Abstract
The determination of gamma heating levels in material-testing reactors (MTRs) is of crucial importance as gamma heating affects both safety and performance parameters of MTRs [Citation1,Citation2]. The required accuracy (5% at one standard deviation) makes it necessary to calibrate bias and uncertainty associated with MTR gamma-heating calculations. Main steps of bias determination for gamma-heating calculations include, first, the development of a calculation methodology with the controlled use of physical approximations; second, the interpretation of gamma-heating measurements with reference calculations so as to determine bias supposed to be mainly due to nuclear data.
1. Introduction
This article presents a methodology to estimate the bias and uncertainty associated with gamma-heating calculations in material-testing reactors (MTRs). We will describe its application for the Jules Horowitz Reactor (JHR), an MTR under construction in the south of France at CEA Cadarache (French Alternative Energies and Atomic Energy Commission).
MTRs are designed to host several irradiation experiments simultaneously in their core and reflector. These experiments help us better understand the complex phenomena occurring during the accelerated aging of materials and the irradiation of nuclear fuels. Gamma heating, i.e. photon-energy deposition, is mainly responsible for temperature rise in non-fuelled zones of nuclear reactors [Citation3,Citation4], including MTR internal structures and irradiation devices. As temperature is a key parameter for physical models describing the behavior of material, precise control of temperature, and hence gamma heating, is required in irradiation devices and samples in order to adequately analyze future experimental results. From a broader point of view, MTR global attractivity depends on their ability to monitor experimental parameters with high accuracy, including gamma heating.
Strict control of temperature levels is also necessary in terms of safety. As MTR structures are warmed up by gamma heating, they must be appropriately cooled down to prevent creep deformation or melting. Cooling power and sizing are based on calculated levels of gamma heating in the MTR. Due to these safety concerns, accurate calculation of gamma heating with well-controlled bias and associated uncertainty as low as possible is all the more important.
There are two main kinds of calculation bias: bias coming from nuclear data on the one hand, and bias coming from physical approximations assumed by computer codes and by general calculation route on the other hand. The former must be determined by comparison between calculation and experimental data and the latter by calculation comparisons between codes and between methodologies.
As for nuclear data, a sound experimental ground of gamma-heating measurements is needed to analyze the lacks of current libraries and to validate calculation schemes. To this aim, experiments were recently conducted in light-water reactors (LWR) at CEA Cadarache, namely in EOLE and MINERVE zero-power facilities:
ADAPH/ADAPH+ [Citation5], dedicated to the study of gamma heating in a light-water-reactor-type (LWR-type) reactor;
PERLE [Citation6], for the study of gamma heating in Generation-III (Gen-III) heavy reflector;
AMMON [Citation7], for the study of gamma heating in a JHR-representative critical mock-up.
Absolute comparison between this Experimental gamma-heating data (E) and data Calculated by a reference calculation route (C) yields the bias (C/E) due to nuclear data on gamma heating calculations. Determination of AMMON (C/E)-values is expected to provide feedback on nuclear evaluation of JHR-specific elements, especially aluminum, hafnium, and beryllium. Also, provided the AMMON experiment is representative enough of JHR (see Section 3.2.3), the AMMON (C/E)-values can be used as correction factors on the raw calculated values of gamma heating in the JHR to yield the “true” values of gamma heating in the JHR, that is, gamma-heating values corrected from the bias due to nuclear data. It especially matters to quantify not only the (C/E)-values themselves, but also the uncertainty associated to these (C/E)-values, as this uncertainty will be associated, after correction of the raw values, to the “true” values of gamma heating in the JHR. This uncertainty should be equal to or smaller than the target uncertainty for MTR gamma-heating calculation, which amounts to 5% at one standard deviation (see Sections 2.3 and 2.4). When quantifying the (C/E)-values, attention must, therefore, be paid to the uncertainty associated with the calculated value C and to the precision of the experimental techniques which provided the measured value E.
As for calculation route, reference gamma-heating calculation is based on three-dimensional (3D) Monte Carlo simulations with simultaneous tracking of neutrons, photons, and charged particles, and tallies on the energy deposited by charged particles. We may call this kind of calculation “reference” because, compared to deterministic computations, it reduces the number of physical approximations necessary to compute gamma heating (self-shielding strategy, neutron and gamma flux solver, energy meshing, etc.). Still, physical model implementation varies between Monte Carlo codes (typically electromagnetic-shower models), resulting in calculation differences that must be determined. Moreover, gamma heating entails various and independent components (such as prompt or delayed heating) that must be separately computed. The way these components are taken into account by global calculation routes is another potential source of bias and it should be handled with care. Calculation/calculation (C/C) comparison is an efficient way to quantify these calculation-route effects.
This article focuses on how to quantify the bias, along with its associated uncertainty, of gamma-heating calculations for MTR, with application to the JHR. We first highlight why a JHR-validated gamma-heating calculation scheme with controlled bias and associated uncertainties is necessary for JHR safety studies. We next tackle the development of a gamma-heating calculation scheme and mention how we intend to determine method bias, thanks to (C/C) comparisons. Finally, we deal with determination of nuclear data bias related to gamma heating and we consequently review recent gamma-heating experiments in Cadarache which provide feedback on nuclear data.
2. Status of gamma heating for the JHR
2.1. JHR presentation
The JHR is an international MTR set to replace the aging European MTR which are bound to end operation in the next 10 years (for instance, OSIRIS MTR reactor at CEA/Saclay near Paris). Its main purpose is threefold: irradiation of material and fuel samples under a very high neutron flux (up to 1015 n cm−2 s−1), production of radioisotopes (technetium-99) for medical applications, and production of doped silicon for high-performance semiconductors. It will help prevent technetium-99 shortages, as the one that happened in Europe in September 2008 right after the unplanned shutdown of the high-flux reactor, a Dutch MTR. It will produce at least 25% of medical radioisotope demand in Europe and up to 50%, if needed.
The JHR is a research tool that will accompany the development of Gen-III and Gen-IV reactors. It will host on average 20 irradiation devices where samples of materials or fuels will be submitted to very high thermal and fast neutron fluxes. Applications are numerous:
Testing of material (for life-extension study of Gen-II-reactor pressure vessel).
Design of new alloys more resistant to high fluence and high temperature (for design and safety study of Gen-III and Gen-IV reactors).
Experimental validation of the present and future nuclear fuel.
2.2. JHR design
The following technical data comes from CEA [Citation8].
JHR is a 100-MW reactor. The core (a cylinder with 600 mm fuel active height) is cooled and moderated with light water. The core will operate with a cold fuel (fuel temperature around 100 °C) and a slightly pressurized light water (primary circuit pressure and water temperature around 7 bars and 35 °C, respectively).
The core is made of an aluminum rack hosting 34–37 fuel assemblies distributed in a so-called “daisy-flower” geometrical motif (see ). The fuel element is of circular shape, consists of a set of curved plates assembled with stiffeners, and comprises a central hole. The core area is surrounded by a reflector made of beryllium elements. The reflector limits neutron leakage and provides intense thermal flux in this area.
Figure 1. Radial cross section of JHR starting core.
About 20 control rods are used to operate the core. They are made of two concentric tubes in hafnium, a neutron-absorber element, which can be inserted in the center of assemblies. The follower tubes in aluminum take the place of rods in the center of assemblies when they are not inserted.
Irradiation devices can be placed either in the core area (in a fuel-element central hole or in place of a fuel element) or in the reflector area. Experiments can be implemented in static locations, but also on displacement systems as an effective way to investigate transient regimes occurring in incidental or accidental situations.
In summary, JHR is a flexible experimental facility. With 220 full-power operation days per year, it will be able to create up to 16 displacements per atom (dpa) a year for in-core material experiments, compared to 6 dpa/year in OSIRIS reactor or 2–3 dpa/year in a standard pressurized-water reactor (PWR). In core, the material samples will undergo a fast flux of neutrons with energy higher than 1 MeV up to 5 × 1014 n cm−2 s−1, whereas in reflector, they will undergo a thermal flux of neutrons with energy lower than 0.625 eV up to 5 × 1014 n cm−2 s−1.
2.3. Gamma heating and JHR performances
JHR is an MTR reactor and will mainly sell irradiation services. It will be in concurrence with other MTRs and its competitiveness lies in its ability to offer innovative and specific irradiations of very good quality. This requires a fine control over irradiation conditions of samples and a large range of available irradiation conditions (total heating, temperature, neutron spectrum, pH, etc.).
In non-fissile zone, such as an experimental device or an inert material sample, gamma heating is the main contributor to total heating. Gamma heating is, therefore, a key input data for thermal physics codes simulating the temperature reached by samples under irradiation. The temperature of samples inserted in the JHR is especially a critical parameter as temperature is a key factor for physical models describing the properties of material. Uncertainty on irradiation temperature of samples generally translates into uncertainty on JHR final experimental results. An important example is the measurement of ductile–brittle transition temperature performed on steel samples aged in an accelerated way in MTR. Those measurements, conducted in the context of safety and life-extension studies of nuclear power plants, can be greatly affected by discrepancies between nominal and actual irradiation temperatures of samples. As, roughly speaking, uncertainty on irradiation temperature works as an upper boundary for such discrepancies, it matters to assure low irradiation-temperature uncertainty. For the JHR, target uncertainty at one standard deviation for sample temperature in experimental devices equals 5 °C (sample temperatures usually being in the range of 300 °C).
Temperature knowledge necessitates knowledge of gamma heating. Consequently, gamma heating strongly influences main design choices for experimental devices and must be determined with precision, as any uncertainty on gamma heating affects the expected temperature levels. The required accuracy for gamma heating in JHR experimental locations amounts to 5% (1σ) [Citation9].
2.4. Gamma heating and JHR safety
As mentioned earlier, gamma heating is mainly responsible for temperature rises of JHR internal structures, such as the aluminum rack and related support structures, beryllium reflector, and hafnium rods. Its calculation is, therefore, required for material-strength safety studies aiming at adequately sizing components and cooling power. Three extensively studied risks, associated with insufficient cooling and too high temperature, are creep deformation of components, melting of components, and local boiling of primary water in the core. Zones under scrutiny are, for instance,
the surroundings of hafnium rods, because of the high neutron-capture rate in those neutron-absorber rods and the local boiling risk resulting from the increased photon production and heating;
aluminum surrounding of MOLFI (MOLybdenum from FIssion) devices, located in reflector, aiming at producing technetium-99 and made of 235U-enriched targets, because of the high fission rate in the device, resulting in the increased prompt photon production and heating.
Moreover, aluminum, crossed by high neutron flux and chosen in the core design for its low capture cross section, possesses the drawback of a rather low melting point, 660 °C. A safety criterion imposes aluminum-rack temperature to be below 70 °C at any time so as to prevent creep deformation and melting.
In summary, in order to meet the safety criteria and to correctly size JHR cooling power, it is necessary to determine gamma heating with sufficient accuracy in different JHR components. The required accuracy amounts to around 5% (1σ) [Citation9].
3. Adopted work plan
In order to quantify the bias of gamma-heating calculations for an MTR, we first need to develop a gamma-heating calculation scheme. The reference character of developed calculation route must be demonstrated through comparisons with other calculation schemes and other codes. For instance, one will try to minimize method bias that is due to physical approximations assumed by codes and that is not related to nuclear data. This is necessary as, in a second step, output results of the calculation route will be compared to gamma-heating measurements in order to yield a (C/E)-bias that is mainly due to nuclear data.
Gamma-heating measurements are carried out in zero-power critical mock-ups in order to get well-controlled experimental uncertainties. Before nuclear-data-induced bias determined with the help of critical mock-ups can be applied to MTR gamma-heating calculations, the feasibility of such a transposition must be studied, taking into account the representativity of experimental mock-ups toward the MTR under study (representativity in terms of geometry, neutron spectrum, etc.). Moreover, zero-power reactors are begin-of-life (BOL) reactors and can only help quantify nuclear-data bias for BOL MTR. Therefore, determination of nuclear-data bias for MTR gamma-heating depletion calculation (i.e. in an MTR with a burnup rate greater than zero) must equally be addressed.
3.1. Gamma-heating calculation route
In this section, we address the development of a gamma-heating calculation scheme for BOL reactors. We begin by recalling some definitions about gamma heating and we will end with the presentation of a calculation route for BOL reactors.
3.1.1. Absorbed-dose calculation
Heating is represented by the physical quantity called absorbed dose. It is usually computed using Monte Carlo simulations or deterministic codes. However, absorbed dose is not directly calculated: actually, other physical quantities (close but different from absorbed dose) are calculated and used as absorbed-dose estimators, such as KERMA (Kinetic Energy Released per unit MAss) or CEMA (Converted Energy per unit MAss). KERMA is defined as the sum of the initial kinetic energies of all the charged particles liberated by uncharged ionizing radiation in a sample of matter, divided by the mass of the sample, whereas CEMA quantifies the energy imparted in terms of the interactions of charged particles, also divided by the mass of the sample. In a heating calculation, conditions of equality between absorbed dose and these estimators should be carefully examined so as to avoid introducing bias due to discrepancies between absorbed dose and its estimators.
From this point of view, CEMA is a more interesting estimator than KERMA. The reason behind this latter statement is the fact that CEMA requires weaker hypotheses than KERMA to equal absorbed dose [Citation10]. In particular, hypothesis of charged-particle equilibrium for all charged particles is not required by CEMA, unlike KERMA. However, the price to pay for fewer physical approximations is computing power as CEMA calculation necessitates computationally expensive Monte Carlo simulation of charged-particle transport in addition to neutron and photon transport. In practice, only transport of light-charged particles (electrons and positrons) is simulated as transport of other, heavier charged particles can be reasonably neglected.
3.1.2. Components of nuclear heating
Nuclear heating is a complex physical quantity made of many different components which must all be taken into account by a calculation route. We propose to detail each of these components. Nuclear heating can be effectively split into prompt and delayed neutron heating on the one hand, and prompt and delayed gamma heating on the other hand [Citation11].
Prompt neutron heating corresponds to heating resulting from recoil energy of nuclei after a neutron collision and from energy deposition of charged particles promptly created by a neutron interaction. For instance, this includes heating caused by fission fragments or by protons and alpha particles released in (n,p) and (n,alpha) interactions.
Delayed neutron heating corresponds to heating resulting from interactions of charged particles created with delay by a neutron interaction. This includes, for instance, heating caused by electrons resulting from beta decays of activation and fission products.
Gamma heating corresponds to heating resulting from energy deposition of charged particles produced by photoatomic and photonuclear interactions. Photons are usually distinguished according to their origin, either prompt or delayed. Prompt photons are emitted right away after a neutron interaction, whereas delayed photons come from decays of activation and fission products. Prompt, respectively delayed gamma heating is, therefore, gamma heating caused by prompt, respectively delayed gammas.
The share of each of these components in total heating strongly varies in a reactor, depending on reactor design and location in the reactor. These ratios also depend on burnup because of additional heating due to actinide and fission-product neutron capture. Likewise, if equilibrium is not reached yet, these ratios will be different because yet-released delayed heating will only be a fraction of delayed heating at equilibrium. A JHR gamma-heating calculation route should be able to determine the share of each nuclear heating component in locations of interest for the specific JHR geometry and different levels of burnup.
3.1.3. Toolbox for a begin-of-life gamma-heating calculation scheme
In order to calculate gamma heating in a BOL reactor, one should dispose of
a Monte Carlo transport code for neutrons and photons with electromagnetic shower simulation;
a point depletion code solving Bateman equation; this is necessary to estimate delayed components of heating;
nuclear data libraries: neutron, photon, charged particles, and atomic relaxation data.
Two codes developed by CEA are used: point depletion code PEPIN-2 [Citation12] and four-particle-transport Monte Carlo code TRIPOLI-4® [Citation13].
Prompt neutron heating and prompt photon heating are accounted for in a single TRIPOLI-4® simulation in a four-particle mode. The calculation is performed on a full 3D description of core geometry. Neutron, photon, electron, and positron tracking is simulated everywhere; however, for reasons linked to available computing power, high cut-off values for charged particles are set for locations far away from the zone of interest. This effectively results in simulating electrons and positrons only in the near surrounding of the zone of interest, where heating resulting from energy deposition of charged particles is tallied. This approximation is legitimate as long as charged particles are simulated in a sphere centered on the zone of interest and of radius greater than the range of charged particles. Indeed, charged particles located further away will not be able to reach the zone of interest and to deposit their energy there.
Delayed heating from fission gammas is accounted for with a coupled calculation. First, fuel is divided in a mesh and fission rates are calculated in each fuel cell with TRIPOLI-4® in neutron-transport mode. The average fission-gamma spectrum in each cell, taking into account the duration of irradiation experiments, is then computed with PEPIN-2. Finally, heating is calculated with TRIPOLI-4® in photon–electron--positron mode using the previously computed gamma sources.
Development is still underway to take into account heating induced by activation product decay. For the PERLE experiment, it was shown to be negligible [Citation3]. In the AMMON experiment, the first estimations reveal that photon heating generated by 27Al activation product amounts to 1%–2% of total heating [Citation14].
3.1.4. Benchmarking
A gamma-heating benchmark should be built in order to compare TRIPOLI-4® performances with those of other Monte Carlo codes. Insight on gamma-heating models, their implementation in Monte Carlo codes, and potential computational bias is at stake.
We envision conducting compared calculations with MCNP (Monte Carlo N-Particle transport code) [Citation15]. The impact of the differences between electromagnetic-shower models of each code (thick bremsstrahlung, electron multiple-scattering formalism, etc.) will be studied.
3.2. Experimental validation of gamma-heating nuclear data
In this section, we first mention the nuclear data we intend to experimentally validate. We then present gamma-heating experiments that recently took place in zero-power reactors of Cadarache. We finally give details of our plan of action regarding these recent measurements.
3.2.1. Presentation of nuclear data
The European library JEFF3.1.1 [Citation16] has been selected for JHR design, operation, and safety studies. This evaluation currently undergoes experimental validation seeking to quantify the bias and uncertainty which must be applied for JHR neutron and gamma parameters calculated with JEFF3.1.1. For the time being, as for gamma-heating data, the accent is put on the validation of photon-production data, especially photon emission following fission, neutron capture, and inelastic neutron scattering. The first two interactions are the main gamma sources in reactors.
Electromagnetic shower data comes from the EPDL97 libraries [Citation17], containing data for photon (EPDL), electron (EEDL), and atomic relaxation (EADL). This work does not intend on validating this data as it is supposed already accurate for our needs, that is, we suppose it does not induce a bias on heating calculations. As an example of this accuracy, uncertainty associated with the EPDL97 photoionization cross sections in the typical energy range of photons in reactors (5 keV to 10 MeV) only equals 2% at the three standard deviations [Citation17]. Therefore, we only intend on validating the JEFF3.1.1 library for the purpose of gamma-heating calculations.
3.2.2. A review of recent gamma-heating experiments for LWR in EOLE and Minerve zero-power reactors
In this paragraph, we present past experiments that provided gamma-heating measurements aiming at improving nuclear data thanks to (C/E) comparisons. We deal with experimental techniques, interpretation methodology at the time, and findings.
3.2.2.1. ADAPH (2006) and ADAPH+ (2010).
The ADAPH experiment [Citation18] took place in the mock-up reactor MINERVE in Cadarache with an LWR configuration, called R1-UO2 configuration. Gamma-heating measurements were carried out with thermo-luminescent dosimeters (TLD) and optically stimulated luminescent dosimeters (OSLD) inserted inside Lucoflex® micro-tubes of conical shape and positioned in aluminum rods in the core. Interpretation of this experiment, using the code TRIPOLI-4® and nuclear-data library ENDF/B-VI, yielded a (C/E) absolute discrepancy of (C–E)/E = −28% ± 7.5% (1σ). Due to limited computer power at the time, the used calculation route had to rest on many physical approximations. Especially, the prompt gamma-heating calculation scheme contained two main steps: a neutron–photon computation on the whole core and a photon--electron computation on a smaller geometry centered on gamma-heating dosimeters.
At the time, the 28% underestimation was interpreted as a lack of photon production data in the libraries used. Since then, methods of measurements were re-investigated and an important work was performed in order to improve measurement accuracy. The will to better understand the causes of the difference observed between measurements and calculations resulted in the ADAPH+ program.
The ADAPH+ experiment [Citation5] consisted in a new set of gamma-heating measurements in the same R1-UO2 configuration of MINERVE reactor. The feedback of ADAPH enabled to improve experimental techniques overall [Citation19], resulting in lower experimental uncertainty with regard to ADAPH. In particular, the use of the previous Lucoflex® micro-tubes was called into question and TLD and OSLD were this time inserted inside aluminum pillboxes specifically designed to achieve better measurement conditions. Also, reading–annealing cycles of dosimeters were optimized to achieve better measurement reproducibility and dosimeters were individually calibrated in order to reduce calibration uncertainty (compared to ADAPH when dosimeters where calibrated batchwise)
The first interpretation of this experiment [Citation19,Citation20] was carried out with Monte Carlo code MCNP and nuclear-data library ENDF/B-VI. Calibration--correction factors for anisotropy and neutron spectrum were introduced: the total effect of these correction factors is an increase of about +10% of the (C–E)/E values. Prompt gamma-heating calculation was based on the two-step scheme described above or on one-go computation on simplified core geometry with simultaneous tracking of neutron, photon, and electron. The results of this interpretation are presented in .
Table 1. Absolute C/E discrepancies of ADAPH+ interpretation.
The C/E values yielded by ADAPH+ interpretation are different from the C/E yielded by ADAPH interpretation. A series of reasons can explain this difference. The first and the most important, the measurement methods with TLD detectors in ADAPH+ have been significantly improved compared to ADAPH, as well as the knowledge of the absolute fission rate of the R1-UO2 configuration given by a calibrated fission chamber. This combined effect might lead to a discrepancy achieving 20%. Second, calibration–correction factors are used in the ADAPH+ interpretation, but not in the ADAPH interpretation: this accounts for a 10% difference. Third, two different Monte Carlo codes were used for the computation of absorbed dose. As absorbed dose computation necessitates the simulation of charged-particle transport, and as there exists a huge variety of electromagnetic shower models which tackle this topic, differences in the implementation of these models between the two codes may result in a difference of a few percent in absorbed dose computation.
These interpretations provide nuclear-data feedback for LWR in general. However, nuclear-data feedback for the JHR from these experiments is limited as the R1-UO2 core is poorly representative of the JHR.
3.2.2.2. PERLE (2008).
The PERLE experiment [Citation6] was conducted in the zero-power facility EOLE in Cadarache. It is a regular PWR reactor with 3.7%-enriched UO2 pins surrounded by a 22-cm thick stainless steel reflector. One purpose of this experiment was to validate gamma-heating calculation locally in a heavy reflector for Gen-III reactors. Measurements were carried out using TLD and OSLD inserted inside steel pillboxes and positioned in the reflector. PERLE interpretation [Citation3] was conducted using TRIPOLI-4® and JEFF3.1.1 with improved evaluations [Citation21] for iron neutron-capture gamma spectra. For the first time, CPU-expensive one-go computations on whole core geometry with simultaneous tracking of neutrons, photons, electrons, and positrons in the surroundings of TLD were used for prompt-heating calculations, instead of previous methods assuming two steps or simplified geometry. The results of this interpretation are presented in .
Table 2. Relative C/E discrepancies for heating measurements in PERLE reflector.
The 3% discrepancy between the uncertainties of the two configurations is due to statistical convergence concern. Agreement between C and E is good but it must be paid attention to the fact these reflector-heating discrepancies were calculated relatively to heating in the PERLE core center and not in absolute terms. This means JEFF3.1.1 data used for gamma-heating calculations in the reflector were experimentally validated regarding JEFF3.1.1 data used for gamma-heating calculation in the core, but there is no validation of the overall level of heating induced by JEFF3.1.1 data.
3.2.2.3. AMMON (2010)
Until here, previous experiments are not representative for the JHR in terms of material, geometry, and neutron spectrum. Consequently, their nuclear-data feedback for the JHR is limited as their results cannot be easily transposed to the JHR, if at all. To address this problem of representativity, the AMMON experiment [Citation7] began in late 2010 in the EOLE reactor and ended in early 2013. One of its purposes is to validate neutron and photon production data of JHR-specific environment containing aluminum, hafnium, and beryllium.
The AMMON reference core includes an experimental zone made of an aluminum rack hosting seven JHR-type circular fuel assemblies; the geometrical pattern of these seven assemblies being identical to the pattern of the seven central assemblies of JHR. The experimental zone is surrounded by a driver zone made of hundreds of PWR-type 3.7%-enriched UO2 pins. Moderation ratio of pins was optimized to reproduce the JHR neutron spectrum (somewhat harder than the standard PWR spectrum). The experimental zone is, therefore, representative for the JHR with respect to material, geometry, and neutron spectrum. The AMMON core is, nevertheless, not entirely JHR-representative, two main differences being the presence of an experimental zone with fuel pins and the absence of a solid beryllium reflector.
Gamma-heating measurements were carried out with TLD and OSLD inserted in pillboxes made either of aluminum, hafnium, or beryllium. These pillboxes were then inserted either in a regular JHR assembly, in a JHR assembly hosting a hafnium rod, or in a beryllium block (which replaced one fuel assembly of the experimental zone). Experimental uncertainty amounts to about 3% (including dosimeter counting, background noise, calibration, and neutron-dose determination).
Interpretation of all the gamma-heating measurements in the AMMON reference configuration (with seven non-rodded JHR fuel assemblies), the AMMON hafnium configuration (with a central rodded assembly and six non-rodded assemblies), and the AMMON beryllium configuration (with a central solid beryllium block) is performed with JEFF3.1.1 data and TRIPOLI-4®, using one-go prompt dose computations as in the above PERLE interpretation. ADAPH+ calibration–correction factors are not used. Preliminary results of this interpretation are presented in .
Table 3. Absolute C/E discrepancies for heating measurements in AMMON core.
The first C/E discrepancy is consistent with the first interpretation of the AMMON reference configuration, which relied on JEF2.2 decay data for delayed dose calculation and yielded absolute discrepancy of (C–E)/E = −8.0 ± 4.5% (1σ) [Citation14]. The complete interpretation of the three AMMON configurations is to follow.
3.2.3. Plan of action for measurement analysis
The first step is to interpret AMMON gamma-heating measurements in aluminum, hafnium, and beryllium environments. We use the calculation route we previously described with JEFF3.1.1 and EPDL97 libraries. Thus, we expect to quantify the JEFF3.1.1 bias for gamma-heating measurements in aluminum, hafnium, and beryllium.
In the second step, we will study the JHR representativity of AMMON and the transposition possibilities toward the JHR of the bias determined in the AMMON experiment. As gamma heating is a local parameter, nuclear data bias on gamma-heating calculation, as determined with a critical mock-up, can be transposed to the JHR under the condition that the critical mock-up is enough JHR-representative. As it stands now:
The AMMON experimental zone is representative for the JHR in terms of material, geometry, and neutron spectrum.
However, the AMMON gamma spectrum in the experimental zone is not totally JHR representative.
The AMMON gamma-spectrum representativity must, therefore, be investigated. We mention two potential issues. First, some photons generating heating in the experimental zone actually come from the driver zone, which is JHR unrepresentative in terms of material, geometry, and uranium-enrichment rate. Between 5% and 22% of photon-energy deposition in the experimental zone, depending on location, is induced by prompt photons emitted in the driver zone [Citation14]. Second, delayed-gamma spectra of AMMON and JHR are different depending on irradiation time (on whether delayed emissions had enough time to reach steady-state equilibrium or not yet).
In the final step, it is necessary to calibrate bias of depletion gamma-heating calculation, taking into account fission-product neutron capture and creation of actinides. In 2012, gamma-heating measurements were carried out in the OSIRIS MTR using a new experimental device, CARMEN [Citation22], designed in the context of the INCORE project [Citation23] for the qualification of JHR neutron and gamma instrumentation. We plan to interpret this gamma-heating experiment which took place in a 70-MW reactor as it will give us some elements to validate JEFF3.1.1 data for a non-zero burnup.
4. Conclusion and perspectives
Gamma-heating calculations with controlled bias and uncertainty are necessary for MTR safety studies. We presented a general work plan aiming at quantifying this bias for JHR heating calculation, mainly based on the development of a reference calculation route for BOL reactors and the interpretation of recent measurements in critical mock-ups of Cadarache. This work plan can be applied for gamma-heating calculation in any MTR as long as experimental data from appropriate and representative critical mock-ups are available.
After this work, the development of a reference gamma-heating calculation scheme for depleted reactors will be the next natural step.
Acknowledgements
The authors wish to thank P. Siréta, J. Pierre, C. Colin, C. Huot-Marchand, B. Pouchin, and S. Ravaux from CEA Cadarache for fruitful discussions.
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