Research Article |
Corresponding author: Evgeny G. Kulikov ( egkulikov@mephi.ru ) Academic editor: Yury Kazansky
© 2022 Gennady G. Kulikov , Anatoly N. Shmelev, Vladimir A. Apse, Evgeny G. Kulikov.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Kulikov GG, Shmelev AN, Apse VA, Kulikov EG (2022) Comprehensive analysis of proliferation protection of uranium due to the presence of 232U and its decay products. Nuclear Energy and Technology 8(4): 253-260. https://doi.org/10.3897/nucet.8.96564
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For a comprehensive assessment of the protection of uranium against proliferation due to the presence of uranium-232 in it, the authors of the article propose and substantiate an integral protection criterion for this material. The criterion is based on the physical barriers against the proliferation of uranium created by uranium-232, namely: (1) the radiolysis of uranium hexafluoride, which hinders attempts to re-enrich uranium and, as a result, a significant critical mass; (2) hard γ-radiation, which leads to incapacity and death of those who try to handle this material without radiation protection; (3) increased heat release, which disables the components of a nuclear explosive device; and (4) a significant source of neutrons that causes predetonation and thereby reduces the energy yield of a nuclear explosive device. These barriers appear at various stages of uranium handling not only in the indicated order but also act simultaneously, mutually reinforcing one another.
Uranium protection, integral protection criterion for uranium, radiolysis of uranium hexafluoride, critical mass, hard γ-radiation, heat release, neutron source
For various scenarios of the proliferation and theft of nuclear materials that can be used to create a nuclear explosive device (NED), it is desirable to have some criterion that would make it possible to estimate the attractiveness of these materials for such purposes. It is extremely difficult to propose such a criterion, since barriers of different physical nature can stand in the way of the unauthorized use of nuclear materials. When various physical barriers are combined into a single criterion, a difficult task arises to assess the contribution of each barrier to the protection of nuclear materials. Thus, the criterion, although based on physical processes, however, does not represent a specific physical quantity but is essentially an expert assessment of a specialist. Of course, such an assessment can be only approximate. Moreover, depending on the parameters included in the criterion, the contribution of each barrier to it, as well as the attractiveness of different materials, may turn out to be different. In this case, the question may well arise why such an indefinite criterion is needed. Unfortunately, in multidisciplinary and multi-physical problems, when it is necessary to take into account and compare various phenomena, nothing better than an expert assessment has been proposed so far. In other words, if it is necessary to choose a solution, then it is better to be guided by at least an assessment than by nothing. In addition, the assessment is offered by experts in this field of knowledge, and it allows the main patterns to be identified, on the basis of which decisions can be made.
In the United States, two national laboratories – at Los Alamos and Livermore – are engaged in the development of nuclear weapons. In Russia, such centers are VNIIEF (Sarov) and VNIITF (Snezhinsk). The laboratories were established in 1942 and 1952 to develop the world’s first nuclear weapon and to accelerate work on the creation of a thermonuclear bomb, respectively. The criterion for the attractiveness of nuclear materials was developed by Dr. Charles Bathke of Los Alamos National Laboratory (
It is supposed to protect the uranium produced in the thorium blanket of a thermonuclear neutron source, i.e., uranium-233. However, nothing prevents us from considering the more general problem of protecting not only uranium-233 but also uranium-235, which we will do below.
The barriers that may prevent the use of uranium containing uranium-232 are listed below. Firstly, if an attempt is made to enrich uranium-233 (or uranium-235) in centrifuges, an intense source of α-particles of the radioactive decay of uranium-232 (T1/2 = 69 years) and daughter nuclides of its decay chain can cause radiolysis of uranium hexafluoride, which can significantly complicate or even prevent the enrichment process. Secondly, if enrichment is not carried out or significant enrichment cannot be achieved, then a second barrier arises – this is the value of the critical mass of the material, which can turn out to be significant, leading to a large weight and size of the NED, i.e., making it difficult to use this material. Thirdly, when trying to make the NED using this nuclear material, the direct executors of this work will encounter hard χ-radiation present in the decay chain of uranium-232 (Tl-208, Eγ = 2.615 MeV with a yield of 100%), which can lead to exposure of the executors and even to a lethal dose with an instant state of coma. Fourthly, after the NED is assembled, due to the heat release associated with the α-activity of uranium-232 and its daughter nuclides, both the nuclear material itself and its surrounding components (for example, chemical explosives) can overheat and fail. And, fifthly, if the NED is intended to be detonated, then, due to a powerful source of neutrons from spontaneous fission of uranium-232, as well as neutrons arising from (α, n)-reactions on unremovable microimpurities (carbon, nitrogen, oxygen, etc.), the explosion power may be significantly less than the nominal power (up to a value of less than 1% of it). This is a case of so-called “predetonation”.
Note that hard γ-radiation will, of course, irradiate the direct executors at the stage of preparing uranium for enrichment. However, this is not considered as an independent barrier, since in this case uranium-232 will be mixed not only in fissile nuclides (uranium-233 and/or uranium-235) but also in raw materials (uranium-238 and (or) thorium-232), which are contained in the fuel several times more.
The first barrier associated with the radiolysis of uranium hexafluoride actually determines the value of the critical mass of nuclear material, which in turn determines all the other barriers. Therefore, the first barrier cannot be taken into account in the criterion along with the others and it has to be considered separately. Apparently, the authors of (
Let us estimate the fraction of uranium hexafluoride molecules subjected to radiolysis. In this case, we take into account that the energy of one uranium-232 α-particle is Eα = 5.414 MeV, and for the radiolysis of one uranium hexafluoride molecule, it needs to transfer the energy Erad ≈ 111 eV. This means that one α-particle is capable of destroying about 48,700 molecules of uranium hexafluoride, if all the energy of the α-particle is used for this. The contribution of other uranium isotopes to the radiolysis is negligibly small. The number of uranium-232 nuclei in time t is described by the equation of its radioactive decay:
N (U-232, t) = N (U-232, 0)⋅2(–t/T),
where N (U-232, 0) is the number of uranium-232 nuclei at the initial moment of time; T is the period of its half-life (68.9 years). The number of α-particles emitted by uranium-232 per second coincides with its activity:
A (t) = | dN (U-232, t)/dt | = N (U-232, 0)⋅2(–t/T)ln(2)/T = N (U-232, t)⋅ln(2)/T.
Then the fraction of destroyed uranium hexafluoride molecules during the time ∆t is determined by the expression
ε = (Eα/Erad)⋅(A (t)/N (U, t))⋅∆t,
where N (U, t) is the number of all the uranium nuclei. Given that the ratio N (U-232, t)/N (U, t) is the content of uranium-232 in uranium (X), we will obtain the following formula:
ε = ln(2)⋅(Eα/Erad)⋅X⋅(∆t/T).
The time during which uranium is in the form of uranium hexafluoride in the enrichment cascade (∆t) depends on many characteristics of the cascade (the number of centrifuges and their productivity, i.e., the cascade power or the number of separative works that the cascade can perform per unit time) as well as on the amount of enriched material, the degree of required enrichment and the content of the target nuclide in the waste material. All these parameters can vary over a wide range and strongly depend on the degree of development of the centrifuge enrichment technology. In (
Fraction of Destroyed Uranium Hexafluoride Molecules in the Process of Centrifugal Enrichment Depending on the Enrichment Time (∆t) and the Content of Uranium-232 in Uranium (X)
Enrichment time, days | U-232 content in U, % | ||
---|---|---|---|
0.01 | 0.1 | 1.0 | |
1 | 0.01 | 0.13 | 1.3 |
7 | 0.09 | 0.94 | 9.4 |
30 | 0.40 | 4.04 | 40.4 |
It obvious that the enrichment process can be seriously disturbed when the content of uranium-232 in uranium is at the level of 0.1–1% with an enrichment time of the order of a week or more.
According to the IAEA documents (
If the critical mass of uranium turns out to be less than 800 kg, then such material will be considered less protected, and if more than 800 kg, then more protected. Approximately the same critical mass is typical for uranium containing 12% uranium-233. The critical mass is determined by the uranium enrichment and the fissile isotope (see Fig.
The calculations of bare uranium spheres with low enrichment were performed using the TIME26 program (
Hard γ-radiation leads to exposure of personnel handling uranium, who, depending on the time of work with the material, can receive a different dose of radiation. To select the dose value as a barrier against the use of uranium in NEDs, we assume that the personnel are not protected from radiation. Otherwise, this barrier does not work, i.e., it is assumed that the violator of the non-proliferation regime does not have remote technologies available in countries with nuclear weapons for handling highly radioactive materials. Table
Dose of radiation, rem | Human health |
---|---|
100 | Death rate in about 10% of cases within a month |
300–500 | Death rate in about 50% of cases within a week |
600–800 | Death rate in more than 50% of cases within a few days |
1000–5000 | Instant coma, death within half an hour |
Over 8000 | Immediate death |
We are interested in the case when the terrorists will actually not be able to work with the material. This corresponds to a situation where, after receiving a single dose, they almost instantly fall into a coma.
The table shows that this will occur when they receive a radiation dose in the range of 10–50 Sv. Let us choose from this range the radiation dose, say, of 20 Sv as the barrier value. Note that in (Lethal Dose of Radiation), 5 Sv was chosen as such. This was apparently done, because this value is considered a lethal dose. However, this does not mean that, when receiving such a dose, the terrorists will be put out of action. Lethal dose means death in about half of the cases and not immediately after receiving the dose.
In our opinion, the heat release barrier value of 4500 W adopted in (
In (
Since plutonium-238 generates approximately 1⋅106 n/(s⋅kg), and the critical mass of reactor-grade plutonium is about 34 kg, the yield of a neutron source from the critical mass of reactor-grade plutonium with 20% plutonium-240 is 34 kg ⋅ 20% ⋅ 106 n/(s⋅kg) = 6.8⋅106 n/s. It is surprising that the authors of (
In order to combine various physical quantities in a single criterion, it is obvious that these quantities must be included in this criterion in a dimensionless form. To do this, let us divide the characteristics of uranium nuclear material, such as its critical mass, the dose load it creates, heat release, and the neutron generation rate by the corresponding barrier values adopted earlier, namely, by the critical mass of uranium enriched up to 20% in uranium-235 (M0 = 800 кг), dose that brings terrorists into a coma state (D0 = 20 Sv), heat release that disables all the NED components five hours after their assembly (Q0 = 2900 W), and neutron source that leads to NED predetonation (S0 = 8⋅107 n/s). In this case, each characteristic of nuclear material is evaluated by how much it exceeds the accepted safety barrier (when the material is protected) or is below it (when the material is poorly protected).
Unfortunately, the barrier associated with the radiolysis of uranium hexafluoride cannot be directly included in the IPC. However, its influence on the protection of uranium was considered earlier, and this barrier is indirectly taken into account in the IPC through the critical mass of uranium.
It is not advisable to formulate the criterion as the product of the indicated fractions, since, at the initial moment of time, pure uranium-232, without its decay chain, does not emit hard γ-radiation and the dose from the material is zero, which means that the material is not mathematically protected. At the same time, such material may have other barriers. Therefore, it is proposed to form the IPC as a sum of individual barriers:
IPC = M/M0 + d (t)⋅X⋅M/D0 + q (t)⋅X⋅M/Q0 + s (t)⋅X⋅M/S0, (1)
where M is the critical mass of a bare sphere of nuclear material, kg; d (t) is the radiation dose rate in 30 cm from 1 kg of uranium-232 and its daughter nuclides, rem/(h⋅kg); q (t) is the heat release rate from 1 kg of uranium-232 and its daughter nuclides, W/kg; s (t) is the neutron source power from 1 kg of uranium-232 and its daughter nuclides, n/(s⋅kg); X is the content of uranium-232 in uranium. The characteristics d (t), q (t), s (t) depend on the storage time of uranium-232, during which the daughter products of uranium-232 decay are formed and, therefore, change with time.
In (
The breeding properties of uranium-232 are somewhat inferior to those of uranium-233 and uranium-235. However, since the low content of uranium-232 in uranium will be considered, it will have little effect on the value of the critical mass of uranium and will be neglected in what follows. For the same reason, we will also neglect the decrease in the critical mass associated with the decay of uranium-232, although time intervals of the order of the half-life of uranium-232 will be considered.
Fig.
It can be seen that all the characteristics increase sharply in the first years, reaching a maximum by about 10 years, and then gradually decrease. The increase in the characteristics is caused by the accumulation of uranium-232 decay products, the amount of which reaches the equilibrium composition after about 10 years. The subsequent decrease in the characteristics is associated with the decay of uranium-232 itself, which is relatively slower than their growth due to the significant value of the half-life of uranium-232. Note that, at the initial moment of time, the heat release and the neutron source rates, although small, are not equal to zero, since uranium-232 itself generates heat as a result of α-decay and neutrons as a result of spontaneous fission and (α, n)-reactions on light nuclei of unremovable impurities. At the same time, the dose rate at the initial moment of time is equal to zero, since it is determined by the hard γ-radiation of the daughter nuclides of uranium-232, which have not yet been formed from uranium-232.
In the analysis, we will consider various values of the critical mass of a bare uranium sphere: from 15 kg, which corresponds to uranium enriched up to 90% in uranium-233, up to 800 kg, corresponding to uranium enriched up to 20% in uranium-235. As other values, we will consider 50 kg for uranium enriched to 90% in uranium-235 and other intermediate values. Let us consider such additions of uranium-232 to uranium that will provide protection of the material, expressed in the IPC at a level of more than unity for a significant time interval (100 years), and after a short initial decay of uranium for several years.
Fig.
Table
Contributions of Components to the Integral Protection Criterion for Uranium with at Least One-Time Protection for 100 Years
Critical mass of a bare sphere, kg | Uranium-232 content, % | Protection degree at maximum, rel. units | Contributions of components to the integral protection criterion of uranium, % (end-to-end limits) | |||
---|---|---|---|---|---|---|
Mass | Heat | Neutrons | Dose | |||
15 | 1.07 | 2.37 | 1–12 | 9–12 | 42–48 | 36–41 |
50 | 0.307 | 2.32 | 3–33 | 7–11 | 32–47 | 28–40 |
150 | 0.0886 | 2.14 | 9–63 | 4–11 | 18–44 | 15–37 |
450 | 0.0159 | 1.61 | 35–91 | 1–8 | 5–31 | 4–27 |
600 | 0.00682 | 1.35 | 55–96 | 1–5 | 2–21 | 2–18 |
700 | 0.00294 | 1.18 | 74–98 | 0–3 | 1–12 | 1–10 |
Tables
Contributions of Components to the Integral Protection Criterion for Uranium with at Least Two-Time Protection for 100 Years
Critical mass of a bare sphere, kg | Uranium-232 content, % | Protection degree at maximum, rel. units | Contributions of components to the integral protection criterion of uranium, % (end-to-end limits) | |||
---|---|---|---|---|---|---|
Mass | Heat | Neutrons | Dose | |||
15 | 2.16 | 4.77 | 0.4–7 | 10–12 | 45–48 | 38–41 |
50 | 0.634 | 4.72 | 1–19 | 9–12 | 39–47 | 33–41 |
150 | 0.198 | 4.55 | 4–44 | 6–12 | 27–46 | 23–39 |
450 | 0.0522 | 4.01 | 14–74 | 3–10 | 12–41 | 11–35 |
600 | 0.0341 | 3.75 | 20–82 | 2–9 | 9–38 | 8–33 |
700 | 0.0263 | 3.58 | 24–85 | 2–9 | 7–36 | 6–31 |
800 | 0.0204 | 3.40 | 29–88 | 1–8 | 6–34 | 5–29 |
Contributions of Components to the Integral Protection Criterion for Uranium with at Least Three-Time Protection for 100 Years
Critical mass of a bare sphere, kg | Uranium-232 content, % | Protection degree at maximum, rel. units | Contributions of components to the integral protection criterion of uranium, % (end-to-end limits) | |||
---|---|---|---|---|---|---|
Mass | Heat | Neutrons | Dose | |||
15 | 3.25 | 7.17 | 0.5–4 | 10–12 | 46–48 | 39–41 |
50 | 0.961 | 7.11 | 1–14 | 9–12 | 41–48 | 36–41 |
150 | 0.307 | 6.95 | 3–33 | 7–12 | 32–47 | 28–40 |
450 | 0.0886 | 6.14 | 9–63 | 4–11 | 18–44 | 15–37 |
600 | 0.0613 | 6.15 | 12–71 | 3–10 | 14–42 | 12–36 |
700 | 0.0497 | 5.98 | 15–75 | 3–10 | 12–41 | 10–35 |
800 | 0.0409 | 5.80 | 17–79 | 2–10 | 10–39 | 9–34 |
1600 | 0.0102 | 4.40 | 46–94 | 1–6 | 3–26 | 3–22 |
For the case of the highest (five-time) protection and the lowest critical mass (15 kg), the content of uranium-232 is significant, reaching approximately 5% (Tab.
Contributions of Components to the Integral Protection Criterion of Uranium with at Least Five-Time Protection for 100 Years
Critical mass of a bare sphere, kg | Uranium-232 content, % | Protection degree at maximum, rel. units | Contributions of components to the integral protection criterion of uranium, % (end-to-end limits) | |||
---|---|---|---|---|---|---|
Mass | Heat | Neutrons | Dose | |||
15 | 5.43 | 11.97 | 0–3 | 11–12 | 47–48 | 40–41 |
50 | 1.615 | 11.91 | 0–9 | 10–12 | 44–48 | 38–41 |
150 | 0.525 | 11.75 | 2–23 | 8–12 | 37–47 | 32–40 |
450 | 0.161 | 11.20 | 5–49 | 6–11 | 25–45 | 21–39 |
600 | 0.116 | 10.97 | 7–57 | 5–11 | 21–45 | 18–38 |
700 | 0.0964 | 10.78 | 8–61 | 4–11 | 19–44 | 16–38 |
800 | 0.0818 | 10.60 | 9–65 | 4–11 | 17–43 | 14–37 |
1600 | 0.0307 | 9.21 | 22–83 | 2–9 | 8–37 | 7–32 |
2400 | 0.0136 | 7.79 | 39–92 | 1–7 | 4–29 | 3–25 |
Table
Fig.
It should be noted that for materials with large critical masses, a smaller source of neutrons is required as protection against propagation than is included in the integral protection criterion, since it is difficult to accelerate large masses to high velocities or quickly implode them with the creation of significant supercriticality. This leads to an increase in the time during which NED predetonation is possible due to the neutron source, resulting in a decrease in its energy output. Numerical evaluation of this issue requires a separate detailed consideration.
The study was supported by a grant from the Russian Foundation for Basic Research (Agreement No. 19-29-02006/19).