Isotopic compositions of uranium and plutonium in spent LWR fuel
The paper addresses to the problems related with protection of the existing and advanced nuclear fuel types against unauthorized proliferation via introduction of some admixtures into their composition. So, the task may be defined as follows: these admixtures must create the barriers difficult to overcome for the use of nuclear fuels in nuclear explosive devices (NED) but, at the same time, these admixtures must preserve (or even enhance) energy potential of nuclear fuels for further peaceful use at civilian nuclear power plants (NPP). Such an approach to proliferation protection of nuclear fuels is often called as an isotopic denaturing. The term “isotopic denaturing” is used to designate any artificial changes in isotopic composition of chemical element which can give some new desirable properties to this element.
2. Protection of nuclear materials in fuel cycle against unauthorized applications
As is known, main raw materials for NPP are natural uranium and thorium. Natural uranium contains 0.71% 235U, and self-sustainable chain fission reaction (CFR) may be maintained by thermal neutrons provided rather large amounts of uranium, graphite or heavy water are available. As for natural thorium, there are no fissile isotopes, like 235U, in its composition at all. So, manufacturing of a small-size NED with uranium charge requires application of isotopic enrichment in order to produce highly enriched (weapon-grade) uranium (HEU, 90-95% 235U). Some artificial fissile materials (plutonium or 233U) can be used as a nuclear charge but they may be produced only under neutron irradiation of natural uranium or thorium in nuclear reactors.
At present, nuclear reactors apply uranium fuels of various enrichments. So, isotopic composition of uranium-based fuel for civilian NPP takes an intermediate position between natural uranium and HEU. Conversion of civilian uranium fuel into HEU, or weapon-grade uranium, requires application of isotopic re-enrichment operations.
Plutonium, suitable element for NED, is produced by nuclear reactors in the process of their operation. As is known, weapon-grade plutonium (WGPu) consists mainly of 239Pu with small content of 240Pu (4-7%) and negligible amounts of heavier plutonium isotopes. WGPu may be produced in the special reactors with short irradiation cycle. Power reactors at NPP are operated with relatively long irradiation cycle and, thus, with high fuel burn-up. So, plutonium produced in power reactors (reactor-grade plutonium, RGPu) contains the larger amounts of heavier plutonium isotopes. Lengthy irradiation of uranium fuel can change significantly isotopic composition of uranium (in particular, isotopes 232U and 236U do appear). As an example, isotopic composition of uranium fuel (initial enrichment - 4.4% 235U) after LWR operation up to fuel burn-up of 4% HM is presented in Table 1. Thus, uranium fuel may be used to produce fissile materials, suitable for NED, in nuclear reactors but it requires application of some special operations.
|Composition of fresh fuel||Composition of uranium and plutonium in spent fuel, %|
(fuel burn-up - 4 % HM)
|4.4 % 235U||Uranium||232U||235U||236U||238U|
|1.4symbol 215 \f "Symbol" \s 9×10-9||1.26||0.59||98.15|
Artificial fissile uranium isotope 233U, high-efficiency material for NED, may be produced by neutron irradiation of natural thorium. However, undesirable by-products are generated in this process including other uranium isotopes, namely 232U, 234U and 236U. In particular, light uranium isotope 232U can complicate significantly any operations with produced uranium.
Radiochemical reprocessing of spent nuclear fuel (SNF) includes extraction of radioactive fission products (FP) whose intense emission of ionizing radiation creates a protective barrier against unauthorized access to fissile materials. So, SNF reprocessing can be regarded as an operation which can remove (or, at least, weaken under incomplete purification) the radiation barrier. SNF partitioning into separate elements or groups of elements can facilitate diversion of fissile materials. In order to reduce the diversion risk, appropriate protective actions should be undertaken. In addition to the organizing measures related with physical protection of nuclear enterprises and technological control, the following barriers against diversion of fissile materials should be considered:
Radiation barrier mainly formed by FP. Such a barrier can be formed in the process of the reactor operation and by a special short-term irradiation of fresh fuel assemblies in the dedicated nuclear facilities. Radiation background of fissile materials is one else component of the radiation barrier.
Incomplete SNF purification from radioactive FP can result in intense radiation fields which make very difficult any further operations with extracted fuel.
Isotopic dilution of 235U, i.e. the use of relatively low-enriched uranium (LEU).
Incomplete separation of uranium from plutonium (or full exclusion of any technological procedures needed for uranium-plutonium separation) in the course of SNF reprocessing. This measure makes it impossible to use these materials directly in NED.
Application of automatic remote technology for fuel, fuel rods and fuel assemblies fabrication. This measure can complicate access to fissile materials.
Dilution (or denaturing) of fissile materials by their isotopes which can complicate the use of fissile materials in NED. A particular case of isotopic denaturing is a well-known dilution of 235U by 238U, i.e. the use of LEU fuel. Another example: neutron irradiation of mixed uranium-thorium fuel in nuclear reactors can produce fissile isotope 233U isotopically diluted by 238U.
If we consider fissile plutonium isotope 239Pu, then the heavier plutonium isotopes (mainly, 240Pu) play the same role of isotopic diluents. In addition, light plutonium isotope 238Pu is an intense source of spontaneous fission neutrons and intense source of thermal energy from -decays (half-life of 238Pu is equal to 87.7 years).
In thorium fuel cycle the same role may be played by 232U (half-life – 68.9 years).
In practice, the measures listed above may be used in combinations. For example, open fuel cycle of power LWR is provided with the following protective barriers:
Isotopic dilution (LEU fuel).
Intense radiation background caused mainly by FP.
SNF contains non-separated mixture of uranium and plutonium.
Just this set of protective barriers represents a basis for the USA standard on SNF proliferation protection (Spent Fuel Standard (USA National Academy of Sciences, 2000)).
As 232U and its neutron predecessor 231Pa are nuclides of low abundance, it seems reasonable to consider their properties in detail.
3. Nuclear properties of 232U and 231Pa
Basic nuclear properties of main uranium isotopes are presented in Table 2 (Reilly et al., 1991; OECD Nuclear Energy Agency, 1997). As it may be seen, some nuclear properties of 232U make it a valuable material for proliferation protection of uranium-based nuclear fuel.
|Specific yield of -particles, 1/(gs)||81011||2.3108||7.9104||1.2104|
|Mean energy of -particles, MeV||5.3||4.76||4.4||4.19|
|Specific yield of spontaneous fission neutrons, 1/(g s)||1.3||5.0210-3||2.9910-4||1.3610-2|
(En 0.0253 eV), barns
232U is a starting isotope for chain of radioactive decays, and some 232U decay products (208Tl, 212Bi) emit high-energy gamma-radiation (2.6 MeV and 1.8 MeV, respectively) that improves detectability of 232U-containing nuclear materials (Gilfoyle & Parmentola, 2001) and complicates radiation conditions, especially for any unauthorized actions. Nuclear properties of main 232U decay products are presented in Table 3.
|Half-life||1.91 years||3.62 days||55.6 sec||0.145 sec||1.01 hours||310-7 sec|
|Energy of -particles, MeV|
|6.78 (100%)||6.09 (9.7%)|
Like 238U, isotope 231Pa can play a role of a fertile nuclide which is not split by thermal neutrons but promotes breeding of fissile materials. Dependencies of radiative capture cross-sections on neutron energy are presented in Fig. 1 for isotopes 238U and 231Pa.
The following two important aspects should be noted here. Firstly, within thermal energy range, 231Pa is a superior neutron absorber as compared with 238U. For example, radiative capture cross sections of thermal neutrons (En 0.0253 eV) for these two isotopes are equal to: σc(231Pa) 227 barns, σc(238U) 3 barns. So, the presence of 231Pa in fuel composition can promote effective generation of fissile isotopes 232U and 233U. Secondly, there is a rather large energy distance between capture resonances of 238U and 231Pa. Capture resonances of 231Pa belong to relatively low energies (below 100 eV). This means the presence of 231Pa in fuel composition can depress thermal region in energy spectrum of neutrons (see Fig. 2).
It can be seen that, although neutron energy spectrum in VVER-1000 contains a certain fraction of thermal neutrons, introduction of 231Pa into fuel composition can remove the thermal fraction completely. That is why stainless steel may be used here as a structural material. Indeed, the absence of thermal fraction in neutron spectrum does not result in additional neutron loss but fuel rods can keep their ability for working up to the higher values of fuel burn-up than with zirconium-based alloys.
Now let us consider nuclear properties of 232U, product of neutron capture by 231Pa and rapid -decay of 232Pa (T1/2 (232Pa) 1,3 days (Babichev et al.,1991)). Like 235U, isotope 232U is a fissile nuclide. Dependencies of fission cross-sections on neutron energy are presented in Fig. 3 for isotopes 235U and 232U.
It can be seen that, within thermal energy range, fission cross-sections of 232U are substantially lower than those for 235U while radiative capture cross-sections of these isotopes are comparable each other. For example, radiative capture cross sections of thermal neutrons (En 0.0253 eV) for these two isotopes are equal to: σc(232U) 73 barns, σc(235U) 99 barns. So, neutron-multiplying properties of 232U are inferior to those of 235U within thermal energy range.
This conclusion can be confirmed by Fig. 4 which demonstrates energy dependency of (νef - 1), i.e. the number of excess fission neutrons per one absorbed neutron.
235U looks superior to 232U within thermal energy range but quite another situation takes place in resonance range. So, it may be expected that introduction of 231Pa into uranium-based fuel composition with aim to increase fuel burn-up will be more efficient just in resonance neutron spectrum.
4. Proliferation resistance of nuclear materials in open fuel cycle. The ways for closure of fuel cycle
Presently, there are different points of view on future development of nuclear fuel cycles. Some countries (USA, Canada, Germany and Sweden) are implementing in practice an open nuclear fuel cycle (Fig. 5) that does not foresee a radiochemical SNF reprocessing in the visible future. One of the reasons for this choice is a wish of decreasing a risk of nuclear weapon proliferation. SNF may be only converted into the forms suitable for long-term safe storage. However, such a strategy of nuclear power development has already resulted in large SNF stockpiles, potentially dangerous nuclear materials (NM). So, the preferable option for future development of nuclear power consists in transition to the closed fuel cycles with SNF reprocessing, separation of radioactive FP and recycling of residual fuel.
LEU is a fresh fuel for open nuclear fuel cycle. Plutonium in spent fuel assemblies is protected by intense gamma-radiation of fission products (Fig. 5). That is why unirradiated materials are more vulnerable for unauthorized proliferation.
Isotopic uranium denaturing may be regarded as an effective method for upgrading self-protection of unirradiated uranium-containing materials. The term “isotopic denaturing” is used conventionally for designation of any artificial changes in natural isotopic composition of a chemical element with aim to give him some new, desirable properties. In practice, uranium may be denatured by the following two ways: direct introduction of intense radioactive isotope 232U into uranium fuel composition or direct introduction of relatively weaker radioactive isotope 231Pa into uranium fuel composition. 231Pa is a neutron predecessor of 232U, main isotope of uranium denaturing. So, only short-term pre-irradiation of fresh fuel assemblies in the research reactors may be sufficient to produce proliferation resistant fuel assemblies, suitable even for export deliveries.
4.1. Isotopic denaturing of uranium as a way for creating an internal source of - particles
Along with progress in development of high-efficiency enriching technologies, potential threat of LEU diversion and re-enrichment up to the weapon-grade level excites more and more apprehensions. These reasons indicate that, besides reduction of uranium enrichment below 20% 235U, other measures may be also required to upgrade LEU self-protection against its unauthorized re-enrichment. Taking into consideration the growing world-wide scope of LEU utilization, including LEU with enrichment in the vicinity of the upper boundary (20% 235U), high LEU vulnerability to unauthorized re-enrichment must be recognized. Particular apprehensions are related with 20%-uranium. So, some additional actions should be undertaken to protect LEU against its unauthorized re-enrichment.
The effects of 232U introduction into LEU are caused by the following specific properties of 232U (see Table 2):
Good neutron-multiplying properties of 232U (Ganesan et al., 2002) and its neutron predecessor 231Pa make it possible to extend time period of continuous reactor operation without refueling up to the values comparable with the reactor life-time. As a result, unauthorized extraction of plutonium from spent fuel assemblies becomes unfeasible.
It is impossible to remove 232U from denatured uranium without application of sophisticated and expensive isotope separation technologies.
232U is a neutron source from spontaneous fission reactions and a source of high-energy -particles. Alpha-particles emitted by 232U are able to dissociate molecules of uranium hexafluoride and, thus, could make it practically impossible to re-enrich denatured uranium up to the weapon-grade level. Besides, -particles are able to initiate (,n)-reactions with impurities of light elements (LE) and, thus, intensify internal neutron generation. Growth of neutron background in the re-enriching process of LEU-uranium containing 0.10.5% 232U can decrease the CFR energy yield by three orders of magnitude. In essence, NED with such a re-enriched uranium is a “dirty” bomb only. Thus, export deliveries of LEU-based fuel assemblies to foreign NPP receive an additional proliferation barrier.
5. Increased burn-up of proliferation protected LWR fuel containing 231Pa
One of specific features in operation of nuclear power reactors consists in a necessity to perform regular refuelings. This necessity is caused by the following effects: depletion of fissile materials, FP accumulation, potential rupture of fuel cladding with intense release of radioactive materials. LWR, the mostly spread type of power reactors, requires refueling every 1-2 years, when fuel burn-up reaches 4-6% HM.
Extension of fuel life-time up to relatively long time periods (several decades, for instance) can reduce drastically the number of refuelings or exclude them at all. Reduction or full exclusion of refueling procedures decreases the demands for fresh fuel and decreases quantity of SNF discharged per unit of produced energy. Those reactors, which are capable to operate for a sufficiently long time without any refueling, may be used as the only energy source in remote regions, at the floating NPP, as energy source for space investigations (research bases on the Moon or Mars, cosmic flights into the outer space). Our studies demonstrated that introduction of 231Pa into LWR fuel composition could extend significantly the fuel life-time and reach ultra-high fuel burn-up.
It should be noted that achievability of ultra-high fuel burn-up was studied here only from the standpoint of neutron-multiplying properties of advanced fuel compositions. The problems of suitable structural materials, evolution of their strength properties and durability for a long fuel life-time are not analyzed here. At present, maximal fuel burn-up (about 30% HM) was achieved in the research fast reactor BOR-60 (Grachev et al., 2003). It may be expected that the higher values of fuel burn-up could be achieved if the following operations would be multiply carried out: partial fuel burn-up (near to the practically achievable value of 30% HM), application of DUPIC-technology for removal of gaseous and volatile FP, re-fabrication of fresh fuel pellets.
5.1. Evolution of neutron-multiplying properties in chains of isotopic transformations
In this section we compared time evolutions of neutron-multiplying properties in two isotopic chains: traditional chain that starts from 232Th (232Th → 233U → 234U → …) and non-traditional chain that starts from 231Pa (231Pa → 232U → 233U → …) (see Fig. 6). Radiative capture cross-sections σc and fission cross-sections σf were calculated for a typical neutron spectrum of VVER-1000 (β-decays were not taken into account).
It can be seen that neutron-multiplying properties in non-traditional chain are gradually improved: the starting isotope 231Pa is a neutron absorber, fission cross-section of the second isotope 232U prevails over its capture cross-section, and the third isotope 233U is a well-fissionable material. So, non-traditional chain represents the combination of two consecutive fissionable isotopes (232U and 233U) while, in traditional chain, the third isotope 234U is a neutron absorber only.
Thus, in non-traditional chain, parasitic neutron absorption by FP and depletion of fissile materials during the reactor operation can be partially compensated by 231Pa feeding. This makes it possible to talk about a possibility for substantial extension of fuel life-time and achievability of ultra-high fuel burn-up. By the way, in traditional LWR fuel, the negative effects caused by FP accumulation and depletion of fissile materials are compensated by 238U(n,γ)239Pu chain significantly weaker than by 231Pa(n,γ)232U(n,γ)233U chain in non-traditional fuel because of lower capture cross-sections: σc(238U) 0.9 barns, σc(231Pa) 43 barns.
So, it can be concluded that non-traditional chain (231Pa → 232U → 233U → …) appears to be more attractive from the standpoint of neutron-multiplying properties (as a consequence, from the standpoint of extended fuel life-time or achievability of ultra-high fuel burn-up) in comparison with traditional chain (232Th → 233U → 234U → …) due to the following reasons:
Combination of two consecutive well-fissionable isotopes (232U and 233U).
High rate of their generation from the starting isotope 231Pa, whose neutron capture cross-section is larger substantially than that for the starting nuclide 232Th in traditional chain of isotopic transformations.
It is noteworthy that 231Pa may be regarded, to a certain extent, as a burnable neutron poison: for fuel life-time 231Pa is burnt up to 80% and converted into well-fissionable isotopes, neutron capture cross-section of 231Pa is substantially larger than that of fertile isotope 232Th.
As is known, the existing LWRs are characterized by thermal neutron spectrum. In advanced LWR designs, for example, in LWR with supercritical coolant parameters (SCLWR), different regions of the reactor core are characterized by different neutron spectra depending on coolant density. Thermal spectrum prevails within the core region containing dense coolant (γ 0.72 g/cm3) while resonance neutron spectrum dominates within the core region containing coolant of the lower density (γ 0.1 g/cm3) (Kulikov, 2007).
Reasonability of 231Pa introduction into fuel composition for the cases of thermal and resonance neutron spectra is analyzed in the next section.
5.2. Reasonability of 231Pa involvement in the case of thermal neutron spectrum
Numerical analyses of fuel depletion process were carried out with application of the computer code SCALE-4.3 (Oak Ridge National Laboratory, 1995) and evaluated nuclear data file ENDF/B-V for elementary cells of VVER-1000. The only exception consisted in the use of martensite steel MA956 (elemental composition: 74,5% Fe, 20% Cr, 4,5% Al, 0,5% Ti and 0,5% Y2O3) instead of zircaloy as a fuel cladding material. Substitution of martensite steel for zirconium-based cladding is caused by the higher values of fuel burn-up.
Traditional (232Th-233U) and non-traditional (231Pa-232Th-233U) fuel compositions were compared for the case of thermal neutron spectrum (coolant density – 0.72 g/cm3). Infinite neutron multiplication factor K∞ is shown in Fig. 7 as a function of fuel burn-up.
It can be seen that substitution of 231Pa for 232Th decreases K∞ at the beginning of cycle, i.e. decreases an initial reactivity margin to be compensated. This effect is caused by different capture cross-sections of these isotopes - 231Pa is a significantly stronger neutron absorber than 232Th. In parallel, thanks to the larger capture cross-section of 231Pa, intense breeding of two consecutive well-fissionable isotopes (232U and 233U) takes place. So, gradual introduction of 231Pa into fuel composition results in the smoother relaxation of neutron multiplication factor in the process of fuel burn-up.
Acceptable fraction of 231Pa in non-traditional fuel composition is limited by the value of neutron multiplication factor (above unity) at the beginning of cycle. So, the effects caused by introduction of 231Pa may take place only in those fuel compositions where fraction of main fissile isotope is sufficiently large. For example, fraction of main fissile isotope 233U may be increased up to the level corresponding to the situation when neutron multiplication factor at the beginning of cycle is equal to about 1.10 at full replacement of 232Th by 231Pa. The calculations showed that this condition may be satisfied at maximal 233U fraction about 30%. Evolution of neutron multiplication factor in the process of fuel burn-up is presented in Fig. 8 for traditional and non-traditional fuel compositions.
As is seen from Fig. 8, traditional thorium-based fuel (30% 233U + 70% 232Th) provides rather high reactivity margin (K∞ (BOC) ≈ 1,9) with achievable value of fuel burn-up about 29% HM. Introduction of 231Pa into fuel composition decreases initial reactivity margin but, at the same time, increases fuel burn-up. If 232Th is completely replaced by 231Pa, i.e. (30% 233U + 70% 231Pa) fuel composition is analyzed, then neutron multiplication factor remains practically unchanged in the vicinity of unity for a full duration of fuel life-time. This means that the negative effects from neutron absorption by FP and depletion of fissile isotope are almost completely compensated by breeding of secondary fissile isotopes from 231Pa. In this case, about 80%-part of 231Pa is converted into secondary fissile isotopes which can provide ultra-high fuel burn-up (near to 57% HM).
If fuel loading in such a reactor is similar to the fuel loading of VVER-1000 (about 66 tons), then achievable value of fuel life-time is near to 40 years for the reactor power of 3000 MWt.
It is interesting to note that 235U as well as 233U may be used to achieve ultra-high fuel burn-up. Moreover, 235U option looks very attractive because of two reasons: firstly, 235U resources are more available than resources of 233U, and, secondly, achievement of the same fuel burn-up will require lower quantity of 231Pa, artificial isotope to be produced in the dedicated nuclear power facilities.
5.3. Reasonability of 231Pa involvement in the case of resonance neutron spectrum
Traditional (232Th-233U) and non-traditional (231Pa-232Th-233U) fuel compositions were compared for the case of resonance neutron spectrum (coolant density – 0.1 g/cm3). Infinite neutron multiplication factor K∞ is shown in Fig. 9 as a function of fuel burn-up.
Comparison of the curves presented in Figs. 7, 9 allows us to conclude that introduction of 231Pa into fuel composition is more preferable from the standpoint of higher fuel burn-up in the case of resonance neutron spectrum. This conclusion can be explained by better neutron-multiplying properties of 232U just in resonance neutron spectrum as compared with thermal neutron spectrum (see Fig. 4).
As it follows from Fig. 9, introduction of only 12% 231Pa increased fuel burn-up twice. Neutron multiplication factor at the beginning of cycle increased too, i.e. neutron-multiplying properties of fuel composition became better.
Like previous analysis, fraction of main fissile isotope 233U may be increased up to the level corresponding to the situation when neutron multiplication factor at the beginning of cycle is equal to about 1.10 at full replacement of 232Th by 231Pa. In addition, potential use of 235U instead of 233U was analyzed to evaluate a possibility for achieving ultra-high fuel burn-up.
So, numerical studies confirmed reasonability for introduction of 231Pa into fuel composition because this introduction results in reduction of initial reactivity margin and in substantial growth of fuel burn-up. Maximal positive effect from introduction of 231Pa may be observed in resonance neutron spectrum. Besides, introduction of 231Pa makes it possible to reach ultra-high fuel burn-up regardless of what main fissile isotope is used, 233U or 235U. In particular, (20% 233U + 80% 231Pa) fuel composition can reach fuel burn-up of 76% HM in resonance neutron spectrum (see Fig. 10).
5.4. Effects of 231Pa on safety of the reactor operation
On the one hand, introduction of 231Pa into fuel composition can provide small value of initial reactivity margin and high value of fuel burn-up. On the other hand, if relatively large 231Pa fraction is introduced into fuel composition, reactivity feedback on coolant temperature becomes positive, and safety of the reactor operation worsens.
Numerical studies demonstrated that, if maintenance of favorable reactivity feedback on coolant temperature during fuel life-time is a mandatory requirement, then, in thermal neutron spectrum, 231Pa fraction in fuel composition is limited by a quite certain value while, in resonance neutron spectrum, introduction of 231Pa is impossible at all. However, this conclusion is correct only for large-sized reactors, where neutron leakage is negligible.
So, only thermal neutron spectra should be considered to provide favorable reactivity feedback on coolant temperature. The results presented in Fig. 11 demonstrate a possibility for increasing fuel burn-up in thermal neutron spectrum by introduction of 231Pa into fuel composition.
As is known, fuel burn-up in VVER-1000 can reach a value about 4% HM. Introduction of 231Pa and higher contents of 235U can increase fuel burn-up by a factor of 8 with the same initial reactivity margin, i.e. more powerful system of reactivity compensation is not required.
Requirement of favorable reactivity feedback on coolant temperature completely excludes any introduction of 231Pa into fuel composition in the case of large-sized reactors with resonance neutron spectra. But, introduction of 231Pa into fuel composition of small-sized reactors does not worsen safety of the reactor operation because of relatively large neutron leakage. This indicates that the mostly attractive area for 231Pa applications is a small nuclear power including small-sized NPP for remote regions, for the floating NPP, for space stations on the Moon or Mars and for cosmic flights into the outer space.
The following conclusions can be made in respect of potential 231Pa applications:
Application of 231Pa as a burnable neutron poison can reduce initial reactivity margin and increase fuel burn-up.
Introduction of 231Pa into fuel composition makes it possible to reach ultra-high fuel burn-up (above 30% HM) both in thermal and resonance neutron spectra.
The actual problem of 231Pa production in significant amounts should be resolved.
6. Proliferation protection of nuclear materials in closed uranium-plutonium fuel cycle
NPP operation in open fuel cycle results in accumulation of huge SNF stockpiles that represents a long-term hazard to the humankind. Ultimate SNF disposal is a difficult technical problem requiring large number of practically “eternal” deep underground repositories. That is why many various options for closure of nuclear fuel cycle (NFC) are currently under research and development including extraction of residual uranium, plutonium and minor actinides from SNF.
As known, closed uranium-plutonium NFC includes reprocessing and recycling of nuclear fuel and evokes a lot of contradictory opinions with respect to potential risk of plutonium proliferation. This connected with two points:
Although plutonium extracted from SNF of power reactors (for example, LWR of PWR, BWR or VVER type) is not the best material for nuclear weapons, nevertheless it can be used in NED of moderate energy yield (Mark, 1993).
Recycled plutonium will be disposed at the facilities of closed NFC, and this will increase the probability of it using for illegal aims (diversion, theft).
Under these conditions, the absence of any internationally coordinated plan concerning the utilization or ultimate SNF disposal enforced the leading nuclear countries to undertake the steps directed to strengthening the nonproliferation regime (IAEA safeguards, Euratom's embargo on the export of SNF reprocessing technology). But several countries, in the first turn the USA, refused from deployment of breeder reactors which are intended for operation in closed NFC, and focused at once-through NFC. On the other hand, the social demand of solving excess fissile materials (plutonium, the first of all) problem which have both civil and military origins, stimulated carrying out the research on plutonium utilization in MOX-fuel. At the same time, the studies of advanced NFC protected against uncontrolled proliferation of fissile materials have been initiated.
6.1. Radiation protection of MOX-fuel. GNEP initiative
Specialists from ORNL (USA) investigated the ways for introduction of -radiation sources into fresh fuel (Selle et al., 1979). Sixty-four -active radionuclides were selected and studied as candidates for admixing into fresh fuel (see Fig. 12).
Radionuclides 137Cs (T1/2 30 years) and 60Co (T1/2 5.27 years) appeared the most preferable candidates. But cesium is a volatile element, and it can be easily removed from fuel by heating up. Intensity of -radiation emitted by 60Co rapidly relaxes.
Specialists from LANL (USA) proposed the advanced version of the international NFC that enhances proliferation resistance of plutonium (Cunningham et al., 1997). This proposal constituted a basis for the US President’s initiative on the Global Nuclear Energy Partnership (GNEP) that was supported by many countries (including Russia) with well-developed nuclear technologies (see Fig. 13).
According to the proposal, spent fuel assemblies discharged from power reactors of a country-user must be transported to the Nuclear Club countries for full-scale reprocessing. Extracted plutonium and minor actinides must be incinerated in the reactors placed on the territory of the International nuclear technology centers. Plutonium is not recycled in power reactors of a country-user. The Nuclear Club countries provide fresh LEU fuel deliveries into a country-user.
Upon exhaustion of rich and cheap uranium resources, nuclear power has to use artificial kinds of fresh fuel (plutonium, 233U or their mixtures). The GNEP initiative does not consider this opportunity. It is proposed to use such power reactors which are able to work without refueling for 15-20 years. After this time interval they must be returned to the Nuclear Club countries for SNF discharging and reprocessing and for insertion of fresh fuel. The concentrated incineration of plutonium and minor actinides in the International nuclear technology centers can lead to unacceptably large local release of thermal energy with unpredictable negative environmental and climatic effects. As for reactors with long-life cores, these are small and medium-sized power reactors. Besides, during transportation and mounting, they can be very attractive sources of plutonium in amounts large enough for manufacturing of several dozens of nuclear bombs.
6.2. Enhancement of LWR MOX-fuel cycle proliferation resistance by plutonium denaturing
Some nuclear properties of 238Pu make this isotope a valuable material for proliferation protection of uranium-plutonium fuel. Firstly, 238Pu is an intense source of thermal energy (T1/2 87 years, specific heat generation - 570 W/kg). So, introduction of 238Pu into plutonium creates almost insuperable barrier to manufacturing of even primitive implosion-type NED. Plutonium heating up by isotope 238Pu can provoke undesirable phase transitions and thermal pyrolysis of conventional explosives applied for compression of central plutonium charge. Secondly, 238Pu is an intense source of spontaneous fission neutrons, even more intense than 240Pu. As a consequence, probability of premature CFR initiation in NED sharply increases while energy yield of nuclear explosion drastically drops down to the levels comparable with energy yield of conventional explosives. Thus, LWR MOX-fuel cycle with ternary fuel compositions (Np-U-Pu) is characterized by enhanced proliferation resistance.
Like uranium, plutonium can be isotopically denatured by two ways: either direct introduction of intensely radioactive isotope 238Pu into MOX-fuel composition or introduction of relatively low intense radioactive isotope 237Np into MOX-fuel composition. 237Np is the nearest neutron predecessor of main denaturing isotope 238Pu. So, only short-term pre-irradiation of fresh MOX-fuel assemblies would be sufficient to produce proliferation resistant fuel assemblies, suitable even for export deliveries to any countries.
6.2.1. The effect of 237Np and 238Pu introduction on Pu protection in LWR fuel
It is proposed that the equilibrium isotope vectors are obtained for MOX-fuel circulating between LWR, spent fuel reprocessing as fuel manufacturing facilities. The fuel feed includes isotopes 237Np, 238Pu and 239Pu is produced in Hybrid Thermonuclear Installation (HTI) blankets.
Using the code GETERA (Belousov et al., 1992) for cell calculations of fuel burn-up, Pu isotopic compositions of MOX-fueled PWR were determined for moments of the beginning and end of cycle. 238Pu fraction in plutonium was adopted to be an index of Pu protection against uncontrolled proliferation. It means that the impact of higher plutonium isotopes on neutronics of chain reaction in imploded plutonium charge of NED was not taken into account.
The fuel being loaded in PWR may be considered as material consisting of two parts: the first part includes equilibrium composition of 238U and plutonium isotopes produced by 238U while the second part ("feed part of fuel") includes equilibrium composition of 237Np, 238Pu and other plutonium isotopes produced entirely by the feed. Equilibrium contents of 238Pu in plutonium of PWR fuel depending on 238Pu contents in plutonium of feed (with different 237Np fractions in "feed part of fuel") for equilibrium multi-cycle operation regime are presented in Fig. 14.
The plot region situated under the bisectrix B is a region where plutonium protection in feed is higher than plutonium protection in fuel. Respectively, the plot region situated above the bisectrix B is a region where plutonium protection in fuel is higher than that in feed. The curves of this figure characterize the correlation between plutonium protection levels in feed and fuel when the "feed part of fuel" contains 237Np in addition to plutonium. Basing on these data, it is possible to select the appropriate equilibrium regime of NFC.
Proper selection of the feed compositions, i.e. fractions of 238Pu and 237Np, makes it possible to attain the same level of fuel plutonium protection for various combinations of 238Pu and 237Np content in feed. For example, 32%-level of fuel plutonium protection can be attained in case of feed containing (0% 237Np, 52% 238Pu) or (20% 237Np, 43% 238Pu) or (40% 237Np, 32% 238Pu). The latter option corresponds to equal level of plutonium protection both in fuel and in feed. The line "S" that connects the right ends of the curves shown in Fig. 14 may be regarded as an "ultimate option" of the (Np-U-Pu) NFC considered here. The points of this line correspond to particular option of the (Np-U-Pu) NFC where 238U is absent in fuel composition, and its fertile functions passed to 238Pu and 237Np. So, this NFC may be called as a (Np-Pu) NFC. In this NFC the highest fuel Pu protection level (65% 238Pu) can be reached with feed Pu protection of 90% 238Pu. As known, the IAEA safeguards are not applied to plutonium containing 80% 238Pu or more (Rolland-Piegue, 1995; Willrich & Taylor, 1974; Massey & Schneider, 1982).
Inherent heat generation of plutonium is considered as a significant factor of its protection. The rates of inherent heat generation for various feed compositions are presented in Table 4. Here, the rates of specific heat generation for weapons-grade plutonium (WGPu) and reactor-grade plutonium (RGPu) are presented as well.
|238Pu/Pu in fuel and in feed|
|( Np/(Np + Pu) in feed )|
|qPu, W/kg Pu||2.3||13.||97||186||248|
|nsfPu, 106(n/sec)/kg Pu||0.06||0.38||0.71||1.06||1.30|
|qfuel, W/kg fuel||---||---||14.9||41.2||99.5|
|nsffuel, 106(n/sec)/kg fuel||---||---||0.11||0.24||0.53|
|---||---||38 / 82 / 402||103 / 194 / 377||176 / 318 / 421|
Basing on the results shown above, it can be concluded that denatured fuel plutonium containing more than 25% 238Pu is characterized by the internal heat generation which exceeds that of RGPu by more than order of magnitude and, by the larger extent, that of WGPu. In addition, denatured fuel plutonium is characterized by the higher neutron background caused by spontaneous fissions. The factors mentioned above enhance plutonium protection against its utilization in NED. The same factors complicate, to certain degree, the handling procedures with such a fuel in nuclear technologies.
Values of specific heat generation and neutron emission due to spontaneous fission of MOX-fuel being loaded for the equilibrium cycle options analyzed are shown in Table 4 also. For comparison, "dry" technology for handling with spent fuel assemblies may be applied if specific heat generation does not exceed 20-35 W/kg fuel. It may be also concluded that plutonium denaturing with 238Pu is restricted by thermal constraints imposed on permissible specific heat generation of fuel. The same tendency exists in connection with spontaneous neutrons emission. These constraints need to be taken into account in fuel fabrication, fuel rods and fuel assemblies manufacturing and transport operations. These complications of fuel management may be considered as certain "payment" for proliferation resistance of MOX-fuel cycle.
Actually speaking, the protection of plutonium in (Np-U-Pu)-fuel cycle is supposed to be enhanced due to addition 237Np and 238Pu into fuel. The degree of fissile nuclides protection depends mainly on magnitude of 238Pu fraction in plutonium. Meanwhile, 237Np itself can be also considered as a potential material for NED. For example, critical mass of 237Np (metal sphere, steel reflector) is about 55 kg (Koch et al., 1997). It’s ten times more than that of 239Pu. The magnitude of critical mass of 237Np is sensitive with respect of its dilution. For example, minimum critical mass of NpO2 is as much as 315 kg (Nojiri & Fukasaku, 1997; Ivanov et al. 1997). Besides, in fuel composition 237Np is present together with plutonium which is characterized by essential neutron source strength due to spontaneous fissions. Therefore, in order to apply extracted 237Np in NED it is needed to perform effective 237Np purification from plutonium (plutonium fraction is restricted by value of 10-4 - 10-3).
6.3. Increase of fuel burn-up in denatured (Np-U-Pu) fuel cycle
Good neutron-multiplying properties of 238Pu and its neutron predecessor 237Np make it possible to extend substantially time period for continuous reactor operation without refuelings. As a consequence, unauthorized extraction of plutonium from SNF becomes practically unfeasible.
Indeed, under reactor irradiation of (Np-U-Pu) fuel it is occurs the following “non-traditional” transition chain (see Fig. 15): 237Np 238Pu 239Pu ... A successive transition of these nuclides leads to enhancement of multiplication properties.
Actually, as it can be seen in Fig. 16, excess neutron generation per one absorption (eff-1) in 237Np is negative for neutrons of all energy range (excepting fast neutrons), positive for neutrons with En > 1 KeV for 238Pu and, as is known, essential positive one for 239Pu.
So, for (Np-U-Pu)-fuel the nuclides we are dealing with can be characterized as follows (Table 5).
At the same time, during irradiation in reactor core FP accumulation results in growth of neutron absorption. So, these tendencies can be counterbalanced and such fuel will be characterized by stabilized neutron-multiplying properties over long burning-up.
Burn-up calculations for mono-nitride fuel in cell of PWR-type reactor with heavy water as a coolant were performed by using code GETERA. The cell parameters were similar to that of VVER-1000 cell (see Table 6):
|"Burnable poison" nuclide||Moderate fissile nuclide|
(En"/> 1 KeV)
|Well-known fissile nuclide|
|Fuel rod diameter||9.1 mm|
|Thickness of stainless steel cladding||0.4 mm|
|Coolant ( heavy water )||D2O|
|Water volume / fuel volume||1.6|
|Fuel||Mono-nitride ( porosity - 30% )|
|Specific heat generation||110 kW/l|
In Fig. 17 it is shown the dependence of K on fuel burn-up for various fuel compositions. For comparison it is demonstrated also a curve of K for LWR-UOX. It can be seen that, actually, there is possibility to attain fuel burn-up of 25-30%HM ( corresponding residence time is about 20-25 years.). It is worth-while mentioning that, according to papers (Ivanov et al. 1997; Bychkov et al. 1997) presented at the International Conference “GLOBAL’97”, vibro-packed MOX fuel in stainless steel cladding was irradiated in fast reactor BOR-60 (Russia) and it was obtained burn-up of 26% HM on standard fuel assemblies and burn-up of 32% HM in experimental fuel rods. No thermal-mechanical and physical-chemical fuel-cladding interaction was observed in any of the analyzed cross-sections.
The results mentioned above referred to so-called "ultimate" fuel compositions which didn't contain 238U. Actually speaking, these results can be considered as preliminary ones to demonstrate scale of benefit. Undoubtedly, it is needed to analyze impact of wide fuel compositions (including 238U) on stabilized multiplication properties of ultra long-life cores taking into consideration reactor safety in both critical and sub-critical regime of operations.
Anyway, application of ultra long-life core concepts will lead to essential decrease of SNF flow rate, reduction of reprocessing, remanufacturing and shipping operations. It’s a factor for internationalization of Nuclear Energy System fuel cycle. Since fuel cycles been discussed are “rich” with respect to excess neutron generation in CFR, there is no necessity to perform fine purification of fuel being reprocessed. It’s a factor of enhancement of the fuel cycles protection.
Application of NPP with ultra long-life core concepts is expected to be profitable for electricity generation in developing countries which have not improved nuclear technology infrastructure.
7. Mixed (Th – U - Pu) fuel cycle
Plutonium has no its own “fertile” isotope. So, it is impossible to protect plutonium by isotopic dilution, like uranium. Upon exhaustion of cheap 235U resources, the isotope dilution principle can be applied to 233U-238U mixture. So, it seems reasonable to consider the following proliferation resistant fuel - (232Th-233U-238U) . If 238U content is small but sufficient for low content of 233U in uranium fraction, then plutonium build-up may be suppressed.
In other words, the mixed (232Th-233U-238U-Pu) fuel cycle should be studied along with “classical” (232Th-233U) and (238U-Pu) cycles. In both “classical” cycles, fissile materials (233U or Pu) may be figuratively called by “highly-enriched” fuel. In the mixed cycle, on the contrary, fissile isotope 233U is diluted with 238U in uranium fraction, and thus (233U-238U) mixture may be regarded as a “low-enriched” fuel. It is noteworthy that homogeneous mixture of two fertile isotopes 238U and 232Th is a more effective neutron absorber than both separate isotopes. This effect can improve neutron-physical properties of the mixed fuel because it can increase fuel burn-up and thus reduce flow rate of spent fuel assemblies for reprocessing (Kulikov, 2007).
In the mixed fuel cycle, the following double-strata structure may be estimated as an effective and proliferation resistant option (Figs. 18, 19): the top stratum includes full-scale reprocessing of spent fuel assemblies in the International nuclear technology centers with complete incineration of plutonium and minor actinides, the bottom stratum includes a simplified thermal-chemical (DUPIC-type) re-fabrication of fresh fuel with feeding by proliferation resistant 233U. Such a closed nuclear fuel cycle may be equally effective in power reactors of PWR and CANDU types.
So, if fuel contains homogeneous mixture of two fertile isotopes 238U and 232Th, the following new qualities do appear:
Fissile isotope 233U produced in neutron irradiation of thorium is diluted with fertile isotope 238U. So, 233U-238U mixture represents, in essence, a kind of “low-enriched” uranium.
Reduced content of 238U suppresses build-up rate of plutonium.
Mixed fuel is highly effective not only in thermal but in resonant neutron spectrum too because fissile isotope 233U has sufficiently good neutron-multiplying properties both in thermal and resonant neutron spectra.
Fissile isotope 239Pu converts rapidly into heavier plutonium isotopes with low neutron-multiplying properties because of larger c/f. So, plutonium loses its attractiveness as a material suitable for NED manufacturing.
As is known (Benedict et al., 1981), fissile isotope 233U can be additionally protected by its denaturing with 232U because this isotope has the following proliferation-resistance properties (Fig. 19):
232U is an intense source of high-energy -radiation emitted by its decay products.
232U is an intense source of spontaneous neutrons, i.e. spontaneous fission neutrons plus neutrons from (,n)-reactions with light impurities.
232U is an intense heat source from its own -decays and from decays of its daughter products.
Qsf (Spontaneous Fission Neutrons) 1.3 103 n/(s kg 232U);
Q,n (Uranium Dioxide) 15 106 n/(s kg 232U) ( 20 – equilibrium);
232U–leader among U isotopes as a spontaneous neutrons generator.
7.1. Proliferation protection of multi-isotope fuel containing uranium generate and protactinium-uranium mixture produced by Hybrid Fusion Facility
Neutron irradiation of natural thorium in blanket region of Hybrid Fusion Facility (HFF) based on (D,T)-plasma can produce many thorium, protactinium and uranium isotopes. High-energy (14 MeV) thermonuclear neutrons are able to initiate some threshold (n,xn)-reactions leading to intense generation of 230Th, 231Pa, 232U, 233U and 234U. The longer irradiation time, the larger content of these isotopes in irradiated thorium. Content of 232U, for example, can reach a value of several percents.
NFC closure and SNF reprocessing can release huge amounts of fissionable materials: about 210 000 tons of uranium regenerate, RGPu and minor actinides, where uranium regenerate is a dominant fraction. Uranium regenerate may be regarded as a fertile material suitable for further use by nuclear power industry. Uranium regenerate will be released in the amounts large enough to feed NPP of total electric power at the level of 1500 GWe, i.e. 4 times higher that total power of global nuclear energy system today.
Uranium regenerate contains the following isotopes: 232U, 233U, 234U (minor fraction) and 235U, 236U, 238U (main fraction). Uranium produced in thorium blanket of HFF contains only isotopes of minor fraction, i.e. 232U, 233U and 234U. So, if HFF-produced uranium is admixed to uranium regenerate, content of only minor fraction increases. Content of minor fraction can be made comparable with content of main fraction. In the extreme case, minor fraction becomes a dominant one, and NFC shifts towards 233U-based fuel.
Thus, uranium fraction of nuclear fuel represents a mixture of practically all significant uranium isotopes: 232U, 233U, 234U, 235U, 236U, 238U. The following three aspects should be noted. Firstly, main fissile isotopes, 233U and 235U, are accompanied by lighter and heavier uranium isotopes, essential neutron absorbers. Secondly, if 232Th and 231Pa are introduced into fuel composition replacing partially uranium regenerate, then plutonium generation rate is suppressed. Thirdly, the presence of 236U in fuel composition can initiate the chain of isotopic transformations leading to accumulation of 232U, 233U, 238Pu, main isotope for plutonium denaturing (De Volpi, 1982):
236U(n,γ)237U(β-, T1/2 7 days)237Np (n,)238Np (β-, T1/2 2.1 days)238Pu
So, produced plutonium will contain not only 240Pu, usually accompanying isotope to 239Pu in power reactors, but 238Pu too.
In mixed (Th-U-Pu) fuel cycle, plutonium plays an auxiliary role only while 233U is a main fissile isotope, and plutonium content in fuel composition may be diminished. Finally, plutonium could be removed from global nuclear energy system for peaceful utilization in the dedicated nuclear power facilities. The GNEP initiative advanced by the US President (Sokolova, 2008) foresees just a similar option. This aspect represents a special significance from the standpoint of plutonium protection against unauthorized diversion to non-energy purposes (Mark, 1993).
Uranium fraction consisting of practically all significant uranium isotopes from 232U to 238U is, in essence, low-enriched uranium with rather small content of main fissile isotopes (233U and 235U). Isotopic enrichment of such a multi-isotope composition will be a very difficult problem for potential proliferators in the case of its unauthorized diversion.
The presence of α-emitters (mainly, 232U, 233U and 234U) in uranium fraction can initiate physical and chemical processes leading to α-radiolysis of uranium hexafluoride including molecular dissociation with generation of minor fluorides, exchange reactions of recombination and coagulation. These processes can provoke serious violations in the correspondence between the order in masses of uranium isotopes and the order in masses of uranium hexafluoride molecules. This correspondence is a necessary condition for successful uranium enrichment.
So, closed mixed (233U-232Th-238U) fuel cycle can offer the following advantages in comparison with “classical” (238U-Pu) and (232Th-233U) cycles:
Fissile isotope 233U is diluted by fertile isotope 238U in uranium fraction of fuel composition.
238U content in fuel composition may be diminished thus suppressing plutonium production. As a consequence, load of the International centers on plutonium utilization may be reduced.
General conclusion can be defined as follows: fuel of mixed (Th-U-Pu) cycle contains fissile isotopes with upgraded level of their protection against any unauthorized attempts of their diversion to non-energy purposes.
8. Probability analysis of risk reduction in non-energy applications of denatured uranium
Proliferation protection of uranium and uranium-plutonium fuel can be quantitatively evaluated within the frames of the concept developed for risk assessment in authorized applications of nuclear materials. The concept includes some relationships which can be used to evaluate probability for a certain chain of unauthorized actions (UAA) to occur and to evaluate damage from potential NED applications.
8.1. Scenarios for UAA with nuclear materials and models for UAA detection
One of main directions in nuclear non-proliferation ensuring is a formation of inaccessibility conditions for NM against any UAA. This is a main strategic function of MPC&A system at any nuclear-dangerous objects. However, the following questions arise:
What can occur with nuclear materials, if these conditions are violated due to some kind of reasons?
How can we estimate the threats?
What must we do under these accidental conditions? Answers to the questions are related to the threats of NM diversion including the threat of NED manufacturing from diverted NM and its military application. In order to give a correct response to these questions, two, at least, conditions must be satisfied:
We must know how to evaluate the threats of NED manufacturing from diverted NM and their military applications.
We must work out the recommendations on effective countermeasures to be undertaken against any UAA.
An important condition for successful counteraction against the use of diverted NM in NED manufacturing consists in development of the control system over illegal NM trafficking. External UAA monitoring system can apply various strategies of the searching process for potential UAA objects.
Unlike authorized activity, unauthorized actions with NM can be characterized by the following specific features:
Secrecy of unauthorized works. The secrecy level is defined by NM properties and financial expenses to be paid by potential proliferators.
Striving for manufacturing of NED with maximal destructive capability.
Striving for maximal shortening of UAA time which follows from the fact that potential proliferator understands properly the threats from external UAA monitoring system.
These tendencies are the conflicting ones from position of potential proliferator who strives to reach his ultimate purpose. For example, proliferator strives for NED manufacturing with maximal destructive capability but this requires application of sophisticated nuclear technologies for processing of diverted NM. In their turn, nuclear technologies require large financial and long time expenses with appropriate reduction of the secrecy level and rising of the detection probability.
So, when analyzing various scenarios of NM diversion, we presumed a rational behavior of nuclear proliferators, i.e. the proliferator has to accept a certain compromise between his striving for manufacturing of NED with maximal destructive capability and rising of the detection probability caused by application of sophisticated nuclear technologies. In any case rather long chain of technological processes is required to manufacture NED from diverted NM.
8.2. Concept of risk of NM applications in destructive purposes
Potential risk of NM application for NED manufacturing and military use by terrorist groups can be evaluated as follows: R PD, where P – probability of NED manufacturing and military use; D – potential damage from the use of NED for destructive purposes.
Probability P depends on proliferator capabilities, initial and final NM states. The probability may be written in the following form: P P(F, SI → SF ), where F – proliferator capabilities (his material and financial funds, available technological basis); SI – initial NM state (mass, physical form, chemical composition, radioactivity, local position, etc); SF – final NM state (design of NED, local position, chemical and isotopic compositions, radioactivity, etc). Potential damage D depends on final NM state only, i.e. D D(SF ).
Assumption on a rational behavior of nuclear proliferator enables us to think that proliferator will follow the well-grounded plan with proper accounting for the detection probability, if sophisticated nuclear technologies are applied for processing of diverted NM (for example, fine NM purification with removal of all significant impurities, isotopic re-enrichment and so on). So, the risk of NED manufacturing and military use can reach a maximal point either within or on the boundaries of the domain that includes all potential UAA undertaken by nuclear proliferators. The maximal risk and its location in UAA domain depends on the level of external UAA monitoring and on financial capabilities of nuclear proliferators (see Fig. 20).
This circumstance can be used to simplify analysis by using a conservative approach to evaluating the maximal risk of NM usage for NED manufacturing. Within the frames of this approach, probability P for successful completion of UAA chain (from initial state SI to final state SF ) can be replaced by the following maximal evaluation:
8.3. Probability to avoid UAA detection
The following problem is considered below: it is required to search for UAA object which was created on a certain territory. Let’s consider a discrete limited set N consisting of n components each of them may be checked up in one identification step. If the set N contains a closed limited subset S that includes s components and characterizes dimensions of UAA object from the viewpoint of the identification process, then probability for successful identification of any component belonging to the subset S is equal to Pdet s/n. Naturally, non-detection probability per one identification step is equal to Pundet 1 – Pdet 1 – s/n.
Let’s assume that UAA object is not moved and UAA can be unambiguously detected by one identification procedure. If the identification rate V dn/dt is a constant value, and UAA object is a sufficiently concealed object, i.e. s << n, then time dependency of non-detection probability may be presented as follows:
where s / n V, parameter of successful detection, is a product of two multipliers, one of them depends on properties of UAA object only.
If UAA can not be detected for one identification step, or if UAA object moves during the identification process, then a necessity arises to perform a repeat examination of the regions which were checked up previously. In this case, time dependency of non-detection probability may be written in the following form:
8.4. UAA chains. Indicators of the searching process for UAA objects
The following main links can be identified in UAA chains resulting in NED manufacturing from diverted uranium-containing NM: NM theft → chemical and physical reprocessing → isotopic re-enrichment → manufacturing of main NED components → military use of NED.
Each link of UAA chain is defined by its duration ti and mean time interval needed to detect the proliferator 1/λi, which are the functions of the proliferator capability F, changes of NM properties (Si-1 → Si ) and efficiency of the searching process. In general case, detection probability is described by exponential function. So, probability Pi for successful completion of the i-th link without detection and suppression can be written in the following form:
where Pundet,i – non-detection probability of diverted NM at the i-th link; Punsup,i – non-suppression probability for UAA performed by detected proliferator at the i-th link. So, risk of NED manufacturing and military use is defined by the following equation:
UAA object can be detected from the really existing indicators including the indicators related with consumption of energy and water resources in the unauthorized activity. The following indicators can be used in the search for UAA aimed at NED manufacturing and military use:
Emission rate (A).
Resource consumption rate (W).
Capital expenses (К).
When searching the UAA-object being to several independent indicators, then total non-detection probability is a product of partial non-detection probabilities for different UAA indicators, i.e.
where – efficiency of the searching process for appropriate UAA indicators.
Relationship between UAA indicators and detection parameters can be derived from the following models for strategic behavior of nuclear proliferator:
The proliferator creates a new infrastructure for his unauthorized activity. According to equation (2), UAA detection parameter in the random searching process for new resources is proportional to the scale of new resources which were put in operation. In the simplest case, the scale is defined by the resource consumption rate W and capital expenses K. So, in this case: λW W W and λK K K.
The proliferator applies already available infrastructure to perform UAA. Let’s assume that industrial enterprises in the search region consumes resources W in accordance with distribution N(W), and frequency of the inspecting actions Fins(W) depends on the resource consumption rate also. Optimal scheme of the searching process can be found from the following optimality criterion: efficiency of the searching process does not depend on the proliferator strategy, i.e. λ(W)∙TP(W) is a constant value for any W, where TP is proliferation time. Naturally, the larger available resources may be used by nuclear proliferator, the shorter time is needed to modify NM for successful NED manufacturing and military application. So, detection parameter depends on power consumed by a nuclear enterprise. Since power W consumed by nuclear enterprises and proliferation time TP are linked by the energy E required to modify NM as T E/W, the following equation can be written: λ(W) ∙ (E / W) const, or λ(W) const ∙ (W / E) W W.
In both models the emission rate parameter is proportional to the territorial area where abnormal emission level was observed, i.e. λA ~ S(A) ~ R2(A) ~ A, or λA A A. So, each addend in equation (7) can be written as a product of two multipliers:
For example, detection parameter λW is equal to the mean UAA detection frequency on the resource consumption rate W. Of course, the UAA detection frequency depends on the sensitivity of the detecting devices to the resource consumption rate W, or to W-indicator. The sensitivity defines efficiency αW of the searching process.
8.5. Comparative evaluations of external UAA monitoring efficiency and enhancement of inherent proliferation protection
The following problems are considered below: it is required to analyze dependency of metal uranium proliferation protection on uranium enrichment at different efficiencies of the searching process, and it is required to analyze the effects of uranium denaturing on its proliferation resistance, if uranium is denatured by admixing small amounts of 232U that intensifies inherent neutron background. Nuclear proliferator does not resort to uranium re-enrichment up o the weapon-grade level, his main goal consists in a NED manufacturing.
Relative values of uranium proliferation protection were calculated for different efficiencies α of the searching process including the case when α 0, i.e. the case of uranium self-protection.
Mark-Hippel-Lyman model (Mark, 1993) of CFR initiation and propagation was used to evaluate damage from NED manufacturing and military use. CFR parameters were calculated by direct mathematical simulation of neutron multiplication process with application of Monte Carlo code MCNP-4B (Briesmeister, 1997) and evaluated nuclear data file ENDF/B-VI (National Nuclear Data Center, 2001). Mathematical model and algorithm for determination of the model parameters correspond to the approach described in paper (Kryuchkov et al., 2008).
The results obtained in calculations of relative proliferation protection (inverse value to the risk) for different monitoring efficiencies and for different levels of uranium denaturing by 232U are presented in Fig. 21.
The following conclusions can be derived from numerical evaluations of metal uranium proliferation protection:
Measures of external monitoring (outside of MPC&A system) are ineffective ones in comparison with the measures aimed at upgrading of uranium self-protection for highly-enriched compositions.
Efficiency of external monitoring can excel efficiency of inherent self-protection for uranium enriched below 20% 235U.
Upgrading of uranium self-protection by its denaturing, i.e. by formation of internal neutron source, weakly depends on uranium enrichment and provides approximately the same effect in a rather wide range of uranium enrichments.
So, nuclear non-proliferation requires maximal restrictions to be imposed on any transactions of pure HEU while free material must be maintained in a self-protected state produced by isotopic denaturing, for instance.