Low-Grade Nuclear Materials as Possible Threats to the Nonproliferation Regime. (Report under CRDF Project RX0-1333)

Transcription

1 Low-Grade Nuclear Materials as Possible Threats to the Nonproliferation Regime (Report under CRDF Project RX0-1333)

2 2 Abstract This study addresses a number of issues related to low-grade fissile materials and their possible threats to the nonproliferation regime. In this connection, critical mass properties have been determined for such materials as uranium with a relatively low enrichment in the isotope U-235, power-grade plutonium produced in different types of nuclear reactors, their dioxides, and different MOX fuels. The study discusses the features of possible mechanisms to reduce the risk associated with direct-use materials. The study has been supported by the John D. and Catherine T. MacArthur Foundation and the Ploughshares Foundation and it has been carried out by the Analytical Center for Non-proliferation under CRDF project RX

3 3 Contents Introduction Data Obtained in Experiments with Reference Assemblies and Quality of Their Computational Description Estimated Critical Masses of Uranium and Uranium Dioxide of Different Enrichment With and Without Reflectors from Natural Uranium Highly Enriched Uranium and Its Dioxide Uranium Containing 10 to 20 Percent of U-235 and Its Dioxide Brief Discussion Neutron Multiplication Rate in the Infinite Medium from Uranium and Uranium Dioxide of Different Enrichment in U Estimated Critical Masses of Plutonium, Plutonium Dioxide and MOX Fuel of Different Isotopic Compositions, With and Without Reflectors from Natural Uranium Monoisotopic Plutonium and its Dioxide Plutonium and Plutonium Dioxide of Isotopic Composition from Different Reactors, With and Without Reflectors from Natural Uranium MOX Fuel Manufactured from Natural Uranium and Plutonium Produced in Different Types of Reactors Neutron Multiplication Rate in the Infinite Medium from Plutonium-Bearing Materials Major Conclusions...33 Summary...37 References...38

4 4 Introduction Nuclear material control and protection criteria that are operated in the framework of nonproliferation and implementation of the IAEA safeguards and provisions of the Convention on the Physical Protection of Nuclear Material rest upon a number of attributes that determine the way, nuclear materials are dealt with. So-called direct-use materials, or fissile materials that can be used directly for the manufacture of nuclear explosive devices, constitute the major source of threat to the nonproliferation regime. As they are meant for the IAEA safeguards purposes, such materials include a) plutonium of different isotopic composition (except plutonium containing more than 80 percent of the isotope Pu-238); b) U-233; and c) highly enriched uranium, HEU (uranium containing 20 percent or more of the isotope U-235). The general level of nuclear threat is characterized by the significant quantity of nuclear material, which is the approximate amount of nuclear material for which the possibility of manufacturing a nuclear explosive device cannot be excluded. Significant quantities are used in establishing the quantity component of the IAEA inspection goal and they are the smallest quantities of fissile materials, diversion of which for illicit purposes should be precluded by IAEA safeguards. Significant quantities of direct-use nuclear materials, as designated by the IAEA, are 25 kg of U kg of U-233 and 8 kg of plutonium (for plutonium containing less than 80 percent of the isotope Pu-238). Significant quantities make about 50 percent of the critical masses of these materials. The IAEA safeguards system uses a special unit called effective kilogram in safeguarding nuclear materials. One effective kilogram of nuclear material is: For plutonium, the mass of 1 kilogram; For uranium with an enrichment of 1 percent or above of the isotope U-235, 1/α 2 kilograms, where α is the content of U-235 in the uranium material. The value of 1 kg of plutonium (of arbitrary isotopic composition) within this system equals to the value of 1 kg of 100-percent-enriched U-235, and the value of 1 kg of uranium enriched to 20 percent in U-235 is 25 times lower than the value of 100- percent-enriched U-235. Some quantitative changes appear when the quantities of nuclear material to be exempted from safeguards at the request of a state are determined. In this case, the quantity of plutonium (of arbitrary isotopic composition) is still measured as its mass, M(Pu); the quantity of HEU (uranium containing 20 percent or more of the isotope U-235) is measured as α M(U); and the quantity of uranium enriched below 20 percent is measured as 5 α 2 M(U), where α is the fraction of U-235 in the uranium material and M(U) is the mass of uranium. Within this quantitative approach, the value of 1 kg of plutonium is still equal to the

5 5 value of 1 kg of 100-percent-enriched U-235, but the value of uranium enriched to 20 percent in U-235 is only five times lower than that of 100-percent U-235. This approach takes into account the threat of possible after-enrichment of uranium, exempted from safeguards, up to the weapons grade. Another type of comparative value ratios between nuclear materials is used in the Convention on the Physical Protection of Nuclear Material for their categorization and determination of corresponding protection levels. Category I nuclear materials, being subject to the most stringent protection, include the following direct-use materials: Plutonium (all plutonium except that with isotopic concentration exceeding 80 percent in plutonium-238) in the amount equal to or more than 2 kg; HEU (uranium enriched to 20 percent U-235 or more) in the amount equal to or more than 5 kg. At that, these materials should have a radiation level equal to or less than 1 Sv/hour at one meter unshielded (criterion of unirradiated material). If the material does not satisfy the criterion of unirradiated material, its category may be reduced by one level, and it may be transferred from Category I into Category II. Note that the value of 1 kg of plutonium within this approach is equal to the value of 2.5 kg of HEU (with any enrichment ranging from 20 to 100 percent of U-235). Category II nuclear materials include: Plutonium (all plutonium except that with isotopic concentration exceeding 80 percent in plutonium-238) in the amount of 0.5 to 2 kg; HEU (uranium enriched to 20 percent U-235 or more) in the amount of 1 to 5 kg; Uranium enriched to 10 percent U 235 but less than 20 percent in the amount of 10 kg or more. These materials should satisfy the criterion of unirradiated material, as well. If the materials do not meet this criterion, they can be transferred from Category II into Category III. The value of 0.5 kg of plutonium within Category II (at its bottom level) is equal to the value of 1 kg of HEU (containing more than 20 percent of U-235) or 10 kg of uranium containing 10 to 20 percent of U-235. Category III nuclear materials include: Plutonium (all plutonium except that with isotopic concentration exceeding 80 percent in plutonium-238) in the amount of 15 g to 0.5 kg; HEU (uranium enriched to 20 percent U-235 or more) in the amount of 15 g to 1 kg; Uranium enriched to 10 percent U-235 but less than 20 percent in the amount of 1 kg to 10 kg;

6 6 Uranium enriched above natural, but less than percent U 235 in the amount of 10 kg or more. Category III materials are also subject to the criterion of unirradiated material. Note that although this Convention assigns irradiated fuel (depleted or natural uranium, thorium or low-enriched fuel with less than 10 percent fissile content) to Category II, it is open to states, upon evaluation of the specific circumstances, to assign it to a different category of physical protection. Also, let us specify the levels of physical protection of different categories of materials in compliance with the Convention of the Physical Protection of Nuclear Material. With respect to their storage: For Category III materials, storage within an area to which access is controlled; For Category II materials, storage within an area under constant surveillance by guards or electronic devices, surrounded by a physical barrier with a limited number of points of entry under appropriate control; For Category I material, storage within a protected area as defined for Category II above, to which, in addition, access is restricted to persons whose trustworthiness has been determined, and which is under surveillance by guards who are in close communication with appropriate response forces. Specific measures taken in this context should have as their object the detection and prevention of any assault, unauthorized access or unauthorized removal of material. With respect to transportation: For Category II and III materials, transportation shall take place under special precautions including prior arrangements among sender, receiver, and carrier, and prior agreement between persons subject to the jurisdiction and regulation of exporting and importing States, specifying time, place and procedures for transferring transport responsibility; For Category I materials, transportation shall take place under special precautions identified above for transportation of Category II and III materials, and in addition, under constant surveillance by escorts and under conditions which assure close communication with appropriate response forces. As follows from the data above, diverse approaches are used for comparative categorization of quantities of different fissile materials. This is caused by the rather long history of establishing the regulations as well as by the fact that diverse control and protection measures pursued specific goals. At the same time, under the new conditions of the escalating threat of nuclear terrorism, it is logical to consider quantitative criteria for different fissile materials within the framework of a single approach, when the level of threat associated with one or another type of materials is determined by its basic attribute, critical mass. We will mostly consider the

7 7 logic connected with the relationships between fissile materials of different types, and will not address the regulation of absolute quantities of materials belonging to some or other types of control or protection. Besides, we will restrict our study only to enriched uranium and plutonium materials of different isotopic compositions, and will leave such materials as U- 233, minor actinides and raw materials beyond the scope of our analysis. The major criterion of the possibility to make explosive devices from a fissionable material is the capability of the latter to reach critical conditions and allow a sustainable chain reaction of nuclear fission to occur. An important parameter is also the time of neutron generation in the process of nuclear fission by neutrons of one generation. These and other functionals for neutron multiplying systems can be determined rather accurately by computations. The study discusses these functionals for spherical systems of different composition using the Monte-Carlo method and the widely used neutron data library ENDF B5. The study focuses on uranium enriched to 10 percent U-235 but less than 20 percent and its dioxide, and on plutonium materials produced by nuclear power reactors, their dioxides and MOX fuel manufactured from those plutonium materials.

8 8 1. Data Obtained in Experiments with Reference Assemblies and Quality of Their Computational Description Measurement accuracy in determining elementary neutron constants that characterize interactions between neutrons and nuclei is generally known to be insufficient for describing critical conditions of neutron multiplying systems measured with high accuracy. That is why it is important to make sure that the evaluated neutron constants of the basic isotopes of uranium and plutonium that are used in computations make it possible to describe rather accurately the value K eff = 1, effective neutron multiplication factor, and the value τ f, average time of neutron generation at nuclear fission by neutrons of one generation, measured for reference critical assemblies. There were used well-known reference assemblies [1]: 1. Godiva R = cm, U , U , U Topsy R 1 = cm, U , U ; R 2 = cm, U , U Jezebel R = cm, Pu , Pu , Pu , Ga Jezebel-2 R 1 = cm, Pu , Pu , Pu , Pu , Ga Flattop-Pu R 1 = cm, Pu , Pu , Pu , Ga ; R 2 = cm U , U Concentration of isotopes is given in nuclei/cm 3. Godiva consists of highly enriched uranium containing 93.7 percent of U-235. Topsy has a core from HEU and a thick ( l ~ 20 cm) reflector from natural uranium. Jezebel consists of plutonium with isotopic concentration of about 95 percent of the isotope Pu-239. Jezebel-2 is characterized by a comparatively high (about 20 percent) content in plutonium of the isotope Pu-240. Flattop-Pu is comprised of a plutonium core with isotopic concentration of about 95 percent of the isotope Pu-239and a thick ( l ~ 20 cm) reflector from natural uranium. Table 1 shows the values of the basic neutron functionals obtained through the Monte- Carlo computations of K eff for the above spherical assemblies using the ENDF-B5 neutron constants.

9 9 Table 1 Basic neutron functionals for a number of critical assemblies obtained using the ENDF-B5 neutron constants Functional Godiva Topsy Jezebel Jezebel-2 Flattop-Pu K eff ν τ f, ns R c R f R γ R el R inel R esc ρ, g/cm ; ; M cr,kg , , In Table 1: ν is the average number of secondary neutrons produced by fission; τ f is the time of generation; R c, R f, R γ, R el, R inel, R esc is the average number of collisions, fissions, gamma captures, elastic and inelastic collisions and escapes from system falling on neutrons per one fission event in the system; R c = R f + R γ + R el + R inel ; (ν-1) R f = R γ + R esc. K eff νrf = R + R + R f γ esc. The data for the Topsy and the Flattop-Pu systems are given as a total for the core and the shell. ρ is the density of materials of critical assemblies; for Topsy and Flattop-Pu densities of the core and the shell are given; M cr is the mass of critical assembly. For Topsy and Flattop-Pu, masses of fissile cores are presented, as well. Data of Table 1 show that the ENDF-B5 neutron constants make it possible to describe K eff = 1 for reference critical assemblies with the accuracy corresponding to the measurement accuracy (1σ = ). At that, the calculated average time of neutron generation in the process of nuclear fission by one-generation neutrons for the plutonium critical assembly Jezebel practically coincides with the experimentally estimated value,

10 10 τ f, exp = 3.03 ns [1]. The calculated value of τ f for the uranium critical assembly Godiva is approximately 10 percent lower than the experimental value, τ f, exp = 5.8 ns [1]. The bottom line of Table 1 shows the masses of these critical assemblies. One can see that uranium enriched to 93.7 percent in U-235, with the density ρ = g/cm 3, has a critical mass of 52.4 kg. Plutonium enriched to 95 percent in Pu-239, with the density ρ = g/cm 3, has a critical mass of kg. Plutonium containing 20 percent of the isotope Pu-240 has a critical mass of kg. The use of the thick ( l ~ 20 cm) reflector from natural uranium significantly reduces the critical mass of fissile materials. Using the ENDF-B5 neutron constants makes it possible to adequately describe the critical conditions of the assemblies with uranium and plutonium of different isotopic composition, on the one hand, and the assemblies with the thick ( l ~ 20 cm) reflector from natural uranium, on the other. Therefore, we will use this methodology in order to computationally estimate the critical masses of different uranium and plutonium compositions relevant to this study. 2. Estimated Critical Masses of Uranium and Uranium Dioxide of Different Enrichment With and Without Reflectors from Natural Uranium The widely used materials of nuclear power industry are: Uranium dioxide of different enrichment; Uranium metal of different enrichment; Natural uranium. Uranium metal of natural isotopic composition is generally known to have no critical mass. This material was used in the first American implosion-type atomic bomb Fat Man as a neutron reflector. This section is focused on numerical estimates of critical mass and other essential neutron functionals of spheres from uranium metal and uranium dioxide of different enrichment in U-235 with and without reflectors from natural uranium. At determining the radius and the mass of spheres in the critical conditions, the computations of K eff were performed to the level Keff 1 0,002 with the statistical accuracy K eff For the purposes of computations, natural uranium was assumed to consist of two isotopes (99.28 percent of U-238 and 0.72 percent of U-235) and to have the density ρ = 18.8 g/cm 3. Uranium dioxide is characterized by the density ρ = g/cm 3 [2].

11 Highly Enriched Uranium and Its Dioxide As highly enriched uranium, let us consider uranium used in the reference critical assembly Godiva enriched to 93.7 percent in U-235. Table 2 provides basic neutron functionals for the critical spheres made of such uranium (Godiva), its dioxide, with and without reflector. As an example, we use a 2-cm reflector from natural uranium. Table 2 Basic neutron functionals for critical-size spheres from enriched uranium and its dioxide, with and without reflector from natural uranium Functional Godiva Uranium from Uranium dioxide Uranium dioxide from Godiva plus from Godiva Godiva plus reflector reflector K eff ν τ f, ns R c R f R γ R el R inel R esc ρ, g/cm M cr, kg R cr, cm The legend is the same as in Table 1. R cr is the outer radius of the critical system (including reflector). As follows from the data of Table 2, the use of highly enriched uranium dioxide increases the critical mass of the sphere by a factor of more than two as compared to uranium metal of the same enrichment. The major cause for this is the lower density of material. The presence of oxygen in the material increases the number of neutron collisions, reduces neutron escape from the system and results in the growth of τ f. Using the natural uranium reflector ( l = 2 cm) in both cases leads to the growth of the total critical mass by a factor of about 1.4, to the reduction of the mass of fissile materials by a factor of 1.45, and to the growth of the number of neutron collisions in the spheres and to the growth of τ f.

12 Uranium Containing 10 to 20 Percent of U-235 and Its Dioxide In compliance with the IAEA regulations, uranium containing less than 20 percent of U-235 does not belong direct-use nuclear materials and therefore presents lesser risk in terms of proliferation. We have performed computations of the basic neutron functionals for uranium and uranium dioxide containing 10 to 20 percent of U-235 with and without reflector from natural uranium. The results of the computations for the critical uranium metal spheres with different enrichment with and without natural uranium reflector are given in Table 3. The estimates for the critical spheres from uranium dioxide of different enrichment with and without natural uranium reflector are presented in Table 4. The legend in Tables 3 and 4 is the same as in Table 1. The data of Table 3 show that variation of enrichment in U-235 from 20 to 10 percent causes the basic neutron functionals of the spheres from uranium metal with the density ρ = 18.8 g/cm 3 to change as follows: Critical radius increases from cm to 37.1 cm; Critical mass increases from kg to 4,021.5 kg; τ f grows from 28.2 ns to 52.9 ns. Of course, the values of all these parameters grow significantly as compared to the values for a highly enriched (93.7 percent) uranium sphere. It is beyond doubt that this complicates manufacturing and use of explosive devices from such materials. However, the use of such materials for making very simple nuclear explosive devices does not seem impossible. The use of 2-cm reflectors from natural uranium metal leads to a physically clear consequence, namely to a smaller quantity of enriched uranium at a greater total critical mass of the spheres. As follows from the data of Table 4, the transition from uranium metal containing 20 to 10 percent of U-235 to its dioxide, with the density of material reduced from 18.8 g/cm 3 to g/cm 3, naturally leads to the further growth of: The critical radius; The critical mass; The average time of neutron generation in the process of nuclear fission by onegeneration neutrons. However, it does not seem impossible in principle to use uranium dioxide containing 20 to 10 percent of U-235 for making nuclear explosive devices. The role of reflector in this case is similar to that in the system with uranium metal.

13 Table 3 Estimated basic neutron functionals for critical-size spheres from uranium metal containing 20 to 10 percent of the isotope U-235 with and without natural uranium reflectors Functional Uranium metal Uranium metal plus reflector, l = 2 cm 20% 18% 16% 14% 12% 10% 20% 18% 16% 14% 12% 10% K eff ν τ f, ns R c R f R γ R el R inel R esc ρ, g/cm ρ ref, g/cm M cr, kg , , , , , , , ,054.2 M fm, kg , , , , , , ,434.8 R cr, cm ρ ref is the density of reflector; M fm is the mass of fissile core without reflector.

14 Table 4 Estimated basic neutron functionals for critical-size spheres from uranium dioxide containing 20 to 10 percent of the isotope U-235 with and without natural uranium reflectors Functional Uranium dioxide Uranium dioxide plus reflector, l = 2 cm 20% 18% 16% 14% 12% 10% 20% 18% 16% 14% 12% 10% K eff ν τ f, ns R c R f R γ R el R inel R esc ρ, g/cm ρ ref, g/cm M cr, kg 1, , , , , , , ,226 2, ,244 7, ,488.6 M fm, kg 1, , , , , , , , , , , ,072.8 R cr, cm

15 Brief Discussion In discussing the numerical values of the basic neutron functionals calculated (Tables 2, 3 and 4) let us note the following: The major distinguishing feature of the neutron multiplying systems is the preservation of the balance between the birth of neutrons and their death as a result of nuclear capture (fission R f and radiation R γ neutron capture) and escape R esc of neutrons from the system: ν R f R f + R γ + R esc ν. At a more thoughtful consideration, one needs to take into account other sources of neutron birth and death, as well. Within the above discussed scenarios, the preservation of this neutron balance is quantified as follows: For uranium metal with 93.7-percent enrichment, Godiva assembly, ν R f + R γ + R esc = ; For uranium dioxide with 93.7-percent enrichment, ν R f + R γ + R esc = ; For uranium metal with 20 to 10-percent enrichment, ν R f + R γ + R esc = ( ) + ( ); For uranium dioxide with 20 to 10-percent enrichment, ν R f + R γ + R esc = ( ) + ( ). Transition from uranium metal to uranium dioxide causes the birth rate of neutrons to reduce by approximately 1 percent in all scenarios. By definition of critical conditions K eff R f 1, one fission event consumes one neutron in all scenarios. All significant changes consist in the conversion of part of escaping neutrons into radiation capture neutrons. Correspondent with the relatively high cross section of radiation neutron capture by the nucleus of U-238, the reduction in the enrichment of uranium in the isotope U-235 is accompanied by a considerable growth of the number of radiation capture neutrons and respective decrease of the number of escaping neutrons. The transition from uranium metal to uranium dioxide promotes this process. The transfer of escaping neutrons into radiation capture neutrons, when the above discussed materials are used in explosive devices, constrains the performance of the latter. Namely the number of escaping neutrons can be used as a criterion of potential use of a fissionable material in explosive devices taking into account their possible utilization for nuclear fission and radiation capture in critical systems.

16 Neutron Multiplication Rate in the Infinite Medium from Uranium and Uranium Dioxide of Different Enrichment in U-235 Infinite medium is a sphere with a radius that allows neglecting the number of escaping neutrons R esc /ν Computations were performed for the infinite medium with a density corresponding to the density ρ = g/cm 3 for uranium metal and ρ = g/cm 3 for uranium dioxide, and different levels of enrichment in U-235. Estimated neutron multiplication rates in the infinite medium α and other basic neutron functionals are given in Table 5. Data of Table 5 indicate the following. The value of α for the infinite medium from uranium metal with the density ρ = g/cm 3 and 93.7-percent enrichment in U-235 makes α = ns -1. At 20-percent enrichment, α = ns -1. Further decrease in the enrichment leads to a reduction of the value of α, and at 10-percent enrichment, α = ns -1.

17 Table 5 Estimated neutron multiplication rates α and other neutron functionals for the infinite medium from uranium metal and uranium dioxide with different enrichment in the isotope U-235 Functional 93.7% K eff α, ns τ f, ns 4.15 ν 2.64 R c 8.03 R f 1.0 R γ 0.88 R el 4.13 R inel 1.26 R fic 1.54 ρ, g/cm Uranium metal with enrichment Uranium dioxide with enrichment 20% 18% 16% 14% 12% 10% 93.7% 20% 18% 16% 14% 12% 10% R fic is the number of fictitious neutron absorptions falling on the neutrons per one fission event

18 18 3. Estimated Critical Masses of Plutonium, Plutonium Dioxide and MOX Fuel of Different Isotopic Compositions, With and Without Reflectors from Natural Uranium No plutonium exists in nature; it is produced in nuclear reactors. Isotopic composition of plutonium depends on the type of reactors and irradiation conditions. The following types of nuclear reactors have been considered in this study: GCR [CO2-graphite reactor] graphite carbon-dioxide-cooled reactor with natural uranium as fuel; PHWR [pressurized heavy-water (moderated and cooled) reactor] reactor with heavy-water moderator, pressurized coolant, and natural uranium fuel; PWR [pressurized water reactor] pressurized nuclear reactor with light-water moderator and coolant and low enrichment uranium fuel; LWGR [light-water(-cooled) graphite(-moderated) reactor] reactor with ordinary water as a coolant, graphite as a moderator and low enrichment uranium as fuel; BWR [boiling water reactor] boiling light-water reactor with low enrichment uranium fuel. Table 6 specifies isotopic compositions for the GCR, PHWR, PWR, LWGR plutonium and weapons-grade plutonium (WGPu) [5]. Table 6 Isotopic compositions of plutonium (in percent) produced by different types of nuclear power reactors Reactor type Plutonium isotopes Pu-239 Pu-240 Pu-241 Pu-242 Pu-238 GCR PHWR PWR LWGR WGPu Plutonium metal, its dioxide and the MOX fuel Pu α U 1-α O 2 (fuel manufactured from oxides of plutonium and natural uranium) can be produced from these types of plutonium. Isotopic composition of plutonium affects the parameters of neutron multiplication in plutonium material and, correspondingly, determines its critical mass.

19 19 This section is focused on the estimates of critical mass and other essential neutron functionals of spheres from different plutonium isotopes, their dioxides, reactor mixtures of plutonium isotopes and their dioxides, MOX fuel with different enrichment and different isotopic composition of plutonium. Like in the case of uranium fuel, the effects of reflector ( l = 2 cm) from natural uranium metal were analyzed. The estimates were made based on the assumption that natural uranium consists of two isotopes (99.28 percent of U-238 and 0.72 percent of U-235) and is characterized by the density ρ = 18.8 g/cm 3, that plutonium dioxide and MOX fuel have the density ρ = g/cm 3, and that plutonium metal is characterized by the density ρ = g/cm 3. When determining the critical radius of a sphere, K eff computations were performed to K 1 0,002 with the statistical accuracy K eff /K eff eff 3.1. Monoisotopic Plutonium and its Dioxide Isotopes of plutonium are characterized by remarkably different fission properties, and materials from them, correspondingly, differ in their neutron multiplication capability. In this connection, critical masses and other neutron functionals were estimated for hypothetical monoisotopic compositions of plutonium and their dioxides. The results of such computations are given in Table 7. The major cause of the growth of critical masses at transition from isotopes to their dioxides is the reduction of material density. However, presence of oxygen in dioxide increases the number of collisions and decreases leakage of neutrons, which is accompanied by the growth of the system s reactivity. Thus, if the ratio of the densities used in the computations yields the estimated variation of the critical mass of δm cr ρ -2 = 1.82, then real variation of critical masses at transition from plutonium metal to dioxide makes 1.44 and 1.34 for the isotopes Pu-239 and Pu-241 that are capable of undergoing fission by neutrons of all energies. At the same time, for the isotopes Pu-240 and Pu-242 that are capable of undergoing fission by neutrons of high energy only, the transition from metal to dioxide results in the growth of critical-mass quantities of plutonium by a factor of 2.05 and 2.98, correspondingly. This circumstance is attributed to the important role, in such cases, of neutron spectrum softening at neutron scattering in the presence of oxygen.

20 Table 7 Estimates of basic neutron functionals for critical-size spheres from monoisotopes of plutonium and their dioxides Functional 239 Pu 238 Pu Plutonium metal 240 Pu 241 Pu 242 Pu Plutonium dioxide 239 PuO PuO PuO PuO PuO 2 K eff ν τ f, ns R c R f R γ R el R inel R esc ρ, g/cm R cr, cm M cr, kg

21 Plutonium and Plutonium Dioxide of Isotopic Composition from Different Reactors, With and Without Reflectors from Natural Uranium Real plutonium produced in different reactors is characterized by the isotopic compositions shown in Table 6. Such a collection of plutonium isotopes is contained in the spent nuclear fuel and can be recovered from it for making explosive devices. Table 8 specifies estimates of the basic neutron functionals for critical-size spheres from plutonium and plutonium dioxide with isotopic compositions from different reactors. Data of Table 8 show that at the density of plutonium ρ = g/cm 3, critical masses make: M cr = 17.6 kg for WGPu; M cr = kg for GCR plutonium; M cr = kg for PHWR plutonium; M cr = 22.3 kg for PWR plutonium; M cr = kg for LWGR plutonium. At the density of plutonium dioxide ρ = g/cm 3, the same values make: M cr = kg for WGPu dioxide; M cr = kg for GCR plutonium dioxide; M cr = kg for PHWR plutonium dioxide; M cr = kg for PWR plutonium dioxide; M cr = kg for LWGR plutonium dioxide. Comparatively small critical masses of plutonium metal with different isotopic composition (from different reactors) are attributed to the relatively high specific content of the isotopes Pu-239 and Pu-241 that are capable of undergoing fission by neutrons of all energies. Critical mass increases with the reduction of these isotopes. Transition to plutonium dioxides is accompanied by the growth of critical mass values due to the reduction of the density of material. At that, even the highest critical mass of LWGR plutonium dioxide, M cr = kg, is appreciably lower than that of highly enriched uranium M cr = 52.4 kg (Godiva assembly, Table 1). Let us note the considerable (approximately by a factor of 2) growth of the average time τ f of nuclear fission by one-generation neutrons at such transition. Table 9 gives the values of neutron functionals for the spheres from plutonium and plutonium dioxide having the same isotopic compositions as in Table 8, but with a reflector from natural uranium with the thickness l = 2 cm. The reflector leads to the reduction of the mass of plutonium metal or dioxide, but to the growth of the total critical mass of the spheres. At that, the values of τ f grow as well, which slows down the rate of neutron multiplication. Fission properties of reactor plutonium are slightly inferior to those of WGPu and are superior to those of uranium enriched to 93.7 percent in U-235.

22 Table 8 Estimates of basic neutron functionals for critical-size spheres from plutonium and plutonium dioxide with different isotopic composition from different types of nuclear power reactors Functional GCR K eff 1.00 ν 3.14 Plutonium metal Plutonium dioxide PHWR PWR LWGR WGPu GCR PHWR PWR LWGR WGPu τ f, ns R c R f R γ R el R inel R esc ρ, g/cm R cr, cm M cr, kg

23 Table 9 Estimates of basic neutron functionals for critical-size spheres from plutonium and plutonium dioxide with different isotopic composition from different types of nuclear power reactors, with 2-cm uranium metal reflector Functional GCR K eff 1.00 ν 3.10 τ f, ns 4.15 R c 7.94 R f 1.0 R γ 0.08 R el 5.17 R inel 1.69 R esc 2.02 ρ, g/cm Plutonium metal Plutonium dioxide PHWR PWR LWGR WGPu GCR PHWR PWR LWGR WGPu ρ ref, g/cm R cr, cm M fm, kg M ref, kg M cr, kg

24 MOX Fuel Manufactured from Natural Uranium and Plutonium Produced in Different Types of Reactors Comparatively low critical masses of the spheres from reactor plutonium metal and its dioxide explicitly point at the possibility of efficient neutron multiplication in the MOX fuel produced from reactor plutonium and natural uranium. Tables provide estimates of the basic neutron functionals for critical-size spheres from the MOX fuel with plutonium from different reactors having different specific content of plutonium. Specific content of plutonium was assumed to be 20, 16, 13, 10 and 7 percent. Table 14 specifies the same data for the case of WGPu. Of course, critical masses of the spheres from the MOX fuel significantly differ from the same values for the spheres from reactor and weapons-grade plutonium dioxide. This is ascribed to the high specific content of the isotope U-238, characterized by low fission properties and high capability to capture neutrons. Apparently, direct use in explosive devices of the MOX fuel with a specific content of reactor plutonium of 7 percent, which is characterized by immense critical masses (hundreds of tons), is hardly possible. However, as for the MOX fuel with the specific content of reactor plutonium ranging from 16 to 20 percent, the possibility of its direct use for making explosive devices cannot be excluded. Critical masses of the MOX fuel containing 10 to 20 percent of power-grade plutonium are rather close to the critical masses of uranium metal with the same enrichment in the isotope U-235. In this connection, it would be appropriate to emphasize that the MOX fuel for fast breeder reactors, whose specific plutonium content is more than 20 percent and isotopic composition of plutonium is close to that of WGPu, undoubtedly belongs to fissionable materials with significant proliferation risk. Along with this, let us note that radiochemical reprocessing of the MOX fuel, as envisaged for fast nuclear reactors, would make it possible to recover plutonium, which would present a more significant threat because plutonium of almost any isotopic composition is suitable for making nuclear explosive devices. At that, the similar threat is posed by plutonium recovered from the spent nuclear fuel of all the above mentioned types of thermal reactors.

25 25 Table 10 Estimates of basic neutron functionals for critical-size spheres from MOX fuel with GCR plutonium as a function of plutonium content Functional 7% 10% 13% 16% 20% K eff ν τ f, ns R c R f R γ R el R inel R esc ρ, g/cm R cr, cm M cr, kg 748, , , , Table 11 Estimates of basic neutron functionals for critical-size spheres from MOX fuel with PHWR plutonium as a function of plutonium content Functional 7% 10% 13% 16% 20% K eff ν τ f, ns R c R f R γ R el R inel R esc ρ, g/cm R cr, cm M cr, kg 5,989,970 7, , ,

26 26 Table 12 Estimates of basic neutron functionals for critical-size spheres from MOX fuel with PWR plutonium as a function of plutonium content Functional 7% 10% 13% 16% 20% K eff ν τ f, ns R c R f R γ R el R inel R esc ρ, g/cm R cr, cm M cr, kg 47,919,760 66,798 2, , Table 13 Estimates of basic neutron functionals for critical-size spheres from MOX fuel with LWGR plutonium as a function of plutonium content Functional 7% 10% 13% 16% 20% K eff ν τ f, ns R c R f R γ R el R inel R esc ρ, g/cm R cr, cm 1, M cr, kg 16,436 3, , ,070.1

27 27 Table 14 Estimates of basic neutron functionals for critical-size spheres from MOX fuel with WGPu as a function of plutonium content Functional 7% 10% 13% 16% 20% K eff ν τ f, ns R c R f R γ R el R inel R esc ρ, g/cm R cr, cm M cr, kg 24,535 3,437 1, Neutron Multiplication Rate in the Infinite Medium from Plutonium-Bearing Materials Infinite medium is deemed to be a sphere, whose radius allows us to ignore the number of escape neutrons R esc /ν As in the section before, the density of material for the purely plutonium medium was assumed to be ρ = g/cm 3, and for plutonium dioxide and MOX fuel, ρ = g/cm 3. Table 15 shows estimated neutron multiplication rates and other neutron fuctionals for infinite media consisting of monoisotopes of plutonium and their dioxides. The values of neutron multiplication rate for monoisotopic media make: α = ns -1 for Pu-239; α = ns -1 for Pu-238; α = ns -1 for Pu-240; α = ns -1 for Pu-241; α = ns -1 for Pu-242. Comparison of these values with the neutron multiplication rate of the medium from highly enriched (93.7 percent of U-235) uranium, α = ns -1, shows that only Pu-242 medium has a lower neutron multiplication rate. Multiplication rates in the infinite media from Pu-239 and Pu-238 are more than twice as high as the multiplication rate in the infinite medium from the said highly enriched uranium.

28 28 Neutron multiplication rates for the infinite media from monoisitopic plutonium dioxides make: α = ns -1 for 239 PuO 2 ; α = 0,160 ns -1 for 238 PuO 2 ; α = 0,076 ns -1 for 240 PuO 2 ; α = 0,120 ns -1 for 241 PuO 2 ; α = 0,041 ns -1 for 242 PuO 2. These values for all the isotopes, except Pu-242, are notably higher than the same values for highly enriched uranium dioxide. Moreover, the dioxides 239 PuO 2 and 238 PuO 2 have a higher, and the dioxode 241 PuO 2, the same α as that of highly enriched uranium. Based on the values of other functionals one can judge about mechanisms and features of neutron kinetics in the monoisotopic plutonium media. Table 16 gives the estimated values of α and other neutron functionals for the infinite media composed of real mixtures of plutonium isotopes produced in reactors, including WGPu, and their dioxides. Tables 17 and 18 show the estimated values of α and other neutron functionals for the infinite medium from the MOX fuel of different reactors with different content of plutonium. High specific content of the isotope U-238, characterized by low fission properties and rather high probability of radiation neutron capture, causes considerable decrease in the value of α.

29 Table 15 Estimated neutron multiplication rates and other neutron functionals for the infinite medium composed of monoisotopes of plutonium and their dioxides Functional 239 Pu 238 Pu Plutonium isotopes 240 Pu 241 Pu 242 Pu Dioxides of plutonium isotopes 239 PuO PuO PuO PuO PuO 2 α, ns ν 3.21 τ f, ns 2.46 R c 6.46 R f 1.0 R γ 0.02 R el 2.37 R inel 0.89 R fic 2.18 ρ, g/cm

30 Table 16 Estimated neutron multiplication rates and other neutron functionals for the infinite medium composed of GCR, PHWR, PWR and LWGR plutonium and plutonium oxide and WGPu Functional GCR K eff 2.88 α, ns ν 3.20 τ f, ns 2.65 R c 6.69 R f 1.0 R γ 0.03 R el 2.54 R inel 0.94 R fic 2.17 ρ, g/cm Plutonium metal Plutonium dioxide PHWR PWR LWGR WGPu GCR PHWR PWR LWGR WGPu

31 Table 17 Estimated neutron multiplication rates and other neutron functionals for the infinite medium composed of the MOX fuel of GCR and PHWR with different plutonium content Functional 20% α, ns ν 2.97 τ f, ns 24.8 R c 44.0 R f 1.0 R γ 0.38 R el 36.9 R inel 4.19 R fic 1.57 ρ, g/cm GCR; Pu α U 1-α O 2 PHWR; Pu α U 1-α O 2 16% 13% 10% 7% 20% 16% 13% 10%

32 Table 18 Estimated neutron multiplication rates and other neutron functionals for the infinite medium composed of the MOX fuel of PWR and LWGR and WGPu with different plutonium content Functional PWR Pu α U 1-α O 2 LWGR Pu α U 1-α O 2 WGPu Pu α U 1-α O 2 20% 16% 13% 10% 20% 16% 13% 10% 20% 16% 13% 10% 7% α, ns ν 2.96 τ f, ns 27.4 R c 47.1 R f 1.0 R γ 0.41 R el 39.8 R inel 4.33 R fic 1.55 ρ, g/cm