Assessing the Risk of Proliferation via Fissile Material Breeding in ARC-class Fusion Power Plants (2024)

2.1 Material needed to build a weapon

Construction of a nuclear weapon requires access to kilogram-scale quantities of fissile isotopes like Pu-239 and U-233. These isotopes occur in low abundances in nature, so large quantities of raw material must be processed and isotopically enriched to build a weapon. An alternative path “breeds” WUM from fertile isotopes in a neutron source (e.g. a fission reactor). Highly abundant, fertile isotopes like U-238 and Th-232 are transmuted into weapons-usable fissile isotopes via neutron capture:

The International Atomic Energy Agency (IAEA) defines a significant quantity (SQ) of fissile material as the approximate amount needed to make a first-generation weapon [6]. For Pu-239 and U-233, one SQ is 8kg or approximately $2\times 10^{25}$ nuclei, and we use that definition in this work. Note that this definition has been criticized by some as being a factor of 2–3 higher than what is needed to make a nuclear weapon [7]. A substantial neutron source - such as a fission reactor - is therefore needed to transmute relevant quantities of fertile material on reasonable timescales. Commercial and researcher neutron generators have much lower source rates, ranging from $10^{7}$-$10^{11}$ neutrons per second, and are therefore incapable of breeding a SQ of fissile material on a timescale relevant to proliferation (months to years). Proposed commercial fusion reactors, however, are expected to have neutron source rates on the order of $10^{20}$ neutrons per second, and are therefore potentially useful for fissile material breeding.

2.2 Proliferation resistance of D-T FPPs under normal operating scenarios

While a normally operating D-T FPP will not generate significant amounts of WUM, it is important to note that it could still be used to support an existing nuclear weapons program through the diversion of Li-6 and/or tritium.Li-6 and tritium, in combination with deuterium, can enhance the performance of nuclear weapons.¹¹1In a fission implosion, D-T fuel provides additional neutrons which increase the yield of the fission device and reduce the amount and/or quality of fissile material needed, a process called boosting. In a two-stage thermonuclear device a large fraction of the total yield is from D-T fusion which is induced by the extreme conditions present after the detonation of a fission primary [9]. An assessment of the risk of diversion of Li-6 and/or tritium from an ARC-class FPP is outside the scope of this work. The amount of tritium and Li-6 present on-site at an FPP will be highly dependent on both the design of a given plant’s fuel cycle, the targeted TBR (which may be higher than the the TBR required for tritium self-sufficiency, pending operator decisions around safety margins) and the operational choices governing its tritium consumption and target tritium reserves.²²2We will note that research into FPP fuel cycle modeling shows that there will be limited excess tritium inventory available at D-T FPPs, suggesting that significant diversion of tritium produced in the blanket is likely to lead to a loss of tritium self-sufficiency in the plant [10, 11]. This is true even considering that these models tend to make optimistic assumptions about the efficiencies of plasma operations, blanket breeding, and fuel cycle components, and do not account for inherent tritium losses due to trapping in components. The fusion community has given significant attention to the topics of tritium and Li-6 diversion. For recent work on this topic, see [12, 13, 14].

2.3 Prior work: fusion power and the breakout scenario

One category of relevant prior research focuses on fission-fusion hybrid plants. A hybrid plant consists of a fusion system coupled to a subcritical fission system such that some of the neutrons produced by fusion reactions interact with the fission section. The primary purpose of the hybrid design may be to produce power, to produce fissile material for use in conventional fission reactors from fertile material or spent fuel, and/or to burn waste actinides for easier disposal. In 1981, Conn et al.published a study on SOLASE-H, a fission-fusion hybrid designed to produce fuel for light water reactors [15]. The authors considered how to ensure SOLASE-H would not be used for the production of WUM, and concluded that the intense radioactivity of the fuel assemblies would be a sufficient deterrent. Note that this concept presents an inherent proliferation risk, because it intentionally utilizes fertile and fissile material as fuel. Sahin et al. also considered fission-fusion hybrids in a series of papers from 1998–2001 [16, 17, 18]. In these works, fusion neutrons are used to breed U-233 from Th-232, and the fissile uranium is then used to fuel the fission plant. They propose fuel denaturing as a strategy to prevent the production of WUM, but this is not an option in breakout scenarios since the proliferator controls the isotopic profile of the fertile material. Vanderhaegen et al.considered a fission-fusion hybrid reactor in 2010 [19] in which ThF₄ and UF₄ are dissolved in a FLiBe blanket attached to an ITER-class fusion device to breed fissile fuel for fission reactors. They concluded that LiF-BeF₂-ThF₄ was an ineffective choice for breeding fissile material, but that LiF-BeF₂-UF₄ resulted in relatively efficient production of fissile fuel. However, the LiF-BeF₂-UF₄ salt also produced a significant quantity of high-grade plutonium in a relatively short time ($<$43 days), which presented a proliferation risk and made the concept less attractive. A 2012 conference paper by R.Moir also considered how fusion neutrons could be used to breed fissile material from thorium, and concluded that the radioactivity of the resulting material (due to an energetic gamma in the decay chain of co-produced U-232) would be a strong proliferation deterrent (see Sec.4.4 for further discussion of this issue).

Santarius et al.[20] considered whether passive proliferation resistance would be possible in a fusion power plant. Their conclusion was that the community should focus on the development of aneutronic fuel cycles if proliferation is considered to be a major risk. Realistically, the first FPPs will likely use the neutronic D-T fuel cycle as this reaction has the lowest requirements on plasma performance needed to achieve ignition.

E.T.Cheng’s 2005 paper [21] explicitly looked at an FPP with a FLiBe tritium breeding blanket, as is also the case in this paper. In the Cheng study, the FPP is used as a neutron source to burn actinide waste from fission plants and/or produce additional fissile fuel from fertile material. This study also notes that (1) actinides are soluble in FLiBe and (2) can be removed from the FLiBe online, which are both points pertinent to this work.

Sievert and Englert’s 2010 paper [22] considers the theoretical possibility of producing WUM from fertile material deliberately placed in the breeding blanket of an FPP, and indicates that proliferation safeguards will likely be needed for any future FPP that utilizes a tritium breeding blanket. Englert et al.considered the possibility of breeding plutonium in a Pb-Li blanket in greater detail [23, 24] under scenarios in which hom*ogeneous mixtures of natural uranium were introduced to the liquid Pb-Li in varying concentrations. These works used a simplified burnup model and suggested that the breeding of SQs of WUM in the blanket would certainly be possible, although the blanket design considered was highly simplified compared to more mature modern designs. Englert et al.noted that the fusion neutron spectrum and expected flux enabled the rapid production of WUM with very high isotopic purity, a finding that is consistent with the results of this work.

Glaser and Goldston performed an analysis of proliferation risks posed by magnetic fusion energy systems in 2012 that considered both clandestine and covert breeding scenarios [25]. For the covert scenario, most pertinent to this work, the authors studied a DEMO class reactor with a Pb-Li blanket using the Monte-Carlo radiation transport code MCNP [26]. The authors suggest that fertile material could be covertly introduced into the blanket as TRISO particles to overcome the poor solubility of uranium and thorium in Pb-Li. They show that heat deposition from fission of fertile isotopes is substantial for uranium but not thorium, and that fusion power might have to be reduced to keep from overwhelming the plant’s heat exchangers. The authors also show that the plant’s TBR is negatively impacted by the introduction of fertile material to the blanket, with thorium being more detrimental than uranium. The authors also discuss how such a covert breeding scenario could be detected, including sampling of the blanket material and detection of characteristic gamma emission from fission products. It is concluded that a fast breeder fission reactor and a fusion reactor could produce WUM at similar speeds assuming they are of comparable power. The authors conclude that fusion systems present a lower proliferation risk than fission systems when appropriate IAEA Safeguards are implemented.

Franceschini et al.provide a useful overview of different schools of thought regarding fusion’s risk within the non-proliferation community in their 2013 paper [27]. The authors point out that proposed fusion power plants would theoretically be able to produce SQs of WUM more quickly than fission reactors, using far less fertile material, and with lower radioactivity of the final product (leading to easier handling of the WUM). As fusion power is still years away, this is not treated as a major concern by the technical community: as long as fission power is on the grid, there is a tendency to assume that any nation intent on proliferation would rely on that technology first. The authors go on to outline the various technical, political, and regulatory conditions that would make fusion-enabled nuclear weapons proliferation more likely, on the assumption that fusion power eventually becomes a standard part of the energy generation mix. A 2023 paper by Diesendorf et al.further outlines the high-level risk scoping of proliferation hazards and the adequacy of existing safeguards in a “mature fusion economy,” in which fusion power is a widespread and common part of the energy mix, and concludes that a more rigorous risk assessment is merited [12].

2.4 Weapons-usable material production and the ARC-class FPP

The LIB is essentially a large volume of molten FLiBe (2LiF-BeF₂) salt that surrounds the first wall/vacuum vessel structure and is contained by a blanket-tank structure. This simple design is advantageous largely because it minimizes the amount of structural material needed for the blanket. This maximizes the amount of breeder volume exposed to neutrons (thus increasing the achievable TBR), enables more efficient heat transfer from the first wall/vacuum vessel structure into the blanket, and enhances shielding of the magnet structures as the low-Z elements of FLiBe are good neutron moderators.

The use of FLiBe makes the ARC-class FPP particularly interesting from a fissile breeding proliferation standpoint, as it is well-established that fertile species are soluble in FLiBe. The most notable example of this fact is the Molten Salt Reactor Experiment (MSRE), which operated at Oak Ridge National Laboratory (ORNL) from 1965–1969 [28]. The MSRE fuel was liquid LiF-BeF₂-ZrF₄-UF₄, with unfueled FLiBe as a secondary coolant. In the decades since, FLiBe has been extensively explored by the fission power research community as a fuel carrier for the general molten salt reactor (MSR) concept [29, 30, 31].

In this work, we investigate what happens when fertile species (U-238 or Th-232) are introduced to the FLiBe LIB in amounts ranging from 5 to 50 metric tons, corresponding to a maximum molar percentage of 1.81% and 1.84% for UF₄ and ThF₄ respectively, assuming a blanket volume of 342m³ (see Sec.3.1). Upon introduction to the FLiBe, U and Th form LiF-BeF₂-UF₄ and LiF-BeF₂-ThF₄, respectively. Our upper limit is similar to fuel molar concentrations present in fission MSR designs [32].

In general, it is expected that an ARC-class FPP would already have on-line chemistry control capabilities, as well as on-site salt purification facilities. FLiBe with impurities and/or fuel compounds is known to be more corrosive to structural materials than pure FLiBe [33].³³3FLiBe chemistry and purity is of present interest to both the advanced fission community [34, 35] and the fusion community [36], with the latter particularly interested in how impurities could impact tritium breeding and extraction. Both are concerned with the long-term structural integrity of FLiBe-facing components. These facilities might be capable of extracting bred WUM from the FLiBe during operation, significantly shortening $t_{\text{SQ}}$. If these facilities are undersized, they may at least furnish a prototype on which operators could construct a dedicated system capable of significant actinide extraction, either during operation or in a batch process afterwards.

Removal of actinides from FLiBe is a well-established process. Fluorination of the fueled FLiBe converts UF₄ to gaseous UF₆, which then bubbles out and is collected [37, 38]. This technique was used to extract uranium from the MSRE fuel salt, but only a negligible amount of the plutonium present was extracted in this process as it did not volatilize [39]. However, it is possible to use the fluoride volatility process to convert PuF₄ to PuF₆ under the correct conditions [40].

3.1 Model Overview

First, we developed a representative geometric model of an ARC-class FPP tritium breeding blanket. Several ARC-class FPP design studies have been published, which we used to guide our chosen design point [1, 2, 3]. Eqs.(3) and (4) describe the poloidal cross section shape of the blanket, which is plotted in Fig.1(a).

where $t$ parameterizes the RZ contour on the interval 0 to 2$\pi$, $R_{0}$ is the major radius of the machine, $a$ the minor radius, $\kappa$ the elongation, and $\delta$ the triangularity. Tab.1 summarizes the values used to generate the OpenMC model. The radial build of the model is shown in Fig.1(b), and consists of six nested toroidal volumes representing the plasma facing components, vacuum vessel (with cooling channel), and blanket tank. Tungsten and V-4Cr-4Ti were selected as the materials for the plasma facing components and vacuum vessel respectively. This RZ contour was then rotated 2$\pi$ radians about the major axis, forming a toroidally symmetric 360-degree model. Notably, this is a simplified model that does not include structures that would be present in a real FPP, such as RF heating and vacuum systems.

The neutron source is defined as a ring centered on the major axis of the device, emitting monoenergetic 14.1MeV neutrons isotropically. We assume that the device is operated at a constant fusion power of 500MW continuously in time for all analyses presented.

3.2 Depletion calculation

We assume in this analysis that fissile material and fission products are not removed online and fertile material is not replenished online. It is thus necessary to consider transmutation and radioactive decay during irradiation, which is referred to as a depletion problem [44]. We allow for the blanket composition to evolve in time by solving the Bateman equation [45] numerically using the OpenMC depletion module [44], allowing the entire calculation to be carried out with just a single code. This is in contrast to codes like MCNP, which do not include a depletion solver and must be coupled to a second code like FISPACT-II [46] to perform such a calculation. This, along with the fact that OpenMC is open-source (enabling the broader fusion community to more easily check these results, or adapt the source code to their own studies), motivates its use for this work.

Notably, none of the prior work discussed in Sec.2.3 makes use of such a self-consistent simulation of fissile breeding. Approaching the calculation in this way is critical to ensure all effects relevant to breeding are resolved. The following phenomena are not captured with a time-independent method:

The time stepping scheme was chosen in accordance with the accuracy criterion for the Chebyshev rational approximation method (CRAM), which is used by OpenMC to compute the matrix exponential for solving the Bateman equations. Since the primary neutron source is unaffected by reaction rates in the blanket, this is a conservative approach which minimizes errors in the methodology applied here.

4.1 Time to breed 1 SQ of weapons-usable material in an ARC-class FPP

The critical parameter to determine the feasibility of breakout is $t_{\text{SQ}}$, the time required to produce one SQ of fissile material. As mentioned above, we assume that for the length of time these calculations represent, no fertile or fissile material is being removed by online chemistry control systems. This assumption minimizes the potential need for modifications to the FPP, but also slows the breeding process. Given that we simulate the system at a set of discrete time steps without knowing $t_{\text{SQ}}$ a priori, we linearly extrapolate between the two time points with fissile masses just above and below a significant quantity to determine $t_{\text{SQ}}$. All results presented in this section assume a natural (unenriched) Li-6 content in the FLiBe of 7.5%.

Fig.2 plots $t_{\text{SQ}}$ as a function of fertile inventory initially dissolved in the blanket. Even for small quantities of fertile material ($\sim$2metric tons), $t_{\text{SQ}}$ is less than one year for both the U and Th fuel cycles. Above 10 metric tons⁴⁴4Ten metric tons corresponds to about 1/2 cubic meter of U or Th metal, or one industry-standard 48Y-shipping container used for transporting natural UF₆. of fertile mass, $t_{\text{SQ}}$ is on the order of 1-2 months for both fuel cycles. For IAEA inspection purposes, it is important to note that the IAEA defines 10 metric tons as the SQ for natural uranium, and 20 metric tons as the SQ for natural thorium [6]⁵⁵5This means that under current IAEA definitions, the diversion of less than 10 metric tons of natural U, or less than 20 metric tons of natural Th, over an inspection period would not trigger concerns of unsanctioned use of fertile material for weapons purposes.. These data can be fit using the following equation:

where $m_{f}$ is the mass of fertile material in metric tons, $t_{\text{SQ}}$ is in units of days, and $A,B,$ and $C$ are the fit coefficients. Their values are given in Tab.2. The fit described by Eq.(5) is empirical and should not be assumed to apply for fertile masses far outside of the 5–50 metric ton range considered here.

We observe a significant difference in $t_{\text{SQ}}$ between the two production schemes, a result of the long half-life (26.98 days) of Pa-233 in the U-233 production chain, which creates a lag between the capture of a neutron by Th-232 and the actual appearance of U-233 in the blanket fluid. As 27days is on the order of $t_{\text{SQ}}$ for all fertile mass inventories investigated, this result is expected. Note that the effect of Pa-233’s long half-life is accurately captured using the self-consistent time-dependent depletion method, but would be lost if a simpler single-transport-calculation approach was used. We note however that this decay process does not need to happen within the FPP or while it is operation, thus the FPP could be shut down before the decay is completed, further reducing $t_{\text{SQ}}$ by reducing losses to fission reactions.

4.2 Fission heating in the blanket

The introduction of fertile material into the tritium breeding blanket means that some rate of fission is expected. Fission reactions are exothermic and thus act as an additional source of heat in the blanket fluid. Fig.3 plots fission power at $t=0$ and $t=t_{\text{SQ}}$ as a function of fertile inventory in an ARC-class reactor blanket. For both production schemes, the fission power in the blanket over the plotted time interval is on the order of tens of megawatts. This represents a perturbation on the order of 10% to 15% of the total fusion power, assumed here to be 500 MW, indicating that excess fission power in the blanket is unlikely to make proliferation untenable unless safety margins on the heat exchanger components are very small. Even if this is the case, a proliferator could reduce the fusion power to create a total blanket heat load tolerable by the heat exchanger. Since the neutron rate is linearly correlated to fusion power, this reduction in source rate would be of the same magnitude as the heat from fission, shown here to be at most 15% of nominal fusion power, increasing $t_{\text{SQ}}$ by the same amount to first order.

For Pu-239 production, fission of the U-238 fertile isotope is the dominant source of fission heating, with the build-up of Pu-239 resulting in only a small perturbation to the total fission power. For U-233 production, fission of the fertile isotopes is small compared to the fission power produced by bred U-233, as is shown by the large change in total fission power between $t=0$ and $t=t_{\text{SQ}}$ in Fig. 3.

4.3 Impact of fertile material on tritium breeding

The blanket of a D-T fueled FPP has three primary functions: it breeds tritium via interactions between the fusion neutrons and lithium in the blanket breeder material; it captures heat that is converted into useful energy; and it shields the magnets from neutron damage. The blanket’s tritium breeding performance is characterized by the TBR, which is defined as the ratio of tritons produced via breeding to tritons consumed by fusion reactions in the plasma. For the reactor to be fuel self-sufficient, it must have a TBR $>$ 1, with additional margin that accounts for fuel cycle and fueling inefficiencies, tritium loss due to decay and uptake in materials, desired tritium inventory doubling time (for startup of new plants), and desired tritium reserve inventory. Therefore the required TBR is dependent on both plant design and operational decisions [11]. Generally, any scenario that results in a decrease of achievable TBR is detrimental to plant operations, and may result in a loss of tritium self-sufficiency (and thus an inability to continue operating the plant).

The use of neutrons for breeding fissile material rather than tritium is expected to detrimentally impact TBR. We characterize the impact of introducing fertile material to the blanket on TBR in Fig.4. TBR monotonically decreases with increasing fertile inventory, although TBR never falls below 1 for the plotted fertile mass range for either production scheme. Nonetheless, such a reduction may cause the TBR to fall below the level required for tritium self-sufficiency. In [11], the TBR required for self-sufficiency in an example ARC-class FPP ranged from 1.012 to 1.113 for the parameters studied. Based on that assessment and the results in Fig. 4, TBR reduction due to the addition of fertile mass in the blanket would not necessarily be a proliferation deterrent. However, it is worth restating that our blanket model is simplified, and that the margin to loss of tritium self-sufficiency in a real FPP may be smaller.

Note that Figure4 only shows data at $t=0$, and does not account for the breeding of fissile material over time. In-blanket fissioning of fissile material boosts neutron flux inside the blanket which boosts TBR. However, this change was determined to be negligible and so time-dependent results were omitted from the plot.

4.4 Isotopic purity of bred fissile material

Isotopic purity of bred fissile material is a key parameter in determining its usefulness as WUM. For example, Pu-239 can capture a neutron and become Pu-240, which is undesirable in a weapons context because of its high rate of spontaneous fission. Isotopic purity is computed at each time step by calculating the ratio of Pu-239 or U-233 nuclides to the total number of plutonium or uranium nuclei respectively. Fig.5 plots isotopic purity as a function of fertile inventory evaluated at $t_{\text{SQ}}$. We find that fertile inventory has little-to-no effect on the total isotopic purity at $t_{\text{SQ}}$, with $>$ 99% purity for both production schemes.

The purity of Pu-239 bred from U-238 is exceptionally high ($>99.8\%$ over the plotted fertile mass range), and well in excess of what is considered to be “weapons-grade material” ($>$93% Pu-239 [47]). This is likely a result of the hardness of the neutron spectrum in the ARC-class FPP blanket, as the capture reactions that degrade isotopic purity are largest at lower neutron energies. Additionally, in this analysis we focus only on the breeding of a single SQ of WUM from metric tons of initial fertile inventory, representing a very low burnup fraction which is already well known in the fission community to correspond to high isotopic purity.

The purity of U-233 bred from Th-232 is also quite high ($>99.6\%$ over the plotted fertile mass range). However, it should be noted that the manufacture of a U-233 based weapon is complicated by the impurity U-232, which is co-produced with U-233 by mechanisms including radiative capture on Th-232 and (n,2n) reactions on the intermediate breeding daughter Pa-233 and U-233 itself [48]. The decay chain of U-232 includes Tl-208, which emits a 2.6MeV gamma ray that makes working with contaminated U-233 very dangerous, complicating the manufacture of a weapon. Even small amounts of U-232 contamination, on the order of 100 ppm, can result in substantial radiation hazards. We find that for all initial fertile masses of Th-232, the concentration of U-232 at $t=t_{\text{SQ}}$ is very high ($>$300 ppm) if the U-233 is allowed to sit in the neutron flux until 1SQ is obtained. Fig.6 plots the concentration of U-232 in bred U-233 at $t=t_{\text{SQ}}$ for this scenario. The problem can be temporarily overcome via chemical processing to remove Tl-208 and other decay products, but dose rates will begin to rise again after a few weeks [49]. The problem can be more significantly overcome if online extraction of protactinium (the intermediate element in the transmutation of Th to U) from the salt is performed during the breeding process, but this requires a more complex modification to the salt purification system.

4.5 Self-protection time

Another consequence of fissile breeding is the production of fission products, which pose a radiological hazard as they decay. If sufficiently intense, this radiation could increase the difficulty of handling the contaminated salt, although this is certain to be much less problematic than handling fission-reactor spent fuel. We seek to determine if the radiation hazard posed by fission products would complicate the removal of the salt for reprocessing, thus increasing the probability of detection or extending the time needed to extract the bred WUM.

NRC regulation 10 CFR §73.6(b) states that material with a dose rate greater than 1 Gy/hr at a distance of 1 meter without intermediate shielding is exempt from physical protection requirements as the radiological hazard is sufficient to prevent theft or diversion. In light of our simplified model, we use this rule to guide our calculation. We define the self-protection time to be the duration after shutdown at $t_{\text{SQ}}$ for which the dose rate 1 meter from the FLiBe is greater than 1 Sv/hr. We chose units of Sieverts instead of Grays as we assume that the dose is deposited in human tissue by gamma rays alone.

The self-protection time was computed by evolving the material composition at $t_{\text{SQ}}$ forward in time in the absence of neutron flux and computing the dose rate at each time step. To compute the dose rate, a simplified Monte Carlo model was used. An infinite 1 meter thick slab of actinide-doped FLiBe with gamma sources distributed uniformly throughout was modeled. The energy and activity of the gamma sources was based on the radionuclides present in the salt at that time step.

Fig. 7 plots self-protection time as a function of fertile mass. We observe that for all fertile mass inventories and both breeding pathways, the self protection time is at most one day. Given that the minimum $t_{\text{SQ}}$ determined above is 14 days, we find that self-protection time does not significantly increase the time to acquire fissile material from breeding nor will it impede its removal for reprocessing for an extended period of time.

4.6 Decay heat in the blanket

Fissile material breeding in the blanket results in fissioning of some fissile elements and the subsequent presence of fission products. Radioactive decay of these products produces excess heat in the blanket.Fig. 8 plots the decay heat in the blanket at $t=t_{\text{SQ}}$. Notably, the decay heat is a strong function of initial fertile mass, and peaks well below the maximum fission power observed. We find that at $t=t_{\text{SQ}}$ decay heat accounts for less than 5 percent of total excess blanket heating, and represents a $<$1% perturbation to total fusion power. Thus, excess decay heat is not expected to be a significant deterrent to FPP operation in a breakout scenario. However if the salt is removed from the FPP for reprocessing, this extra heat will need to be removed. With volumetric heating densities of 1.5 - 9 kW/m³ (depending on initial fertile inventory), heat removal for reprocessing is nontrivial. However, the decay heat magnitude decreases steadily: in uranium-doped FLiBe, decay heat drops by an order of magnitude after $\sim$20 days, and in thorium-doped FLiBe the decay heat drops by an order of magnitude after $\sim$100 days.

4.7 Impact of Li-6 enrichment

Li-6 enrichment has been widely considered as an option for improving the TBR of FPP blanket designs. This is because Li-6 has a large $1/v$ cross section for tritium breeding, while Li-7 has a non-zero tritium breeding cross-section only at very high neutron energies ($>$9 MeV).

We scanned Li-6 enrichment from 2.5% (below natural levels, which are $\approx$7.5%) to 90% enrichment to analyze its impact on the six breeding quantities of interest discussed in Sections 4.1-4.6 above. Overall results are presented in Figs.9 and 10.

4.7.4 Li-6 enrichment and isotopic purity of bred fissile material

Figs.9(d) and 10(d) plot total isotopic purity of the bred WUM as a function of Li-6 enrichment. A maximum percentage of isotopic purity, more prominent for lower fertile mass inventories, is observed in both production schemes. However, at all conditions assessed here, the isotopic purities obtained are very high ($>$99%) and more than sufficient for use in a nuclear weapon. Li-6 enrichment thus does not impact proliferation resistance from the standpoint of total isotopic purity.

Fig.11 plots the concentration of the U-232 impurity in U-233 at $t=t_{\text{SQ}}$ as a function of Li-6 enrichment. We find that Li-6 enrichment increases U-232 concentration for all fertile mass inventories studied, but the effect is larger for smaller inventories. Like the increase in $t_{\text{SQ}}$ resulting from Li-6 enrichment, this increase in U-232 impurity content further motivates Li-6 enrichment as a tool for proliferation resistance.

4.8 Localization of WUM breeding in the liquid immersion blanket

It is sometimes assumed that fissile breeding is maximized further into the blanket, where the neutron spectrum is more thermal, as the relevant cross sections are highest at lower neutron energies. However, the OpenMC model indicates that WUM breeding is highest in the region closest to the plasma. This is visualized in Fig.13, which plots the reaction rate for U-238 neutron capture on a poloidal cross section of the liquid immersion blanket in the ARC-class FPP modeled in this work. Geometrically, the neutron flux is highest closer to the plasma neutron source (1/$r^{3}$ dependence); this effect outweighs the difference in cross section between higher and lower neutron energies.

This result shows that while our blanket model is simplified and slightly larger than a typical ARC-class device, we are completely capturing the relevant blanket regions for this phenomena and are not artificially introducing extra breeding volume. In fact, our use of a larger than necessary blanket is a conservative assumption in light of this result as the extra blanket material dilutes the dissolved fertile material, reducing the density of nuclides in the region of highest breeding and thus the breeding rate for a given fertile mass inventory. We note, however, that in a true system the actual volume of blanket material would be larger than the blanket tank volume alone, as some extra fluid must be present to be pumped through the heat exchanger and tritium extraction facilities. This reduces the conservativeness of this assumption.

4.9 2D plots of relevant breeding parameters

So far, we have examined the dependence of $t_{\text{SQ}}$, fission power in the blanket, isotopic purity of bred WUM, TBR, decay heat, and self-protection time on fertile mass and Li-6 enrichment. Fig.14(a) and (b) present this data in one plot for both production schemes, allowing quick identification of the 2D parameter regions that are most concerning for proliferation. We have opted not to include decay heat, isotopic purity, or self-protection time as these quantities have been shown to have no substantive impact on the feasibility of fissile breeding anywhere in the parameter space studied.

These plots summarize the key results of this work. Enriching the FLiBe blanket in Li-6 has dual benefits of improving TBR (the usual motivation for lithium enrichment) and significantly increasing $t_{\text{SQ}}$. Importantly, a region where $t_{\text{SQ}}$ is $>$ 1yr appears only for Li-6 enrichment $>$ 20%. At 90% enrichment, this region covers about half of the fertile masses studied. Thus a large portion of the 2D parameter space visualized is of possible proliferation concern. While in this work we are unable to definitively set limits on quantities like TBR and fission power which might limit a proliferation scenario, we hope that future more detailed reactor design studies could make use of similar plots to analyze their vulnerability to this proliferation pathway.

4.10 Uranium impurities in beryllium and implications for plutonium production

Natural beryllium can be significantly contaminated with impurities, including uranium. Therefore, it is well known that fusion concepts using significant amounts of beryllium as a neutron multiplier should consider the effects of uranium contamination, including plutonium production, and consider standards for beryllium purity. ITER research teams in particular have given this matter significant attention as beryllium was long-intended to be used as a first wall material in the device (although this changed in 2023). One calculation determined that Pu-239 production in ITER would be on the order of a gram after five years of operation (for 1 wppm of U impurity in beryllium), but could be on the order of 10 kg in DEMO-class plants [50].

Here, we consider how uranium impurities in beryllium could result in plutonium production in the ARC-class FPP under normal operating conditions for uranium impurity levels of 50, 100, 150, and 200 weight parts per million (wppm), representing 2.4, 4.8, 7.2, and 9.6 kilograms of fertile mass, respectively. To put these values into context, Materion specifies its S-65 grade of beryllium as having a maximum of 150 wppm of U impurity [51]. Beryllium mined from Russia or Kazakhstan were found to have an average of 5.2 wppm uranium impurities (with different Be samples ranging from 0.16 to 18 wppm U content) [52]. Beryllium obtained for use in the Advanced Test Reactor was determined to have an average uranium impurity content of 71 wppm (with concentrations ranging from 23–105 wppm) [53].

To perform this analysis, we used the same geometric model described in Sec.3.1, but implemented a new material definition that allowed the quantity of uranium in the blanket to be specified as a weight fraction of the beryllium in the FLiBe. We made use of a independent depletion calculation, which assumes that the flux spectrum in the blanket is negligibly perturbed by the evolution of its composition. Given the very small amount of fertile and fissile material involved, this is assumption is well justified. Results are shown in Fig.15, which plots the mass density of Pu-239 as a function of time in the blanket assuming continuous full power operation. We observe that it takes nearly a decade for the concentration of Pu-239 to reach its peak. For the liquid immersion blanket modeled here, with a volume of 342 cubic meters, this corresponds to a peak total Pu-239 mass of $\approx$ 3kg for the 200wppm impurity case, less than half of a significant quantity of WUM but possibly enough for a weapon [7].

We also observe that after a decade the quantity of Pu-239 in the blanket becomes approximately constant for the next two decades of operation, indicating that the rate of Pu-239 production and loss are approximately equal. Thus, while the total mass of plutonium in the blanket never exceeds a significant quantity, if plutonium was removed occasionally, a significant quantity could be accrued over time. Notably, it would take decades to produce 1 SQ of Pu-239 from a single ARC-class FPP based on this model (especially at uranium impurity levels $<$200wppm, as would be expected from most naturally occurring beryllium). However, similar timescales have applied to other national weapons programs. It is also possible that 1 SQ could be amassed by collecting the outputs from multiple ARC-class FPPs, reducing the time needed to accrue a significant quantity. In general, uranium impurities in beryllium are not expected to pose an urgent breakout risk. At the same time, the amount of Pu-239 produced in the blanket from impurities is not necessarily trivial: at 100wppm uranium impurity in the beryllium, a kilogram of Pu-239 will be amassed in the blanket at five years of full-power operation. In general, though, breakout risk posed by naturally occurring uranium impurities can be effectively mitigated by mandating lower allowable uranium impurity levels in the FLiBe.