Introduction

ITER will be the largest Tokamak ever constructed, and it will produce orders of magnitude more neutrons than its predecessor (up to 107 times more), JET1, and other current private initiatives2. According to French nuclear licensing procedures, ITER is classified as Installation Nuclear de Base INB-174 under French regulation. Ensuring that the expected radiation conditions do not pose challenges and risks to equipment and humans, has made nuclear analysis a relevant computational discipline in support of the ITER design and licensing during the last two decades. The radiation safety case of ITER, structured around the computational codes MCNP3 and D1SUNED4, receives growing attention as the construction progresses. Monte Carlo method accuracy and code robustness accumulated over decades of use are the basis for MCNP selection by ITER Organization, while D1SUNED is an extension to boost MCNP performance needed to deal with ITER nuclear analysis computational particularities. Independent examination has explicitly identified the need to provide additional robustness to the prediction of three-dimensional radiation fields5.

ITER presents particularities requiring adaptations and innovations in the discipline. Geometry representation in MCNP stands as one of the most relevant ones. Materials as different as steel, water, beryllium, copper and air are deployed in intricate cm-scale shapes over dozens of meters. Homogenization of materials can result in large distortions of the radiation field prediction, the sense and size of which cannot be anticipated, thus representing an undesired approach6. Thanks to the development of tools such as Spaceclaim (www.spaceclaim.com) for geometry handling and SuperMC7 for computer-aided design (CAD) geometry translation to MCNP format, an ever-growing degree of detail has been captured over the years in successive models.

However, this approach implied an increased workload to prepare simulation inputs. To save time and to standardize the modeling of the environment to any simulation, ITER Organization coordinated a strategy of making reference models available to any user. They are arranged in two families: the Tokamak models8,9,10 and the Tokamak Complex models11,12,13 (representing the nuclear buildings). Despite the increased computational demand, most of the analyses conducted for ITER have been successfully carried out using them. Nevertheless, due to the usability of the models and computational limitations, it was necessary to keep both families apart.

Considering separate reference models for the machine and the building entails raising concerns. Situations in which the source of radiation is represented in a different model than the region of interest cannot be characterized with one single simulation. The same applies to situations in which the sources and/or regions of interest transcend the boundary between reference models of both families. Topics of relevance for the ITER safety case are affected.

To date, different artifacts have been considered to deal with this limitation on a case-by-case basis. All of them present drawbacks regarding the practicality, accuracy, codes licensing policies, compatibility with the ITER-specific environment of nuclear analysis tools, and/or simplicity of the analysis. They represent obstacles for an agile design process and affect the robustness of the safety case5.

The development of a heterogeneous model of the complete ITER Tokamak10 advances in the computational performance of D1SUNED, and a set of tools in support of weight windows technique14,15 have brought the possibility of joining the reference model families in a single integral model of the ITER facility, including both the Tokamak and the Tokamak Complex: the ITER full model. We present the model and two illustrative applications of high relevance for the ITER design and the safety case assessment. Model usability and computational viability to provide clean evaluations while avoiding the use of any artifact is thus demonstrated.

This work represents the culmination of a two-decade-long effort of ITER modeling8,9,10,11,12,13, methods development11,16, and implementation of tools7,17,18 to predict the radiation conditions in the ITER facility. It involves the simplification of the safety-related analysis for the benefit of clarity and standardization of the approach and reduces both human and computational resource demands. In practical terms, it means abandoning artifacts for the benefit of improved robustness of the nuclear analysis.

ITER MCNP reference models

The reference models of the ITER Tokamak have been in use and constant improvement for over two decades following or even triggering methodological advances. The number of MCNP surfaces is a good indicator of the complexity of a model. Initial versions consisted of <2000 surfaces to represent a single 20° sector of the machine. The adoption of CAD-to-MCNP translation tools, prominently SuperMC7, the inclusion of SpaceClaim (www.spaceclaim.com) in the workflow, and the development of guidelines and standardized approaches represented steep advances and boosted international collaboration. A successful 40° model series was developed over 12 years for applications related to regular sectors of the machine: A-lite, B-lite, C-lite, and C-model8. A similar development took place for the 80° irregular sector of the machine9 (containing the Neutral Beam Injector). In 2020, the first 360° model of the ITER Tokamak was built: E-lite10. In parallel, diverse MCNP models of the ITER Tokamak Complex were created in 201011, 201612, and 202013. Details on the number of surfaces are given in Table 1.

Table 1 Date of issuance and surface numbers of the different ITER reference models
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The complexity captured in the Tokamak models increased by a factor of ~100 in ~12 years. A similar trend is observed for the Tokamak Complex models, involving rising computational loads in either case19. This was the motivation to keep the Tokamak and the Tokamak Complex reference models apart.

Use of the current reference models

Note the mentioned ITER reference models contain, by definition, a non-exhaustive representation of the facility. They include either sectors of the machine inside the bio-shield, or the Tokamak Complex beyond the bio-shield. The same logic applies to radiation source representations considered within these models and to the regions of interest that can be studied: their maximum spatial extent will be delimited by the boundaries of the models. This feature is referred to as a partial representation captured in the models. Working in such conditions is referred to as a local approach, and it becomes more valid as the range of the dominant interactions gets narrower.

A myriad of local studies used the partial reference models to successfully address specific design topics and have constituted the core of the discipline. Numerous aspects of the radiation field of ITER were identified and accurately characterized thanks to the complexity captured in the reference models. For example, the role of the particles streaming through the gaps in the shutdown dose rates20 (SDDR), SDDR cross-talks between adjacent ports21, the nuclear heating peak values in the Vacuum Vessel inner shell22, or integral heating in the Blanket Shield Modules6. Note, however, that all of them are conducted in a local approach since they consider models dismissing regions either from the geometry or the radiation source. This has been widely acceptable since a relative evaluation or a confined phenomenon was addressed, rather than an absolute judgment of long-range aspects of the radiation field. Note this approach is sufficient, and even efficient, under certain circumstances.

Local approach shows, however, limitations when the geometries, radiation sources and/or regions of relevance become wider and eventually transcend the model's boundaries. This situation has manifested in the last years in a set of works, and diverse attempts to mitigate it have been set in place.

A group of works23,24,25,26,27 took the approach of locally expanding the ITER reference models (A-lite23,24, B-lite25,26 and C-model27) in terms of geometry to address nuclear analysis of the Torus Cryopump Port #12 port cell25,26, the equatorial port bio-shield plug23 or the Neutral Beam Injector Cell24 and a dedicated shielding cabinet for the Radial Neutron Camera27. This permitted to include radiation sources of relevance and tallies over regions of interest. To some extent, this approach can be understood as increasing the study domain by extending the models. This is, building ad hoc dedicated larger-but-still-partial models. While it serves the purpose of facilitating a given study, the lack of generality of this approach is evident. Further, it remains difficult to quantify the impact of this approach.

Differently, other works explored the possibility of sewing simulations using different models to build a wider domain of study by concatenating studies in subsequent domains. This is made by transferring radiation transport information from one simulation to the next one. The radiation impinging on the boundary of a model needs to be characterized and reconstructed in the next one. The simplest procedure is the setting of a tally, inspecting it, and inferring an SDEF card (the standard approach for sources definition in MCNP) from it, which was made in some cases to study the upper launchers28, the upper port #1829 and a bio-shield plug generic design30. Note, however, that the SDEF cards are limited to one-level variable dependencies, which prevents proper modeling of the dominating effect of radiation streaming (focused, locally intense and highly energetic radiation beams). Furthermore, this approach is accompanied by an avoidable field distortion due to binning unapproachable to the date. Methods for uncertainty propagation associated with this approach are largely missing.

More generally, the use of WSSA files (i.e. binary surface source writing file), recording weight, coordinates, velocity vectors, and energy of impinging histories, permits to carrying out of such an operation, capturing the full complexity of the radiation field in the model's boundary, as it was considered in to study the equatorial port #1131 and the In-vessel Viewing System32,33. Its main drawback is, however, the cap in the sampling of source particles. The number of particles registered in the initial simulation is the maximum number of particles that can be simulated in the subsequent one. This can entail convergence problems. In addition, it may involve the manipulation of source description files occupying GBs, sometimes impractical.

Lastly, the limitations of the use of WSSA files were addressed with a dedicated tool, named SRC-UNED34. It automatically infers probability distribution functions in user-defined bins from WSSA files, which permits unlimited sampling with lighter files (~MB). On the other hand, in comparison with the SDEF card approach, it permits higher-level variable dependencies, while the field distortion due to binning remains. Note that SRC-UNED is an artifact embedded within an already complex workflow, requiring a documented verification and validation (V&V) plus a case-by-case binning validation. SRC-UNED has been used in works such as the shielding design to protect electronics35, the design of lower ports bio-shield plugs36, the assessment of the radiation conditions during in-vessel components extraction13, the bio-shield lid design37 and the production of radiation atlases16.

Thus, attempts to overcome the partial nature of the local studies derived from the use of the current ITER reference models exist, reaching what can be considered pseudo-integral representations. With different degrees of success, none of them is fully satisfactory, bringing different problems such as the proliferation of new models, lack of generality, or unassessed distortions in the radiation field. The underlying problem to all of them is the constant avoidance of an obvious situation: the integral representation of the facility requires models including everything.

ITER safety case and the need for an integral representation

Differently, to design tasks, a local approach based on partial representations results unsatisfactory for the safety case assessment. Most of the safety-relevant responses must be determined all through the facility and considering all relevant sources of radiation, with the aim of reaching a global and absolute perspective. It will demonstrate compliance with the limits for radiation exposure to the public, workers and electronics, as well as the minimization of the occupational radiation exposure (ORE) known as the As Low As Reasonably Achievable (ALARA) strategy. This will involve a collection of studies considering a few radiation sources and large regions of the facility.

The safety case will deal with several neutron and photon sources spread all across the entire facility (shown in Figs. 1 and  2): (1) plasmas of different species, (2) Deuterium—Deuterium (DD) and Deuterium–Tritium (DT) reactions in the Neutral Beam Injector components38, (3) high-energy particles following runaway electrons events, (4) activated structures and components39, (5) activated corrosion products across the Tokamak cooling water system (TCWS)40, (6) activation of water in the TCWS41 (16N and 17N, photon and neutron emitters), and (7) activated Tokamak dust impregnating components42.

Fig. 1: Main sources in relation to the facility.
figure 1

The plasma neutron source and the Tokamak Cooling Water System 16N photon source geometrical arrays are shown both in orange in the context of the ITER facility. The bio-shield and Lid are highlighted in blue. Note that the HV deck stands for a high-voltage deck, and the NB cell stands for a neutral beam cell. Courtesy of ITER Organization.

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Fig. 2: Spatial distribution of radiation sources across the ITER Tokamak Complex.
figure 2

The bio-shield is highlighted in a white dashed line. Note that NBI stands for Neutral Beam Injector.

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Timewise, instances of these radiation sources may dominate the radiation field during the pre-fusion power operation, during the fusion power operation phase, during machine shutdown and maintenance, as well as during the decommissioning. Space-wise, the full Tokamak pit, over 600 rooms in the Tokamak complex, which includes over 4500 penetrations in the walls, as well as the full extension of the ITER site up to the fence, are subject to study.

Facing the ITER safety case as a collection of local studies is unsatisfactory in terms of robustness, simplicity, and clarity5. Composing a global view as a patching of hundreds of local studies results is impractical. As explained, it requires artifacts introducing unassessed uncertainties and resulting more cumbersome as the study domain becomes wider or global for a simple reason: representing a single facility with two mutually exclusive models to determine the long-range situation is artificial from a methodological perspective. There is a growing perspective that an integral representation in a unified model might offer a more streamlined process for safety demonstration.

Results

ITER full model in MCNP

The natural boundary between the Tokamak models and the Tokamak Complex models has been the bio-shield: a cylindrically shaped reinforced concrete structure with a 2.5 m-thick wall (Fig. 1). The ITER full site MCNP model has been built, inserting an updated version of E-lite10 inside the Tokamak Complex model 202013 bio-shield (copy/pasting MCNP cells and surfaces definitions). Note the last one already contained representations of the neutral beam cell, high-voltage deck (HV deck) and the TCWS. Further updates were later implemented to the resulting model.

Updates to E-lite43 before inclusion in the ITER full model are depicted in Table 2. With respect to bio-shield, occurring in both models, the bio-shield cells used in the Tokamak Complex model were preserved. Some components transcending the boundary between the two models were present in either model. A cookie-cutter approach was followed to extend them and preserve them in the resulting joined model.

Table 2 Updates to E-lite before inclusion in the ITER full model
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Once assembled, the resulting model has been amended. All the bio-shield plugs MCNP models have been updated. MCNP models of the Drain Tank Room were added to the model, the contents of all the In-Vessel Viewing System ports, plus LP #2 and #4, EP #8, #10, #15, #16, UP #1 and #16 have been updated from plasma to the gallery and included in the new model (both inside and outside the bio-shield). These models account for the extra number of cells and surfaces observed in Table 3. The ITER full model is shown in Fig. 3.

Table 3 Computational consumptions for a single process of the ITER full model and its constituents with D1SUNED v4.1.2 parallelized with OMP + MPI
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Fig. 3: ITER full model in MCNP model (Z = 60 cm).
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Cross-section view of the ITER full model. The MCNP model in horizontal plane corresponding to Z = 60 cm is shown in the figure.

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Thus, the construction of the ITER full model in MCNP has been a process of updating E-lite, assembling it with the Tokamak Complex model, and updating the resulting model. Such a relatively standard process resulted in challenges, given the size of the models involved. Identifying cells (required, e.g., to void the in-bio-shield region of the Tokamak Complex model or to set priority in clashes) and debugging lost particles were particularly tedious. Loading time and plotting times in the range of hours were incompatible with the usual approach to visualize the geometry. And the inexistence of a CAD model of E-lite added difficulty to the task. This was resolved by three strategies. First, both E-lite and the Tokamak Complex models are profusely commented on. Studying and using the headings and comments was particularly useful in identifying cells. Secondly, batches of hundreds of MCNP plots of the two separate models and the joint one were produced by sending tasks to a queue manager to produce them in parallel, one picture per processor. Third, the information that MCNP reports in the output following a lost particle in the case of a cell clash was processed with a dedicated script. It resulted, thus, relatively immediate to identify which cells clash; the resolution of the clash was then implemented by negating one cell from another with a “#” operator according to the hierarchy just explained.

The process to construct the ITER full model was tailored since it was a prototype starting from two already large models. The strategies just mentioned suffice in the unlikely event that another prototype is to be built again. Nevertheless, should the ITER full model in MCNP get consolidated, it should be built from the scratch with a different approach incorporating lessons learnt which are all explained the section named “Future work”.

Modifications of D1SUNED and computational performance

The computational consumption of the ITER full model is shown in Table 3 in comparison with its constituents, considering no tally in any of the cases. The loading and running time referred to herein were obtained using Intel Xeon 8160 processors. To make the model usable, two improvements were developed in D1SUNED v4.1.2. First, OMP-based parallelization was implemented to handle the large RAM memory needs of the model. OMP (Open Multi-Processing) is a library for parallel programming in the symmetric shared-memory processors model, so all threads share memory and data. Second, some parts of the geometry loading and processing have also been parallelized in OMP. The loading time has been reduced by a factor of 4 from pure message passing interface (MPI) to OMP + MPI in 48-processor nodes, permitting a more agile debugging process.

The practicality and robustness of the consideration of the ITER full model are shown in coming examples intended to illustrate its advantages to address long-range simulations without artifacts to couple models. We show it considering the two most pertinent sources of radiation expected in ITER: the DT plasma and the 16N radioisotopes in the TCWS. Note these are representative instances of the studies still needing to be addressed satisfactorily for the safety case assessment. The simulations shown here are only to illustrate the practicality and benefits of the ITER full model. They are not intended to forecast any creditable ITER radiation field. Thus, considerations about results crediting and safety margin are irrelevant and excluded.

Neutron flux in the Tokamak Complex

The DT plasma source will be fully contained within the ITER Tokamak vacuum chamber (thus, in E-lite model currently), thus excluded and relatively far from the Tokamak Complex MCNP model.

Before this work, the most advanced approach to determine its influence across the entire Tokamak Complex involves the use of SRC-UNED34 to reconstruct the respective radiation conditions recorded in the bio-shield, the natural boundary where the Tokamak Complex MCNP model starts10. Despite recent improvements to tool44, SRC-UNED relies on a dedicated V&V, and it introduces case-dependent unapproachable uncertainties due to the space, energy, and angle of user-defined binning, as mentioned. SRC-UNED has been instrumental in the production of the two last editions of the ITER radiation atlases, but it also stands as one of the improvable points of the safety case.

The consideration of the ITER full model renders the use of SRC-UNED, WSSA files, or any other approach, unnecessary to simulate the influence of the plasma source in the Tokamak Complex. Furthermore, any distortion to the neutron field prediction due to binning is simply avoided. The neutron flux due to the DT plasma source during a 500 MW pulse in the entire facility, simulated in a single direct run, is shown in Fig. 4, avoiding any artifact to sew simulations (simplicity) and the associated distortions (enhanced robustness). This is a quantitative difference with respect to the state-of-the-art approaches with marked benefits for the preparation of the safety case.

Fig. 4: Neutron flux in the facility due to the DT plasma source during a 500 MW shot.
figure 4

It considers a threshold at 10 n cm−2 s−1, and it is computed with the ITER full model. Note B1, L1, and L2 levels are stories of the edifice hosting the lower, equatorial and upper levels of the Tokamak.

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Elaboration on the computational viability is pertinent. Showing the compatibility of radiation levels with the allocation of safety-related electronics (currently assumed as 10 n cm−2 s−1) is one of the most computationally demanding calculations. It represents a reduction of ~13 orders of magnitude in the neutron flux from the dominant radiation source, the plasma. Figure 4, showing acceptable statistical errors (ε) for all the values above the limit, confirms it can be achieved with the ITER full MCNP model. Most of the map shows reliable (ε < 0.1) or questionable (0.1 < ε < 0.2) results. Minor regions show values creditable within a factor of a few (0.2 < ε < 0.5) and only, very exceptionally, useless values are observed (ε > 0.5). The calculation required a number of Monte Carlo histories of 1.2 × 1011 considering only the transport of neutrons (mode N) and considering the global variance reduction technique14. The simulation required ~460,000 cpu h, while no stopper was identified, preventing affordable further running of histories to reach higher convergence if needed. This indicates the practicality of the ITER full model to address similar safety-related studies derived from the influence of the plasma source across the Tokamak Complex.

Sky-shine due to decay of photons from 16N

The 16N source contained in the TCWS following the irradiation of cooling water with 14.1 MeV DT fusion neutrons presents a span of 10 orders of magnitude in intensity41 in an intricate distribution across the entire facility crossing the bio-shield. The high-energy photons following the decay of 16N are known to compete with, or even outpace the plasma source influence in diverse locations beyond the bio-shield in the Tokamak Complex and outside it. It produces a remarkable leakage upwards37, and the subsequent sky-shine phenomenon. It is relevant since it affects the spatial domain of safety to public, starting in the facility fence. While the highest specific activity is found in the pipes inside the bio-shield, most of the activated water volume of the TCWS lies outside the bio-shield. Simulating the TCWS influence with state-of-the-art approach considering the Tokamak Complex reference model presents a challenge: the dominant region of the source (inside the bio-shield) would need to be included in an unrepresented region of the model: the region inside the bio-shield is empty in the Tokamak Complex reference model. This is using a model beyond its scope, which consequences have been unapproachable so far. WSSA or SRC-UNED could also be considered with the already mentioned limitations.

Alternatively, a tailored extension of the Tokamak Complex MCNP model with the pertinent geometry could be implemented. However, tailoring MCNP models for specific safety demonstrations is subtly challenging. The need to document all the models, to carry out independent verifications of each of them, and the potential design evolution requiring simultaneous updates to all the models, are undesired workload multiplication factors. Resources limitation often stalls this approach; some models are abandoned or more worryingly, unconsciously obsoleted. These reasons are, once more, the manifestation of the unsatisfactory approach of considering separate reference models for the regions inside and outside the bio-shield.

The use of the ITER full model resolved most of the previous considerations. In Figs. 5 and 6 the biological dose due to the 16N radioisotopes contained in the TCWS during a 500 MW pulse is shown. The pattern shown clearly corresponds to a sky-shine phenomenon that originated in the pipes immediately below the bio-shield lid carrying the highest concentrations of 16N. At ground level, the ε is lower than 10% near the fence. The calculation required a number of Monte Carlo histories of 5 × 1010 with global variance reduction and a computational load of ~260,000 cpu h, showing the practicality of the ITER full model once more.

Fig. 5: Top view of the biological dose rate during operation at ground level due to 16N decay (Z = −140 cm).
figure 5

The gray-out area corresponds to the Hot Cell complex region unrepresented in the ITER full model and excluded to avoid misleading conclusions.

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Fig. 6
figure 6

Front view of the biological dose rate during operation in the middle plane due to 16N decay (X = 0).

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Discussion

A heterogeneous MCNP model, including the Tokamak and the Tokamak Complex of ITER, is presented in this work: the ITER full model. We have shown how it permits to address integral nuclear analysis across the entire facility. It permits avoiding sophisticated artifacts to sew partial simulations and the associated unassessed uncertainties. This results in reinforced analysis robustness which will facilitate the preparation of a more reliable safety case in the years ahead. Relevant examples of qualitative improvements thanks to this model are given for (i) the determination of the neutron flux across the Tokamak Complex due to plasma, and (ii) the determination of the biological dose rate outside the Tokamak Complex due to the 16N in the TCWS. Both cases, run in single dedicated simulations, were subject to cumbersome patching and noticeable assumptions before the present work. Note that the ITER safety case is important for the rest of the industry in many aspects.

The consideration of this full model as a basis for future works may save computational resources and facilitate the explanations of radiation conditions predictions. It represents an important support to the ITER safety case assessment.

We identify the need to produce a consolidated model to promote the adoption of the approach by the community and to smooth its application to the ITER safety case. On the one hand, it should be built based on a new and specifically conceived universe structure, reconcile the numbering of cells, surfaces, materials and universes implemented in E-lite, and it must be implemented with a GIT-like version control system. It must be fully commented as well to facilitate its use. Importantly, it should permit easy traceability of the assumptions, so the model can be switched from a “best estimate model” to a “conservative model”. On the other hand, the model computational load can be reduced with the implementation of negative universes, the conception of simpler universe containers, the elimination of redundant geometry words, flattened negations, and cell splitting. It would permit addressing relevant scoping studies for uncertainties quantification. Finally, it is also possible to implement modifications that could nearly automate the extraction of partial models for local/specific non-safety studies, thereby facilitating the overall management of ITER nuclear analyses by centralizing studies around a single, traceable, verified and validated nuclear analysis model.

Methods

Production of MCNP models

The MCNP models other than E-lite10 and the Tokamak Complex 202013 that have been incorporated into the ITER full model have been produced following the sequence: (i) simplification, healing, and refurbishment of CAD model with Spaceclaim (www.spaceclaim.com), (ii) translation to MCNP with SuperMC7, (iii) lost particles debugging with MCNP3 and D1SUNED4. Automatic void generation was considered. The models were integrated by universe allocation.

Calculations

All the calculations conducted for this work have been executed with D1SUNED4 v4.1.2. Global Variance Reduction technique14 was considered. The nuclear data considered for neutron transport corresponds mainly to FENDL3.1 c/d45. The photon transport library considered was MCPLIB8446 in any case. Results in MCNP mesh format were converted to vtk format and plotted with Paraview47. The voxel size considered for the determination of neutron flux inside the Tokamak Complex was 1 × 1 × 1 m3. The voxel size considered for the determination of the biological dose rate outside the Tokamak Complex was 5 × 5 × 5 m3.