# Assessing the Risk of Proliferation via Fissile Material Breeding in ARC-
class Fusion Reactors

John L. Ball  Ethan E. Peterson  R. Scott Kemp  Sara E. Ferry  Plasma Science
and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139,
USA  Laboratory for Nuclear Security and Policy, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA

###### Abstract

Construction of a nuclear weapon requires access to kilogram-scale quantities
of fissile material, which can be bred from fertile material like U-238 and
Th-232 via neutron capture. Future fusion power plants, with total neutron
source rates in excess of $10^{20}$ n/s, could breed weapons-relevant
quantities of fissile material on short timescales, posing a breakout
proliferation risk. The ARC-class fusion reactor design is characterized by
demountable high temperature superconducting magnets, a FLiBe liquid immersion
blanket, and a relatively small size ($\sim$ 4 m major radius, $\sim$ 1 m
minor radius) [1, 2, 3]. We use the open-source Monte Carlo neutronics code
OpenMC [4] to perform self-consistent time-dependent simulations of a
representative ARC-class blanket to assess the feasibility of a fissile
breeding breakout scenario. We find that a significant quantity of fissile
material can be bred in less than six months of full power operation for
initial fertile inventories ranging from 5 to 50 metric tons, representing a
non-negligible proliferation risk. We further study the feasibility of this
scenario by examining other consequences of fissile breeding such as reduced
tritium breeding ratio, extra heat from fission and decay heat, isotopic
purity of bred material, and self-protection time of irradiated blanket
material. We also examine the impact of Li-6 enrichment on fissile breeding
and find that it substantially reduces breeding rate, motivating its use as a
proliferation resistance tool.

###### keywords:

ARC, proliferation, fissile, fertile, breeding, FPP

††journal: Nuclear Fusion

##  1 Introduction

In this work, we consider the proliferation risk associated with the operation
of an ARC-class fusion power plant (FPP) in a breakout scenario. In the
context of nuclear non-proliferation work, a “breakout scenario” describes the
deliberate misuse of nuclear technology intended for peaceful purposes for the
production of weapons-usable material (WUM). Deuterium-tritium (D-T) fueled
FPPs do not produce WUM under normal operating conditions. However, this does
not imply that an FPP is inherently proliferation resistant. The D-T plasma is
a high-flux, high-energy neutron source that can be used to transmute non-
weapons-usable fertile material into weapons-usable fissile material. Using
OpenMC [4], an open-source radiation transport code, we analyze the potential
for an ARC-class FPP to produce a weapons-relevant quantity of fissile
material in less than one year of operation. This paper shows that it is
theoretically possible to use an ARC-class plant to breed significant
quantities of WUM in a short amount of time.

The purpose of this work is not to argue against the pursuit and adoption of
fusion power. Nor is it to argue against the deployment of liquid breeder
blanket concepts, which offer significant advantages with regards to tritium
breeding and heat removal. Rather, we hope to show that breakout proliferation
risk is a sufficiently serious concern for certain FPP concepts that it should
be accounted for early in the design process. In 2008, the U.S. Nuclear
Regulatory Commission issued a Rule (a policy with the force of law) stating
it expects fission reactor designers to consider diversion of weapons-usable
material in the design phase [5]. The fusion community should continue to
analyze breakout risks associated with new designs, engage early with the
relevant regulatory bodies to ensure that their operating plans are compliant
with regulation and best practices, and proactively address public concerns.
It is also important to devote resources to the development of technological
strategies that can be incorporated into an FPP to achieve true proliferation
resistance, including in the low-probability/high-risk breakout case.

First, we provide an overview of the basics of weapons proliferation and of
prior work on the proliferation risk associated with fusion energy. We then
discuss why the ARC-class tokamak is a particularly interesting case to study.
Next, we detail the neutronics model used to complete this analysis. In the
results section, we examine how adding between 5 and 50 metric tons of either
natural uranium or thorium to the ARC-class FPP breeding blanket impacts the
following metrics: time to breed a significant quantity of weapons-usable
material ($t_{\text{SQ}}$), extra heat in the blanket due to fission, tritium
breeding ratio (TBR), isotopic purity of produced fissile material,
radiological hazards associated with the breeding of fissile material, and
excess heat from radioisotope decay. We also consider how the isotopic
enrichment of lithium in the blanket affects these parameters. Finally, we
discuss the feasibility of this scenario in the context of the global
nonproliferation regime and IAEA Safeguards, drawing upon historical examples
for guidance.

The code and data that support the findings of this study are openly available
at the following URL: https://github.com/jlball/arc-nonproliferation

##  2 Background: nuclear weapons proliferation and fusion technology

###  2.1 Material needed to build a weapon

Construction of a nuclear weapon requires access to kilogram-scale quantities
of fissile isotopes. These isotopes occur in low abundances in nature,
requiring large quantities of raw material to be processed and isotopically
enriched to build a weapon. Alternatively, fertile isotopes like U-238 and
Th-232, which are far more abundant in nature, can be transmuted into weapons-
usable fissile isotopes via neutron capture:

$^{238}\textrm{U}+\textrm{n}\rightarrow\,^{239}\textrm{U}\xrightarrow[23.5~{}\textrm{min}]{\beta^{-}}\,^{239}\textrm{Np}\xrightarrow[2.356~{}\textrm{d}]{\beta^{-}}\,^{239}\textrm{Pu}$
(1)

$^{232}\textrm{Th}+\textrm{n}\rightarrow\,^{233}\textrm{Th}\xrightarrow[21.8~{}\textrm{min}]{\beta^{-}}\,^{233}\textrm{Pa}\xrightarrow[26.98~{}\textrm{d}]{\beta^{-}}\,^{233}\textrm{U}$
(2)

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 8 kg or approximately
$2\times 10^{25}$ nuclei. We adopt these values because they are a standard
and would account for process losses, although they have been criticized by
some as being a factor of 2–3 too high [7]. A substantial neutron source is
therefore needed to transmute relevant quantities of fertile material on
reasonable timescales. Proposed commercial fusion reactors, with total source
rates on the order of $10^{20}$ neutrons per second, are one of the only
technologies other than fission reactors which could be reasonably used for
such a breeding process.

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

Fission power plants pose an “inherent” proliferation risk because they
generate weapons-usable fissile material by default [8]. D-T fueled fusion
power plants are expected to produce large quantities of neutrons, but under
normal operation are not expected to pose a significant proliferation risk as
only a small amount of fertile or fissile material is expected to be present
in the plant. Possible sources of fertile or fissile material on-site at an
FPP include:

  * 1.

The uranium coating inside fission chamber tubes, which may be used as a
neutron diagnostic. This represents only a few grams of uranium and is not
relevant to the production of significant quantities of weapons-usable
material.

  * 2.

Depleted uranium getter beds, which may be deployed in the fuel cycle system
to capture hydrogenic isotopes. These getter beds represent small amounts of
fertile uranium.

  * 3.

Uranium impurities that may be present in structural materials or breeder
materials. It is possible that non-trivial amounts of fissile material could
be produced in the blanket if adequate chemical purity standards are not
implemented. A quantitative discussion of this issue as it pertains to FLiBe
blankets is provided in Section 4.10.

While the risk of proliferation via fissile breeding of an FPP without fissile
or fertile material present is negligible, it is important to note that a D-T
FPP in which no fertile material is introduced could still be used to support
an existing nuclear weapons program through the diversion of Li-6 and/or
tritium from the plant. Both Li-6 and tritium, in combination with deuterium,
can enhance the performance of nuclear weapons. In 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 possibility 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.111We 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]. Furthermore, existing models tend to make optimistic assumptions
about the efficiencies of plasma operations, blanket breeding, and fuel cycle
components, as well as 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
considering a fission-fusion hybrid, SOLASE-H, 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 to achieve ignition.

E. T. Cheng’s 2005 paper [21] explicitly looked at an FPP with a FLiBe tritium
breeding blanket, which is the focus of 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 homogeneous 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. note that the fusion spectrum and expected flux
enables 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

This work focuses on the ARC-class FPP, a relatively recent design that is
presently of significant interest to both the research and private fusion
sectors. As explained below, the high-power-density and use of molten fluoride
salt in the breeder blanket makes the ARC-class FPP a particularly interesting
proliferation case study. ARC-class D-T FPPs were first proposed in 2015 [1],
with several subsequent design studies published since [2, 3]. They are
defined by the following broad characteristics:

  * 1.

The use of high-temperature superconducting (HTS) REBCO magnets with
demountable joints to enable easy access to the interior of the plant for
component maintenance and replacement

  * 2.

A compact, high-power-density design enabled by the high magnetic fields
accessible with HTS magnets

  * 3.

A replaceable vacuum vessel adjacent to the first wall structure _inside_ the
tritium breeding blanket

  * 4.

A Liquid Immersion Blanket (LIB) for tritium breeding, currently assumed to
use molten FLiBe salt as the breeding material

Prior to undertaking any quantitative analysis, we expect that an ARC-class
FPP might present a breakout proliferation risk for the following reasons, and
is therefore worthy of further study:

  * 1.

Fertile material is known to be soluble in FLiBe. Fueled FLiBe has been
studied experimentally and used practically.

  * 2.

Actinide material is known to be removable from the FLiBe breeder via well-
established processes.

  * 3.

The ARC-class FPP will have on-line and on-site capabilities that could be
used for or modified to be capable of the addition, monitoring, and removal of
actinide material.

  * 4.

The ARC-class FPP has a high power density and high solid angle coverage of
the neutron source with the breeder material, making it a potentially
efficient breeder of WUM.

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 342 m3 (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. These 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. FLiBe
with impurities and/or fuel compounds is known to be more corrosive to
structural materials than pure FLiBe [33]. FLiBe 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.

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 [39]. However, it is possible to use the fluoride volatility
process to convert PuF4 to PuF6 under the correct conditions [40].

##  3 Methodology: OpenMC neutronics analysis

The neutronics analysis for this work was carried out using OpenMC, an open-
source Monte-Carlo radiation transport code [4]. The code has been benchmarked
against MCNP [26] and Shift [41] for an ARC-class FPP model and shows good
agreement [42]. The OpenMC depletion module, used extensively in the analysis
presented below, has also been shown to agree well with FISPACT-II in fusion
shutdown dose rate calculations[43].

###  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.
eqrefeq:R and (4) describe the poloidal cross section shape of the blanket,
which is plotted in Figure 1(a).

Major radius $R_{0}$ | 4 m
---|---
Minor radius $a$ | 1 m
Blanket thickness | 1 m
Elongation $\kappa$ | 1.6
Triangularity $\delta$ | 0.5
Table 1:  Plasma geometry parameters used in Eqs. 3 and 4 to determine the
plasma-facing component (PFC) contour.

$R(t)=R_{0}+a\cos{(t+\delta\sin{t})}$ (3) $Z(t)=\kappa a\sin{t}$ (4)

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. Table 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 about the
major axis 2$\pi$ radians, forming a toroidally symmetric 360-degree model.
Notably, this is a simplified model that does not include many structures
which would interrupt the blanket 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 14.1 MeV neutrons isotropically. We assume that
the device is operated at a constant fusion power of 500 MW continuously in
time for all analyses presented.

(a) Plot of the poloidal cross section of the ARC-class FPP liquid immersion
blanket studied in this work. The shape was generated using eqs. 3 and 4 and
the values in table 1.

(b) Radial build of the OpenMC model of the ARC-class breeding blanket studied
in this work.

Figure 1: The geometry and materials used to model the ARC-class FPP breeding
zone in OpenMC for this work.

###  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:

  * 1.

Loss of bred fissile material to neutron reactions during breeding

  * 2.

Additional neutrons and heat from fission of bred fissile isotopes, which
produce secondary neutrons and additional fission products.

  * 3.

Neutron reactions on fission products

  * 4.

Radioactive decay of unstable nuclei, particularly the decay chains of fissile
breeding reactions

  * 5.

Impurity-producing neutron reactions on intermediate daughter products in
fissile breeding decay chains

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 Results

###  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 use a natural (7.5%)
Li-6 enrichment.

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$2 metric tons), $t_{\text{SQ}}$ is less than one year for both the U
and Th based schemes; and $t_{\text{SQ}}$ becomes largely insensitive to the
fertile mass once the mass exceeds about 10 metric tons222Ten 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., which is
at or below the IAEA’s lower limit for accountability [6]. These data can be
fit using the following equation:

$t_{\text{SQ}}(m_{f})=A/m_{f}-Bm_{f}+C$ (5)

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.

Fit Coef. | U-238 $\rightarrow$ Pu-239 | Th-232 $\rightarrow$ U-233
---|---|---
$A$ | 330 $\pm$ 3.6 | 420 $\pm$ 8.2
$B$ | 0.12 $\pm$ 0.014 | 0.25 $\pm$ 0.033
$C$ | 15.0 $\pm$ 0.62 | 37 $\pm$ 1.4
Table 2:  Fit coefficients for Eq. (5), which is fit to the data plotted in
Fig. 2.

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. The long half-life of this intermediate daughter
creates a lag between the capture of a neutron by Th-232 and the actual
appearance of U-233 in the blanket fluid. As 27 days 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 reactor or
while it is operation, thus the reactor could be shut down before the decay is
completed, further reducing $t_{\text{SQ}}$ by reducing losses to fission and
allowing earlier extraction of the material.

Figure 2: Plot of time to breed one significant quantity ($t_{\text{SQ}}$) of
fissile material versus mass of fertile material dissolved in a representative
ARC-class FPP liquid immersion blanket (see Sec. 3.1) for two different
fissile material breeding pathways (U-238 $\rightarrow$ Pu-239 and Th-232
$\rightarrow$ U-233; 1 SQ = 8 kg for both). We find that even for small
amounts of fertile material input, ARC-class fusion reactors can produce 1 SQ
of fissile material in less than 6 months, posing a possible proliferation
risk.

###  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 neutron rate is
linear in 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 the
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.

Figure 3: Plot of fission power in the blanket as a function of fertile
inventory. The bottom curve of each colored region corresponds to fission at
$t=0$, when only fertile material is present, and the top curve corresponds to
$t=t_{\text{SQ}}$, when 1 SQ of fissile material has been produced in the
blanket. While we observe a substantial change in fission power as fissile
material builds up in the blanket, fission power never exceed $\approx$ 15% of
total fusion power (500MW) making it unlikely to limit a proliferation
scenario.

###  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, although this condition depends heavily
on the plant design and operational parameters. 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 the results in Figs. 2 and 4, TBR reduction
due to the addition of fertile mass in the blanket would not automatically be
a deterrent to continued plant operation. However, it is worth noting that our
blanket model is simplified and neglects important structures which would also
reduce TBR like RF heating systems and vacuum ducts.

Note that Figure 4 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, helping to lessen the
detrimental effect on TBR. However, this change was negligible in the single-
SQ breeding scenario analyzed here and so time-dependent results were omitted
from the plot.

Figure 4: The tritium breeding ratio (TBR) in the model ARC-class FPP liquid
immersion blanket is plotted as a function of fertile mass dissolved in the
blanket for the fertile materials U-238 and Th-232. The presence of fertile
material decreases the TBR, although not necessarily by an amount expected to
render tritium self-sufficiency impossible. This determination depends heavily
on the plant design and operational parameters.

###  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 which 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 2.6 MeV
gamma ray that can make 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 1 SQ 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.

Figure 5: Plot of isotopic purity versus fertile inventory in the ARC-class
FPP blanket. At all fertile masses considered, the isotopic purity achieved is
well in excess of what is considered to be weapons-usable material. Figure 6:
Plot of U-232 impurity concentration in bred U-233 at $t=t_{\text{SQ}}$ in
units of atomic parts per million (appm). The impurity U-232 has Tl-208 in its
decay chain, a very active gamma emitter which can create substantial
radiation hazards even in small concentrations (¿100 appm U-232), thus
increasing the difficulty of manufacturing a weapon from contaminated
material.

###  4.5 Self-protection time

Another consequence 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 the problem 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,
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 salt 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 timestep. To compute the dose rate a simplified Monte
Carlo model was used, where the material was represented as an infinite 1
meter thick slab of actinide-doped FLiBe with gamma sources distributed
uniformly throughout with energy and activity 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
impede its removal for reprocessing.

Figure 7: Plot of self-protection time, defined as the interval after shutdown
for which the dose rate at 1 meter is greater than 1 Sv/hr, as a function of
initial fertile mass. We find that if the reactor is shutdown at
$t_{\text{SQ}}$ the self-protection time is at most a day for both breeding
pathways and all mass inventories studied, thus not significantly impeding
proliferation via fissile breeding.

###  4.6 Decay heat in the blanket

Another consequence of the production of fission products from fissile
breeding is excess heat from the radioactive decay of these products. Delayed
heat from radioactive decay is a well known issue in fission systems, as heat
must continue to be extracted from the fission reactor’s core after shutdown
to prevent the fuel from melting, and extracted spent fuel must be cooled and
shielded as well. 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 $kW/m^{3}$ depending on initial
fertile inventory, heat removal for reprocessing is nontrivial. However this
heating decays in time, with the decay heat in uranium-doped FLiBe reducing by
an order of magnitude after $\sim$20 days, and the heat in thorium-doped FLiBe
reducing by an order of magnitude after $\sim$100 days.

Figure 8: Plot of decay heat at $t=t_{\text{SQ}}$ versus initial inventory of
fertile material, where $t_{\text{SQ}}$ is the time at which 1 SQ of fissile
material exists in the blanket. Decay heat is a small ($<$5%) fraction of
total excess heat and represents a $<$1% perturbation on total fusion power
(500MW). Thus decay heat is unlikely to limit the feasibility of a
proliferation scenario.

###  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 only has a non-zero tritium breeding cross-
section 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.

Figure 9:  Plots of six relevant breeding parameters as a function of Li-6
enrichment for fertile mass inventories from 5–50 metric tons in the U-238
$\rightarrow$ Pu-239 production scheme. (a) Plot of time to 1 SQ vs. Li-6
enrichment. We observe a strong suppression of fissile breeding with
increasing Li-6 enrichment, greatly increasing $t_{\text{SQ}}$ and motivating
Li-6 enrichment as a proliferation resistance tool. (b) Plot of fission power
at $t=t_{\text{SQ}}$ vs. Li-6 enrichment. We observe a reduction in fission
power with Li-6 enrichment up to 30% enrichment, after which fission power is
approximately constant. (c) Plot of TBR vs. Li-6 enrichment. We observe that
Li-6 enrichment increases TBR until $\approx$ 30% enrichment, after which TBR
is slightly reduced. However, fertile mass slightly increases TBR at these
high enrichment levels from neutron multiplication reactions. (d) Plot of
total isotopic purity vs. Li-6 enrichment. While we observe variations in
purity with Li-6 enrichment, all purities remain in excess of 99%, well above
what is needed for use in a nuclear weapon. (e) Plot of self-protection time
vs. Li-6 enrichment. We find that self-protection time decreases monotonically
with Li-6 enrichment, which is expected given the increase in $t_{\text{SQ}}$
and reduction in fission rate. However self-protection time never exceeds two
days, and thus does not impact the viability of fissile breeding as a
proliferation pathway. (e) Plot of decay heat at $t=t_{\text{SQ}}$ in the
blanket material vs. Li-6 enrichment. We observe a monotonic reduction in
decay heat with Li-6 enrichment. The magnitude of decay heats observed remains
low ($\leq$ 1%) across all Li-6 enrichments studied.

Figure 10:  Plots of six relevant breeding parameters as a function of Li-6
enrichment for fertile mass inventories from 5–50 metric tons in the Th-232
$\rightarrow$ U-233 production scheme. (a) Plot of time to 1 SQ vs. Li-6
enrichment. We observe a strong suppression of fissile breeding with
increasing Li-6 enrichment, greatly increasing $t_{\text{SQ}}$ and motivating
Li-6 enrichment as a proliferation resistance tool. (b) Plot of fission power
at $t=t_{\text{SQ}}$ vs. Li-6 enrichment. We observe a reduction in fission
power with Li-6 enrichment up to 30% enrichment, after which fission power is
approximately constant. (c) Plot of TBR vs. Li-6 enrichment. We observe that
Li-6 enrichment increases TBR until $\sim$ 30% enrichment, after which TBR is
slightly reduced. Unlike in the U-238 $\rightarrow$ Pu-239 production scheme,
no boost in TBR from neutron multiplication is observed. (d) Plot of total
isotopic purity vs. Li-6 enrichment. While we observe variations in purity
with Li-6 enrichment, all purities remain in excess of 99%, well above what is
needed for use in a nuclear weapon. However U-233 is complicated by very low
levels of U-232, which is discussed in sec. 4.10 and fig. 11. (e) Plot of
self-protection time vs. Li-6 enrichment. We find that self-protection time
decreases monotonically with Li-6 enrichment, which is expected given the
increase in $t_{\text{SQ}}$ and reduction in fission rate. However self-
protection time never exceeds three days and for most cases is zero, and thus
does not impact the viability of fissile breeding as a proliferation pathway.
(e) Plot of decay heat at $t=t_{\text{SQ}}$ in the blanket material vs. Li-6
enrichment. We observe a monotonic reduction in decay heat with Li-6
enrichment. The magnitude of decay heats observed remains low ($\leq$ 1%)
across all Li-6 enrichments studied.

####  4.7.1 Li-6 enrichment and $t_{\text{SQ}}$

Figs. 9(a) and 10(a) plot $t_{\text{SQ}}$ vs. Li-6 enrichment for the U-238
$\rightarrow$ Pu-239 and Th-232 $\rightarrow$ U-233 production schemes
respectively. Li-6 enrichment is a strong lever on $t_{\text{SQ}}$, with 90%
enrichment increasing $t_{\text{SQ}}$ by about an order of magnitude over
natural lithium for both production schemes. This creates a novel motivation
for lithium enrichment in fusion systems as a tool for improving proliferation
resistance as well as boosting blanket TBR.

####  4.7.2 Li-6 enrichment and fission heating

Figs. 9(b) and 10(b) plot fission power at $t=t_{\text{SQ}}$ in the blanket as
a function of Li-6 enrichment. We observe that fission power is reduced with
increasing Li-6 enrichment up to 30% enrichment, after which there is little
to no change. We observe this effect in both production schemes. This is
likely a result of the hardening of the neutron spectrum with increasing Li-6
enrichment, which is discussed further in sec. 4.7.7.

####  4.7.3 Li-6 enrichment and TBR

Figs. 9(c) and 10(c) plot TBR as a function of Li-6 enrichment. Unsurprisingly
we observe that increasing Li-6 enrichment increases TBR, but only up to 30%
enrichment, after which there is little to no gain or even a slight reduction
in both production schemes. In the U-238 $\rightarrow$ Pu-239 production
scheme we also observe a slight boost in TBR with increasing fertile mass for
enrichments above 30%, likely the result of uranium’s high rate of neutron
multiplication and low probability of absorption in the faster spectrum
created by Li-6 enrichment. For further discussion of Li-6 enrichment’s impact
on the neutron flux spectrum see sec. 4.7.7. We observe no such boost in TBR
in the Th-232 $\rightarrow$ U-233 production scheme, and see an even greater
reduction in TBR with fertile mass at lower enrichments, in line with the
result of sec. 4.3.

####  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.

Figure 11: Plot of U-232 impurity concentration in bred U-233 (without online
Pa removal) at $t=t_{\text{SQ}}$ as a function of Li-6 enrichment. We observe
that Li-6 enrichment increases U-232 concentration for all fertile mass
inventories, further motivating Li-6 enrichment as a proliferation resistance
tool. See sec. 4.10 for further discussion of the impact of U-232 on fissile
material bred from Th-232.

####  4.7.5 Li-6 enrichment and self-protection time

Figs. 9(e) and 10(e) plot self-protection time as a function of Li-6
enrichment. We observe that Li-6 enrichment monotonically decrease self-
protection time for both production pathways, with notably all enrichments
above 20% having zero self-protection time for the U-233 production pathway.
Given that self-protection time was already found to be very short for natural
Li-6 enrichment, this result does not change the conclusion drawn in sec. 4.5
that self-protection time does not substantially impact the feasibility of
fissile breeding in ARC-class reactors.

####  4.7.6 Li-6 enrichment and decay heat

Figs. 9(f) and 10(f) plot the decay heat in the breeder material at
$t=t_{\text{SQ}}$ as a function of Li-6 enrichment. We observe a monotonic
decrease in decay heat with Li-6 enrichment, which is expected given the
reduction in fission rate with increasing Li-6 enrichment. The difference
between fertile masses varies widely over the range of Li-6 enrichments
studied, with low Li-6 enrichments seeing much larger variations with fertile
mass than higher Li-6 enrichments. The absolute magnitude remains small
($\approx$ 1% of total fusion power) for all enrichments studied, indicating
that decay heat is not likely to impact a proliferation scenario at any
natural or greater Li-6 enrichment.

####  4.7.7 Li-6 enrichment and the neutron flux spectrum in the blanket

To better understand the mechanism by which Li-6 impacts the fissile-material
breeding process, we examine the average flux spectrum in the blanket tank as
a function of Li-6 enrichment. Fig. 12 plots the average neutron energy flux
spectrum in the blanket tank in arbitrary units for Li-6 enrichment ranging
from 2.5–90% for a 20 metric ton fertile inventory. We see a clear trend:
increasing Li-6 enrichment significantly increases the average neutron energy.
Fission and neutron capture reactions in fertile and fissile material tend to
have cross sections that peak at low neutron energies. These nuclear reactions
are suppressed by the presence of Li-6, which tends to capture neutrons before
they have time to be moderated to lower energies or interact with other
nuclides. Note also that the Li-7 tritium breeding reaction produces neutrons,
whereas the Li-6 tritium breeding reaction does not. Higher percentages of
Li-7 in the FLiBe will contribute to the softening of the neutron spectrum by
providing a source of lower energy neutrons.

Figure 12: Plot of neutron energy spectrum in the ARC-class FPP FLiBe blanket
tank with 20 metric tons of fertile material as a function of Li-6 enrichment.
Increasing Li-6 enrichment increases average neutron energy in the blanket, as
fusion neutrons are more likely to be consumed in a Li-6(n,$\alpha$)T reaction
before they are thermalized in the blanket and/or captured by fertile or
fissile material via neutron capture and fission reactions. This increase in
the average neutron energy with Li-6 enrichment is responsible for many of the
trends, including suppression of fissile breeding, observed in sec. 4.7.

###  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; this effect outweighs the difference in
cross section between higher and lower neutron energies.

Figure 13: Tally of U-238(n,$\gamma$)Pu-239 reactions as a function of
location in the blanket. The rate plotted is absolute and toroidally
integrated, and is not volume normalized, but is normalized with respect to
the maximum value obtained. Pu-239 production is highest closest to the
neutron source (the plasma).

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 $>$ 1 yr 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.

Figure 14: Plots of three breeding-relevant parameters (time to 1 SQ
($t_{\text{SQ}}$), TBR, and fission power) as a function of Li-6 enrichment
and fertile mass in the blanket for both the U-238 $\rightarrow$ Pu-239 and
Th-232 $\rightarrow$ U-233 production schemes. These plots summarize some of
the key results presented in figs. 9 and 10 in a way that allows for easier
comparison across parameters and bounding of regimes concerning for
proliferation. Given the simplicity of the model used in this study and
remaining uncertainties in aspects of plant design like the tritium fuel
cycle, we can make no definitive assertions about boundaries separating
concerning and non-concerning regions, but suggest them as a tool for future
studies to rapidly communicate the results of their proliferation analyses.

###  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 satisfied. 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 mass of Pu-239 of $\approx$ 3 kg for the 200
wppm 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 $<$200 wppm, 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 100 wppm 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.

Figure 15:  Plot of Pu-239 mass density accumulated in the ARC-class FPP
liquid immersion blanket for varying levels of naturally occurring uranium
impurities in the beryllium of the FLiBe breeder. Total blanket volume is 342
m3, so 1 g/m3 of Pu-239 corresponds 0.342 kg. At 100 wppm uranium in the
beryllium, therefore, there is $\approx$1 kg of Pu-239 in the blanket after
five years of full-power operation. These results indicate that it would take
decades to amass 1 SQ of Pu-239 (8 kg) from naturally occurring uranium
impurities in a single ARC-class FPP, although the amounts of Pu-239 produced
are not trivial.

##  5 Discussion

Table 3 reviews some of the key findings from Sec. 4 and summarizes their
implications on the breakout proliferation risk associated with the ARC-class
FPP modeled in this work. In general, the results indicate that an SQ of high-
purity WUM can be rapidly produced in the breeding blanket of an ARC-class
FPP. In this section, we discuss how this might affect global security and the
emerging fusion industry.

The feasibility of the proliferation scheme outlined here ultimately depends
on the technical sophistication of the state attempting it. In general, states
operating FPPs will probably have a baseline level of expertise that is more
than adequate to initiate a program to produce WUM. Acquiring the raw fertile
material (U or Th) in the needed ton quantities is straightforward. These
elements are about as abundant as tin, and virtually every country has
adequate resources for a weapons program. The periphery of sandstone aquifers
and phosphate mines are especially rich sources. Iraq, for example, acquired
the uranium for its nuclear-weapons program by re-milling the tailings from a
phosphate mine [54]. The technology for large-scale salt cleanup may need to
be custom built, but if the FPP comes with an online salt-purification system,
that system might provide the required template. The weapons technology itself
is eighty years old, demonstrably within reach of states like North Korea, and
much simpler than an FPP to model and understand. In general, there are very
few technical barriers to making nuclear weapons once the fissile material is
in hand [55].

The decision to proliferate is constrained primarily by politics, but when
national leaders become motivated to acquire nuclear weapons, they tend to
view the effort as essential to their continued existence as a nation [56, 57,
58]. As such, even high-value assets, like FPPs, can be conscripted into
service: of the 32 countries [58] that have entertained nuclear-weapons
programs, an estimated 70% drew up plans to use their civilian nuclear-power
infrastructure to jumpstart weapons production [59]. The potential to exploit
peaceful energy technologies for weapons motivated the creation of the IAEA in
1957, but that agency lacks the resources to stop proliferation—its best hope
is early detection, followed by a drawn-out international review of anomalies
followed by a collective international action, as occurred most recently with
Iran [60]. This process is not fast. For example, the IAEA opened its formal
investigation of Iran’s nuclear program in the summer of 2002, but it took
more than four years before the first United Nations resolution finding Iran
in noncompliance was passed in December 2006. The weeks-to-months breakout
timelines discussed here are much faster than the international community can
typically respond.

IAEA Safeguards are designed to confirm the non-diversion of 1 SQ of fissile
material once every year from declared facilities that routinely process
Special Fissionable or Source Materials [61]. Under normal operation, FPPs
would not be routinely inspected because they are not expected to possess
qualifying nuclear materials. Putting this legal issue aside, there is a
practical problem with inspecting FPPs. Fission plants can be inspected
effectively on an annual basis because the fissile material in them ($\gg\\!1$
SQ) is stored in solid fuel bundles, which are quick to verify by counting. By
contrast, the fissile-material breeding process described here is more akin to
a bulk processing facility, such as occurs in reprocessing plants, where
safeguards inspections need be very frequent or continuous.333In fact, the
IAEA doesn’t have the resources to meet its inspection goals for all bulk-
process plants, and there are comparatively few such plants in the world. A
fusion future would put enormous strain on the IAEA if a bulk-plant standard
were needed. If the IAEA were to adopt the goal of detecting proliferation at
FPPs, rather than merely confirming non-diversion of declared material,
inspections may be needed on timescales of the $t_{\text{SQ}}$ estimates
identified above.

In point of fact, however, IAEA Safeguards have not actually detected
proliferation activities. Inspections are choreographed events known to the
inspected state well in advance.444Special Inspections theoretically give the
IAEA the power to inspect any sites with very limited warning, but these
inspections have not been routinely used for fear of political repercussions
[62, 63]. The Additional Protocol allows Complementary Access at routinely
inspected sites, with one day notice, but under present rules this option
would not apply to FPPs because the Additional Protocol doesn’t apply to sites
that don’t routinely process Special Fissionable or Source Materials per
Article XX of the IAEA Statute. This limitation of Safeguards has led some
countries to take matters into their own hands. Israel, for example, used
military attacks in 1981 and 2007 to stop nuclear reactors from making weapons
in Iraq and Syria, respectively; the United States went to war with Iraq
notionally for this purpose; and the United States has used coercion in
numerous other cases555Successfully for Taiwan and South Korea, and
unsuccessfully for India, Pakistan, and North Korea.. As such, actual
proliferation prevention depends on the ability of powerful nations to detect
weapons programs on their own, and on having adequate and timely options to
reverse the program, be they diplomatic or military in nature.

Nevertheless, the key risk for the proliferator is early detection that might
lead to an effective intervention. The preparatory activities for fissile
breeding can probably be carried out with virtually no risk of detection [64].
We also showed that the excess heat from fission during the breeding process
was small, and could easily be offset by slightly reducing the fusion power,
making detection by thermal emission infeasible. If there is tamper-proof
monitoring of the blanket by the international community, then its use for
fissile material breeding would be readily detected. There may also be
signatures that could be detected at the fence-line of the plant [59].
However, these do not ensure that the response will be timely or adequate.
Because a kinetic military strike against an operating FPP could result in
tremendous radiological release and subsequent health consequences,
counterproliferation actions might be limited to political options, which
depend entirely on the equities of the state doing the proliferating. In other
words, there may be no ex-post-facto technological fix once a state commences
WUM production.

In view of these considerations, ARC-type FPPs might be regarded by
governments as presenting nontrivial proliferation risks. Because the ability
to stop proliferation might rest heavily on the identity of the proliferator,
restrictions on FPP export may be an important element in preventing their
eventual misuse.666Even so, political relationships are unpredictable. In the
1970s, the United States was an enthusiastic exporter of nuclear technology to
Iran, only to regret that decision a decade later. Designing FPPs to be more
intrinsically resistant to proliferation may help abate these concerns. Li-6
enrichment can help extend the breakout timelines, giving more time for a
response, although this can be partially overcome if domestic FLiBe production
is possible. Exporting plants incapable of tritium self sufficiency would be a
way to ensure a continued dependence on a supplier nation that could monitor
the use of the plant; but it seems unlikely that FPP buyers will be
enthusiastic to make multi-billion dollar investments that permanently tie
their energy security to a supplier nation. It would also require that
supplier nations operated FPPs that could produce enough excess tritium to
keep other nations operating. This two-tier system ultimately requires buyers
to go along with the restriction, and in the event there are multiple
international suppliers, competition may lead other suppliers to undercut this
scheme.

Table 3: Key findings for both the U-238 $\rightarrow$ Pu-239 and Th-232 $\rightarrow$ U-233 breakout scenarios in an ARC-class FPP, and possible implications of the quantitative results on breakout proliferation risk. Consideration |  U-238 $\rightarrow$ Pu-239 |  Th-232$\rightarrow$U-233 |  Summary
---|---|---|---
Amount of fertile mass required to breed 1 SQ in $<$ 1 month |  $\approx$ 20 metric tons of U-238 needed (approximately 1 m3). Natural uranium is 99.3% U-238. |  Requires $>$ 50 metric tons of Th-232 (beyond range considered here) because of 27 day intermediate daughter half-life. |  Obtaining raw material not a major deterrent for U-238; possibly for Th-232
Amount of fertile mass required to breed 1 SQ in $<$ 2 months |  $\approx$ 7 metric tons of U-238 needed ($<$ 0.5 m3) |  $\approx$ 15 metric tons of Th-232 needed ($\approx$ 1.3 m3). Natural thorium is 99.98% Th-232. |  Obtaining raw material not a major deterrent
Amount of fertile mass required to breed 1 SQ in $<$ 1 year (approx. IAEA inspection timeline) |  $\approx$ 1 metric ton (calculated with empirical fit given in sec. 4.1) |  $\approx$ 1.3 metric tons (calculated with empirical fit given in sec. 4.1) |  Obtaining raw material not a major deterrent
Addition of fertile mass and impact on tritium breeding |  For fertile masses plotted, TBR does not drop below levels required for tritium self-sufficiency in any ARC-class FPP scenarios modeled in [11]. |  For fertile masses plotted, TBR does not drop below levels required for tritium self-sufficiency in any ARC-class FPP scenarios modeled in [11]. |  Addition of fertile mass not expected to affect tritium breeding to the point that plant is no longer able to operate.
Impact of excess heat due to fission in the blanket |  Increase of 10-15% in total power handled by blanket |  Increase of 5–10% in total power handled by blanket |  Not an issue to plant operation, unless heat exchange systems are designed with very small safety margins for excess power
Impact of excess heat due to radioactive decay of fertile and fissile material in the blanket |  Negligible perturbation to total power in blanket, reduces by order of magnitude $\sim$20 days after shutdown at $t_{\text{SQ}}$ |  Negligible perturbation to total power in blanket, reduces by order of magnitude $\sim$100 days after shutdown at $t_{\text{SQ}}$ |  Not an issue to plant operation, but may create a challenge for external reprocessing.
Quality of fertile material produced at $t_{\text{SQ}}$ |  Purity above 99.0% for all cases studied |  Purity above 99.0% for all cases studied, but substantial ($>$100 ppm) U-232 contamination |  For both Pu-239 and U-233 production schemes, resultant purity is well in excess of what is considered adequate for weapons-usable material, but U-233 made less usable by U-232 impurity.
Self-protection time |  Self-protection time is short ($\sim$1 day or less) |  Self-protection time is short ($\sim$few hours) |  The radiological hazard posed by fission products in the salt is unlikely to prevent the removal of the salt from the plant or greatly complicate its reprocessing, thus it does not impact the feasibility of fissile breeding.
Li-6 enrichment |  Li-6 enrichment increases $t_{\text{SQ}}$ at all fertile masses considered. It also tends to increase TBR (except at very high Li-6 enrichment), decrease fission power in the blanket, decrease self-protection time, and decrease decay heat. |  Li-6 enrichment increases $t_{\text{SQ}}$ at all fertile masses considered. It also tends to increase TBR (except at very high Li-6 enrichment), decrease fission power in the blanket, decrease self-protection time, and decrease decay heat. |  Li-6 enrichment may be an effective way to add proliferation resistance by making it much harder to breed an SQ of WUM in between inspection periods.

##  6 Conclusion

In this paper we have analyzed the risk of a fissile breeding breakout
proliferation scenario in an ARC-class FPP by using the OpenMC Monte-Carlo
neutronics code to perform a fully self-consistent time-dependent simulation
of a simplified ARC-class blanket model. We examined the impact of two initial
conditions: mass of fertile material in the breeding blanket and Li-6
enrichment of the breeding material, on six relevant breeding parameters:
$t_{\text{SQ}}$, TBR, fission power, isotopic purity of bred WUM, self-
protection time, and decay heat. We performed this analysis for two fissile
breeding production schemes, U-238 $\rightarrow$ Pu-239 and Th-232
$\rightarrow$ U-233. We find that for all fertile mass inventories analyzed
(5–50 metric tons) and a natural Li-6 enrichment (7.5%), a significant
quantity of WUM can be bred in less than six months of full power operation.
This result indicates that ARC-class FPPs could pose a non-negligible
proliferation risk if other mechanisms do not limit the feasibility of these
scenarios.

We found that with a natural Li-6 enrichment of the blanket material, TBR,
isotopic purity, fission power, self-protection time, and decay heat did not
represent definitive limitations on the feasibility of this scenario. However
we noted that U-233 bred from Th-232 is contaminated with a substantial amount
of U-232, greatly increasing the radiological hazard posed by the final
reprocessed fissile material, reducing its weapons usability.

We also varied the Li-6 enrichment of the breeding fluid and examined its
impact on fissile breeding. Most consequently, we observed a substantial
suppression of fissile breeding with increasing Li-6 enrichment, leading to a
large increase in $t_{\text{SQ}}$. This alone provides a strong motivation for
additional study of Li-6 enrichment as a tool for proliferation resistance. We
also observe reductions in other relevant breeding parameters like fission
power, self-protection time, and decay heat. TBR is sightly increased with
Li-6 enrichment, as expected. The impact of introducing fertile material on
TBR changes substantially over the enrichment interval studied, with lower
Li-6 enrichments being more sensitive to the introduction of fertile material
than higher enrichments. Total isotopic purity does vary with Li-6 enrichment,
but not to any level that would impact its weapons usability. The
concentration of U-232 in U-233 however does monotonically increase with Li-6
enrichment, further motivating the use of Li-6 enrichment for proliferation
resistance.

We suggest that future work focus on the following:

  * 1.

Improving available workflows for self-consistent time-dependent fissile
breeding calculations

  * 2.

Use of more complete geometric models to better estimate TBR and parasitic
neutron absorption in structural materials

  * 3.

Exploration of detection and mitigation technologies

  * 4.

Analysis of pathways for fertile material introduction / fissile material
removal in various blanket types

In this work we have shown that, left unaddressed, ARC-class FPPs could pose a
proliferation risk via fissile breeding. However, we have also shown that
options exist for increasing the intrinsic proliferation resistance of D-T
fusion reactors through Li-6 enrichment of the blanket material. While plans
exist to build fusion pilot plants within the next ten years, it is unlikely
that the issue of proliferation will become a barrier to fusion deployment
until a global industry seeks to deploy many FPPs around the world.
Nonetheless our technical understanding of fusion’s proliferation risks
requires further study, and must be expanded before the technology sees
widespread adoption. We feel that this work shows that the risk of
proliferation via fissile breeding is substantial enough that proliferation
resistance should be considered in the design of all future D-T FPPs, and
further research into the detection and mitigation of these scenarios pursued.
This includes studies of appropriate safeguards and regulatory frameworks as
well as technology for intrinsic resistance and detection. We feel pursuing
these issues now will be critical to ensuring the safe and widespread
deployment of fusion energy in the future.

## References

  * [1] B.N. Sorbom, J. Ball, T.R. Palmer, F.J. Mangiarotti, J.M. Sierchio, P. Bonoli, C. Kasten, D.A. Sutherland, H.S. Barnard, C.B. Haakonsen, J. Goh, C. Sung, and D.G. Whyte.  ARC: A compact, high-field, fusion nuclear science facility and demonstration power plant with demountable magnets.  Fusion Engineering and Design, 100:378–405, 2015.
  * [2] A.Q. Kuang, N.M. Cao, A.J. Creely, C.A. Dennett, J. Hecla, B. LaBombard, R.A. Tinguely, E.A. Tolman, H. Hoffman, M. Major, J. Ruiz Ruiz, D. Brunner, P. Grover, C. Laughman, B.N. Sorbom, and D.G. Whyte.  Conceptual design study for heat exhaust management in the ARC fusion pilot plant.  Fusion Engineering and Design, 137:221–242, 2018.
  * [3] S.J. Frank, C.J. Perks, A.O. Nelson, T. Qian, S. Jin, A. Cavallaro, A. Rutkowski, A. Reiman, J.P. Freidberg, P. Rodriguez-Fernandez, and D. Whyte.  Radiative pulsed l-mode operation in ARC-class reactors.  Nuclear Fusion, 62(12):126036, Oct. 2022.
  * [4] Paul K. Romano, Nicholas E. Horelik, Bryan R. Herman, Adam G. Nelson, Benoit Forget, and Kord Smith.  Openmc: A state-of-the-art monte carlo code for research and development.  Annals of Nuclear Energy, 82:90–97, 2015.  Joint International Conference on Supercomputing in Nuclear Applications and Monte Carlo 2013, SNA + MC 2013. Pluri- and Trans-disciplinarity, Towards New Modeling and Numerical Simulation Paradigms.
  * [5] U.S. Nuclear Regulatory Commission.  Policy statement on the regulation of advanced reactors.  Federal Register, Vol. 73, No. 199, p. 60612, Oct. 2018.
  * [6] IAEA Safeguards Glossary.  Number 3 in International Nuclear Verification Series. International Atomic Energy Agency, Vienna, 2022.
  * [7] Braden Goddard, Alexander Solodov, and Vitaly Fedchenko.  IAEA “significant quantity” values: time for a closer look?  The Nonproliferation Review, 5–6(23), Aug. 2016.
  * [8] Gregory Jones.  Reactor-grade plutonium and nuclear weapons: ending the debate.  The Nonproliferation Review, 1–2(26), May 2019.
  * [9] Bruce Goodwin.  Nuclear weapons technology 101 for policy wonks.  Technical report, Lawrence Livermore National Laboratory, 2021.
  * [10] Mohamed Abdou, Marco Riva, Alice Ying, Christian Day, Alberto Loarte, L.R. Baylor, Paul Humrickhouse, Thomas F. Fuerst, and Seungyon Cho.  Physics and technology considerations for the deuterium–tritium fuel cycle and conditions for tritium fuel self sufficiency.  Nuclear Fusion, 61(1):013001, 2020.
  * [11] Modeling and analysis of the tritium fuel cycle for ARC-and STEP-class DT fusion power plants.
  * [12] Mark Diesendorf, David Roser, and Haydn Washington.  Analyzing the nuclear weapons proliferation risk posed by a mature fusion technology and economy.  Energies, 16(3):1123, 2023.
  * [13] M. Kovari, M. Coleman, I. Cristescu, and R. Smith.  Tritium resources available for fusion reactors.  Nuclear Fusion, 58(2):026010, Dec. 2017.
  * [14] Fusion energy and nonproliferation workshop summary report.  Technical report, Princeton Plasma Physics Laboratory, 2023.
  * [15] R.W. Conn, S.I. Abdel-Khalik, G.A. Moses, G.L. Kulcinski, E Larsen, C.W. Maynard, MMH Ragheb, I.N. Sviatoslavsky, W.F. Vogelsang, WG Wolfer, et al.  Fusion-fission hybrid design with analysis of direct enrichment and non-proliferation features (the solase-h study).  Nuclear Engineering and Design, 63(2):357–374, 1981.
  * [16] Sümer Şahın, Hüseyin Yapici, and Ertuǧrul Baltacioǧlu.  Fusion breeder with enhanced safeguarding capabilities against nuclear weapon proliferation.  Energy Conversion and Management, 39(9):899–909, 1998.
  * [17] Sümer Şahin and Hüseyin Yapici.  Neutronic analysis of a thorium fusion breeder with enhanced protection against nuclear weapon proliferation.  Annals of Nuclear Energy, 26(1):13–27, 1999.
  * [18] Sümer Sahin, Hüseyin Yapici, and Necmettin Sahin.  Neutronic performance of proliferation hardened thorium fusion breeders.  Fusion Engineering and Design, 54(1):63–77, 2001.
  * [19] Matthias Vanderhaegen, Greet Janssens-Maenhout, Paolo Peerani, and André Poucet.  On the proliferation issues of a fusion fission fuel factory using a molten salt.  Nuclear Engineering and Design, 240(10):2988–2993, Oct 2010.
  * [20] J.F. Santarius, G.L. Kulcinski, and L.A. El-Guebaly.  A passively proliferation-proof fusion power plant.  Fusion Science and Technology, 44(2):289–293, 2003.
  * [21] E.T. Cheng.  Performance characteristics of actinide-burning fusion power plants.  Fusion Science and Technology, 47(4):1219–1223, May 2005.
  * [22] Fabian Sievert and Daniel Johnson.  Creating suns on earth: Iter, life, and the policy and nonproliferation implications of nuclear fusion energy.  Nonproliferation Review, 17(2):323–346, 2010.
  * [23] M. Englert, F. Balloni, and W. Liebert.  Possible proliferation risks of future tokamak reactors.  In 51st Annual INMM Meeting, July 2010.
  * [24] M. Englert, G. Franceschini, and W. Liebert.  Strong neutron sources - how to cope with weapon material production capabilities of fusion and spallation neutron sources?  In 7th INMM/Esarda Workshop, 2011.
  * [25] Alexander Glaser and Robert J. Goldston.  Proliferation risks of magnetic fusion energy: clandestine production, covert production and breakout.  Nuclear Fusion, 52(4):043004, 2012.
  * [26] Joel Aaron Kulesza, Terry R. Adams, Jerawan Chudoung Armstrong, Simon R. Bolding, Forrest Brooks Brown, Jeffrey S. Bull, Timothy Patrick Burke, Alexander Rich Clark, Robert Arthur Forster, III, Jesse Frank Giron, Tristan Sumner Grieve, Colin James Josey, Roger Lee Martz, Gregg Walter McKinney, Eric J. Pearson, Michael Evan Rising, Clell Jeffrey Solomon, Jr., Sriram Swaminarayan, Travis John Trahan, Stephen Christian Wilson, and Anthony J. Zukaitis.  MCNP® Code Version 6.3.0 Theory & User Manual.  Technical Report LA-UR-22-30006, Rev. 1, Los Alamos National Laboratory, Los Alamos, NM, USA, Sep. 2022.
  * [27] Giorgio Franceschini, Matthias Englert, and Wolfgang Liebert.  Nuclear fusion power for weapons purposes: An exercise in nuclear proliferation forecasting.  The Nonproliferation Review, 20(3):525–544, 2013.
  * [28] Paul N. Haubenreich and J.R. Engel.  Experience with the molten-salt reactor experiment.  Nuclear Applications and Technology, 8(2):118–136, 1970.
  * [29] Thomas J. Dolan, editor.  Molten Salt Reactors and Thorium Energy.  Woodhead Publishing, 2017.
  * [30] Bahman Zohuri, editor.  Molten Salt Reactors and Integrated Molten Salt Reactors.  Academic Press, 2021.
  * [31] Robin Roper, Megan Harkema, Piyush Sabharwall, Catherine Riddle, Brandon Chisholm, Brandon Day, and Paul Marotta.  Molten salt for advanced energy applications: A review.  Annals of Nuclear Energy, 169:108924, 2022.
  * [32] W.R. Grimes.  Chemical research and development for molten-salt breeder reactors.
  * [33] Stephen S. Raiman and Sangkeun Lee.  Aggregation and data analysis of corrosion studies in molten chloride and fluoride salts.  Journal of Nuclear Materials, 511:523–535, 2018.
  * [34] Jeffrey E. Seifried, Raluca O. Scarlat, Per F. Peterson, and Ehud Greenspan.  A general approach for determination of acceptable flibe impurity concentrations in fluoride-salt cooled high temperature reactors (fhrs).  Nuclear Engineering and Design, 343:85–95, 2019.
  * [35] Jinsuo Zhang.  Impurities in primary coolant salt of fhrs: Chemistry, impact, and removal methods.  Energy Technology, 7(10):1900016, 2019.
  * [36] Charles Forsberg, Guiqiu Zheng, Ronald G. Ballinger, and Stephen T. Lam.  Fusion blankets and fluoride-salt-cooled high-temperature reactors with flibe salt coolant: common challenges, tritium control, and opportunities for synergistic development strategies between fission, fusion, and solar salt technologies.  Nuclear Technology, 206(11):1778–1801, 2020.
  * [37] Lixin Sun, Yongsheng Niu, Congwei Hu, Xiaohe Wang, Zhongqi Zhao, Jingen Chen, Xiangzhou Cai, Haiying Fu, Qiang Dou, and Qingnuan Li.  Behavior and distribution of nuclides in the fluoride volatility process of uranium containing molten salt fuel.  Journal of Fluorine Chemistry, 261-262:110016, 2022.
  * [38] Jan Uhlíř.  8 - chemical processing of liquid fuel.  In Thomas J. Dolan, editor, Molten Salt Reactors and Thorium Energy, pages 209–230. Woodhead Publishing, 2017.
  * [39] R B Lindauer.  Processing of the MSRE flush and fuel salts.
  * [40] Jan Uhlíř, Martin Mareček, and Jan Škarohlíd.  Current progress in r & d of fluoride volatility method.  Procedia Chemistry, 7:110–115, 2012.  ATALANTE 2012 International Conference on Nuclear Chemistry for Sustainable Fuel Cycles.
  * [41] Tara M. Pandya, Seth R. Johnson, Thomas M. Evans, Gregory G. Davidson, Steven P. Hamilton, and Andrew T. Godfrey.  Implementation, capabilities, and benchmarking of shift, a massively parallel monte carlo radiation transport code.  Journal of Computational Physics, 308:239–272, 2016.
  * [42] Jin Whan Bae, Ethan Peterson, and Jonathan Shimwell.  AR reactor neutronics multi-code validation*.  Nuclear Fusion, 62(6), Apr 2022.
  * [43] Ethan E. Peterson, Paul K. Romano, Patrick C. Shriwise, and Patrick A. Myers.  Development and validation of fully open-source r2s shutdown dose rate capabilities in openmc*.  Nuclear Fusion, 64(5):056011, mar 2024.
  * [44] Paul K. Romano, Colin J. Josey, Andrew E. Johnson, and Jingang Liang.  Depletion capabilities in the openmc monte carlo particle transport code.  Annals of Nuclear Energy, 152:107989, 2021.
  * [45] H. Bateman.  Solution of a system of differential equations occurring in the theory of radioactive transformations.  Proceedings of the Cambridge Philosophical Society, Mathematical and physical sciences, 15:423 – 427, 1910.
  * [46] J.-Ch. Sublet, J.W. Eastwood, J.G. Morgan, M.R. Gilbert, M. Fleming, and W. Arter.  Fispact-ii: An advanced simulation system for activation, transmutation and material modelling.  Nuclear Data Sheets, 139:77–137, 2017.  Special Issue on Nuclear Reaction Data.
  * [47] Nonproliferation and arms control assessment of weapons-usable fissile material storage and excess plutonium disposition alternatives.  pages 37 – 39.
  * [48] Andrzej Wojciechowski.  The u-232 production in thorium cycle.  Progress in Nuclear Energy, 106:204–214, 2018.
  * [49] Charles W. Forsberg, C.M. Hopper, J.L. Richter, and H.C. Vantine.  1998\.
  * [50] G. Cambi, D. G. Cepraga, L. Di Pace, F. Druyts, and V. Massaut.  The potential presence and minimisation of plutonium within the irradiated beryllium in fusion power plants.  Fusion Engineering and Design, 85(7):1139–1142, Dec 2010.
  * [51] Materion.  Spec Sheet, S-65 Beryllium Grade, Rev. E, April 2018.
  * [52] B.N. Kolbasov, V.I. Khripunov, and A. Yu Biryukov.  On use of beryllium in fusion reactors: resources, impurities and necessity of detritiation after irradiation.  Fusion Engineering and design, 109:480–484, 2016.
  * [53] G.R. Longhurst and R.D. Rohe.  Beryllium use in the advanced test reactor.  Technical Report INL/CON-07,12959, Idaho National Laboratory, 2007.
  * [54] R. Scott Kemp.  On the feasibility of safeguarding uranium mines.  Nonproliferation Review, 13(2):417–425, Dec. 2006.
  * [55] Nonproliferation and arms control assessment of weapons-usable fissile material storage and excess plutonium disposition alternatives.  Technical Report DOE/NN-0007, U.S. Department of Energy Office of Arms Control and Nonproliferation, Jan. 1997.
  * [56] Robert F. Goheen.  Problems of proiferaiton: U.s. policy and the third world.  World Politics, 35(2):194–215, Jan. 1983.
  * [57] Bradley A. Thayer.  The causes of nuclear proliferation and the utility of the nuclear non-proliferation regime.  Security Studies, 4(3):463–519, 1995.
  * [58] Ariel E. Levite.  Never say never again: Nuclear reversal revisited.  International Security, 27(3), Winter 2002/03.
  * [59] R. Scott Kemp.  The iran nuclear deal as a case study in limiting hte proliferation potential of nuclear power.  Nature Energy, 4:99–106, Feb. 2019.
  * [60] IAEA safeguards: Aims, limitations, and achievements.  Technical report, International Atomic Energy Agency, 1983.
  * [61] IAEA Statute.  International Atomic Energy Agency, Vienna, 1976.
  * [62] The Evolution of IAEA Safeguards.  Number 2 in International Nuclear Verification Series. International Atomic Energy Agency, Vienna, 1998.
  * [63] Olli Heinonen.  Iaea inspections in perspective.  In Reassessing the Assumptions Driving Our Current Nuclear Nonproliferation Policies. Nonproliferation Policy Education Center, May 2012\.
  * [64] R. Scott Kemp.  Environmental detection of clandestine nuclear weapon programs.  Annual Review of Earth and Planetary Sciences, 44(Volume 44, 2016):17–35, 2016.