Neutronic Performance of a Compact 10 MWe Nuclear Reactor with Low Enrichment (ThxU1−x)N Fuel

Recent interest in compact nuclear reactors for applications in space or in remote locations drives innovation in nuclear fuel design, especially non-oxide ceramic nuclear fuels. This work details neutronic modeling designed to support the development of a new nuclear fuel concept based on a mixture of thorium and uranium nitride. A Monte Carlo N-Particle Version 6.2 (MCNP-6) model of a compact 10 MWe reactor design which incorporates (ThxU1−x)N fuel is presented. In this context, a “compact” reactor is a completely assembled reactor which may be emptied of coolant and transported by specialized commercial vehicle, deployed by a C130J aircraft, or launched into space. Core geometry, reflector barrels, and the heat exchange zones are designed to support reduction of overall reactor volume of core components while maintaining criticality with a fixed total fuel mass of 4500 kg. Dense mixed nitrides of thorium nitride (ThN) additions in uranium nitride (UN) in 5 wt.% increments between 0.05≤x≤0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.05 \le x \le 0.5$$\end{document} have been considered for calculation of k∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{\infty }$$\end{document} and keffective\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{{\text{effective}}}}$$\end{document}. ThN additions in UN results in a slight increase in the magnitude of the temperature coefficient of reactivity, which is negative by design. The isotopic distribution of the principal actinide inventory as a function of burnup, time, and initial fuel composition is presented and discussed within the context of the proliferation risk of this core design.


INTRODUCTION
Energy abundance in remote locations could enable a broad mission space, yet such technologies require significant investment and development. The evident need for safe, reliable, and affordable high energy density systems exceeds the capability of available technology. In space applications, solar panels and radioisotope thermoelectric generators (RTG) are utilized to generate<1 kW of power for a limited period of time before material degradation or source decay renders the power production below that of the operational requirements of the mission. 1 In remote terrestrial applications, diesel generators are most commonly used to provide power suitable for the function of remote forward operating bases or research stations; while terrestrial operations allow resupply, constant supply of fuel is expensive, and maintenance of supply lines may place personnel at risk in the case of numerous military applications. 2 Nuclear power has historically been utilized on naval craft as a means of high energy production for long periods of time, but such reactor designs are not made for portability nor may they operate in a mode of reliable self-regulation. No available portable technologies exist which allow significant power production (>10 MWe) for long operating times (10-15 years). 3 Very small, compact nuclear reactors can readily address the needs of power production in remote locations, and could support applications which are typically powerlimited.
Low-power compact nuclear reactors (< 10 kWe) have been manufactured and utilized for application in space. The first disclosed use of a nuclear fission power system in space was a 0.5-kWe Systems for Nuclear Auxillary Power (SNAP-10A) satellite launched by the United States in 1965. The SNAP program was then adapted to support the Apollo missions. Around this time frame the USSR began the Radar Ocean Reconnaissance Satellite (ROR-SAT) program, in which over 31 nuclear-powered Kosmos satellites were launched between 1965 and 1987. The Kosmos satellites utilized a fast spectrum BES-5 reactor, which produced 2 kWe. Two additional, higher power (5 kWe) TOPAZ satellites were also launched as part of the RORSAT program. Given the enormous costs associated with payload mass, all the designs used in the SNAP and RORSAT programs were highly enriched (> 90% 235 U) fast reactors, which considerably reduced the mass of both the fuel and the coolant compared with thermal reactors of equal power output. These missions may be viewed as successful demonstrations of the feasibility of fission power in space, and programs like the Space Reactor Prototype (SP-100) and the Safe Affordable Fission Engine (SAFE) at NASA continued the research and development into the potential application of fission reactors for space propulsion. 4 Transportable compact reactors for use in terrestrial applications could serve numerous roles. Recent reports from the Defense Science Board strongly advocate for the development of compact nuclear reactors for use in military applications, disaster relief, and in remote locations. 2,5 In a comprehensive survey of all available energy systems, a task force on Energy Systems for Forward/Remote Operating Bases concluded that it was in the best interest of the Department of Defense (DOD) to invest in compact nuclear reactor technology in order to provide for current and growing future energy needs; this assessment was based on operational requirements, transportability, automatic or passive operation, safety, and proliferation risk associated with compact reactors in comparison to other energy production systems. 2,6-8 While compact reactors may readily serve existing needs, the energy requirements associated with projecting US military capability is expected to increase in the coming decades. 5 This work details neutronic modeling designed to support the development of compact, transportable reactors using a new nuclear fuel concept based on a mixed thorium and uranium nitride fuel. The MegaPower reactor concept under development by Los Alamos National Laboratory (Patent No. US 20160027536 A1) represents an early stage design iteration aimed toward high energy output, transportable, compact nuclear reactors. This compact reactor design is intended to be transportable in a cargo container on a semi-trailer truck, and may be rapidly deployed or removed. 9 In the event of complete loss of coolant, the reactor will automatically shut down and will dissipate heat to the surrounding air. This reactor utilizes a fast neutron spectrum with low uranium enrichment (< 20 at.% 235 U). In comparison to water, the use of liquid salts for the heat transfer fluid allows miniaturization of the heat transfer system. Reflector drums and control rods are used to control the reactivity of the system. The armored, shielded cask doubles as a neutron reflector, which effectively shields any personnel from receiving a neutron dose. The core is designed to operate on a single fuel charge for over a decade, which eliminates the need for fuel shuffling. The strong negative temperature coefficient of reactivity contributes to the inherent safety of this design, and allows for the reactor to operate in a semi-load-following operation. In the event of complete loss of coolant to the core, the reactor automatically shuts down and passively radiates decay heat to the surrounding atmosphere. The choice of materials and the hexagonal geometry of the bundles results in a more homogeneous thermal profile and an even burnup of the fuel. The properties of the fuel strongly influence the potential power level, operating time, safety profile, and the proliferation risk of the reactor. Keeping in mind the initial requirement of compact nuclear reactors (i.e., transportability, safety, self-regulation, long operating life, and $10 MWe power output), the fuel composition can be tailored to optimize the reactor performance.
Part of the operational flexibility of this reactor design can be attributed to the mixed thorium and uranium nitride fuel. This choice of material is motivated, in part, by the higher actinide density and significantly improved thermophysical properties compared with reference oxide and carbide fuels. [10][11][12][13][14][15][16][17] In comparison to oxide or mixed oxide fuels, non-oxide ceramic fuels (i.e., carbides, nitrides, silicides) have marginally lower melting points but significantly higher thermal conductivity. [11][12][13] In particular, ThN and UN have favorable thermophysical properties for reactor applications and the properties and applications of mixtures of this material are the subject of ongoing research. 11,14,18 For the case of fixed linear power density from fission across the fuel and for the same period of fuel burnup, the increase in thermal conductivity associated with switching from oxide to nitride fuels results in reduced centerline temperatures and a reduction in the thermal gradients. Nitride fuels, which retain higher thermal conductivity as a function of burnup, exhibit less pronounced temperature-dependent degradation by fuel swelling, grain growth, and fission gas release. 15,19 Research on the synthesis, fabrication, and characterization of UN and PuN has advanced significantly in recent years. UN and (U x Pu 1Àx )N fuels have been synthesized for characterization, with emphasis on tailoring the initial materials properties for application in gas-cooled fast reactors (GFR), sodium-cooled fast reactors (BN-1200), leadcooled fast reactors (BREST), seed-and-blanket transuranic (S&B) burner concepts, space propulsion systems for the SP-100 program, and various light water reactor concepts. [20][21][22][23][24][25][26] The varied requirements of these designs necessitate a Neutronic Performance of a Compact 10 MWe Nuclear Reactor with Low Enrichment (Th x U 1Àx )N Fuel comprehensive view of the materials properties of nitride fuel forms. The thermal and mechanical properties of UN and, to a limited extent, (U x Pu 1Àx )N, have been measured as a function of temperature and pressure. 15,[27][28][29] A comprehensive summary of these material properties is presented in, 29 and is used as a key reference for point of comparison. Irradiation testing of UN and mixed UN and PuN has been carried out over the past few decades. The thermoconductivity of UN has been determined as a function of fission damage, and volumetric swelling as a function of burnup has been determined up to 3% and modeled, with reasonable extrapolation, to end-of-service life. [30][31][32] Interestingly, fission-induced swelling only appears after 3% burnup; 15,33 comparative irradiation experiments indicate that fission gas swelling of nitride fuels is significantly lower than that of the carbide. 18 While the irradiation data on UN and PuN is not comprehensive, modeling the initial finding will guide future prototype and commercial-scale applications of nitride fuels. The data needs for ThN are considerable, given the 25-year lag in the development cycle compared with the other actinide nitride fuel candidates. Recent findings suggest that the favorable thermal properties of ThN lend readily to mixtures of UN and, potentially, UN/PuN. 34 This work details advanced neutronic modeling of the neutronic performance of (Th x U 1Àx )N from 0:05 x 0:5 within the framework of both an infinite reactor and in the specific application of a modified-MegaPower core design. These models operate with a fast neutron spectrum. An infinite reactor model, while a simplification of the true neutronic environment, is very useful for motivating a discussion of the neutron multiplication properties of (Th x U 1Àx )N as a function of ThN addition in a UN matrix. This model indicates the maximum thorium content for a given enrichment of 235 U or 233 U in 238 U. While highly enriched uranium enables favorable design aspects concerning the size reduction of the core, it is practical to limit the uranium enrichment to 'low enriched' so as to simplify security concerns related to the manufacture of the fuel. In the Results and Discussion that follow, the uranium enrichment is fixed at 19.5 at.%. In order to accommodate low enrichment, it is assumed that all nitrogen in the nitride fuel is enriched to 15 N, in order to reduce parasitic absorption. 35 This assumption may be relaxed if higher enrichments are used. The output of the modified-MegaPower core model outlines the maximum reasonable operating time of a single charge of fuel as a function of initial fuel composition, while also tracking the populations of all isotopes consumed or produced by fission. Such a result allows a discussion on the potential proliferation risk the (Th x U 1Àx )N fuel and waste present. Neutronic modeling was accomplished through Monte Carlo N-Particle Version 6.2.

NEUTRONIC MODELING OF REACTIVITY AND BURNUP
Boundary Condition: k 1 Reactor models of infinite dimension are used to determine k 1 , which is the ratio of the number of neutrons in successive generations. Calculations of this parameter are a useful starting point given that the computational resources needed are minimal. Thus, the geometry and composition of the model can be quickly adjusted before committing significant resources to higher fidelity models. Calculation of k 1 serves as an approximate measure of the neutron economy in a simplified model. The effect of neutron leakage and core size associated with a finite reactor are discussed in ''K eff '' section. k 1 has been determined as a function of thorium addition. The cross section of the infinite reactor is shown in Fig. 1. Magenta regions are the inner ring of fuel pins, the blue regions are the outer ring of fuel pins, the white regions are heat pipes which carry coolant, the yellow region is aluminum nitride, and the green bars are moderators comprised of yttrium hydride. The inner and outer fuel rings are identified separately in order to consider differences in burnup as a function of location in the core. Different structural material, such as HT-9 steel, is being considered in place of aluminum nitride; however, substitution of this material has minimal impact on the calculated multiplication factors. In this model, there is assumed to be no gap between the fuel and the clad (zircaloy) or the surrounding structural framework (aluminum nitride).
For this model, k 1 is plotted as a function of atom fraction of thorium in (Th x U 1Àx )N in increments of 5 at.%, from 0 at.% to 70 at.%, in Fig. 2. The k 1 of UN fuel in this configuration is 1.38 (supercritical). Incremental additions of ThN result in a linear decrease in the multiplication factor until a maximum concentration of ThN is reached at 58 at.%. In reality, given neutron leakage and the anticipated decrease of reactivity with time, thorium should be limited to lower quantities than this limit. The ultimate upper limit of thorium will be set by burnup calculations, given the design requirements of how long the core should operate at a given power level. The interesting conclusion drawn from this observed relationship between k 1 and thorium content is the apparent insensitivity of such additions. However, this should not be surprising, since one non-fissile isotope ( 238 U) is being replaced by another ( 232 Th).

K eff
While 232 90 Th is not fissile, a series of neutron absorptions starting with 232 90 Th will produce 233 92 U and 234 92 U, which are fissile and fissionable, respectively. Initially, neutron absorptions by 232 90 Th are parasitic and act to reduce k 1 . This is useful, given that the system must be supercritical and downregulated by controlling neutron leakage or by parasitic absorption in burnable poisons. As fuel burnup accumulates, the fissile and fissionable isotopes produced by 232 90 Th contribute to neutron generation by introduction of t 233 92 U À Á Á R F and t 234 92 U À Á Á R F . While not desirable from a non-proliferation stand point, a small contribution from plutonium isotopes [t 239 94 Pu À Á Á R F and t 240 94 Pu À Á Á R F ] generated from absorption on 238 92 U will also increase neutron generation. One of the practical consequences of additions of ThN in UN is that it minimizes the reduction of k 1 over the lifecycle of the reactor. The cross section and scaled representations of the finite reactor model used for determination of K-effective (k eff ) as a function of burnup and of initial thorium addition are shown in Fig. 3. For scale, the design shown is intended to fit within a standard shipping container. The reflector drums sit within a shielding matrix of low Z material in order to protect operators. The heat exchange system and turbine are not shown. Reflectors are shown in the shutdown orientation, and may rotate up to 180 degrees to reduce neutron leakage.
The reactor can be shut down with control rods or with the reflector drums. k eff as a function of time is plotted in Fig. 4 for 5 at.% incremental additions of ThN in (Th x U 1Àx )N from 0:05 x 0:5 in the case of continuous operation at a power level of 10 MWe. The observed decrease in k eff , especially at startup, is shown in calculations of k 1 in Fig. 2. The percent reduction in k eff as a function of thorium content at 8 years is less than the effect at startup due to accumulation of 233 92 U and 234 92 U from neutron capture on 232 90 Th. Indeed, the slope of k eff vs time is reduced by 14.7% from the most dilute composition The benefit of a more uniform neutron multiplicity over time is that less burnable poisons are required in the initial fuel charge. While thorium additions up to x ¼ 0:50 ð Þare possible, the composition (Th 0.25 U 0.75 )N was chosen as a reasonable balance between the resultant thermal and mechanical properties of the mixture, published in parallel with this modeling work, while still retaining sufficient neutron multiplication to remain critical for up to a decade of continuous operation at 10 MWe.

Temperature Coefficient of Reactivity
The temperature coefficient of reactivity, a T ; is a measure of the reactivity change in response to the Neutronic Performance of a Compact 10 MWe Nuclear Reactor with Low Enrichment (Th x U 1Àx )N Fuel change in temperature of the reactor. Core reactivity, q t; T ð Þ, is given by Eq. 1, and a T is given by Eq. 2: Changes in core temperature affect neutron multiplication, primarily through changes in resonance absorption in the fuel due to Doppler broadening, and changes to the neutron energy spectrum due to changes in the density of the moderator. The temperature coefficient of reactivity is plotted as a function of temperature in Fig. 5 for all compositions studied.
The temperature coefficient of reactivity is a measure of the inherent safety of the core, and is an essential design parameter of the fuel to assure that increases in reactor power result in a decrease in reactivity on a response time-scale proportional to the change in power. The increase in fuel temperature leads to an increase in resonance absorption, primarily among the fertile isotopes ( 238 U, 240 Pu, 232 Th, 234 U). However, in a fast reactor the neutron energy spectrum spans the resonance absorption of both fertile and fissile nuclei ( 235 U, 233 U, 239 Pu, 241 Pu). a T is plotted in Fig. 5 at the onset of the reactor lifecycle, and so the only dominant contributions are from the initial fertile and fissile materials in the fuel: 238 U, 232 Th, and 235 U. Potential effects of the evolved fertile and fissile nuclei are discussed in the context of fuel breeding in the following sections. It is shown in the figure above that there is an increase in the magnitude of the negative temperature coefficient of reactivity with increasing thorium content, due primarily to an increasingly negative Doppler coefficient. This indicates that the core will have a  Neutronic Performance of a Compact 10 MWe Nuclear Reactor with Low Enrichment (Th x U 1Àx )N Fuel prompt tendency to self-regulate, and allows the reactor to operate in a mode of pseudo load-following. That is to say, increased power demand will extract additional heat from the coolant, which will result in a temperature decrease in the core and cause an increase in reactivity. The opposite will also be true, especially in the event of a rapid core power excursion. Additions of ThN to UN greatly enhances the built-in safety of the fuel, the effect of which increases with increasing temperature of the fuel.

Burnup-Isotopic Distribution of Key Actinide Species
The population of key isotopes as a function of time and thorium addition was determined. The primary isotopes of concern are the fissile and fertile isotopes, both included in the initial fuel charge and generated by neutron absorptions during normal operation of the reactor. The primary absorption pathways for the breeding of fissile isotope 233 U are shown in Fig. 6: Neutron absorption reactions are denoted n; 2n ð Þ and n; c ð Þ; the cross section of each absorption or fission is dependent on the neutron energy and the temperature of the fuel. While other reaction pathways are possible, those shown in Fig. 6 are the dominant reactions leading to the creation of additional fissile isotopes during reactor operation. While not shown here, 237 Np, which is fissionable in a fast neutron spectrum, is produced by successive neutron absorptions on uranium isotopes or by n; 2n ð Þ reactions on isotopes of plutonium. It is found in this study that less than 800 g of 237 Np accumulate over a 10-year operating cycle, regardless of the initial nitride mixture utilized. Compared with the rest of the fissile inventory, this quantity of material is sufficiently low so as to be excluded from the discussion of reactor performance. This amount of material is also insufficient for a critical mass, and therefore will not be included in a discussion of the proliferation risk presented by the spent fuel. 36 This reactor is not designed to be a breeding reactor; the conversion ratio is less than 1. Rather, the additional fissile material created by transmutation serves to increase k eff in the later years of reactor operation (> 5 years) and thereby extend the service life of the core. The balance in the uranium economy as a function of time and initial fuel composition is shown in Fig. 7. In the plot of 235 U utilization vs time, the relative consumption of 235 U increases with increasing thorium content. In the case of high thorium content x ¼ 0:5 ð Þ , 61% of the 235 U is used over the life of the reactor, while the minimal thorium loading x ¼ 0:05 ð Þ only utilizes 43% of the initial fissile uranium. However, the enrichment of 235 U to 238 U is fixed at 19.6 at.%. The high thorium loading design uses 10.6 kg less of 235 U compared with (Th 0.05 U 0.95 )N, where $41 kg of 235 U undergoes fission. Thus, the apparent increase in utilization observed in the plot is due to the fact that 235 U is initially being consumed at the same rate in all compositions, but there is less material present in the starting composition with increasing thorium concentration. More interesting is the apparent reduction in slope seen at later years in the 235 U utilization curves at all compositions. The reason is that the inventory of 233 U created from neutron absorption in 232 Th builds considerably over time, and, in the case of x ¼ 0:5 ð Þ , eventually accounts for as much as 34% of the total quantity of fissile uranium isotopes in the fuel.
In order to discuss the impact of absorption on 238 U and the production of minor quantities of plutonium, the total fissile and fertile inventories are plotted in Fig. 8. In the dilute limit of thorium addition, $5.2 at.% of all fertile material, which is nearly all 238 U, undergoes transmutation. Adding 50% thorium results in a 2.7% increase in the total utilization of fertile materials, which indicates that thorium undergoes neutron capture at nearly twice the rate of 238 U. This was also observed to be the case in the reduction of the slope of the k eff curve over time. It is interesting to note that the total utilization of fissile species decreases with increasing thorium content. The magnitude of this effect amounts to a nearly 20% reduction in the utilization of the available fissile material. That is to say, nearly 20% of additional fissile material is created in years 4-10 in the case of higher thorium loading. Increasing the initial enrichment of 235 U would reduce parasitic absorption by 238 U and would allow considerably higher thorium concentration. While not included in this study, further modeling of mixed nitrides as a function of higher 235 U enrichment > 20 at:% ð Þ for higher thorium loading 0:5 x 0:70 ð Þcould expand the potential design space to allow for extended operation beyond the initial 10-year design requirement.

Proliferation Risk
The transmutation reactions starting with 238 U which lead to the production of plutonium are shown schematically in Fig. 9. 241 Pu and 242 Pu are produced in negligible amounts, and are not included in the following analysis. Given the compact nature of this reactor design, the total quantity of plutonium isotopes bred by neutron absorption on Z N Fig. 6. The reaction pathways for the generation of additional fissile material starting with neutron capture on 232 Th. Fertile species are marked as red. Z is the proton number and N is neutron number. 238 U is relatively small, and this quantity decreases with increasing thorium content. However, the plutonium inventory as a function of time must be understood, as this could be a significant proliferation risk for this core design. Understanding the rate of generation and consumption of plutonium isotopes as a function of time and initial fuel composition will illustrate how the initial fuel composition might be tailored so as to reduce the risk of proliferating special nuclear material (SNM) which could be readily formed into a weapon.
Reactor-grade plutonium is a term coined for the typical isotopic distribution of plutonium found in spent fuel from light water reactors and describes a mixture of primarily 239 Pu with at least 19 at.% 240 Pu. This definition is applied to large thermal reactors utilized for commercial power production. However, production of plutonium in fast reactors occurs at a reduced rate compared with thermal reactors. 37 239 Pu can be used for nuclear weapons, and has favorable characteristics compared with uranium-based weapons. The bare sphere critical mass of 239 Pu is significantly less than that of 235 U; indeed, a reflected critical sphere would weigh $5-6 kg, and an explosively compressed mass would be considerably smaller. 38,39 Another key advantage is that plutonium can be readily chemically separated from uranium by PUREX processing. 40 However, reactor-produced 239 Pu is rarely suitable for use in a weapon, since it is generally formed with an appreciable quantity of 240  Neutronic Performance of a Compact 10 MWe Nuclear Reactor with Low Enrichment (Th x U 1Àx )N Fuel unsuitable for use in nuclear weapons, and separation of 239 Pu from 240 Pu is not practical. 41 The definition of weapons-grade plutonium allows no more than 6 at.% 240 Pu as an impurity in 239 Pu. While it is possible to accommodate higher levels of impurities of 240 Pu, such designs would be very sophisticated, implosion-type devices. 42 From the perspective of proliferation assessment, it is assumed that countries which have access to such sophistication in nuclear weapon design are not the agents likely to seize a compact nuclear reactor for access to SNM. Rather, it is assumed that theft of this reactor or diversion of the fuel would be perpetrated by states or state sponsored agents which do not otherwise have access to these materials through a state sponsored nuclear weapons program.
In Fig. 10, the regions of concern of material proliferation are highlighted in red. This region may be eliminated, or reduced by controlling the initial composition of the fuel. Indeed, for sufficiently high thorium content 0:35 ! x ð Þ , there is sufficient 240 Pu so as to render the plutonium unfavorable for diversion. This is shown by the composition lines in the plot to the right which are in excess of the maximum impurity level before the assumed minimum mass of 239 Pu is generated at $ year 4. This implies two important results. The first is that if an adversarial state were to pursue mixed nitride fast reactor technology, the initial composition of 238 U must be carefully considered in order to anticipate the evolution of plutonium isotopes over time. In the case of manufacture and service of these types of reactors for the DOD, the second result is that the initial enrichment of 235 U and addition of 232 Th may be chosen to be sufficiently high that the remaining 238 U is too dilute to pose significant risk of transmutation. This is an important result for the development of compact reactors, as it outlines how the initial fuel composition might be modified so as to lower the proliferation risk. While the argument might be made that the remaining 235 U or 233 U may be sufficient for a nuclear weapon, this would require isotopic separation of 232 U, 233 U, 235 U, 236 U, and 238 U present in the spent nuclear fuel. While this may be technically possible, the severe radioactivity of the decay products of this mixture, such as the 2.6 MeV gamma ray emitted from 208 Tl, a decay specie from 232 U, makes reprocessing and separation impractical. 43 Isotopic separation of 235 U from 238 U is a mature technology and would be considerably easier to apply, as opposed to attempting to produce parallel methods on such a diverse, highly radioactive mixture.

CONCLUSION
The neutronic performance of (Th x U 1Àx )N from 0:05 x 0:5 was presented and discussed within the framework of both an infinite reactor and in the specific application of a compact reactor design under development by Los Alamos National Laboratory. k 1 calculations for the infinite core model were determined as a function of atom fraction of thorium in (Th x U 1Àx )N in increments of 5 at.%, from 0 to 70 at.%. The infinite model remains critical from 0 x 0:58, which indicates that UN is fairly insensitive to thorium addition. This model assumed an enrichment of 235 U to 238 U of 19.6 at.% for all compositions studied. k eff was determined for the case of a finite reactor as a function of time and of initial thorium addition. Additions of ThN in UN leads to a reduction in the slope of k eff over the lifecycle of the reactor. A maximum composition of (Th 0.35 U 0.65 )N remains supercritical beyond 10 years at the assumed power level. The service life of the reactor can be extended for higher concentrations of ThN if higher enrichments of 235 U are considered. The temperature coefficient of reactivity was found to become increasingly negative as both a function of temperature and of thorium addition to the fuel. This is due to an increasingly negative Doppler broadening coefficient. In an analysis of the isotopic distribution as a function of burnup and initial fuel composition, it was found that the maximum thorium loading resulted in significant creation of 233 U by transmutation. As much as 34% of the fissile uranium inventory was 233 U by year 10. It was found that negligible quantities of 237 Np, 241 Pu, and 242 Pu were created at any composition over the time range studied. 239 Pu and 240 Pu were discussed within the context of proliferation risk. It was determined that there exists a vulnerable window wherein the reactor may be at risk of diversion. This window may be eliminated by setting the initial fuel inventory to contain higher uranium enrichment, or by adding a few atom percent 240 Pu to make a mixed (Th x U 1Àx )N initial fuel charge. While not included in the scope of this study, plutonium or actinide additions could work favorably in more highly enriched (Th x U 1Àx )N fuels for the purpose of actinide burning.