D1SUNED system for the determination of decay photon related quantities

Fusion Engineering and Design 151 (2020) 111399

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D1SUNED system for the determination of decay photon related quantities 1,

1

P. Sauvan *, R. Juárez , G. Pedroche, J. Alguacil, J.P. Catalan, F. Ogando, J. Sanz

T

Dept. Ingeniería energética, Universidad Nacional de Educación a Distancia (UNED), Calle Juan del Rosal 12 Madrid 28040, Spain

ARTICLE INFO

ABSTRACT

Keywords: Direct-one step method MC transport simulation Nuclear data ITER Operational radiation exposure ALARA

The neutron fields alter the radioactive inventory of the irradiated materials leading to subsequent decay photon fields. In some cases, these fields are of relevance either intended or undesired, normally involving safety and economics aspects. The determination of these fields can be of paramount complexity if high spatial resolution is required. The determination of these fields requires both radiation transport and activation calculations. The Direct-one-Step methodology, under the assumption that the radioactive inventory activity is lineal with the neutron flux, can address the problem with only one coupled neutron-photon transport calculation. In this paper the D1SUNED code for the calculation of decay photon field and related quantities using D1S methodology is presented. Calculation capabilities including the determination of 3D decay photon sources, filtering options, and other relevant features are presented. In terms of computational load, D1SUNED, which is based on MCNP5 code, presents improvements with respect to MCNP. It can save a 79% of the RAM memory used to store the geometry, a 98% of the loading time, and an acceleration of a factor two by controlling the decay photon emission, boosting the simulations for ITER-like problems. D1SUNED has been validated with the FNG benchmark experiment considering the null hypothesis rejection test and the C/E ratio with very positive results. As a consequence, D1SUNED has become a reference tool for the design of ITER, and other relevant nuclear fusion facilities.

1. Introduction The neutron fields can alter the radioactive inventory of the irradiated materials, giving rise to a subsequent decay radiation field. Usually, the decay radiation field is negligible with respect to the prompt radiation field produced during the neutron irradiation. However, after the end of irradiation it becomes the main field of concern in the facility. An example of beneficial and intended creation of decay radiation fields are those from radioisotopes for medical applications, produced after irradiation of precursors in fission reactors, or particle accelerators. An example of an undesired situation resulting from the decay radiation field is the exposure of workers conducting maintenance activities in reactors. Provided that safety and economics aspects are always involved in their presence, the determination of the decay radiation field has been an active research field in the computational neutronics in the past years. It has been particularly intense in relation to the ITER project design needs for planned in-situ maintenance activities. It has triggered the development of a large set of tools [1–9] and analysis [10–34]. The source term of the decay radiation field is characterized by a set of first order differential coupled equations of constant coefficients. Its

general resolution has been subject of study for a long time and diverse computational tools were created to this end (FISPACT [35], ORIGEN [36], ACAB [37] or ALARA [38]). However, the use of this information to accurately determine the consequences of the decay fields with high spatial resolution requires the use of sophisticated mesh-based Rigorous-Two Steps (R2S) codes like R2SUNED [1]. The R2S methodology performs the activation calculations using dedicated inventory codes. On return, this approach results in intricate, long and cumbersome calculations, unpractical in many situations [16] and prone to human errors. However, under certain circumstances, some approximations can be introduced in the general system of equations. Provided isotopes burnups are negligible, and the radioactive daughter is produced involving just one neutron capture, a simplified expression of the equations can be obtained. It shows a linear dependence between the activity of the radioisotope of interest “d” and its production rate, as shown in Eq. (1), what is the basic assumption of the D1S method.

A d (x, T) =

d Nd (x,

Where,

Corresponding author. E-mail address: [email protected] (P. Sauvan). 1 Both authors contributed equally to this work. ⁎

https://doi.org/10.1016/j.fusengdes.2019.111399 Received 26 June 2019; Received in revised form 28 September 2019; Accepted 4 November 2019 0920-3796/ © 2019 Elsevier B.V. All rights reserved.

T) = S(x)h(T),

(1)

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• A (x, T) is the activity of the radioisotope at point x after an irradiation scenario T. λ • and N (x, T) are the decay constant and the concentration of the radioisotope at point x after an irradiation time T. • S(x) is the radioisotope production rate. h(T) is a parameter, de-

In this paper we present and describe the system D1SUNED v3.1.2, a new implementation of the D1S approach implemented in MCNP v5.16 [39] that overcomes all the previously mentioned limitations shown by other D1S implementations. It is as powerful as the most powerful R2S system (like R2S-UNED [1]), offering for the first time a solid alternative to R2S method with the benefits of the D1S approach. D1SUNED deploys a large and complete variety of computational capabilities and a boosted computational performance. In addition, we have conducted a verification and validation exercise to determine photon decay related quantities of relevance for ITER applications explained in this work. All these features motivate that D1SUNED has become a reference tool in the ITER design [12,13,15,20,21].

d

d

d

pending of irradiation scenario T, which describes the activation process. It is usually referred as correction factor.

This assumption was introduced for the first time by Valenza et al. [7] in 2001, and it is the basis of the Direct-One Step (D1S) methodology. In practice it allows coupling the neutron and decay photon transports and carry them out simultaneously in the same Monte Carlo simulation. This approach leads to much simpler calculations of the decay photon field than R2S methodology. The implementation of this methodology requires the modification of the transport code and the use of dedicated cross-section libraries, so that the activation reaction and the subsequent photon decay are treated as any other prompt reaction. Some adjustments are needed a posteriori to account for the irradiation scenarios and the radioisotopes lifetimes. D1S approach requires the characterization of the radioisotopes of concerns and the reactions producing them a priori. In addition, whether the radioactive inventory activities show lineal dependence with the flux must be confirmed by the user in each case. The D1S approach has been implemented in diverse tools [7,8]. However, up to now these tools were missing important aspects. Their main and most obvious limitations to the date were three. Firstly, the production of D1S modified transport libraries was not automatic. On the one hand, a limited number of libraries lead to a very constrained set of addressable problems. Stainless steel activation for cooling times in the range of 106 s have been relatively well simulated before [7,8]. Nonetheless, other materials commonly found in fusion reactors like copper-, aluminum- and tungsten-based alloys or concrete, or simply different cooling time could not be properly simulated. On the other hand, the choice of reference cross-section libraries evolves in time for long-term projects like ITER and DEMO. This situation leads to an obsolescence of the D1S modified libraries, so they need a timely upkeeping that has been hardly followed. Secondly, the analysis capabilities of the previous implementations were not as powerful as those from the R2S based systems, at least for geometries as complex as ITER. Production and portability of external decay photon files was not possible, limiting the revisability of the calculation and limiting the compatibility of tools. Change of geometrical configurations during irradiation and shutdown scenarios was not feasible, so situations like liquids drainage during maintenance or the insertion of temporary shields were not addressable. The consideration of different irradiation scenarios for different components was not available, excluding the study of situations of coexistence of components with different lifetimes. Finally, the simulation with D1S schemes was very heavy in terms of computational resources when considering geometries as complex as ITER, provided they are NP simulations. Sensitivity studies, in example varying impurities content, might require larger computational loads than R2S systems. In summary, previous D1S implementations allowed computing only a limited set of problems and many times making use of obsolete nuclear data sets. In the past, these implementations were encompassed with many of the ITER needs and they have played an important role. However, as the ITER design progresses, the situations to simulate show an increasing complexity, normally beyond the capabilities of those tools. The limitations of previous tools have prevented the D1S methodology from replacing the R2S approach in the design of important nuclear fusion facilities. Even when it offered a drastic improvement in terms of performance, sophistication, and other aspects, it has been considered, as most, a complement to the R2S method. It is relevant also to note a new recent hybrid approach [9] that might be of significance in future demanding D1S tools to make a step forward remain useful along the years.

2. D1SUNED system for the determination of decay photon related quantities The D1SUNED system consists of the following tools:

• A script that produces the modified D1S transport libraries (libraries including information of decay photon emission). • A script to determine the “correction factors” which are the ratio •

between production rate of the radioisotope of concern and its activity. This factor captures the details of the irradiation history and the lifetimes of the radioisotopes involved. A patch code to be applied on MCNP5 to build the D1SUNED transport code. Note that all the primitive MCNP features are kept, and some have been extended.

Beyond specific decay photon field calculation features, which will be described below, D1SUNED system can be tuned for a large set of problem (e.g., D1S modified transport library for any parent isotope can be produced easily). It incorporates new developments to enhance the performance of the native code MCNP5 in terms of computational demands. 2.1. Modified D1S transport library D1S methodology requires the use of modified transport libraries to consider the information on the production of decay photons by nuclear disintegration. Such D1S-specific libraries should be produced ex professo for all precursor isotopes and reactions of interest. The prompt photon information of the original library is replaced by decay photon information of interest. Nowadays, different nuclear data libraries are considered in ITER depending whether transport or activation calculations are performed. In D1S methodology transport and activation are performed in the same simulation, although the activation calculation is performed implicitly through the application of the correction factors to nuclear reaction rate. During the transport calculation the neutron interaction, the subsequent outgoing channel (scattering, absorption, neutron emission) and its angular-energy distribution should be evaluated with transport nuclear data. As the photons involved in D1S methodology are decay photons emitted by a radioisotope produced during the neutron interaction, activation cross section should be used to estimate the decay photon production rate. The energy and yield of the decay photons are provided by decay nuclear data. The mixing of both type of data is possible thanks to the structure of ENDF and ACE nuclear data format where the photon production cross section can be defined as an explicit cross section. In this case the prompt decay photon production cross section can be easily substituted in the library by decay photon production cross section and used during the transport simulation. This allows reproducing the activation process with the intended dedicated nuclear data. A python script has been conceived to process original transport libraries in ENDF format into D1S modified transport libraries. The resulting D1S library is later processed with NJOY software [40] to convert it to ACE format, ready for MCNP5. It has been used to produce nuclear data libraries for a set of parent isotopes covering all the 2

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radioactive inventory of interest for the needs of ITER applications for in-situ planned maintenance situations. For each new type of simulation, the user must determine the radioisotopes of concern and the reactions producing them from the original materials. After confirmation that they can be treated within D1S assumptions (validity of Eq. (1)), the user must consider the required data from the mentioned data set.

photon weight with its corresponding correction factor. The other labels are used to identify the parent isotope or the location photon emission. This information is used to identify contributions for specific user defined tally (parent or source contribution).

2.2. Evaluation of the correction factors

D1SUNED has preserved all the capabilities of MCNP5. This means, for instance, full compatibility with the variance reduction techniques, use of surface source read and write function, or continuing a simulation to a higher number of histories. The tally options from original MCNP5 have been preserved in D1SUNED, what includes both cell and mesh tally, and the possibility to apply multiplying factors on them. Either FM or DE&DF cards can be used. Thus, decay photon field intensity can be tallied, as well as biological doses from it (referred to as shutdown dose rates). The computation of new quantities has been implemented. The first one, called the “decay photon source” (DPS), records in a mesh tally the map of the decay photon source intensity. The computation of this quantity is mandatory in the R2S method, and it is still important in D1S method. It provides a valuable source of information to analyze of the decay photon field. The visualization of the DPS is also a powerful way to confirm the correctness of the derived decay photon field. D1SUNED can read the DPS to run an only-decay photons simulation. Finally, D1SUNED can produce the DPS in the Common Decay Gamma Source (CDGS) format that is compatible with all the relevant R2S systems. Note that the statistical error of the DPS can be also determined, what is a relevant indicator of the quality of the calculation. The second quantity called “source importance” (SI) computes, using a mesh tally, the contribution of the decay photon source to a specific tally. The SI function produces a map with the contribution of each source location to a specific target tally set by the user. This capability is of relevance in shielding analysis, as it highlights the regions that contribute to the dose at a specific location. Filtering options in the decay photon quantities have been also implemented, both in cell and mesh tallies. The quantities, like the DPS or the decay photon field or derivations of it, can be broken down. One filtering options splits the tallies by radioisotopes of concern that produce the decay photons. Another filtering option splits the tallies by the MCNP cells in which the decay photons were produced. The filtering options are of extreme importance to analyze quantities as complex as the Shutdown Dose Rate. With it, one can obtain a clean view of the drivers of the decay photon fields. An example is the determination of the role that cobalt impurities may play. Another example is the identification of regions of the geometry which activation is of concern for a given maintenance task, so a shielding can be placed accordingly. Different irradiation histories and different cooling times can be applied to different MCNP cells. In addition, the allocation of material and density to each cell can be considered different for the transport of the neutrons and the decay photons. In practical terms, these features enable the simulation of complex scenarios. D1SUNED can simulate components with different lifetimes in a reactor, the inclusion of temporary shields and/or the absence of components only during maintenance periods. The liquids drainage during the maintenance periods can be also simulated. All these advanced features, excepting the filtering applied only to tallies, are novel and unique to D1SUNED; they can be all combined in the same run, what has unlocked the simulation of a large set of complex situations at once with the subsequent saving of computational resources. This is one of the reasons why D1SUNED is being widely used in the design of ITER. Examples of the use of the aforementioned features applied to ITER can be found in [10–12,14,19].

3. Calculations capabilities

D1S methodology assumes the activity of the radionuclide directly proportional to the production rate of this radionuclide regardless the neutron flux spectrum. The ratio of the activity over the production rate is called “correction factor” and it depends only on the radioisotope features and the irradiation scenario. This factor plays the implicit role of the activation process. Eq. (1) is the condensed form of the relation between the nuclide activity and the reaction rate in the D1S approximation. An extended form of this equation after the irradiation of the jth step with duration Tj, is written as

A dj (x) = S(x)f j (1

e

d Tj)

+ A dj 1 (x)e

d Tj,

(2)

fj being a factor proportional to the irradiation pulse intensity. Assuming there is no nuclide d at the beginning of the irradiation scenario, the initial activity to be considered in the first irradiation step (j = 1) is zero. With this condition the activity after the jth irradiation (or cooling) steps is

A dj (x) = S(x)hj

(3)

hj is the recursive function

hj = f j (1

e

d Tj )

+ hj

1e

d Tj,

(4)

with h0 = 0. The value of hj in Eq. (4) can be solved easily with a simple iterative scheme, allowing an analytical evaluation of the correction factor. A python script calculates such correction factors for all radioisotopes involved in the calculation and for a given irradiation scenario. The script produces an output file ready to use by D1SUNED. 2.3. D1SUNED transport code D1SUNED computational flow needs three input files. The main one is based on the MCNP5 input file. It contains the geometry description, the source definition, the materials definitions with cross-sections allocations, and the tallies. Few more cards that govern the additional computational and analysis features of the code (e.g. the cooling time/s to be considered in the simulation) have been implemented following the MCNP input standards. No additional skills with respect to MCNP5 are required to write a D1SUNED input. The two other input files are related to treatment of the activation by D1SUNED. One of the files called “reaction file” contains all specific activation reaction channels to be considered in the D1SUNED simulation. The other file called “irradiation file” contains the correction factors for all the radioisotopes defined in the “reaction file”. The working scheme of the implementation of the D1S methodology in D1SUNED is as follow. In the transport process of MODE N P (neutron and photon transport), a photon emission is sampled after each neutron interaction (even if the neutron interaction does no involved photon production). This is a non-analog photon production method where the weight is adjusted by the probability of the photon production after a neutron interaction. These photons will be emitted only if they are produced by a reaction listed in the reaction file. The decay photon produced is tagged with different parameters corresponding to the reaction channel and the location of the event, no additional weight modification is applied at this step. The photon is transported with usual MCNP algorithm. When the photon is tallied, the label of the reaction originating the neutron emission is used to identify the daughter radioisotope and to adjust the

4. Enhancement of the code performance D1SUNED is conceived to be used in complex nuclear analysis. A good example of such complexity is the determination of Shutdown Dose Rates (SDDR) in ITER. It involves the use of a very complex model, usually 3

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modifications of Cmodel [41], the use of intensive variance reduction [42,43] and High Performance Computing to reach the desires statistical errors in the regions of interest. Under such conditions very high computational demands have been observed, arising from the MCNP5 v1.6 performance, and shared by all the common tools to determine SDDR. A short review of the implications is suitable at this point. A very long time for the initialization of the simulation may be required. This reduces the efficiency of parallel computation. The slave processors are waiting for hours for the master to process the input file. Let us assume a computational load request of 5000 processors for 24 h, a prototypical large simulation of nuclear analysis in HPC infrastructure, like former Helios or current Marconi [44]. If the loading time is 5 h, then, the 20% of the simulation time is wasted, adding about 25.000 cpu.hr, or 2.85 cpu.yr. In the case of C-model, the RAM memory load for the geometry storage is about few Gigabytes. When simulating in parallel using MPI libraries, this memory is allocated to each process. Usually, this large RAM memory demand per process exceeds the total memory available

on the computational node. In these cases, less processes per node must be allocated to reduce the total budget of memory of the simulation, what is another source on inefficiency and implies wasting computational resources. Node loads (i.e. processes allocated divided by node processors) as low as 25% have been observed for instance for ITER applications on Marconi computer. This corresponds to a waste of the 75% of the computational time. Finally, the incorrect definition of the geometry, defined as the violation of the univocal definition of every region of the space and manifested as “lost particle events”, can bias the results and reduce the simulation efficiency. These errors in the cell definition must be fixed in a debugging process, being the most obvious approach the use of the MCNP plotter to seek dotted red lines illustrating the issue. However, complex models like Cmodel [41] present multiple universes levels, with profusion of nesting at different parts of the geometry. One of the consequences of this complexity is that the time required to plot with lines in the MCNP plotter becomes virtually infinite. The debugging process relies then in indirect approaches, leading to a significant increment of time. D1SUNED presents modifications to loading-, storing- and plottingrelated routines of the MCNP5 v1.6 code mitigating these three situations with noticeable improvements[45]. The MCNP model, produced for the nuclear analysis of the ITER EP#16 [15] and containing the European TBMs, has been considered to illustrate them. In Table 1 the performances of MCNP5 v1.6 and D1SUNED are compared. A reduction of the 79% is observed for the RAM memory, and a 98% for the loading time. In Fig. 1, the EP#16 geometry integrated in C-model is displayed with lines.

Table 1 Computational loads of MCNP5 and D1SUNED involved in the simulation of the ITER EP#16 [15]. Parameter

MCNP5

D1SUNED

Reduction

RAM memory Loading time Plotting time

10.2 GB/cpu 304 min ∞

2.2 GB/cpu 6.5 min 50 min

79% 98% ∞

Fig. 1. Cross section view of the MCNP model integrated in C-model v1 R2.1 [41]. 4

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The implications are as follows. To run the model with MCNP5 in Marconi computer, in SKL partition (maximum 24 h runs), a 20% of the simulation is wasted in the loading of the input, and 63% is wasted due to the reduction of number of process per node (computing nodes have 192 Gb of RAM each, so the maximum load to the nodes was 37%), while in D1SUNED execution the simulation can be carried out with the full computing power. This means that D1SUNED can run about 3.3 times more histories than MCNP5 on the same computer and time period. MCNP5 is unable to plot the geometry with lines, while the model can be plotted with lines in few minutes with D1SUNED (Fig. 1). Finally, the debugging time of the process is significantly reduced thanks to these enhancements. A last feature of D1SUNED to speed up the simulation is related to the control of the decay photon emission. The photon transport in CModel with MCNP in N P mode may represent a significant fraction of the total simulation time (around 60%). However, and depending on the problem specification, many of the photons produced have no effect on the region of interest, where the locally produced photons dominate. In these circumstances a large fraction of the photons is transported for nothing. To avoid this waste of simulation time, D1SUNED can switch off the decay photon emission in the simulation from cells or from entire universes known to contribute negligibly to the region of interest. In the case of the ITER EP#16, where the region of interest for the SDDR was the port interspace, the decay photon emission from the blanket shield modules and the divertor was turned off, as shown in [15]. The SDDR results did not change, but the simulation run a factor x2 faster than considering the emission of such decay photons.

5. Verification exercises D1SUNED has been verified with a set of computational exercises described in this section. A comparison with the analytical solution of the one step radioisotope production differential equation has been conducted. A thin layer of 10−4 cm and 1 cm2 has been simulated to be exposed to a planar flux of 1 n. cm-2.s-1. One irradiation pulse of 107 s was considered, and results have been evaluated at 105 and 106 s after the end of the pulse. Each case has been run four times, each considering a mono-energetic flux of 14, 1, 0.1 and 10-6 MeV. Activities of the resulting radioisotopes were determined and compared between the analytical solution and with D1SUNED results. The exercise considered a set of elements commonly found as relevant in ITER applications: Iron, Cobalt, Copper, Nickel, Tantalum, Tungsten and Sodium. The results of the comparison showed an agreement over 99% in all the cases. A benchmark capturing some relevant features of the determination of the SDDR in ITER exist [46], usually referred to as “ITER cylinder benchmark”. It has been addressed many times before to check the consistency between the different tools. One of the most robust resolutions of the benchmark corresponds to R2SUNED [1]. This benchmark has been repeated with D1SUNED and compared as shown Fig. 2. The small differences are due to the R2S approximations. It considers averaged neutron fluxes over cells inside a voxel for the activation and binned energy for the neutron flux and decay photons, while D1S makes a point-wise treatment of these three. The results show very good agreement between both codes. Furthermore, a verification test suite on top of the MCNP standard release has been defined and passed successfully. 6. FNG experimental validation exercise D1SUNED has been validated experimentally with a neutron irradiation experiment performed using the Frascati Neutron Generator (FNG) [47]. The material assembly is suitable to generate a neutron flux spectrum similar to that anticipated for the outer vacuum vessel region of ITER. The experimental set-up is shown in Fig. 3. The mock-up was irradiated for a time sufficiently long to create a level of activation monitored by dosimeters and other radiation detectors after shutdown. The experiment configuration was designed to allow the validation of dose rate calculations in a typical and complex shield geometry, compatible with the intensity of the available neutron source and its capability to induce sufficiently high dose levels in the mock-up. It was conceived as relevant for ITER applications. Null hypothesis testing has been conducted. The null hypothesis is H0: The experiment and simulation results belong to populations with

Fig. 2. Results of the cylinder benchmark with D1SUNED and R2SUNED.

Fig. 3. Schematic view of the experimental set-up. 5

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the same mean value. This is, indexing populations from the experiment as “1” and from the simulation as “2”, μ1=μ2. This is checked with the statistics Z described as

z=

x 2 1

Table 2 Radioisotopes of concern, production pathways from their precursors and correction factors considered in the resolution of the FNG exercise.

y +

2 2

(5)

Daughter Radioisotope

Pathway

24

27

Na

Being x and y measurements of the experiment and the simulation respectively, and σ1 and σ2 their standard deviation. A Gaussian distribution has been assumed for Z. A significance level for hypothesis rejection of α = 5% has been selected. Thus, if p = P(|Z| > |z|) < 5%, we can correctly reject that the D1SUNED and the experiment are measuring the same in the 95% of the cases. The discussion on the null hypothesis testing here is supported with a discussion on C/E ratio. Activation calculations have been performed with ACAB code [36] using EAF2007 activation cross-sections libraries [46] to check that the radioactive inventory of interest is dominated by reactions with the expression from Eq. (1). In Table 2, the radioisotopes contributing at least a 99% of the contact dose rate at any cooling time are shown. With them, the reactions leading to the production of at least the 99% of those radioisotopes. These have been considered in the D1SUNED simulations with the quoted correction factors. The D1SUNED libraries were built with the FENDL3.1c/d [48] for transport and EAF2007 [49] for activation. MCPLIB84 has been considered for photon transport [50]. During irradiation, the cavity has been considered empty and the lateral access hole plugged, whereas in the measurement phase the detectors were considered inserted and connected through the lateral opening. These changes in the geometry configuration from irradiation to shutdown have been modelled in D1SUNED. Two experiments were conducted with two irradiation scenarios and different initial conditions and detectors. In experiment 1, a GeigerMüller (GM) was used to measure doses at cooling times of 1, 7, 15, 30 and 60 days. The total experimental uncertainty is quoted to be ± 10%. For experiment 2, a plastic scintillator NE-105 was considered to measure doses, and a liquid scintillator NE-213 was considered to measure photon flux. The cooling times for experiment 2 were 2.08, 15.9, 25.2 h; and 4, 8.2, 12.2 and 19.3 days. The experimental uncertainty for NE-105 is quoted as ± 3.9%, while for NE-213 it is ± 4.6%, ± 4.2%, ± 5.0%, ± 5.8%, ± 5.8%, ± 6.8% and ± 6.6% for each of the cooling times. To model the GM and NE-213 detectors, air-to-kerma conversion coefficients from ICRP-74 were considered [51]. To model the NE-105 detector, flux-to-dose conversion coefficients from ANSI/ANS 6.1.1.1977 have been considered [52] for “effective dose”. The simulations were run until the statistical errors were lower than 3%. A deep discussion on the uncertainties in the estimation of decay photon related quantities with D1SUNED exceeds the scope of this paper. Only a tentative estimation of the uncertainties in the current simulation is made as an initial approximation to the issue. In Table 3 a list of uncertainties in the simulation related to diverse sources is shown. In most of the cases, these are guesses, and they are all already propagated to the quantity under study with simplified or approximated approaches. Note the other sources of uncertainties have been omitted, such as the correspondence between the MCNP model and the real arrangement, the chemical composition of the materials, or the source modelling. No traceable information on them has been found to estimate a value. Adding the errors in quadrature, for results involving ANSI/ANS 6.1.1.-1977 the error is assumed to be 26%. For the rest, 17%. Given the unassessed sources of uncertainty, these seem reasonable assumptions. In Tables 4–6 the experimental and simulation results are shown, as well as the probability of the acceptance of the null hypothesis testing having z > Z. For experiments #1 and #2, H0 cannot be rejected in any of the

48

Sc

51

Cr

54

Mn

56

Mn

59

Fe

57

Co

58

Co

60

Co

57

Ni Cu

64 74

As As 89 Zr 76

89m

Y

92m

Nb

96

Nb

99

Mo

99m

Tc

Correction factor Exp. 1

Al (n, α) 24Na Al (n, α) 24mNa (IT →) 24Na 48 Ti (n, p) 48Sc 49 Ti (n, np) 48Sc 51 V (n, α) 48Sc 50 Cr (n, γ) 51Cr 52 Cr (n, 2n) 51Cr 54 Fe (n, α) 51Cr 55 Mn (n, 2n) 54Mn 54 Fe (n, p) 54Mn 56 Fe (n, t) 54Mn 58 Ni (n, pα) 54Mn 55 Mn (n, γ) 56Mn 56 Fe (n, p) 56Mn 57 Fe (n, np) 56Mn 57 Fe (n, d) 56Mn 58 Fe (n, t) 56Mn 59 Co (n, α) 56Mn 58 Fe (n, γ) 59Fe 59 Co (n, p) 59Fe 62 Ni (n, α) 59Fe 58 Ni (n, np) 57Co 58 Ni (n, d) 57Co 59 Co (n, 2n) 58Co 59 Co (n, 2n) 58mCo (IT →) 58Co 58 Ni (n, p) 58Co 58 Ni (n, p) 58mCo (IT →) 58Co 59 Co (n, γ) 60Co 59 Co (n, γ) 60mCo (IT →) 60Co 60 Ni (n, p) 60Co 60 Ni (n, p) 60mCo (IT →) 60Co 61 Ni (n, np) 60Co 61 Ni (n, np) 60mCo (IT →) 60Co 61 Ni (n, d) 60Co 61 Ni (n, d) 60mCo (IT →) 60Co 63 Cu (n, α) 60Co 63 Cu (n, α) 60mCo (IT →) 60Co 58 Ni (n, 2n) 57Ni 63 Cu (n, γ) 64Cu 65 Cu (n, 2n) 64Cu 75 As (n, 2n) 74As 75 As (n, γ) 76As 90 Zr (n, 2n) 89Zr 90 Zr (n, 2n) 89mZr (IT →) 89Zr 92 Mo (n, α) 89Zr 92 Mo (n, α) 89mZr (IT →) 89Zr 90 Zr (n, 2n) 89Zr (β+/E.C →) 89mY 90 Zr (n, 2n) 89mZr (IT →) 89Zr (β+/E.C →) 89mY 92 Mo (n, α) 89Zr (β+/E.C →) 89mY 92 Mo (n, α) 89mZr (IT →) 89Zr (β+/E.C →) 89mY 93 Nb (n, 2n) 92mNb 92 Mo (n, p) 92mNb 96 Mo (n, p) 96Nb 97 Mo (n, np) 96Nb 97 Mo (n, d) 96Nb 98 Mo (n, t) 96Nb 98 Mo (n, γ) 99Mo 100 Mo (n, 2n) 99Mo 98 Mo (n, γ) 99Mo (β− →) 99mTc 100 Mo (n, 2n) 99Mo (β− →) 99mTc 27

Exp. 2

8.12·10−1

1.50

−1

5.23·10

7.01·10−1

5.11·10−2

5.56·10−2

4.66·10−3

5.00·10−3

1.09

3.18

3.21·10−2

3.48·10−2

5.35·10−3

5.74·10−3

2.03·10−2

2.19·10−2

7.57·10−4

8.12·10−4

5.86·10−1 8.37·10−1

8.19·10−1 1.65

7.82·10−2 6.82·10−1 3.49·10−1

8.60·10−2 1.04 4.26·10−1

1.32·10−1

1.48·10−1

7.14·10−1

1.13

3.97·10−1

4.96·10−1

measurements or cooling times, as p > α in any case. In other words, we cannot exclude that the experiment and the simulation are taking measurements belonging to populations with the same mean. The C/E ratio for experiment #1 is comprised within the range of 0.82 < C/E < 1.05 for all the cooling times, while for experiment #2, it is in the range from 0.79 < C/E < 1.11. In many cases the C/E is 6

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source contribution to a specific tally, iii) the filtering of these new quantities by radioisotope and/or cell of production of the decay photon, iv) the consideration of multiple irradiation scenarios and cooling times in the same run and v) the consideration of different materials allocation during neutron transport and decay photon transport. These new features have unlocked the determination of decay photon fields in an unprecedented extended range of problems complexity, with special relevance in ITER to the date. Another aspect of remarkable improvements brought by D1SUNED is the reduction of the computational demand in terms of geometry initialization time, RAM memory consumption, and time to plot with lines. Examples of relevance show reductions in the range of the 80% and beyond. The possibility to control the decay photon emission can also accelerate the calculations in a factor two in addition. Such enhancements make D1SUNED most suitable to address problems of paramount complexity, like those normally found in ITER nuclear analysis. D1SUNED has been verified versus simple analytical calculations, as well as in comparison with other computational tools in a computational benchmark with showing a robust agreement. D1SUNED has been validated with the FNG experiment considering the null hypothesis rejection test and C/E ratio. With a significance level of the 5%, we cannot reject that the code and the experiment are taking measurements from populations with the same mean. The C/E ratios are comprised between 0.79 and 1.11 showing that the D1SUNED offers results systematically close to the experiment. Disagreements can be attributed to approximated and missing uncertainties of both the experiment and calculation. Under these conditions, D1SUNED can be considered validated for the determination of decay photon fields in ITER and similar facilities.

Table 3 Estimated uncertainties considered in the simulations of the FNG experiments. Uncertainty

Exp 1 kerma

Exp 2 – effective dose

Exp 2 – decay p flux

Mat. density & cross-section for n transport Mat. density & cross-section for p transport Cross-sections for activation Source power Selection of isotopes Irr. time profiles Conversion factors Statistical error Total

6%

6%

6%

15%

15%

15%

3% 3% 2% 1% – < 3% 17%

3% 3% 2% 1% 20% < 2% 26%

3% 3% 2% 1% – < 2% 17%

Table 4 Results of the FNG experiment #1, GM detector. Cool. Time

Experiment (μSv/h)

Simulation (μSv/h)

p(%)

C/E

1d 7d 15d 30d 60d

2.46 0.699 0.495 0.416 0.316

2.01 0.647 0.506 0.432 0.333

28.5 68.9 91.2 84.9 79.5

0.82 0.93 1.02 1.04 1.05

Table 5 Results of the FNG experiment #2, NE-105 detector. Cool. time

Experiment (μSv/h)

Simulation (μSv/h)

p(%)

C/E

2.08 h 15.9 h 25.2 h 4d 8.2 d 12.2 d 19.3 d

375 11.7 3.56 1.22 0.759 0.667 0.613

300 10.4 3.34 1.32 0.846 0.73 0.653

34.7 63.8 80.3 77.2 69.7 74.1 81.8

0.80 0.89 0.94 1.08 1.11 1.09 1.07

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements

Table 6 Results of the FNG experiment #2, NE-213 detector. Cool. time

Experiment (p cm-2 s-1)

Simulation (p cm-2 s-1)

p(%)

C/E

2.08 h 15.9 h 25.2 h 4d 8.2 d 12.2 d 19.3 d

13000 523 179 67.6 38.2 33.7 27.3

12720 442 142 56.9 37.8 33.2 30.2

90.4 29.8 15.0 30.8 95.2 93.6 58.9

0.98 0.85 0.79 0.84 0.99 0.99 1.11

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