Integral analysis of the effect of material dimension and composition on tokamak neutronics

The neutronics performance of a tokamak has been identified as an important factor in designing a fusion power plant. The design of the tokamak should not only meet operational parameters such as sufficient tritium breeding, but also safety parameters such as low structural material activation. This paper investigates the impacts of the neutronics metrics for the ARC-class tokamak, a compact tokamak with an immersion blanket, by perturbing the first five layers of structural material—first wall, inner vacuum vessel, coolant salt channel, neutron multiplier, and outer vacuum vessel. The goal of this work is to provide insight into shaping and scaling the flux on each layer to obtain optimized operational and safety metrics through quantification of the responses from each perturbation. Results show that increased first wall thickness can increase the tritium breeding ratio (TBR) in specific configurations with high 6Li  enrichments and that vacuum vessels decrease TBR for low-6Li  enrichment configurations. It was also found that the neutron multiplier can either increase or decrease TBR depending on the configuration. The response of metrics to the change in layer thickness and enrichment also varies depending on the vacuum vessel material. The integral impacts of 6Li  enrichment, layer thicknesses, and vacuum vessel material choice are investigated and presented in this paper.


Introduction
Fusion energy can offer the possibility of contributing to the world's carbon-neutral electricity needs [1], and many organizations are now developing fusion device designs.Fusion plants need to functionally produce energy, sufficiently breed tritium, and have manageable activation; therefore, highfidelity neutronics are crucial to understanding the operational and safety metrics of the fusion device.Fusion neutronics is the analysis of how the neutrons generated from a fusion reaction (e.g.deuterium-tritium fusion generates ∼14.06 MeV neutrons) interact with the surrounding materials.
The neutronics analyses of larger research fusion devices, such as the ITER project [2][3][4][5][6] or Joint European Torus (JET) [7,8] focus on safety calculations, including shutdown dose rate [9,10].Traditionally, the neutronics performance of a fusion device has not been a major driver for design.However, the newer fusion device designs that aim to produce electricity have different neutronics considerations than the traditional research tokamaks.
Proposed commercial designs, such as the ARC-class tokamak from Commonwealth Fusion Systems (CFS) [11], have higher power densities; they are smaller than research tokamaks and operate more frequently (i.e.longer pulse lengths).This arrangement increases the flux and consequently the fluence, on the materials, thereby increasing heat deposition and material activation.Additionally, to sustain operation of the tokamak, a sustainable fusion fuel cycle must be developed.Although a supply chain exists for deuterium, which can be readily extracted from seawater, the tritium supply remains uncertain [12].Known external sources of tritium include the Tritium Producing Burnable Absorber Rod (TPBAR) [13] and Canada Deuterium Uranium (CANDU) reactors [14], but these sources are not sufficient for a commercial fusion device.Thus, a commercial fusion device design should be capable of a sufficiently high tritium breeding ratio (TBR) to maintain a self-sustaining tritium fuel cycle.

Tritium breeding ratio
Because the tritium fuel cycle is a critical aspect of commercial fusion power plant deployment, TBR is considered one of the most important neutronics metrics for the feasibility of fusion device designs.TBR in fusion neutronics is calculated as the total number of tritium-generating reactions per generated source neutron.Therefore, this TBR value must be higher than 1.0 to realistically have a self-sufficient tritium cycle, accounting for tritium losses before its extraction and reinsertion into the plasma.The exact threshold TBR to maintain a self-sufficient tritium cycle is unclear because of uncertainties in nuclear data [15,16], neutronics modeling [17,18], and tritium loss and extraction mechanisms [19,20], which vary on the system temperature, surrounding materials, and tritium-breeding material.Additionally, the 'required' TBR strongly depends on the tritium fuel cycle design, technology, and reliability, availability, maintainability, and in-spectability (RAMI) [21] considerations [22][23][24].Efforts are ongoing to understand tritium breeding and behavior for a molten salt blanket, namely the Liquid Immersion Blanket: Robust Accountancy (LIBRA) experiment at the Massachussets Institute of Technology (MIT) [25].However, the discussion of tritium transport [26][27][28] and breeding margin are beyond the scope of this paper and will be explored in future work.Instead, this paper provides insight into the TBR response to fusion device structural design and material selection, and how designs can be adjusted for optimal TBR performance.

Structural material activation
During operation, the tokamak structural material undergoes neutron irradiation, which causes its components to become activated (i.e.transmuted into radioactive isotopes).The activated material then decays and emits various radioactive particles as well as decay heat.For the vacuum vessel's safe operation and waste disposal, activity after discharge must be minimized.Additional criteria to consider include material properties after irradiation and operability at high and low temperatures [29].These criteria guided the downselection of materials investigated in this work.

Previous work
Previous work in this area includes the investigation of different materials and thicknesses for various fusion device structures.Segantin et al [30] and Bocci et al [31] investigated the effect of vacuum vessel material choice, channel and neutron multiplier thickness, and Li 2 BeF 4 enrichment on TBR.Another study by Segantin et al investigates the neutronics impact of different shielding compounds [32].Other studies have investigated the effects of TBR for DEMOnstration power plant (DEMO) for first wall material and thickness as well as divertor geometry with the Helium Cooled Pebble Bed (HCPB) design [33,34], and a similar study investigated a Li 2 O blanket [35].This work is novel because it uses a fully 3D explicit geometry for modeling, and it explores the integral effects of the vacuum vessel material selection, layer thicknesses, and lithium enrichment on TBR and vacuum vessel activation.

Methods
This section describes the tools used in this work.This analysis focuses on the ARC-class tokamak, a compact tokamak with an immersion salt blanket.The salt acts as a coolant, tritium breeder, and a shield to the magnets [11].

ARC-class tokamak
The ARC-class tokamak is a compact tokamak design with a power output of 525 MW of fusion power [11].Molten salt-Li 2 BeF 4 -flows in coolant channels between the vacuum vessels and in the larger blanket outside the outer vacuum vessel.The neutrons and the generated gammas deposit energy into the structural materials and Li 2 BeF 4 .The heat is removed from the structural materials to the Li 2 BeF 4 , which then goes through a heat exchanger.Additionally, the neutron interactions with Li 2 BeF 4 components (mostly lithium isotopes) generate tritium, which is processed and deployed back into the plasma.The thick salt blanket also acts as a neutron shield to the outer structures.
For conservatism, the maximum estimated amount of impurities considered for each alloy is modeled.A visualization of the computer-aided design (CAD) geometry used in this work is shown in figure 1.From the plasma, the first layer is the tungsten first wall, followed by the inner vacuum vessel, salt coolant channel, beryllium neutron multiplier, outer vacuum vessel, and the salt blanket.

FERMI
With the increased importance of neutronics in a tokamak, the Fusion Energy Reactor Models Integrator (FERMI) team at Oak Ridge National Laboratory (ORNL developed a workflow to design fusion devices and assess their neutronics performance.This paper investigates the neutronics performance changes from structure thicknesses, material selection, and salt lithium enrichment, highlighting the importance of spectrum shaping and scaling of 14.06 MeV neutrons for optimized fusion neutronics performance. FERMI is being developed as a modeling and simulation tool for fusion devices.The neutronics framework can provide the full suite of analyses pertinent to fusion neutronics including tritium breeding ratio, material activation, volumetric power deposition, magnet neutron fluence, and shutdown dose rate [37].The neutronics framework supports usage of three Monte Carlo (MC) particle transport codes-Monte Carlo N-Particle Transport Code (MCNP) [38], OpenMC [39], and Shift [40]-by developing Python Application Programming Interfaces (APIs) that generate inputs for each code from a standardized input format.

Neutronics workflow.
For this paper, OpenMC [39] is used as the MC transport code, for its convenient Python API for input generation and output parsing.The FERMI neutronics workflow starts with a CAD model and comma-separated values (CSV) file listing the material compositions for each CAD volume.In this work, the 3D 90-degree sector CAD model and the material listing are generated parametrically by the Tracer module [41], which generates fusion device CAD models from a set of parameters, including layer thickness and major and minor radii.
Tracer is a python package that leverages the Cubit [36] python API.The package contains a set of classes that represent typical tokamak building blocks.It relies on a vertex-based definition, allowing for the representation of design-specific elements surrounding the plasma.This feature enables representation of any design within the framework.The layers surrounding the plasma are built out from the set of vertices via a transformation that ensures equal thickness of a material.Hence, the user can specify any material thickness and add or remove any material layer.The ARC-class tokamak was represented using Tracer classes that allow perturbation of the material thickness and many other design features.The geometry is constrained to preserve device size, by constraining the surface of the first wall facing the plasma and outer surface of the blanket.The transformation changes the thicknesses of the material layer surrounding plasma.This transformation does not preserve volumes (i.e. the thickness change of one material will change the volume of all materials positioned on the outside of that material).This is necessary to build a well constrained volume without gaps and overlapping volumes.
The CAD file is then imported into Cubit, cleaned, labeled, and exported to a DAGMC [42] file using the DAGMC Cubit plugin [43], in which the CAD geometry is represented by tessellated surfaces.The DAGMC file is used for the transport calculation in OpenMC.During this step, the volumes of each cell are stored in a separate file for use in postprocessing (e.g.volume normalization of track length tallies for flux).OpenMC tallies the 1597-group multigroup (MG) flux [44] on the first wall, inner and outer vacuum vessel, neutron multiplier, coolant channel, and blanket and the volume-integrated tritium breeding reaction rate in the coolant channel and blanket volume.This entire workflow is automated for the combination of parameters listed in table 1.
An activation calculation is then performed by SCALE/ORIGEN [45] using the MG tallies and material compositions.For this work, the vacuum vessels are activated for 2 effective full power years (EFPYs) and cooled for a day.The total activity of the activated vacuum vessel material is then normalized by the total mass of the inner and outer vacuum vessel.
The ENDF-v7.1 nuclear data [46] library is used for transport, and JEFF-3.1/A[47] is used for activation.Furthermore, each simulation includes 20 million particles to ensure good MC statistics for the metrics.The relative error (standard deviation divided by mean) for volume-averaged tallies, such as TBR tallies, are less than 0.04%.

Parameters.
The thicknesses of the first wall, the beryllium neutron multiplier, and the vacuum vessels were perturbed.Additionally, the 6 Li enrichment and the selection of vacuum vessel materials was explored.The coolant channel thickness remains constant at 2 cm.The selections for the parameter values are shown in table 1.This set of parameter choices generates a total of 729 unique configurations.The vacuum vessel material compositions assumed in this work are also shown in table 2. The values were obtained from CFS and are based on industrial knowledge and experience.
The parameter values and material selections were chosen based on communication with CFS about their design space for the ARC-class tokamak.The vacuum vessel material candidates were selected based on manufacturability and feasibility with operating conditions.

Response space
The response metrics considered for this work are the TBR and vacuum vessel specific activity after 2 EFPY and one day of cooling to allow very short-lived isotopes to decay out.These two variables depend not only on the flux magnitude but also on the flux spectrum because important reactions, like the (n,Xt) reaction of 6 Li , have energy-dependent cross sections.This work also explores the different responses from high breeding salt enrichment (90% 6 Li ) and natural enrichment (7.5% 6 Li ) and the integral effects of layer thicknesses.Depending on the enrichment, the TBR of the system responds differently to the flux energies (figure 2).Similarly, the specific activity of the vacuum vessel depends not only on the flux spectrum and magnitude but also on the total volumes of the vacuum vessels.For example, increasing the thickness of the first wall increases the total volume of the subsequent layers, even as their thicknesses remain constant.

Results
The impact of vacuum vessel material selection on TBR and specific activity was examined first by plotting the distributions for all cases (figure 3).The following insights can be obtained: 1. Configurations with Inconel 718 tend to have lower TBR values compared to other vacuum vessel materials.2. Configurations with V-4Cr-4Ti have significantly lower specific activity.3. Configurations with Inconel 718 show a wider, more normal distribution of TBR, while configurations with V-4Cr-4Ti and F82H have left-skewed distributions.
This evaluation, of course, only considers the neutronics properties rather than other factors, including material cost and material properties such as tensile strength and melting temperature.
A more in-depth analysis can be performed to assess the effect to TBR and specific activity of other parameters besides vacuum vessel material.Figure 4 shows the distribution of the metrics for each vacuum vessel material; colors denote the 6 Li enrichment (left) and beryllium thickness (right), while different markers indicate first wall (tungsten) layer thickness.This figure shows the general trend of metrics with the change in the parameters.For all configurations, increasing the enrichment increases TBR and lowers activity.Increasing the beryllium thickness can increase or decrease TBR, depending on the other parameters, such as salt enrichment.For lower enrichment, a higher beryllium thickness can actually reduce TBR, owing to the reduction of fast flux in the blanket salt.
From the general insight gained from figures 3 and 4, the following subsections discuss the sensitivities of the metrics Distribution of TBR (x-axis) and specific activity (y-axis) with respect to changes in salt 6 Li enrichment (left), beryllium thickness (right), and first wall thickness (markers) for different vacuum vessel configurations.A notable separation between colors on the left plot illustrates the high impact of 6 Li enrichment to the metrics, while the clustered distribution illustrates the low impact of beryllium thickness to the metrics.
to each parameter as well as the integrated effects of other parameters, such as 6 Li enrichment.For example, if a thicker layer causes the flux spectrum on the Li 2 BeF 4 to be more thermal, then the TBR will increase for highly 6 Li -enriched configurations but not so much for the natural-enrichment configurations.

Differences in vacuum vessel specific activity and dose rate
The specific activity of each vacuum vessel material was calculated by using the multigroup flux from the cases with the median values from the design candidates (1.5 cm first wall, 5 cm inner and outer vacuum vessel, 1 cm beryllium, and 30% 6 Li enrichment).The flux values were used to irradiate the material for 2 EFPYs, and the resulting specific activity was evaluated after 1 d of cooling and after 2 years of cooling.
The contributions to activity for each activated vacuum vessel material are shown in figures 5 and 6, at 1 d and 2 years after shutdown, respectively. 55Fe , which makes up a majority of the activity contribution in F82H, decays via electron capture to stable 55 Mn , and has a low-energy emission that does not normally pose an external exposure hazard.By contrast, V-4Cr-4Ti has an order of magnitude lower specific activity after discharge and cools to 2 orders of magnitude lower after 2 years.
Another metric to consider for structural material activation is the dose rate from the activated materials.The dose rate at 30 cm from the activated vacuum vessel is calculated  by creating a separate transport model of a simple slab geometry with the activated composition.The dose rate at 30 cm is chosen over the contact dose rate to take into account the self-shielding of gamma emissions and different attenuation impacts for each material.The width and height of the slab is 400 cm, and the thickness is 5 cm.The 400 cm was selected to model the approximate dimensions of the vacuum vessel.The decay gamma emission spectra as well as the total activity for scaling, were obtained using the OpenMC Python API.Then, a 10 cm radius sphere region was placed 30 cm away from the surface of the slab, in which the dose rate tally was measured, using the photon dose-to-flux ratio from the ICRP-74 report [48].
Figure 7 shows the 30 cm standoff dose rate and specific activity for each vacuum vessel material over time after irradiation.Inconel 718 has the highest specific activity and dose rate up to days after discharge.V-4Cr-4Ti, for days after irradiation, has a higher dose rate than F82H, despite having a lower specific activity, because ∼58% of F82H activity comes from 55 Fe , which is not a significant dose contributor.For the same reason, despite F82H having a higher specific activity 2 years after irradiation compared to Inconel 718, the dose rate of F82H is lower.In most cases, V-4Cr-4Ti has a dose rate and specific activity that are orders of magnitude lower than those of F82H and Inconel 718.

Differences in TBR and specific activity with layer thickness
This section discusses the impact to both TBR and specific activity from each layer thickness.For the visualization, a nominal case with the median sampled values is compared with perturbations of the layer of interest (i.e.one-at-atime method).For example, to investigate first wall thickness impact, all other layer thicknesses were set to the median values.The sensitivities are demonstrated by two measures-a metric heat map, showing the metric values in a grid, and a flux spectrum relative difference plot, showing how the changes in layer thicknesses change the neutron flux spectrum on the relevant material layer.

First wall thickness effect on TBR and vacuum vessel activation.
Tungsten is the first layer that the deuteriumtritium neutrons face, so understanding its interactions is important for shaping the neutron flux in the tokamak.The tungsten layer has three major interactions: neutron multiplication, scattering, and absorption.Furthermore, although not hugely impactful, the increase in first wall thickness increases the total volume of the subsequent layers (inner/outer vacuum vessel, Li 2 BeF 4 channel, multiplier) even though their layer thicknesses are constant.This factor could also contribute to the increase in TBR.The increase in volume is less than 2% for each layer for first wall thicknesses from 0.5 to 3 cm.
Figure 8 shows the change in TBR with first wall thickness.The rows denote first wall thickness, and the columns denote different vacuum vessel and 6 Li enrichment configurations.The three-column clusters denote a vacuum vessel configuration with varying 6 Li enrichments.The bottom row denotes the metric ratio between the thickest first wall thickness design and the thinnest first wall thickness.A value higher than one means that a thicker first wall increases the TBR, for that vacuum vessel and 6 Li enrichment configuration.
The TBR response with first wall thickness should be assessed in conjunction with vacuum vessel and salt enrichment configurations.Increasing the first wall thickness generally decreases the TBR in low-enrichment configurations (i.e.max/min is less than 13 ), as noted by previous studies [33].However, for higher enrichment cases, increasing the first wall thickness can slightly increase TBR because of the neutron multiplication reaction of tungsten isotopes.Because 90% enriched Li 2 BeF 4 has a relatively higher thermal energy (n,Xt) cross section and lower fast-energy-region (n,Xt) cross section, the neutron multiplication reaction acts to increase the total TBR, whereas for lower-enriched cases, it decreases the total TBR.This effect is increased for thinner vacuum vessel configurations, and decreased for thicker vacuum vessel configurations.However, for V-4Cr-4Ti, increase in first wall thickness decreases TBR for all salt enrichment configurations.For some cases, the 1.5 cm first wall thickness value yields the highest TBR, which shows the competing effects of first wall thickness, in which the benefits of a thicker first wall (neutron multiplication and thermalization) competes with the drawback (neutron absorption).The thermalization of the neutrons can be a benefit to TBR, but can also be a drawback because thermalized neutrons have a higher probability of absorption into structural materials.
To explore the impacts of the thicker wall on TBR further, the flux spectra on the Li 2 BeF 4 channel and blanket are compared for each configuration.The flux spectra are measured as a cell volume-averaged multi-group flux tally.Figure 9 shows the 252-group flux ratio between the different first wall thickness configurations, with the 0.5 cm thickness configuration as the base.The flux energies are cut off at 10 eV because of two reasons: (1) the flux below that energy is very low (on average less than 0.2% of total flux) and does not contribute significantly to TBR (on average 1.5% of total TBR), and (2) the ratios are high due to poor Monte Carlo statistics, which makes the scaling of higher-energy fluxes, which are more impactful to TBR, difficult to discern.Comparing the flux differences among first wall thickness configurations reveals that increased first wall thickness causes lower fast flux and higher intermediate-energy flux in the Li 2 BeF 4 channel, which explains the change in TBR mentioned above.The flux relative difference is calculated for each energy bin g by subtracting the perturbed flux from the base flux and then dividing by the base flux value (equation ( 1)) Flux relative difference g = ϕ perturbed,g − ϕ base,g ϕ base,g . ( In the blanket, the fast flux is also decreased.The reduction in fast flux causes the low-enrichment configurations to have a greater reduction in TBR because a higher fraction of their tritium generation comes from the fast spectrum.Note that the relative flux shape differences with first wall thickness are slightly different depending on the vacuum vessel configuration.Increase in first wall thickness leads to a higher thermal flux for Inconel 718 configurations, lower thermal flux for V-4Cr-4Ti configurations, and mixed for F82H configurations.This is because of the differences in scattering and absorption cross sections of the vacuum vessel materials, and highlights the importance of an integral analysis to fusion tokamak design for neutronics.The increased first wall thickness' impact on TBR can also be explained by observing the channel and blanket TBR change (figure 10).This figure shows that increased first wall thickness increases TBR in the channel for most cases, with a stronger increase with higher 6 Li enrichment.On the other hand, in the blanket, the TBR change with first wall thickness varies depending on the vacuum vessel material.
Increasing the first wall thickness also reduces vacuum vessel activation because of the increased attenuation and absorption of neutrons, which decreases the generation of radioisotopes (figure 11).Again, two effects are at play.First, increasing the first wall thickness increases the volume of the vacuum vessel layers and therefore the total mass.However, the increase in volume is not too significant (up to 2% difference between thinnest and thickest first wall configuration).Second, the increased first wall thickness increases interactions with the neutrons via absorption and multiplication, which are competing effects for vacuum vessel activation.

Vacuum vessel thickness effect on TBR and activation.
Increased vacuum vessel thickness decreases the TBR because it absorbs neutrons (figures 12 and 13).The flux ratio plot between thinner and thicker vacuum vessel thickness configurations shows that a thicker vacuum vessel leads to a lower flux in the Li 2 BeF 4 channel and blanket, decreasing the TBR (figure 14).However, increased 6 Li enrichment reduces the TBR sensitivity to vacuum vessel thickness.This is due to the increased TBR reliance on thermal flux, which increases in the blanket with vacuum vessel thickness.
Increasing the vacuum vessel thickness decreases the specific activity for vacuum vessels (figure 15), and this factor is not sensitive to the enrichment configuration.The decrease in specific activity is primarily due to the increase in the volume (and thus the mass) of the vacuum vessel and the shielding provided by the added thickness.

Beryllium multiplier thickness effect on TBR and activation.
The effect of beryllium thickness depends strongly on the 6 Li enrichment configuration and the thickness values of other layers.At higher enrichment, increased beryllium thickness generally increases the TBR.Three effects are in play: (1) the neutron multiplication from the (n,2n) reactions of beryllium, (2) neutron scattering from beryllium, and (3) the increase in outer vacuum vessel volume with increasing multiplier thickness.TBR increases by a maximum of approximately 3% when the beryllium thickness increases from 0.01 cm to 2 cm (figure 16) for configurations with a 1.5 cm first wall.For lower enrichments, TBR decreases with beryllium thickness by up to about 6%.The TBR benefit of the multiplier also depends on the inner vacuum vessel thicknessa thinner vacuum vessel configuration increases the positive TBR effect of a thicker multiplier layer.However, this increase only applies for high 6 Li enrichment configurations.Increased vacuum vessel thickness causes lower fast flux, which reduces the (n,2n) reaction from the multiplier, effectively decreasing the effectiveness of a neutron multiplier.If the effectiveness of the neutron multiplier is dampened by the lack of fast neutrons, then the multiplier layer will only decrease TBR regardless of enrichment because it will increase the volume of the outer vacuum vessel, thereby decreasing TBR since the neutron flux on the blanket is decreased.In other words, for thin (⩽2 cm) beryllium multipliers, the multiplier only increases TBR when the vacuum vessels are thin and the 6 Li enrichment is high.The biggest increase in TBR with multiplier thickness is 7.6%, which occurs in configurations with thinnest first wall and vacuum vessel thickness, with 90% 6 Li enrichment with Inconel 718.Conversely, the biggest decrease is −9.17%, which occurs with F82H, with the thickest first wall and vacuum vessel thickness, with natural 6 Li enrichment.
Increasing the beryllium thickness increases the thermal fluxes on the vacuum vessel and the Li 2 BeF 4 channel and decreases the fast and epithermal fluxes.The increase in beryllium thickness decreases the specific activity of vacuum vessels (figure 17), which is caused by a reduction of flux.However, for F82H, the increased thermal flux contributes largely to the activation of tungsten isotopes, increasing the specific activity (figure 18).

Discussion
This study provided two distinct strategies for fusion tokamak design for TBR: (1) the thermal configuration-in  which the design maximizes thermal flux the blanket and coolant channel to breed tritium from 6 Li , and (2) the fast configuration-in which the design maximizes overall neutron flux and minimizes thermalization of neutrons, in which higher tritium breeding occurs with 7 Li in the fast energy range.The thermal configuration will aim to have a thick first wall and an optional beryllium multiplier layer for (n,2n) reactions and a highly- 6 Li -enriched blanket.The fast configuration will aim to have a thin first wall and beryllium multiplier layer and low- 6 Li -enriched blanket.
With V-4Cr-4Ti vacuum vessels, it is shown that a non- 6 Lienriched salt with no beryllium multiplier layer can have a TBR of up to 1.102 with 2 cm vacuum vessels and 0.5 cm first wall (figure 19).However, the reduced absorption from the  layers might increase the magnet fluence, which might reduce magnet lifetime.This is future work and can be mediated with a good magnet shield design.

Conclusions and future work
This study explored the effects to TBR and vacuum vessel activation from different fusion device layer thicknesses, vacuum vessel materials, and Li 2 BeF 4 6 Li enrichment levels.Three different vacuum vessel materials were investigated: Inconel 718, F82H, and V-4Cr-4Ti.
The TBR response from parameter perturbations is strongly influenced by the 6 Li enrichment configuration.A highly enriched configuration can achieve a high TBR with a decrease in total flux by increasing the thermal flux (thermalization of the neutron spectrum).Increasing the first wall (tungsten) thickness can increase the TBR in highly enriched configurations with thin vacuum vessel thickness because of the (n,2n) reactions in tungsten isotopes, but in most cases, increased first wall thickness decreases the TBR.Increasing the vacuum vessel thickness always decreases the TBR because of increased neutron absorption.Increasing the beryllium multiplier thickness can increase TBR up to ∼7% for highly-enriched configurations, but can also decrease the TBR by ∼9% for lowenriched configurations.Additionally, the effectiveness of the multiplier also depends on the vacuum vessel material and thicknesses-a thicker vacuum vessel will reduce the effectiveness of the multiplier layer.
A notable finding is that the lithium enrichment changes the nature of the trends that both the first wall thickness and beryllium thickness have with respect to TBR.Increases in both lead to increases in TBR only with configurations that have high enrichments of 6 Li , while the opposite is generally true for low-enriched configurations.This is especially significant because working with beryllium and enrichment of lithium are difficult processes, making this a feasible strategy to reduce two difficult design features in the tokamak.Additionally, with a low-enriched lithium configuration, there's no need to work with a thick tungsten layer, for neutronics purposes.
After 2 EFPYs, the majority of the contribution to specific activity comes from the composition of the vacuum vessel material.The high nickel content in Inconel 718 causes it to have a much higher specific activity compared with the other two materials.However, after 2 years of cooling (decay), F82H had a higher specific activity than Inconel 718 (although an order of magnitude lower standoff dose rate).The V-4Cr-4Ti has an order of magnitude lower specific activity than the other two materials, and this value decreases to 1% of its discharge value after 2 years.Increasing first wall and vacuum vessel layer thicknesses lowers the specific activity of the vacuum vessels by decreasing the flux, thereby decreasing neutron absorption.However, the increase in thermal flux caused by the beryllium multiplier can cause a higher specific activity for F82H owing to its tungsten isotopes.For V-4Cr-4Ti and Inconel 718, increasing the beryllium multiplier reduces the specific activity.
Another major conclusion of this work is that V-4Cr-4Ti has both a higher TBR and lower activation than the other materials considered and improves many of the key metrics, all things being equal.This analysis also motivates future work, which is to scale vacuum vessel layer thickness based on the key mechanical property parameter.For example, future analyses should likely consider the design case (e.g.disruption induced stress) and compare the thickness of the vacuum vessel material with an equivalent stress loading.This work is ongoing in the FERMI team with the integration of the DIABLO code [50].
The insight gained from this work can help analysts design and optimize the neutronics performance of a fusion device by elucidating the trade-offs between design choices and metrics.

Figure 1 .
Figure 1.The CAD-geometry of the ARC-class tokamak used in this work, visualized in Cubit [36].The left figure shows the entire 90-degree sector geometry, and the right figure is zoomed in to show the layers.From the plasma to radially outward, the layers are-first wall, inner vacuum vessel, coolant channel, beryllium multiplier, and outer vacuum.The coolant channel thickness is not varied in this study.

Figure 3 .
Figure 3. Distribution of TBR and specific activity from each vacuum vessel material configuration.There are 243 samples for each configuration.

Figure 4 .
Figure 4.Distribution of TBR (x-axis) and specific activity (y-axis) with respect to changes in salt6 Li enrichment (left), beryllium thickness (right), and first wall thickness (markers) for different vacuum vessel configurations.A notable separation between colors on the left plot illustrates the high impact of6 Li enrichment to the metrics, while the clustered distribution illustrates the low impact of beryllium thickness to the metrics.

Figure 5 .
Figure 5. Pie chart of activity contributions of isotopes from irradiation, 1 d after shutdown.

Figure 6 .
Figure 6.Pie chart of activity contributions of isotopes from irradiation, 2 years after shutdown.

Figure 8 .
Figure 8. Change in TBR with first wall thickness for each vacuum vessel material and enrichment configuration.The last row lists the ratio between the metric values from the thickest configuration over the thinnest configuration.

Figure 10 .
Figure10.TBR change with first wall thickness, separated by material, and color-coded by6 Li enrichment.

Figure 11 .
Figure 11.Change in vacuum vessel specific activity with first wall thickness for each vacuum vessel material and enrichment configuration.The last row lists the ratio between the metric values from the thickest configuration over the thinnest configuration.

Figure 12 .
Figure 12.Change in TBR with inner vacuum vessel thickness for each vacuum vessel material and enrichment configuration.The last row lists the ratio between the metric values from the thickest configuration over the thinnest configuration.

Figure 13 .
Figure 13.Change in TBR with outer vacuum vessel thickness for each vacuum vessel material and enrichment configuration.The last row lists the ratio between the metric values from the thickest configuration over the thinnest configuration.

Figure 14 .
Figure 14.Flux ratio for configurations with Inconel 718 vacuum vessel (top), F82H (middle), and V-4Cr-4Ti (bottom) with 2, 5, and 7 cm inner vacuum vessel thickness for 30% salt enrichment.A similar trend is observed for other salt enrichment configurations.The shaded region denotes the ±3 standard deviation.

Figure 15 .
Figure 15.Change in vacuum vessel specific activity with inner (top) and outer (bottom) vacuum vessel thickness for each vacuum vessel material and enrichment configuration.The last row lists ratio between the metric values from the thickest configuration over the thinnest configuration.

Figure 16 .
Figure 16.Change in TBR with beryllium multiplier thickness for each vacuum vessel material and enrichment configuration.The sensitivity of beryllium thickness to TBR depends on the inner vacuum vessel thickness.The top figure shows the sensitivities for 2 cm inner vacuum vessel thickness, and the bottom figure shows the sensitivities for 7 cm inner vacuum vessel thickness.

Figure 17 .
Figure 17.Change in specific activity with beryllium thickness for each vacuum vessel material and enrichment configuration.

Figure 18 .
Figure18.Change in isotopic activity contribution (top six isotopes) from inner and outer vacuum vessel for F82H, with different beryllium thicknesses, using median thickness values for the other layers and 30%6 Li enrichment.

Figure 19 .
Figure 19.Change in TBR with vacuum vessel and first wall thickness for V-4Cr-4Ti vacuum vessel and natural lithium enrichment salt configurations with no beryllium multiplier layer.The contours are generated from datapoints using the Matplotlib tricontour function [49].

Table 1 .
Parameter space sampled for the study.A total of 729 configurations were sampled.
a 0.01 cm is chosen to model a case with no beryllium multiplier layer.