Impact of fusion reactor neutronics modeling for transmutation and thermal feedback

Fusion neutronics calculations provide important metrics pertinent to fusion device operations, such as tritium breeding ratios (TBRs) and data on heat deposition, material activation, and damage. Because of the high computational burden required to generate a high-fidelity Monte Carlo simulation of a 3D fusion device, various assumptions are made to reduce computational time by simplifying the reactor model or the calculation iteration. This paper explores the impact of fusion neutronics metrics such as the TBR and decay heat of structural materials based on assumptions of material composition in the fusion reactor and temperature modeling of materials. Results show that for compact tokamaks with high power and long operational cycles, the transmutation of structural materials is significant enough to cause a substantial change in the flux spectrum and decrease the TBR by 1.68% after 2 years of full power operation. Additionally, assuming a constant temperature and material density can impact the TBR calculations up to 3%.


Introduction
In compact tokamaks, high-fidelity fusion neutronics analysis takes on increased significance.Compact tokamaks have DE-AC05-00OR22725 with the US Department of Energy (DOE).The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes.DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
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higher neutron fluence as a result of their increased power density and operational lifetime.Compact designs leave less room for shielding around sensitive components and increase the significance of neutron streaming pathways.
Fusion neutronics is a comprehensive assessment of phenomena related to the transport of the fusion neutrons and their interactions with system components, including tritium breeding ratio (TBR), material activation, heat deposition distribution, and shutdown dose rate.Although these analyses vary in complexity, the metrics are all derived from the neutron flux.Therefore, it is very important to calculate an accurate and well-converged neutron flux for fusion neutronics.
Historically, fusion neutronics calculations have been built upon the assumption that the density and isotopic composition are not changing throughout operation.This leads to the assumption that the neutron flux spectrum, obtained from transport calculation with a 'fresh' or unirradiated material composition, is constant throughout operation.For example, for the rigorous two-step (R2S) shutdown dose rate calculation method [1][2][3], the neutron transport calculation is performed on the unirradiated model.The flux spectrum calculated from the transport calculation is assumed to be constant, and is used for transmutation calculations until shutdown time.In previous applications with low neutron fluence from the short operational times, low power (i.e.lower neutron flux), and larger device size, the transmutation of materials was not considered to be of significant impact in terms of neutronics feedback.However, there have been work exploring the impact of modeling transmutation feedback to transport [4,5], primarily focused on the impact of transmutation on TBR, with no replacement of breeder material.
The work presented in this paper investigates the neutronics impact of material activation and heating feedback, and quantifies the impact of each assumption.This work addresses the Affordable, Robust, Compact (ARC)-class tokamak presented in Sorbum et al [6], as a representative model.

Significance of this work
This work explores the necessity of fusion neutronics model activation iteration during operation, as well as multiphysics iteration.For example, if the activation of the materials does not significantly change the neutron flux spectrum, then there will not be a need to reflect material activation in the neutron transport models throughout the operational cycle.However, if the neutron flux spectrum does change significantly with materials activation, then iterations to the components' composition will be required to obtain an accurate neutron flux over time.Similarly, if the temperature feedback in the structure or coolant material significantly alters the neutron flux, and thereby alters important metrics such as TBR, then tighter multiphysics coupling between neutronics and computational fluid dynamics (CFD) simulations will be necessary.

ARC-class tokamak design
An ARC-class tokamak is a compact tokamak design with 525 MW of fusion energy [6].Molten salt-Li 2 BeF 4 -is used as a coolant, a shield, and a tritium breeding material.The Li 2 BeF 4 flows in a channel between the vacuum vessels and in the larger blanket.The neutrons and the generated gammas deposit energy into the Li 2 BeF 4 , which then goes through a heat exchanger.Additionally, the interaction of neutrons with Li 2 BeF 4 components (mostly lithium isotopes) generates tritium, which is processed and deployed back into the plasma.In this analysis, the Li 2 BeF 4 is assumed to have an enriched 6 Li content of 90% instead of the natural abundance of 7.59%.The thick salt blanket also acts as a neutron shield to the outer structures.The radial layers outside the plasma (neutron source) are listed in table 1.More details of the tokamak design and setup can be found in [7,8].A visualization of the computer-aided design (CAD) geometry used in this work is also shown in figure 1.This work uses the preliminary design, which uses Inconel 718, a nickel alloy for its inner and outer vacuum vessel and blanket tank.

Methods
Two separate variables and their impacts were explored in this work: (1) the material compositions of the tokamak components and the blanket, and (2) the temperature feedback of the materials and the blanket.The material composition study first explored the potential impact of the tokamak's pulsed operation on activation modeling.This exploration was based on similar modeling assumptions in molten salt fission reactors [10] in which explicit modeling of the flowing fuel slug compared to a continuous irradiation can yield different results.
Next, the neutronics impact of transmuted materials were investigated by comparing the neutron flux spectra and the TBR of the nominal case (i.e.fresh components) and the activated materials case.The thermal feedback of the materials was explored by changing two values from the nominal model: the cross section evaluation temperature, and the material density.The temperature was evaluated using a 2D representation of the ARCclass tokamak geometry.A 2D conjugate heat transfer (CHT) problem was solved using Open-source Field Operation And Manipulation (OpenFOAM) with a volumetric power deposition source evaluated with Monte Carlo N-particle (MCNP) transport code (see section 2.1.5for details of the OpenFOAM problem definition) as shown in figure 2. In addition to the volumetric heat in each layer, a first wall heat flux load of 0.5 MW m −2 was also included.Next, the temperature values were used to determine the material density for each volume based on known correlations.Using the new temperature and density, another transport calculation was performed to calculate the TBR and flux spectra.

Fusion Energy Reactor Models
Integrator.The objective of the Fusion Energy Reactor Models Integrator (FERMI) project is to develop a framework for fusion reactor multiphysics simulations.The framework contains tools for geometry preparation, plasma physics, neutronics, CFD, and structural mechanics.A detailed description of the framework and its capabilities can be found in Badalassi et al [8].This framework is a tool that allows for agile development and testing of  fusion reactor designs.The work presented in this paper is a preliminary scoping study to develop neutronics coupling and iteration schemes for FERMI.The FERMI neutronics module and part of the CFD module is used for this work.

MCNP.
MCNP [11] is a general-purpose Monte Carlo (MC) particle transport tool that is widely used for fusion neutronics applications [12], including ITER [13][14][15][16][17]. Traditionally, the geometry in MCNP uses surfaces such as planes, spheres, cones, and tori, which can be combined to create solids of arbitrary complexity.In MCNP6, the code now has the capability to run transport on an unstructured mesh geometry.This development enables two core capabilities: (1) direct use of CAD models of fusion reactor geometries, and (2) finer calculation of the neutronics metrics' spatial distribution.
Previously, MCNP calculations relied on superimposed cylindrical or Cartesian mesh tallies, which were adequate for traditional fission reactors because they are composed of simpler geometries (e.g.pins and rectangular assemblies).However, tokamaks have much more complex and inhomogeneous geometries.This makes superimposing a Cartesian or cylindrical mesh a poor approximation of the geometry because multiple materials may lie on a single mesh cell in which the metrics would be homogenized.However, with unstructured mesh tallies, finer detailed neutronics metrics such as volumetric power deposition can be obtained for use with, for example, 3D high-fidelity CFD tools.
For the work presented in this paper, the MCNP calculations were used with the unstructured mesh geometry to obtain TBR and the cell volume-averaged multigroup (MG) flux spectra for activation.In here, the 'mcnp cell' is a set of unstructured mesh cells that denote a structural part, like the first wall layer.For all MCNP calculations, the ENDF-VII.1 nuclear data library [18] was used .

Geometry preparation.
MCNP supports two types of geometry input: (1) constructive solid geometry (CSG) and (2) unstructured mesh (UM) geometry.The CSG uses Boolean operations to create volumes called cells.However, this approach is not practical for complex geometries of tokamaks.The UM geometry can represent complex geometries taken directly from the CAD file.The CAD file must be meshed and exported into Abaqus mesh file format.
The geometry preparation is automated in FERMI, and uses Cubit [9] for geometry cleaning, meshing, and conversion.The geometry cleaning assures there are no gaps or overlapping volumes.This is necessary to imprint and merge geometry for a consistent mesh.After this step, the geometry can be meshed and exported to Abaqus format.The Abaqus mesh format contains information about element blocks (referred to as 'elsets') which are then used to assign materials to volumes in the MCNP input file.For this work, a 90-degree model CAD of the ARC-class tokamak was received from Commonwealth Fusion Systems (CFS), along with the materials used for each CAD volume.The converted Abaqus file is used with reflective surface boundary conditions bounding the two edges of the geometry.For Inconel 718, the maximum considered amount of impurities were used (e.g.titanium, copper, cobalt, etc).
The neutron source is modeled as a 14.06 MeV monoenergetic, isotropic volumetric source which is uniformly sampled from the plasma torus volume.

Oak Ridge Isotope GENeration. Oak Ridge Isotope
GENeration (ORIGEN) is a computational tool used for isotopic activation, decay, decay heat, and radiation source-term calculation [19].A coupling scheme was developed to pass MG flux tallies from MCNP to ORIGEN to perform activation calculations.In this work, MG neutron flux tallies are obtained from MCNP transport calculations for the first wall, the inner and outer vacuum vessels, the coolant channel, the beryllium multiplier, and the salt blanket.The MG spectra are then used in ORIGEN, along with the power scaling factor for the ARC-class tokamak (525 MW of D-T fusion) and the irradiation time.

OpenFOAM.
OpenFOAM [20] is an open-source framework used for CFD modeling and simulation.In this work, OpenFOAM-v1912 is used to simulate the Li 2 BeF 4 flow and heat transfer through the cooling channel and blanket.The neutronic heat deposition is read as a .csvfile which stores the cell-by-cell heat deposition value from MCNP simulations.The OpenFOAM mapFields utility is used to map the heat deposition from the tetrahedral neutronics mesh to the hexahedral CFD grid.This approach uses a nearest neighbor technique for volumetric data interpolation between two grids for overlapping domains.The CFD grid (with an average y+ of about 30) and the heat deposition from neutronics mapped onto that grid are shown in figure 3. Next, the OpenFOAM buoyantPimpleFoam solver is modified to include the volumetric heat deposition as a source term in the energy equation.This solver is used to simulate the flow and heat transfer through the channel and blanket.Since a sector of the full tokamak domain is simulated here, cyclic boundary conditions for all variables are used on the wedge faces.All walls are considered as no-slip walls with prescribed average temperatures from the 2D simulation results shown in figure 2. The fluid inlet is prescribed at the cooling channel and the outlet at the blanket such that flow is predominantly downward in the channel and upward in the blanket.A uniform inlet velocity of 2 m s −1 and temperature 800 K is used with no slip walls and fixed solid temperatures.Three different turbulence models-the k − ϵ, k − ω, and k − ωSST modelsare used to analyze the differences in their predictions.The flow and temperature fields are shown in figure 4. The difference in results will be studied in detail in a future publication since it is beyond the scope of the present one.Presently, the objective was to get an estimate of the range of temperatures we might expect in ARC-class blankets from different turbulence models.Furthermore, constant thermophysical properties of Li 2 BeF 4 (ρ = 1940 kg m −3 , µ = 0.006 kg (m•s) −1 , Pr = 14.4,c p = 2400 J (kg•K) −1 ) are assumed.Once the simulation reaches steady state, the temperature field obtained from the simulation can be used to obtain a realistic density distribution of Li 2 BeF 4 as a post-processing step using the relation ρ (kg m −3 ) = 2415.6− 0.4907 × T (K) [21].Future simulations will use realistic thermophysical properties (which  will directly compute the density and include its feedback on the velocity field) and CHT analysis for improved boundary conditions.

Modeling thermal feedback
In neutronics analysis, material temperature determines material density and changes material cross sections.The importance of thermal feedback is application-dependent and will be investigated here for tokamak conditions.The temperature used in this study was evaluated using the 2D OpenFOAM model [22].The 2D solution was volume averaged to determine the volume-averaged temperature for each material (table 2).These temperature values were used to incorporate the temperature-dependent cross sections and material densities.

Temperature evaluation of cross section.
Pseudomaterials method was used to capture changes to material cross sections due to thermal feedback.The concept of pseudomaterials was introduced by Conlin et al [23] to represent the material at the correct temperature if the cross section library at that specific temperature does not exist.The pseudo-materials were created by mixing of cross sections at different temperatures, in which the mixing is performed with linear interpolation of the square root of the temperature.For material at temperature T, the two closest libraries are selected: one at a lower temperature T L , and one at higher temperature T H .The fractions of the material at T L and T H can be evaluated as follows: and the resulting cross section will become:  Relative change of density as a function of temperature for tungsten [24], Inconel 718 [25], Li 2 BeF 4 [26] and beryllium [27].The data were normalized by density at T = 800 K to enable comparison.

Temperature feedback scenarios
The operating temperature of materials in a reactor is not always known, especially at the earlier stages of the design.
To quantify the uncertainty associated with the lack of thermal feedback information, two scenarios, in addition to the thermal feedback (TF) scenario, are considered.In the first scenario, there is no prior knowledge about the thermal feedback.This scenario is referred to as the no prior knowledge (NPK) model.
The assumed temperature of the structural materials is chosen as T = 293.15K, and Li 2 BeF 4 is at its melting temperature of T = 732.25 K [26].Although 293.15 K is a non-sensible temperature assumption for fusion reactors, this scenario represents the default temperature in MCNP, when the analyst does not define a specific temperature.The second scenario assumes that the analyst has limited prior knowledge about the system.This scenario is referred to as the limited prior knowledge (LPK) model, and it assumes that the temperature is equal to T = 1000 K for all materials, representing a bounding case of the system's state.

Uncertainty propagation
Two primary metrics are compared in this paper-TBR and material activity.The relative difference (RE) of TBR and the associated uncertainty is calculated as follows: For propagating the uncertainty of MC MG flux tallies to activation calculations, each MG flux result is randomly resampled 100 times using the MC mean and standard deviation output for each energy bins from the MC MG tally (figure 6).Each generated MG flux values are then used to run activation calculations (i.e. 100 activation calculations).The results from the 100 activation runs (decay heat and specific activity) are then collected into a distribution to get the mean and the standard deviation.These distributions are then compared between each cases.

Results
This section first presents the impact of neutron flux group structure and activation timestep representation on activation calculation results.Then, the impacts of material activation and temperature (and corresponding density) on the neutronics-namely, the TBR-are presented.

Impact of neutron flux group structure for activation
First, the impact of the MG structure on the depletion result was investigated.ORIGEN traditionally uses 252-group structures for thermal fission reactor physics and criticality calculations [28].Fusion reactor activation calculations such as R2S calculations use the Vitamin J 175-group structure [3,29] or the CCFE 709 group structure [30].In this work, the ORIGEN 252-group structure and the new 1597-group structure [28], which focuses on fine resolution in the fast spectrum, were compared for activation calculations.The Vitamin J 175-group structure could not be compared because ORIGEN, when used within SCALE, can only be used with flux spectra with pre-generated SCALE MG structures.
The comparison was made by obtaining 252-and 1597group volume-average cell flux tallies from the full 3D ARCclass tokamak model using MCNP.The flux tallies are then used in ORIGEN, with the respective MG libraries, to perform the activation calculation.The materials were activated for 730.5 effective full power days (EFPDs).MCNP was run with 500 million particles to ensure that good statistics would be obtained for each flux spectrum tally.For energy bins above 10 eV, the maximum relative MC error (standard deviation divided by the mean) for a flux tally was 0.7%, and the mean relative error was 0.11%.The flux tallies are volume-averaged for each region (e.g.coolant channel, blanket), and no variance reduction method was needed, since the regions of interest are not heavily shielded.Plotting the obtained spectra per unit lethargy shows that the 252 group does not capture the detailed fluctuations in the epithermal region (figure 7).
The coarsening of the flux spectra caused minor differences in isotope inventory and waste metric calculation.The activation calculation results using the 252-group flux and the 1597-group flux tallies were compared at shutdown and after 2 years of decay (table 3).The five isotopes listed are significant contributors of decay heat and activity for vacuum vessel activation.Results show that there could be a difference of up to ∼ 2% in total activity after 2 years of shutdown, depending on the neutron flux energy group structure for activation.

Impact of assumed steady-state operation
Assumed steady-state operation denotes the way irradiation over time is modeled for fusion reactors.Because tokamaks have pulsed operation, the neutron flux is expected to oscillate between full power and zero power.In the ARC-class tokamak, the period is assumed to be 15 min on and 1 min off [31].
This mode of operation can be modeled in three different ways: (1) assuming full power operations throughout for the EFPDs, (2) assuming scaled power for the full operational time, or (3) assuming explicit modeling of full power operation and shutdown.Similar studies have been performed for molten salt fission reactors in which the flowing fuel moves in and out of the core, thus experiencing different flux environments [10].
The impact of assumed stead-state operation was investigated by comparing the activation results of three cases: • full power for EFPDs (fp) • scaled power for total operational days (scaled) • explicit irradiation-and-shutdown cycle for total operational days (explicit) In all three cases, the total amount of fluence that the material is exposed to (total amount of EFPDs) remains the same, but the time-dependent flux scaling is different.The impact of such modeling is more prevalent in fission reactors, in which the equilibrium fission product inventory is proportional to the flux magnitude.These methods were tested for an example scenario in which the inner and outer vacuum vessels were in the ARC-class tokamak for 182.625 EFPDs (0.5 effective full power year (EFPY)) at a power level of 525 MW.First, the 1597-group flux spectrum was obtained from the MCNP flux tally on the two vacuum vessel components.These flux values are then used in ORIGEN and scaled appropriately for each case.For the first two cases (fp and scaled), the irradiation times were divided into 100 irradiation steps with constant flux magnitude.For the explicit case, 39 644 irradiation steps (19 822 on, 19 822 off) were used to explicitly model the  ).This results in the irradiation curve shown in figure 9.The explicit method curves show an oscillation as a result of the on-and-off irradiation modeling, whereas the other two methods' curves are smoother because of the constant-flux irradiation.
The specific activity and decay heat of the activated inner and outer vacuum vessels are shown in table 4. The scaled method's results have a relative difference of −0.87% for decay heat and −0.74% of activity compared to the explicit method's results, whereas the full-power-year method overestimates results by an average of 4.28% for decay heat and 4.35% for activity at shutdown.After 2 years of cooling, the difference diminishes to less than 1% for decay heat and activity for the full-power method, and less than 0.005% for the scaled case.
As a conservative estimate, the full-power method can be used for activation, but the scaled method is preferred because it returns more accurate results and does not increase computational costs.An appropriate modeling of the irradiation scheme, and thus the accurate estimation of the decay heat and activity, will be important for transient calculations and waste profiling calculations.

Impact of activated materials on neutron flux and TBR
Three cases are compared: (1) a fresh case (i.e.no activation), (2) a case in which all materials are activated for 730.5 EFPDs, and (3) a case with activated materials but with fresh salt (Li 2 BeF 4 ).The goal of the comparison is to investigate the activation of the structural materials' impact on the neutronics of the tokamak.The objective of the third case with the fresh Li 2 BeF 4 is to model the Li 2 BeF 4 flowing and its    replacement and processing at a higher frequency than the structural materials.The nominal MCNP file was run with the 1597-MG neutron flux tallies on the first wall, inner vacuum vessel, Li 2 BeF 4 channel, beryllium multiplier, outer vacuum vessel, and Li 2 BeF 4 blanket.These flux tallies were then used in ORIGEN with the ARC-class tokamak power scaling to obtain the materials' activated composition after 730.5 EFPDs.The activated compositions are read for each material and implemented into a new MCNP input for the activated case.For the activated case with fresh Li 2 BeF 4 , the fresh Li 2 BeF 4 composition was used, not the activated composition.
Activation isotopes such as 185 W and osmium does not exist in the ENDF-7.1 neutron data library [18].The concentrations of those isotopes are replaced with the most common isotope in the original composition (the most common isotopes listed in table 5).
Results show a 1.68 ± 0.0181% decrease of TBR with activated salt and structural materials (table 6), coming from a lower 6 Li concentration in the salt, which decreases from a atom fraction of 25.7% in fresh salt to 24.9% in the channel and 25.6% in the blanket.This can be better visualized by plotting the tritium-breeding reaction macroscopic cross section ratio (figure 10).Since the salt is flowing, it is unlikely that salt will be continuously irradiated for 730.5 EFPDs, but this analysis highlights the impact of salt irradiation to TBR degradation, and provides insight into the frequency of salt replacement (or refueling) for sustained TBR.
Assuming a fresh salt composition with transmuted structural materials, the TBR decrease is less significant (1.11 ± 0.018%), especially in the coolant channel, but it is still non-negligible.This small decrease is caused by the change in the flux from source neutrons interacting with transmuted isotopes (figure 11).The thermal flux for the fully activated case is higher than the fresh case because of the reduced 6 Li concentration, since 6 Li is a strong thermal neutron absorber.
The decrease in TBR from transmuted materials is analyzed by investigating the reaction rates for each cases in different layers.There is a 9.96% and 7.5% increase in the absorption reaction rate in the first wall layer for activated and activated with fresh salt cases, which is caused by an increase in the absorption cross section from 185 Re, 187 Re, and 181 Ta, which have a higher neutron absorption cross section in the 10 4 -10 6 eV region compared to the tungsten isotopes.The three isotopes make up ∼0.6% of the atom fraction after irradiation.
Comparing the flux spectrum ratio plots between the three cases (figure 11) show that activated materials lead to higher absorption and a lower flux on the channel and blanket, except that for salt-activated cases, the thermal flux is higher due to the decrease of thermal neutron absorption from 6 Li.

Impact of thermal feedback
The uncertainty of the thermal feedback was assessed under two assumptions: (1) NPK of the material temperature (in which material temperatures are assumed to be T mat = 293.6K with the exception of Li 2 BeF 4 , which is set at the melting point temperature, 732.25 K, and (2) LPK, in which all material temperatures are assumed to be T mat = 1000 K.These cases were compared with the thermal feedback case, in which temperatures were evaluated based on a 2D CFD model of the tokamak, later referred to as TF.Material densities and cross section were changed accordingly to investigate the impact on the neutron flux and TBR.Table 7 includes comparison of material densities between different scenarios.Figure 13 shows the comparison of neutron flux spectrum for the Li 2 BeF 4 channel and blanket.For elevated temperatures (consider LPK to NPK), there are two competing factors: the increased resonance absorption caused by Doppler broadening, and the decreased absorption resulting from a lower density.Figure 12 shows the MG relative flux ratio and absorption reaction rate ratio on the tungsten layer for each cases, relative to the thermal feedback (TF) case.The LPK underestimates the temperature by 142 K, and NPK underestimates the temperature by 849 K.It shows a higher flux in the thermal region in both cases due to the underestimation of temperature (relative to TF), and in the case of NPK there is a depression in the absorption reactions in the resonance region, despite the higher flux, which illustrates the impact of lower temperature modeling.
The NPK case, which underestimates the temperature, has a higher thermal flux (relative to TF case) resulting from less Doppler broadening, and a lower fast flux resulting from higher density (thus higher absorption).The flux is lower for the blanket in all energies because of the higher density, but it maintains the relative flux ratio shape of the higher thermal flux.The LPK case, which overestimates the temperature, has a higher flux in most energy ranges because of the lower material densities.
Table 8 presents the comparison of TBR in the channel and blanket.In the channel, the LPK case has a higher flux than the TF case, but it has a lower TBR because of the lower density (thus lower macroscopic cross section), which results from the higher temperature.In the blanket, the LPK case has a higher flux (because of the low densities causing less absorption), which results in a higher TBR, despite the lower density.The NPK case shows higher channel TBR as a result of the higher thermal flux and density, and a lower blanket TBR because of the lower flux.To better understand the combined impacts of the Doppler broadening, flux spectrum, and density perturbation, the TBR can be visualized as an energy-dependent  cumulative reaction rate plot (figure 14), which helps illustrate the energy region in which most of the tritium-breeding reactions occur.The majority of the TBR comes from neutrons with energy in the range of 100 eV to 1 MeV, due to the 90% enriched 6 Li.Overall, not taking the thermal feedback of the tokamak's materials into account can lead to a difference of up to 3.4 ± 0.011% in local TBR because of the density and cross section data differences.Despite the neutron spectrum being very hard, the less energetic neutrons play an outsized role in a system where the major target isotope for TBR is 6 Li.This emphasizes the importance of using an appropriate temperature-evaluated cross section library.The density change with temperature also plays a significant role, especially for materials with a high-temperature-density sensitivity like Li 2 BeF 4 .

Conclusion
This work investigates the impacts of modeling assumptions that have been traditionally used in the fusion neutronics space.Commercial compact fusion power plants, such as the ARC-class tokamak, will be under a much higher fluence than the large research fusion reactors like ITER.This work quantifies the neutronics feedback of the transmutation of device components, as well as the thermal-neutronics feedback.
Using a coarse (252) MG structure for activation, compared to a fine (1597) MG structure, yielded a minor difference (∼1%) for the activity and decay heat of the irradiated vacuum vessel materials after discharge.Modeling the pulsed operation of the fusion reactor as continuous irradiation yields ∼4.3% relative difference in decay heat and activity from the case in which the irradiation is modeled explicitly.The scaled method, in which the neutron flux scaling term is reduced by the ratio of full power and total cycle length, yields a result that is closer (∼1%) to the explicit modeling of pulsed irradiation.
The transmutation of the ARC-class tokamak components for 730.5 EFPDs at 94% duty cycle causes a reduction of less than 1.11% in TBR as a result of the small reduction in the flux caused by the activation products.However, the TBR reduction is slightly greater (1.68%) with irradiated salt because of the depletion of 6 Li, the isotope most responsible for breeding tritium.This highlights the need for salt replacement for sustained TBR throughout the operation cycle.
The temperature modeling in fusion neutronics can impact the flux spectrum, because of the discrepancies in material density modeling and cross section temperature evaluation.If the temperature is overestimated, then the decreased density lowers the reaction rates (absorption, multiplication, breeding), and the increased Doppler broadening in the resonance region leads to a lower thermal flux.The integral impact and the sensitivity of temperature feedback depends on the system and the metric.For example, for non-6 Li-enriched Li 2 BeF 4 , the response with higher temperature will be different, since most tritium-breeding reactions will occur in higher neutron energies.In this work, underestimation of temperature led to a non-significant total TBR difference, but a TBR difference of ∼3% in the channel due to the increased thermal flux and salt density.

Figure 1 .
Figure 1.The CAD-geometry of the ARC-class tokamak used in this work, visualized in Cubit [9].The brown-gray region is the blanket (left).The zoomed image on the right shows the thin radial layers between the plasma and blanket, which are the first wall, inner vacuum vessel, salt coolant channel, neutron multiplier, and outer vacuum vessel layers.

Figure 2 .
Figure 2. A 2D CHT model of the vacuum vessel and blanket of the ARC-class tokamak with temperature in red and neutronic heat deposition in black.

Figure 3 .
Figure 3.The CFD mesh and mapped heat deposition from neutronics.

Figure 4 .
Figure 4. Effect of turbulence models on flow field and temperature field.

Figure 6 .
Figure 6.Flowchart for propagating MG flux MC uncertainty to activation calculation.

Figure 7 .
Figure 7.The 252-and 1597-group flux spectra on the inner and outer vacuum vessel volume, normalized by unit lethargy.

Figure 8 .
Figure 8. EFPDs of irradiation with modeling time (left), and modeled irradiation cycle (right) for each case.

Figure 9 .
Figure 9. Specific decay heat (left) and specific activity (right) curves with irradiation for three different methods.

Figure 10 .
Figure 10.Macroscopic cross section ratio between the fresh salt composition and the activated salt compositions for the tritium-breeding reaction.

Figure 11 .
Figure 11.The 252-group neutron flux ratio of activated cases to the fresh case.

Figure 12 .
Figure 12.The 252-group flux ratio (left) and absorption reaction rate (right) of the NPK and LPK cases divided by the TF case for the first wall.The shaded regions represent ±2σ.

Figure 13 .
Figure 13.252-group flux ratios of the NPK and LPK cases divided by the TF case for the channel and blanket volume.The shaded regions represent ±2σ.

Figure 14 .
Figure 14.Energy-dependent cumulative (high to low) tritium breeding ratio for each case for the channel and blanket volume.

Table 1 .
Layers leading up to the blanket and associated thickness moving radially outward from the plasma neutron source.

Table 2 .
Volume-averaged temperature for each layer. ) 2BeF 4 shows the highest sensitivity to temperature changes, with a variation that is approximately 10% within the applicable range.Inconel and beryllium show similar sensitivities to temperature with a 3%-4% change.Tungsten density shows the lowest sensitivity to temperature with a 1.3% change.

Table 3 .
Activation calculation differences between 252-and 1597-group fluxes on the inner vacuum vessel.

Table 4 .
Specific activity and decay heat of vacuum vessel components after 730.5 EFPDs.

Table 5 .
Replacement isotopes for each material with mass fraction of material replaced.The mass fraction is the sum of all the activated isotopes not in the ENDF-VII.I neutron library.

Table 6 .
Tritium breeding ratio impacts of activated structural material and coolant salt after 730.5 EFPDs.Monte Carlo standard deviations are shown in parentheses.

Table 8 .
Tritium breeding ratio impacts of thermal feedback assumptions.The values in the parentheses are MC standard deviation a .MCNP reports relative errors (standard deviation divided by the mean) for tallies, and only reports up to four decimal points.The reported relative error values for all the tallies were 0.0001. a