling time of minor actinides bearing blankets in fast reactors

. In the heterogeneous minor actinides transmutation approach, the nuclei to be transmuted are loaded in dedicated targets often located at the core periphery, so that long-lived heavy nuclides are turned into shorter-lived ﬁ ssion products by ﬁ ssion. To compensate for low ﬂ ux level at the core periphery, the minor actinides content in the targets is set relatively high (around 20 at.%), which has a negative impact on the reprocessing of the targets due to their important decay heat level. After a complete analysis of the main contributors to the heat load of the irradiated targets, it is shown here that the choice of the reprocessing order of the various feeds of americium from the fuel cycle depends on the actual limit for fuel reprocessing. If reprocessing of hot targets is possible, it is more interesting to reprocess ﬁ rst the americium feed with a high 243 Am content in order to limit the total cooling time of the targets, while if reprocessing of targets is limited by their decay heat, it is more interesting to wait for an increase in the 241 Am content before loading the americium in the core. An optimization of the reprocessing order appears to lead to a decrease of the total cooling time by 15 years compared to a situation where all the americium feeds are mixed together when two feeds from SFR are considered with a high reprocessing limit.


Introduction
Minor actinides are three heavy nuclides created in reactors core as by-products of the chain reaction by successive captures on uranium and plutonium isotopes. Several isotopes of these elements can be found in spent nuclear fuel, namely: -237 Np for neptunium, produced by captures on 235 U or (n,2n) reactions on 238 U -241 Am, 242m Am and 243 Am for americium, produced by captures on plutonium and decay of 241 Pu -242 Cm, 243 Cm, 244 Cm, 245 Cm, 246 Cm for curium, produced by captures on americium isotopes. -Higher isotopes of Berkelium and Californium are rarer but some of them, such as 252 Cf can be dimensioning to their very high neutron source. They are mostly produced in thermal reactors loaded with MOX fuel.
In the context of a closed fuel cycle where plutonium is multi-recycled in fast reactors [1], minor actinides become the main responsible for the long-term radiotoxicity of the nuclear waste [2]. Additionally, they are generating most of the decay heat of the waste packages, which is a dimensioning parameter of final deep geological reposito-ries [3]. However, it is possible to effectively remove the minor actinides from the waste by implementing minor actinides transmutation.
Transmutation is the process of submitting minor actinides to a neutron flux in order for them to undergo fission and then obtain shorter-lived fission products. A successful removal of all the minor actinides from the waste would reduce the long-term radiotoxicity of the spent fuel by two orders of magnitude while divide by two the volume to be excavated and save 33% in the total footprint of a deep geological repository taking into account all common infrastructures [4] Thermal reactors are not adapted to minor actinides transmutation due to unfavorable capture to fission ratio and the necessity of a closed fuel cycle associated with transmutation, as discussed in [5]. Consequently, this paper will focus on minor actinides transmutation in fast reactors, and more specifically, sodium fast reactors. Furthermore, since complete destruction of a significant mass of minor actinides in a single irradiation is currently not achievable due to material resistance constraints (see the prohibitively long residence time discussed in [6] for instance) multirecycling of the minor actinides will be considered here.
Two main approaches can then be highlighted for transmutation in fast reactors: -The homogeneous approach, in which minor actinides are mixed with the fuel and loaded at the core center. In this case, they are exposed to a high neutron flux, which increases the efficiency of the process. However, this leads to a hardening of the neutron spectrum of the core which has negative impacts on the core integral feedback coefficients [7]. Additionally, this leads to a "pollution" of the entirety of the fuel cycle plants, along with a lack of flexibility in the irradiation conditions of the minor actinides as these would depend on industrial constraints linked with fuel depletion. -The heterogeneous approach, in which minor actinides are loaded in dedicated targets, generally located at the core periphery. In this approach, the perturbation on the core neutron spectrum is very limited and no modifications of the feedbacks coefficients can be observed. However, as the targets are located in a low-flux zone, the transmutation process is less efficient than in the homogeneous case. To compensate for this, the residence time is generally increased along with the mass loaded in the blankets. However, this has a negative impact on the decay heat of the irradiated targets, which ultimately leads to prohibitively long cooling times.
This paper will focus on the heterogeneous approach to minor actinides transmutation and especially americium heterogeneous transmutation. Indeed, 237 Np has a half-life of 2.16 Â 10 6 years, making it relatively harmless while americium isotopes are shorter-lived, with a half life of 7370 years for 243 Am and 432 years for 241 Am, which are the main isotopes to be found in the waste. Curium is generally not considered in transmutation studies as its very high decay heat and neutron source highly complicates the manufacturing of curium-bearing fuels [8][9][10].
Irradiation of americium in radial blankets leads to the production of curium isotopes which have a very high neutron source and decay heat rate. Prior to reprocessing, the assemblies must be removed from the core, washed from the residual sodium and transported to a reprocessing plant. Due to technological limitations linked to the temperature of the assemblies and handling devices during all these operations, such assemblies requires longer cooling times to reach acceptable heat load before reprocessing can occur. This increases the total inventory of minor actinides in the fuel cycle (either in the core, in manufacturing or cooling down), while this inventory should be minimized in order to limit the movements of minor actinides in the fuel cycle. The dependency of the cooling time to the americium isotopic vector will be analyzed here and various strategies will be discussed to limit the cooling time of the minor actinides bearing blankets (MABB).
2 Position of the problem and methodology 2.1 Analysis of the problem Current industrial limitations considered regarding reprocessing of MABB can be divided into two categories [11]: -Short term handling of the assemblies for movement to external storage. Depending on the technology considered, various limitations can be taken. For a revolving drum similar to the Superphénix design, the assembly heat load can be arbitrarily high. However, if an external cask is used, a maximal decay heat can be fixed at 40 kW for sodium cooling cask and 30 kW for cask with cooling by forced gas convection. -Sodium washing of the assemblies before transportation to the reprocessing plant. After an initial cooling period in sodium, the assemblies must be drained of their sodium content and washed using various techniques (carbonation, sodium water reaction) to remove residual sodium before they can be stored under water in cooling pools. Industrial limitations on washing of the spent fuel assemblies depend on technological research, therefore a minimal and a maximal value of respectively 2.5 and 7.5 kW will be considered here, as done in [11].
In this study, a minimal cooling time of 5 years will be considered before sodium washing can occur and it will be supposed that reprocessing occurs directly after sodium washing has been performed. Five years of minimal cooling time is a standard hypothesis of the French scenarios studies, as it can be found in [12].
If we consider a reference MABB, loaded with U 0.8 Am 0.2 O 2 with 75% of 241 Am and 25% of 243 Am and irradiated for 4100 EFPD in a SFR-V2B reactor, as discussed in [13], it is possible to analyze the contribution to decay heat and neutron source after 5 years of cooling, as it is done in Table 1. The depletion calculations were carried out using the DARWIN code system [14]. Nearly 98% of the heat is produced through alpha-decay of heavy nuclides, with 244 Cm being the main heat emitter with close to 50% of the total power production, followed by 238 Pu and 241 Am. Concerning neutron source, spontaneous fissions of 244 Cm is responsible for 96% of the total neutron source of the spent fuel [14]. 242 Cm has a very weak contribution to decay heat after 5 years of cooling due to its short half-life.
Considering this, it is necessary to study the formation route of these nuclei, as it is done below in equation (1). It is thus possible to split the contribution to decay heat depending on the half-lives of the nuclei considered and their parent-nuclei. Thus, the long-term decay heat will be more dictated by 241 Am and 238 Pu, thus depending on the initial 241 Am content while neutron source and shorterterm decay heat will be depending on 244 Cm and thus on 243 Am initial content. 241 Am concentration will also play a role for the very-short term handling of the irradiated fuel, Going back to the reprocessing limits considered above, it can be observed that depending on the current reprocessing limit, the main contributor to the decay heat will not be same. Consequently, the cooling time of the assemblies will depend both on the americium isotopic vector loaded in the blankets and on the reprocessing limit, as shown in Figure 2. In this figure, the cooling time was plotted with regards to the fraction of 241 Am in the americium irradiated for various decay heat limit.
It is observed that the slope of the cooling time evolution changes of sign depending on the limit considered. For high decay limit, the cooling time decreases with the 241 Am fraction as the short-term decay heat depends on 244 Cm production. Consequently, the decay of 244 Cm only is sufficient to reach an acceptable decay heat, and any decrease in the 243 Am content will decrease the 244 Cm production. On the other hand, for low limits, the cooling time increase with the 241 Am fraction. Indeed, in this case, the decay of 244 Cm is not sufficient to achieve a final decay heat lower than the limit, and it is necessary to wait for 241 Am and 238 Pu decay to reach the limit, which requires a much longer time. Consequently, an increase in the 241 Am fraction will increase the cooling time for such cases.
Considering this, it is postulated here that depending on the industrial constraint for reprocessing and on the availability of various americium fluxes in the fuel cycle, an optimization can be carried out to minimize the cooling time of the irradiated targets at any given time.

Analysis of the available americium feeds
The americium isotopic vector present in the fuel depends on various parameters which are: -The initial fissile content of the fuel : an UOX fuel will generate more 241 Am than 243 Am compared to a MOX fuel. -The neutron spectrum: 243 Am production will be higher in a thermal spectrum than in a fast spectrum due to increased captures on 242 Pu. -The fuel burn up : a higher burnup will increase the production of 243 Am due to increased captures on 242 Pu. -The plutonium isotopic vector used in the fuel: a higher quality of the plutonium will limit the production of 243 Am, where the quality of the plutonium is defined by its content in "good" fissile elements, e.g. 239 Pu and 241 Pu. The plutonium isotopic vectors used in this study are given in Table 2. -The spent fuel cooling time before reprocessing: once reprocessing is carried out, the production of 241 Am from the decay of 241 Pu is stopped. A short cooling time will limit the amount of 241 Am produced and then increase the 243 Am content in the americium, while a longer cooling time will increase the content in 241 Am.
An analysis of the various isotopic vectors that can be obtained is shown below in Table 3. At unloading, the ratio of 241 Am to 243 Am is found to be between 78% and 51% depending on the core considered, while after 5 years of cooling, which is the minimal time of cooling generally considered, this ratio oscillates between 85 and 65%. Considering a 2 kW reprocessing limit in Figure 2, this amounts to a difference of 23 years in the cooling time,  which is not negligible. For a 2.5 kW limit, the difference is only of 2 years. If we consider a very long cooling time during which all the 241 Pu decays, the final ratio varies between 83 and 94%, still leading to a significant difference for low reprocessing limit.
We will consider here heterogeneous transmutation of americium for three cases, in which either the americium from various sources will be mixed or a specific strategy will be used depending on the isotopic vector. For each case, the impact of the decay heat limit will be analyzed. The radial blankets will be irradiated in a SFR V2B fast reactor with a design corresponding to [16] for 4100 EFPD in the form of The impact on short term decay heat and neutron source will also be analyzed in these calculations. For each case, the total inventory in the fuel cycle will be analyzed by considering the mass unloaded at the end of irradiation, its cooling time, and the mass not transmuted. 2413 kg of americium can be loaded in the blankets for the configuration considered. The americium isotopic vector will be characterized by its 241 Am content over the total americium, the remaining fraction being 243 Am.

Case 1: PWR UOX and MOX
In this case, the americium vector between both cases is relatively similar as it is mainly dependent on the neutron spectrum in thermal reactors, with the use of MOX fuel simply increasing the total production of americium. Consequently, no specific calculations are required to draw a conclusion here. To avoid prohibitively long cooling times, either the reprocessing limit must be increased or the time before reprocessing and unloading must be shortened to prevent production of 241 Am.

Case 2: PWR MOX and SFR MOX with low quality plutonium
In this case, the americium isotopic vector between both cases is very dissimilar, with a significantly higher production of 243 Am in the SFR case due to the high content in 242 Pu in the low quality plutonium. Three approaches can be considered here: transmute first the americium from the MOX reactor and then the americium from the SFR, which will have more time to decay; transmute first the americium from the SFR, and then the americium from the MOX;  We considered here that a first loading of americium was irradiated while the equivalent mass was stored awaiting reprocessing. At the end of the 4100 days of irradiation, the second mass was loaded in the core while the first was stored until the limiting decay heat was obtained. The corresponding cooling times are shown in Table 4. A wide variation range depending on the isotopic vector considered can be observed, with differences increasing with the reprocessing limit. It can also be observed that the americium consumption only slightly depends on the isotopic vector, with the consumption increasing with the 243 Am content.
Considering the results shown in Table 4, it is interesting to plot the total quantity of americium corresponding to the initial mass of 4826 kg to be loaded in the blankets. This is done in Figure 3, which shows the evolution of the americium in the fuel cycle depending on the strategy and the reprocessing limit. When the mass reaches 0 kg, the total of the remaining americium loading has reached decay heat value lower than the limit and can be reprocessed. It can be observed that the reprocessing of the SFR one followed by the MOX one leads to a faster total cooling for limits of 7.5 and 5 kW. On the other hand, this approach yields the worst result for a 2.5 kW limit, with a mixing strategy yielding the best results. Indeed, for high decay limit, it appears more interesting to reprocess the americium feed with the highest 243 Am content first so that it decays during the irradiation of the second feed, than starting with the feed with the lowest cooling time and then going one with the second one. For low decay heat level, it appears more interesting to homogenize the two feeds so as to limit the total content in 241 Am in both cases.

Case 3: SFR MOX with low and high quality plutonium
This case is slightly similar to the previous one, with the high quality feed with a low 243 Am production replacing the MOX feed, with the main difference being that the two sources are producing the same mass, which means the mixing of the two vectors will yield different isotopic vectors. The results are shown in Table 5, with the evolution of the mass in the fuel cycle shown in Figure 4. The reprocessing of low quality and then of the high quality is optimal in the case of 7.5 kW limit, as the low quality vector has the time to cool down during the irradiation of the high quality vector, which itself has a short cooling time. For lower reprocessing limit, it appears that reprocessing first the high quality feed id optimal, as it limits the relative content of 241 Am in the irradiated americium, and thus the long term cooling time.   As a conclusion, it appears that no significant gain can be achieved by choosing PWR UOX or MOX americium isotopic vector for reprocessing. However, it was shown that for high decay limit, reprocessing and transmuting first the feed with the highest 243 Am fraction is optimal, while for lower decay heat limit, it was more interesting to homogenize the americium feed so as to limit the 241 Am content in the irradiated americium. In the next part, the impacts on the short term decay heat and on the neutron source of both strategies will be analyzed.

Neutron source and short term decay analysis
Reprocessing and irradiating first the americium feed with the highest 243 Am content has a negative impact on the neutron source of the irradiated targets. On the other hand, waiting for 241 Pu decay dilutes the 243 Am and thus decreases the amount of 244 Cm produced during irradiation. As no specific industrial limitations exists on the    4, 11 (2018) maximal neutron source allowed for handling irradiated targets with a high neutron source, no criterion can be defined with regards to their acceptance. Additionally, comparison of the neutron source is pertinent only for relatively short cooling time corresponding to a 7.5 kW limit, as for longer cooling times, most of the 244 Cm will have decayed. The neutron source of each of the initial americium feed is shown in Figure 5. It can be observed that transmuting first the feed with the highest 243 Am content will have significant impact on the neutron source of the irradiated assemblies, which is twice as high in the low quality plutonium case than in the other cases.
Regarding short term decay heat of the irradiated assemblies, the conclusion is reversed, as this parameter depends on the 241 Am fraction. This can be observed in Figure 6. The low quality plutonium feed has a significantly lower short term decay heat than the other feeds. However, the decrease in the handling time for a 40 or a 30 kW limit is limited to around 30 days which is not significant compared to the entire fuel cycle.

Conclusions
The impact of the choice of the americium feed in the reprocessing of the americium loaded targets for heterogeneous minor actinides transmutation has been analyzed in this paper. It has been shown that the short and long term decay heat of the targets was governed by the 241 Am content while the mid term decay heat and neutron source were dependent on the 243 Am content. It was shown that, for high decay heat limit, reprocessing first the feed with a high 243 Am content was more interesting to limit the total cooling time of the targets, while if a lower reprocessing limit was considered, it was more interesting to reprocess first the feed rich in 241 Am. Adequate choice of transmutation and reprocessing orders appears a potential solution to limit the cooling time of minor actinides bearing blankets by more than 10 years depending on the reprocessing limit considered. It is planned to consolidate these preliminary results by using a complete analysis based on industrial electronuclear scenarios.