ISSN 10637788, Physics of Atomic Nuclei, 2015, Vol. 78, No. 11, pp. 1274–1286. © Pleiades Publishing, Ltd., 2015. Original Russian Text © V.E. Marshalkin, V.M. Povyshev, 2013, published in Voprosy Atomnoi Nauki i Tekhniki. Seriya: Fizika Yadernykh Reaktorov, 2013, No. 3, pp. 12–29.

Breeding of 233U in the Thorium–Uranium Fuel Cycle in VVER Reactors Using Heavy Water V. E. Marshalkin and V. M. Povyshev Russian Federal Nuclear Center AllRussian Research Institute of Experimental Physics (VNIIEF), pr. Mira 37, Sarov, Nizhny Novgorod oblast, 607188 Russia email: [email protected] Received June 17, 2013

Abstract—A method is proposed for achieving optimal neutron kinetics and efficient isotope transmutation in the 233U–232Th oxide fuel of watermoderated reactors with variable water composition (D2O, H2O) that ensures breeding of the 233U and 235U isotopes. The method is comparatively simple to implement. Keywords: reactors kinetics, light water reactors, heavy water reactors, reactors with mixture of light and heavy water, oxide nuclear fuel, fuel breeding. DOI: 10.1134/S1063778815110113

INTRODUCTION At present, light water reactors, e.g., VVERs, PWRs, and BWRs, and heavy water reactors (PHWRs) are the most advanced, safest, and most widespread reactors in the world. These are uraniumuranium oxide fueled reactors with plutonium bred in an open nuclear fuel cycle. Their operation is characterized by lowefficiency use of produced uranium and breeding of highactivity waste (spent fuel) with a longlived actinide activity and a relatively large amount of plu tonium, ~1% of heavy metal, which is continuously accumulated and arouses anxiety about potential pro liferation of fissile materials to produce nuclear explo sive devices of high destructive power. The solution of this and other problems of modern nuclear power engineering involves use of fast neutron reactors that ensure breeding of active plutonium iso topes and, consequently, practicability of closing the uranium–plutonium fuel cycle. In this case, the over whelming portion of mined uranium can be burned by nuclear fission reactions, which would increase the fuel resource by two orders of magnitude, conse quently decrease the actinide component in radioac tive waste, and stop accumulation of plutonium. How ever, halfacentury efforts of several generations of experts in leading nuclear countries to create a fast neutron reactor to operate in a closed uranium–pluto nium fuel cycle have not been successful. The Super phenix reactor was shut down because of difficulties in securing safe operation, reactors in Japan were shut down, and in the United States the ban on government financing of developments of fast reactors has not been lifted. The Soviet BN350 and BN600 reactors oper ated, and the BN600 reactor continues to operate on highly enriched uranium rather than on MOX fuel,

and thus the intended goal has not been completely met. This negative historical experience in development of fast neutron reactors and closing of the uranium– plutonium fuel cycle forces us to go back and investi gate the feasibility of a closed thorium–uranium fuel cycle. Creation, operation, and the results of repro cessing the spent U–Th oxide fuel of the LWBR in Shippingport [1] inspire further investigations in this sphere. The following possibilities have been proven exper imentally: —cachieving breeding of 233U in U–Th fuel, —using ordinary water as a coolant, and —radiochemical reprocessing of irradiated fuel to separate uranium that contains the radiologically haz ardous 232U isotope. BACKGROUND OF NECESSITY OF STUDYING THE CLOSED THORIUM– URANIUM FUEL CYCLE A proposal to breed 233U for weapons and, after wards, for reactor fuel was put forward almost simulta neously with a proposal to breed 239Pu [2]. However, the possibilities for production of 239Pu and 233U appeared to be qualitatively different. The presence of ~0.7% of the 235U isotope in natural uranium split by neutrons of any energy and the absence of such an iso tope in thorium predetermined a decision in favor of breeding weaponsgrade plutonium. In his letter to the Minister of the USSR Medium Equipment Industry [2], I.V. Kurchatov did not reject the idea of producing the 233U isotope on the basis of thorium for weapons and nuclear power generation, but reasoning from

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Table 1. Values of fission cross sections σf(ε) of the 233U, 235U, 239Pu, 240Pu, 241Pu, and 242Pu isotopes and cross section of radiative capture of neutrons σγ by them, values of the mean number of fission neutrons γ (0.025 eV), and values of the resonance integrals and numbers η of the secondary neutrons per one absorbed neutron Isotopes 233

U U 239Pu 240 Pu 241 Pu 242 Pu 235

γ (0.025 eV) 2.49 2.42 2.87 2.9 2.93 2.93

ε = 0.025 eV

ε > 0.5 eV

ε ⯝ 100 keV

σγ

σf

η

Iγ

If

η

σγ

σf

η

45.5 98.3 269.3 289.5 358.2 18.5

529.1 582.6 748.1 0.056 1011.1 <0.2

2.29 2.07 2.11

137 144 220 8100 162 1115

760 275 301 8.8 570 5

2.11 1.59 1.66

0.24 0.37 0.24 0.32 0.32 0.25

2.28 1.57 1.51 0.05 2.13 0.015

2.25 1.96 2.48 0.39 2.55 0.17

2.16

capacities limited at that time, 1953, preference was given to breeding plutonium, concentrating the effort on uranium rather than thorium. Solutions to scien tific, engineering, and technological problems, including creation of plutonium breeders and technol ogies for separation of metal plutonium, predeter mined the development of the peaceful nuclear power industry on the basis of the uranium–plutonium fuel cycle. In the past five decades, the peaceful nuclear power industry has adapted the weaponsgrade plutonium breeders to generation of energy but has failed to introduce a closed uranium–plutonium fuel cycle despite huge capital investments and efforts of many experts. However, a large amount of reactor pluto nium, ~200 t in Russia, has been bred that can be used to produce 233U on the basis of thorium and change the power industry over to a closed thorium–uranium fuel cycle. Thus, the problem that impeded the develop ment of this fuel cycle in the 1950s has been overcome. A necessary condition of a closed fuel cycle is pos sibility of breeding fissionable nuclei, which, first of all, is determined by the number of the secondary neu trons η resulting from fission of the nuclei per neutron absorbed by these nuclei γ ( ε )σ f ( ε ) η ( ε ) =  , σf ( ε ) + σγ ( ε ) where σf(ε) and σγ are the cross sections of the fission and the radiation capture of a neutron with energy ε, respectively, and γ (ε) is the number of the secondary neutrons per fission event of the nucleus that absorbed the neutron. In Table 1, the values of these characteristics [3] are presented for the isotopes that participate in the ura nium–plutonium and the thorium–uranium fuel cycles at certain values of the incident neutron energy. It can be seen that only two isotopes, 233U and 241Pu, have the value η > 2 at any energy of the neutron that causes their fission. Therefore, only upon neutron induced fission of these nuclei is the number of sec PHYSICS OF ATOMIC NUCLEI

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ondary neutrons simultaneously generated sufficient to maintain the chain reaction, the fission of the next nucleus, and to breed a fissile isotope during the radi ative neutron capture by the fertile isotopes (232Th, 234U, 236U, 238U, 240Pu, etc.), which are characterized by a threshold dependence of the fission cross section but are unable to ensure selfbreeding. Even the main energyreleasing 235U and 239Pu isotopes used in the modern nuclear power industry can maintain the fis sion chain reaction in an intensely operating reso nance region of the neutron energy; however, they cannot ensure selfbreeding. In the uranium–pluto nium fuel cycle, selfbreeding of the 239Pu and 241Pu isotopes is possible only in reactors with a high fraction of fast neutrons, fast reactors, which have been attempted for half a century. In the LWBR [1], a breeding ratio (BR) of 1.013 was achieved in the thorium–uranium oxide fuel through strict economy of the neutrons: (i) absence of burnable poisons and control rods that absorbed neutrons; (ii) use of a closepacked lattice with a limited con tent of the coolant (light water); and (iii) leakage neutrons were absorbed in a thorium blanket with production of 233U. Thus, a possibility of breeding 233U using 232Th as a raw material has been proven experimentally. The wellknown possibility of economy of neutrons by using heavy water, D2O, as the moderator and the coolant instead of light water, H2O, owing to a large difference—of about three orders of magnitude—in the D and H neutron absorption cross sections is used in heavy water reactors. In Fig. 1, the energy dependence of the cross sec tions of elastic neutron scattering by H, D, and Na nuclei is shown that determines moderation of the neutrons when using light water, heavy water, and sodium as the coolant. An increase in the cross sec tions of neutron scattering by hydrogen relative to D can be seen at neutron energy ε ⱗ 3 MeV, which increases by ~30% at ε ⱗ 1 MeV, and at ε ⱗ 100 keV the increase reaches ~4 times and continues with a

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MARSHALKIN, POVYSHEV Crosssection, b

102

1 101 3 2

100 102

103

104

105

106

107 Energy, eV

Fig. 1. Energy dependence of the cross sections of elastic neutron scattering by the H, D, and Na nuclei: (1) H1\3\2\ENDFB 6\NGE\H1 (MAT = 125) (QM = 0, QI = 0); (2) H2\3\2\ENDFB6\NGE\H2 (MAT = 128) (QM = 0, QI = 0); and (3) Na23\3\2\ENDFB6\NGE\Na23 (MAT = 1125) (QM = 0, QI = 0).

further decrease in the neutron energy. The difference in moderation of the neutrons is additionally increased by enhanced drop in the neutron energy in the scattering event on hydrogen relative to deuterium. This large difference in the moderating capacity of H2O and D2O with their practically coinciding physi cal and chemical properties provides a unique possi bility of additional softening of the neutron spectrum during operation of the reactor using heavy water in the initial state, subsequently diluted with light water. In Fig. 2a, the energy dependence of the fission cross sections of 233U, 235U 239Pu, and 241Pu nuclei is presented. The fission cross sections of 233U, 235U, and 241 Pu are characterized by the minimum at ε ⱗ 0.8 MeV; increase inconsiderably, by less than ~20%, at ε ⱗ 2 MeV; and grow much faster with decreasing energy of the neutrons. An especially rapid growth occurs upon nuclear fission by the neutrons of the S wave at ε ⱗ 10 keV. The fission cross section of the 239Pu nucleus is characterized by the minimum at ε ⱗ 100–200 keV; increases considerably, by ~30%, with the neutron energy decreasing to ε ⱗ 2 MeV; slowly increases with the neutron energy decreasing to ε ⱗ 10 keV; and, according to the 1/ ε law, increases with a further decrease in the neutron energy. The fission cross sections of the threshold 234U, 240Pu, and 242Pu isotopes (Fig. 2b) is small below ε ⱗ 100 keV, grows rapidly with the increasing neutron energy, and reaches ~1.6 b at ε ⱗ 2 MeV. The fission thresholds of 232Th and 238U are especially great and these fertile nuclei are split only by fast neutrons with ε ≥ 1.5 MeV.

An increase in the nuclear fission cross sections with decreasing neutron energy, ε ⱗ 0.8 MeV, especially at ε ⱗ 10 keV, and a unique possibility of softening of the neutron spectrum in this energy region by diluting heavy water with light water can enable maintaining the reactor criticality during both burnup of the fis sionable nuclei and production of the neutron absorb ers. Figure 3 presents the energy dependence of the cross sections of the radiative capture by the main fer tile 232Th and 238U isotopes and by bred 234U and 240Pu isotopes and the neutron captures that accompany production of the fissionable 233U and 239Pu and 235U and 241Pu nuclei, respectively. The following can be seen: (i) a rapid decrease in the capture cross section at ε ⲏ 1 MeV with increasing neutron energy; (ii) an almost constant value at an energy 0.1 ⱗ ε ⱗ 1 MeV; and (iii) a growth in the cross section at ε ⱗ 100 keV. Such a dependence of the neutron radiative capture cross section with breeding of fissionable nuclei makes a good contribution to the burnup rate of nuclei by the breeding rate upon softening of the neutron spectrum and can ensure their breeding. For the sake of completeness, we should note that the inelastic scattering of neutrons by heavy nuclei effectively moderates neutrons with energy ε ⲏ 2 MeV and drastically decreases the moderating efficiency with decreasing energy of the neutrons owing to a decrease in the cross section and a decrease in the

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Crosssection, b 5.0 (a) 4.5

2

4.0

3

3.5 3.0

4

2.5 2.0 1.5

1

1.0 0.5 0

104

105

106

2.0 (b)

1.8 1.6 1.4

3

1.2 1.0

4

0.8 1

0.6

2

0.4 0.2 0

104

105

106 Energy, eV

Fig. 2. Energy dependence of (a) nonthresholdfissionable (1—Pu239\3\18\ENDFB6; 2—Pu241\3\18\ENDFB6; 3—U 233\3\18\ENDFB6; and 4—U235\3\18\ENDFB6) and (b) thresholdfissionable (1—Pu240\3\18\ENDFB6; 2—Pu 242\3\18\ENDFB6; 3—U 234\3\18\ENDFB6; and 4—U236\3\18\ENDFB6) uranium and plutonium isotope cross sec tions.

dropped energy. Thus, in watermoderated reactors, the fission spectrum neutrons with energy ε ⲏ 1–2 MeV are effectively moderated under inelastic scattering on heavy nuclei, and at ε ≤ 1 MeV, by water, and espe cially by light water. The neutronic calculations of the neutron kinetics and isotope transmutation in a watermoderated reactor whose critically is maintained by a variable neutron spectrum through dilution of heavy water with light water were carried out using the techniques of [4]. PHYSICS OF ATOMIC NUCLEI

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CALCULATION METHODS AND TESTING PROCEDURE The methods for calculation of the neutronic func tionals and the isotope transmutation in the thermal reactor multiregion cell and the procedure for testing these methods are set forth in detail in [4]. Here, we only point to the main results of testing. The accuracy and the reliability of the calculated results according to the developed methodology are determined by the accuracy and the reliability of func

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MARSHALKIN, POVYSHEV Crosssection, b 1.4 1.2 1.0 0.8 0.6 0.4

2 1

3

4

0.2 0

104

105

106 Energy, eV

Fig. 3. Energy dependence of the cross sections of the radiative capture of neutrons by thorium, uranium, and plutonium isotopes: (1) U238\3\102\ENDFB6; (2) U234\3\102\ENDFB6; (3) Th232\3\102\ENDFB6; and (4) Pu240\3\102\ENDFB6.

tioning of its main programs: the Monte Carlo code and the isotope kinetics code. In [4], the results of calculating Keff for critical assemblies of various geometries and heterogeneities with uranium and plutonium and a relatively highly variable content of hydrogen are reported. The used set of assemblies seems to be sufficiently complete in Table 2. Initial concentration of the isotopes in the cell components (atom/cm3) Isotope 232

Th

238Pu 239Pu 240Pu 241Pu 242Pu

Cr Mn Fe Ni Zr C H O

Average over the cell 6.45 + 21 2.97 + 18 1.83 + 20 7.10 + 19 2.35 + 19 1.46 + 19 1.99 + 20 1.26 + 19 5.20 + 20 2.24 + 20 4.27 + 21 1.60 + 18 2.86 + 22 2.78 + 22

Fuel

Cladding Moderator

2.11 + 22 9.72 + 18 5.99 + 20 2.32 + 20 7.69 + 19 4.78 + 19 8.14 + 19 3.20 + 20 2.11 + 19 1.60 + 20 8.46 + 20 3.76 + 20 4.37 + 22 2.68 + 18 4.80 + 22 4.41 + 22 2.40 + 22

terms of testing the possibility of describing the laws and the specific features of neutron kinetics in a water moderated reactor. The calculated values of Keff are, for most assemblies, in a reasonable agreement, <2σ, with experimental data [4] and the calculated results by other authors, including those obtained via the widely used MCNP code. The efficiency of the isotope kinetics methodology was tested by describing the computational test exper iment proposed by an IAEA working group for deter mination of neutronic functionals for a PWR cell. The results of computations carried out in the world’s lead ing laboratories are reported in [5]. Comparison of the results of our computation on this cell with the reported data is of undoubted methodological interest. The cell geometry has the following parameters: outer fuel radius RF = 0.47 cm, outer fuel cladding radius Rc = 0.54 cm, and outer water radius Rw = 0.85 cm. The fuel is a mixture of thorium dioxide and plutonium dioxide. The values of the partial density of the isotopes and the elements in the cell in terms of atom/cm3 for the fuel, the cladding, and the modera tor zones are reported in Table 2. Mean fuel tempera ture Tf = 1023 K and mean water temperature Tm = 583 K. Specific power in the cell P = 211 W/cm. In [4], the computed results obtained by us are compared with those by other authors over a wide range of functionals. Here, we present only the data on isotope transmutation of plutonium and breeding of Am, Cm, 233U, and 233Pa depending on energy output

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Table 3. Dependence of the isotope transmutation on energy output B (MW d/kg) 239

N(Pu, B)/N(Pu)

N(Am, Cm, B)  N(Pu)

241

N( Pu, Pu, B)  N(Pu, B)

B

233

233

N( U, Pa, B)    239 241 N( Pu, Pu)

Data obtained Data Data obtained Data Data obtained Data Data obtained Data obtained in other labora obtained in other labora obtained in other labora obtained in other labora tories at VNIIEF tories at VNIIEF tories at VNIIEF tories at VNIIEF 0 30 40 60

1 0.425 0.30 0.142

1 0.40…0.43 0.28…0.31 0.12…0.16

0.7 0.409 0.336 0.211

0.7 0.39…0.42 0.29…0.34 0.12…0.23

B of the reactor. In Table 3, the following ratios are given: (i) the current content of all plutonium isotopes N(Pu, B) to their starting content N(Pu); (ii) the current content of fissionable plutonium isotopes N(239Pu, 241Pu, B) to the current content of all plutonium isotopes N(Pu, B); (iii) the current content of Am and Cm isotopes N(Am, Cm, B) to starting plutonium content N(Pu); and (iv) the current content of the bred 233U and 233Pa isotopes N(233U, 233Pa, B) to the starting content of fis sionable plutonium isotopes N(239Pu, 241Pu). Comparing the results obtained by us with those obtained in other laboratories, we can suggest that (i) the obtained values lie within the spread of the values obtained in the world’s leading laboratories and (ii) the entire numerical material corresponds to watermoderated reactors. In all probability, if light water replaced by heavy water and plutonium by uranium, the accuracy of computations will be on the same level. DEPENDENCE OF THE CONTENT IN THE CELL WITH THE 233U–232Th FUEL IN THE CRITICAL STATE ON THE WATER COMPOSITION Substitution of heavy water for light water in the reactor (cell) will be accompanied by (i) decreased neutron capture by the moderator and (ii) hardening of the neutron spectrum and, accordingly, decreased neutron capture by the fission products, a number of actinides, etc. In this case, the criticality of the 233U–232Th fuel will be characterized by the increased mass of 233U and the density of the neutron flux will increase with the same power. In other words, such replacement of the moderator will be accompanied by especially consid erable changes in the neutron kinetics and the isotope transmutation in the cell/reactor core. Therefore, consideration of the dependence of the content of 233U OF

233U

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0 0.035 0.0462 0.0677

0 0.0315…0.046 0.0428…0.0612 0.06…0.087

0 0.384 0.457 0.532

0 0.32…0.4 0.37…0.48 0.42…0.54

required to ensure the criticality of the 233U–232Th fuel in the cell with a changing moderator mixture C = αD2O + (1 – α)H2O is of undoubted interest. These values are presented in Table 4. From Table 4, a sharp dependence of the 233U con tent with a small amount of admixed light water and a weak dependence upon half dilution can be seen. Admixing H2O to D2O at a level of ~5% decreases the specific content of 233U in the fuel by ~12.5 kg/t while maintaining the criticality of the cells/reactor, which corresponds to a dilution rate of ~5 × 10–4 %/h. Admixing of ~20% decreases by ~25 kg/t the value of 233U required to maintain the fuel criticality. Thus, it can be seen that the criticality of the cell/reactor with the 233U–232Th fuel and its operation with burning up of 233U can be maintained by softening the neutron spectrum, which is attained by appropriate dilution of heavy water with light water in the cell/reactor moder ator. In a real reactor, it is practicable to use a blanket with thorium to increase breeding of 233U by absorbing the leakage neutrons. The highest specific content of the 233U isotopes in the 233U–232Th fuel when heavy water D2O used as a moderator in the starting state of the reactor can be considered to be the reactivity margin of the system that does not need compensating by the neutron absorbers. Admixture of light water in the moderator is a way to realize this reactivity margin to maintain the criticality of the cell/reactor (to control the reactor) as the starting 233U burns up as a result of the fission reac tion and the neutron absorbers are produced provided they are efficiently saved. Neutron absorbers have to be used only when the reactor is shut down. The same method can be used at the stage of plutonium utiliza tion during its burning together with thorium to pro duce 233U. Table 4. Calculated values of the specific content of 233U (kg/t) in a cell with the 233U–232Th fuel in the critical state as a function of the dilution rate α of heavy water with light water

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α 233U

(kg/t)

1 45

0.95 0.90 32.5 25.5

0.8 20

0.75 18.5

0.5 16

0 15.1

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Thus, we think that a method has been found for ensuring the optimal neutron kinetics and the effective isotope transmutation in the 233U–232Th fuel of a watermoderated reactor which is characterized by highlevel breeding of the 233U and 235U isotopes and is comparatively simple to implement. RESULTS OF COMPUTATION OF THE ISOTOPE TRANSMUTATION OF THE THORIUM–URANIUM FUEL IN THERMAL REACTORS WITH A VARIABLE WATER COMPOSITION It seems to be practicable to consider the isotope transmutation in this cell starting with heavy water under two conditions: (i) The starting content of the 233U–232Th fuel is brought to the level of the critical state of the cell (K∞ ≈ 1). (ii) The criticality is maintained during irradiation by continuously diluting heavy water with light water. The computations were carried out as applied to the same standard IAEA cell with outer diameters Rw = 0.85 cm and Rw = 0.7 cm. The Standard IAEA Cell In Table 3, relatively deep burnup of the fissionable and 241Pu isotopes with relatively lowlevel breeding of 233U and 233Pa isotopes is illustrated by example of a PWR cell loaded with nonweapons grade plutonium and thorium. However, these values are also overestimated since they were obtained with out considering absorption of neutrons by burnable absorbers and at such high power output values that are unattainable in real PWRs. Nevertheless, utiliza tion of plutonium in the existing watermoderated reactors can and must be considered as an alternative to convert plutonium into 233U. In Table 5, the values of the reaction rates in a cell with the 233U–232Th fuel in the critical state (K∞ = 1) are presented as a function of the irradiation time (power output) with specific power P = 211 W/cm. The total values of reaction rate R and neutron flux density Φ are presented for every time point T as well as their division into groups: <0.625 eV–5.53 keV–0.821 MeV–10 MeV. In this case, the neutron balance is naturally achieved: the production rate is equal to the absorp tion rate. It can be seen that the main reactions, Rf, Rγ(U), and Rγ(Th) prevail and, in the cases where Rγ(Th) ≥ Rf, selfbreeding of 233U can be expected. The constancy of Rf(t) during irradiation is recorded by the reactor power. An increase in the values of Rγ(Th) is possible by means of decreased values of absorption rates Rγ(i) on the rest of the nuclei. The task of increasing the breeding of 233U consists in increas 239Pu

ing the values of Rγ(Th) by means of decreased values of Rγ(i). From the data of Table 5, it can be seen that, in this scenario of the reactor operation, the breeding of 233U in the presence of reactions of parasitic radiative cap ture of neutrons Rγ(Akt) + Rγ(233U) + Rγ(233Pa) + Rγ(frag) + Rγ(water) + Rγ(met) remains sufficient to breed the 233U and 235U isotopes for at least three years. In this case, in the reactions Rγ(233U) and Rγ(233Pa), not only the neutrons are absorbed but also the 233U nuclei and the bred 233Pa nuclei burn up. As a result of the βdecay reaction of Pa(β), the bred 233Pa is directly converted into 233U. With increasing radiation time, the neutron spectrum softens and the flux density value decreases. The loss of the coolant at the initial time point is accompanied by a decrease in the value of K∞ from 1 to 0.69. Table 6 presents the specific values (in kg/t) of the content of the starting and the bred actinides and the products of their decay as a function of the radiation time in a reactor with a periodicity unit, i.e., the cell under consideration with specific power P = 211 W/cm. The content of 233U is determined by the starting loading, breeding, and burnup. The balance of the fissionable nuclei is determined by the difference between their content at the given moment of irradia tion, on one hand, and the content in the starting loading, on the other hand. From the data of Table 6, it can be seen that, at radiation time t ≤ 3 yr, the con tent of 233U + 233Pa + 235U exceeds the starting amount of 233U. The problem is to increase this excess fuel. One can observe burnup of 232Th and production of actinides and their decay products, including 234U, 236U, and 237Np as well as 232U, 231Pa, 228Th, and 208Pb. In this case, the contents of 236U and heavier transura nium elements are characterized by a small portion of burnable 232Th. The content of the 232U, 228Th, and 208Pb characterizes the level of the hard gamma radia tion of the irradiated nuclear fuel. The data in Table 7 demonstrate the dominating burnup of the 233U isotope as a result of the fission reaction, an increase in the fission of the 235U nuclei as they accumulate, and the fission of the 232Th nuclei. Table 8 presents the specific values (in kg/t) of the isotopes that were subjected to the neutron radiative capture and their total amount as a function of the radiation time. One can see not only the amount of isotopes (232Th, 234U, …), the occurrence of the (n, γ) reaction on which is accompanied by breeding of fis sionable nuclei but also the amount of 233U and 233Pa isotopes that burn up with the neutron being absorbed and the wellfissionable 233U isotope leaving the fis sion process. One can see a small portion of the numbers of neu tron radiative capture by 236U and heavier transura nium elements relative to the number of the neutron captures by 232Th.

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Table 5. Values of reaction rates in a cell with the 233U–232Th fuel (K∞ = 1) as a function of the radiation time at specific power P = 211 W/cm T (year) Rf 0 1.31E+13 1.17E+12 1.02E+13 1.31E+12 5.00E+11 0.03 1.31E+13 1.18E+12 1.02E+13 1.28E+12 5.05E+11 0.05 1.31E+13 1.27E+12 1.01E+13 1.25E+12 4.96E+11 0.14 1.31E+13 1.39E+12 1.00E+13 1.21E+12 4.98E+11 0.25 1.31E+13 1.49E+12 9.97E+12 1.18E+12 4.98E+11 0.5 1.31E+13 1.57E+12 9.92E+12 1.15E+12 5.02E+11 1 1.31E+13 1.77E+12 9.77E+12 1.11E+12 4.98E+11 2 1.31E+13 2.20E+12 9.44E+12 1.00E+12 4.94E+11 3 1.31E+13 2.57E+12 9.16E+12 9.17E+11 4.92E+11 4 1.31E+13 3.13E+12 8.70E+12 8.22E+11 4.86E+11

Rγ (Act) 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.52E+10 4.44E+08 1.44E+10 3.84E+08 2.40E+07 3.22E+10 8.48E+08 3.06E+10 7.79E+08 4.91E+07 7.96E+10 2.23E+09 7.53E+10 1.98E+09 1.28E+08 1.46E+11 4.41E+09 1.37E+11 3.66E+09 2.38E+08 2.71E+11 9.15E+09 2.54E+11 7.25E+09 4.87E+08 4.59E+11 1.99E+10 4.25E+11 1.36E+10 9.40E+08 7.81E+11 4.56E+10 7.10E+11 2.34E+10 1.74E+09 1.01E+12 7.70E+10 9.01E+11 3.12E+10 2.48E+09 1.20E+12 1.22E+11 1.04E+12 3.66E+10 3.12E+09

Rγ (232Th) 1.69E+13 3.18E+11 1.26E+13 3.88E+12 2.00E+11 1.68E+13 3.22E+11 1.24E+13 3.81E+12 2.02E+11 1.66E+13 3.50E+11 1.23E+13 3.74E+12 2.00E+11 1.63E+13 3.85E+11 1.21E+13 3.62E+12 2.00E+11 1.60E+13 4.15E+11 1.19E+13 3.54E+12 1.98E+11 1.57E+13 4.34E+11 1.17E+13 3.41E+12 1.99E+11 1.51E+13 4.83E+11 1.12E+13 3.19E+12 1.95E+11 1.37E+13 5.96E+11 1.01E+13 2.82E+12 1.89E+11 1.31E+13 7.05E+11 9.63E+12 2.57E+12 1.88E+11 1.24E+13 8.80E+11 9.02E+12 2.33E+12 1.85E+11

Rγ (233U) 1.89E+12 1.11E+11 1.64E+12 1.42E+11 3.41E+09 1.91E+12 1.12E+11 1.66E+12 1.39E+11 3.40E+09 1.90E+12 1.20E+11 1.64E+12 1.36E+11 3.37E+09 1.90E+12 1.31E+11 1.64E+12 1.31E+11 3.34E+09 1.90E+12 1.41E+11 1.63E+12 1.27E+11 3.29E+09 1.90E+12 1.49E+11 1.62E+12 1.24E+11 3.34E+09 1.89E+12 1.67E+11 1.61E+12 1.18E+11 3.30E+09 1.87E+12 2.07E+11 1.56E+12 1.05E+11 3.21E+09 1.86E+12 2.39E+11 1.52E+12 9.42E+10 3.14E+09 1.82E+12 2.89E+11 1.45E+12 8.29E+10 3.00E+09

Rγ (233Pa) 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.07E+11 7.77E+08 1.01E+11 4.97E+09 1.83E+08 1.88E+11 1.48E+09 1.78E+11 8.56E+09 3.20E+08 3.33E+11 2.88E+09 3.15E+11 1.46E+10 5.64E+08 4.01E+11 3.79E+09 3.79E+11 1.74E+10 6.82E+08 4.22E+11 4.23E+09 4.00E+11 1.79E+10 7.34E+08 3.94E+11 4.57E+09 3.73E+11 1.62E+10 7.00E+08 3.57E+11 5.19E+09 3.38E+11 1.32E+10 6.29E+08 3.42E+11 5.88E+09 3.24E+11 1.15E+10 6.04E+08 3.21E+11 7.04E+09 3.03E+11 1.00E+10 5.74E+08

Pa(β) Rγ (frag) Rγ (water) Rγ (met) Φ 0.00E+00 0.00E+00 2.39E+11 5.46E+11 6.98E+14 4.43E+12 2.54E+14 3.45E+14 9.49E+13 3.80E+12 1.27E+11 2.40E+11 5.35E+11 6.92E+14 4.56E+12 2.51E+14 3.40E+14 9.60E+13 6.68E+12 1.78E+11 2.40E+11 5.29E+11 6.83E+14 4.89E+12 2.48E+14 3.36E+14 9.47E+13 1.18E+13 3.13E+11 2.41E+11 5.25E+11 6.70E+14 5.40E+12 2.42E+14 3.28E+14 9.51E+13 1.44E+13 4.92E+11 2.44E+11 5.06E+11 6.62E+14 5.79E+12 2.39E+14 3.22E+14 9.48E+13 1.53E+13 8.29E+11 2.44E+11 4.96E+11 6.48E+14 6.00E+12 2.32E+14 3.14E+14 9.54E+13 1.48E+13 1.40E+12 2.42E+11 4.75E+11 6.23E+14 6.64E+12 2.21E+14 3.01E+14 9.41E+13 1.35E+13 2.24E+12 2.46E+11 4.31E+11 5.80E+14 8.07E+12 2.02E+14 2.77E+14 9.30E+13 1.28E+13 2.91E+12 2.54E+11 4.07E+11 5.54E+14 9.37E+12 1.91E+14 2.61E+14 9.34E+13 1.22E+13 3.49E+12 2.67E+11 3.90E+11 5.27E+14 1.16E+13 1.79E+14 2.44E+14 9.34E+13

Rf—fission rate of heavy nuclei; Rγ (Act)—rate of radiative capture of neutrons by all actinides excluding separated 232Th, 233U, and 233Pa; Rγ (232Th)—rate of radiative capture of neutrons by the 232Th isotope; Rγ (233U)—rate of radiative capture of neutrons by the 233U isotope; Rγ (233Pa)—rate of radiative capture of neutrons by the 233Pa isotope; Pa(β)—rate of β decay of 233Pa; Rγ (frag)—rate of radiative capture of neutrons by nuclear fission fragments; Rγ (water)—rate of radiative capture of neutrons by water; Rγ (met)—rate of radiative capture of neutrons by the cladding metals and impurities in water; Φ—neutron flux density value determined by the cell power P = 211 W/cm. PHYSICS OF ATOMIC NUCLEI

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Table 6. Specific content (kg/t) of actinides as a function of the radiation time and the power output Radiation time (years) Actinides

0

0.25

0.5

1

2

3

4

Power output (MW d/kg) A

Z

0

3.215

6.429

12.853

25.683

38.496

51.3

237 236 235 234 233 233 232 232 231 228 208

93 92 92 92 91 92 90 92 91 90 82

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 4.50E+01 9.55E+02 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.01E–06 1.25E–04 1.77E–02 5.47E–01 1.58E+00 4.38E+01 9.51E+02 7.91E–04 1.18E–02 6.59E–07 1.21E–08

1.50E–05 9.48E–04 6.69E–02 1.10E+00 1.68E+00 4.38E+01 9.47E+02 2.76E–03 2.34E–02 4.35E–06 1.72E–07

2.29E–04 6.52E–03 2.28E–01 2.11E+00 1.63E+00 4.40E+01 9.39E+02 9.09E–03 4.14E–02 2.86E–05 2.41E–06

2.60E–03 3.94E–02 6.96E–01 3.84E+00 1.49E+00 4.34E+01 9.23E+02 2.70E–02 6.54E–02 1.64E–04 3.03E–05

9.71E–03 1.06E–01 1.25E+00 5.29E+00 1.41E+00 4.20E+01 9.09E+02 4.79E–02 8.17E–02 4.15E–04 1.22E–04

2.35E–02 2.05E–01 1.78E+00 6.55E+00 1.34E+00 4.00E+01 8.96E+02 6.95E–02 9.19E–02 7.60E–04 3.12E–04

Table 7. Specific content (kg/t) of fissioned isotopes as a function of the radiation time and the power output Radiation time (years) Actinides

0

0.25

0.5

1

2

3

4

Power output (MW d/kg) A

Z

235 92 234 92 233 91 233 92 232 90 232 92 232 91 Total

0

3.215

6.429

12.853

25.683

38.496

51.3

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0

2.93E–04 4.18E–04 4.79E–04 3.32E+00 6.61E–02 2.49E–06 1.96E–07 3.38995

2.27E–03 1.70E–03 1.20E–03 6.64E+00 1.32E–01 5.74E–05 8.57E–07 6.77993

1.62E–02 6.64E–03 2.65E–03 1.33E+01 2.62E–01 7.07E–04 3.51E–06 13.55988

1.04E–01 2.47E–02 5.31E–03 2.65E+01 5.16E–01 4.30E–03 1.36E–05 27.11981

2.95E–01 5.21E–02 7.78E–03 3.96E+01 7.64E–01 1.17E–02 3.00E–05 40.68004

6.06E–01 8.73E–02 1.01E–02 5.25E+01 1.01E+00 2.30E–02 5.38E–05 54.24076

The Standard IAEA Cell with a Decreased Water–Fuel Ratio A reserve of enhanced breeding of 233U is decreas ing the water–fuel ratio. In this case, in accordance with the hardened neutron spectrum, the content of 233U in the fuel increases and the parasitic capture of neutrons by water as well as by fission fragments and, probably, by metals and actinides decreases. To evalu ate the impact of these factors, water radius Rw = 0.85 cm was replaced by Rw = 0.7 cm. In Table 9, the computed results similar to those of Table 6 are pre sented; therefore, the comments to Table 6 are also applicable to Table 9. Comparison of the values from Tables 9 and 6 demonstrates the presence of some changes.

With a constant fission rate, the neutron capture rate by Th increases and the neutron capture rate by 233U decreases, which enhances the breeding of 233U. The loss of the coolant at the initial time point is accompanied by a decrease in the value of K∞ from 1 to 0.98. The content of the sum of the 233U + 233Pa + 235U isotopes upon irradiation to T = 8 yr exceeds the start ing content of 233U, which illustrates ensured self breeding of active isotopes at high power output val ues. The main isotope that experiences the radiative capture of neutrons is 232Th. Together with it, the 233U, 234U, 235U, 236U, 231Pa, and 233Pa isotopes are also sub jected to the radiative capture of neutrons.

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Table 8. Specific content (kg/t) of isotopes experiencing radiative capture as a function of the radiation time and the power output Radiation time (years) Actinides

0

0.25

0.5

1

2

3

4

Power output (MW d/kg) A

Z

237 93 236 92 235 92 234 92 233 90 233 91 233 92 232 90 232 91 232 92 231 91 Total

0

3.215

6.429

12.853

25.683

38.496

51.3

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0

8.20E–09 1.49E–06 1.26E–04 1.81E–02 8.20E–05 7.25E–02 4.91E–01 4.21E+00 5.52E–07 2.84E–06 6.05E–04 4.79255

2.58E–07 1.84E–05 9.63E–04 6.99E–02 1.64E–04 1.80E–01 9.81E–01 8.29E+00 2.28E–06 2.39E–05 2.45E–03 9.52371

7.75E–06 2.61E–04 6.76E–03 2.49E–01 3.25E–04 3.91E–01 1.96E+00 1.62E+01 8.64E–06 2.84E–04 9.30E–03 18.80868

3.47E–04 3.09E–03 4.24E–02 8.38E–01 6.37E–04 7.78E–01 3.91E+00 3.10E+01 2.92E–05 1.72E–03 3.15E–02 36.54588

2.04E–03 1.21E–02 1.18E–01 1.65E+00 9.48E–04 1.14E+00 5.83E+00 4.47E+01 5.81E–05 4.62E–03 6.23E–02 53.52596

6.91E–03 3.12E–02 2.36E–01 2.62E+00 1.27E–03 1.48E+00 7.73E+00 5.78E+01 9.43E–05 9.08E–03 9.93E–02 70.00242

RESULTS AND DISCUSSION A reactor can operate under selfbreeding of active uranium isotopes provided that two, in fact, contra dictory conditions are met: (i) a sufficiently large specific content of nuclei fis sionable by neutrons with all energies to ensure the criticality and (ii) guaranteed conditions for the maximum absorption of neutrons by the reproducing isotopes. The thorium–uranium fuel requires an additional reactivity margin to offset the burnup of the 233U nuclei and its delayed reproduction caused by a com paratively long halflife (T1/2 = 27 days) of bred 233Pa nuclei. Use of water of two modifications, heavy D2O and light H2O, with their content ratio continuously vary ing at an acceptable rate during the operation of the reactor offers a unique possibility for meeting all these requirements. Use of D2O at the beginning of reactor operation ensures an increased content of 233U in the fuel and decreased neutron capture by water and heavy ele ment nuclei, including 233U itself, especially with a decreased water–fuel ratio. Continuous burnup of 233U with its reproduction delayed by decay of 233Pa can be compensated by continuously diluting heavy water with light water, maintaining reactor criticality. At the initial stage, the maximum rapid breeding of 233Pa is ensured, which decays into 233U and, ulti mately, makes up for the burnup of the latter. As the fraction of H2O in the water increases, the neutron spectrum in the reactor softens and the para PHYSICS OF ATOMIC NUCLEI

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sitic capture of neutrons by hydrogen, fission frag ments, the bred actinides, and the nuclei of 233U itself increases. This requires an increase in the specific content of 233U in the fuel to maintain criticality and thus ensure increased breeding of 233U. Figures 4 and 5 show the energy dependence of the neutron flux density on the radiation time for IAEA cells with Rw of 0.85 cm and 0.7 cm, respectively. From the figures, one can see that, at the initial stage of irra diation, the neutron flux density in terms of its magni tude and energy dependence approaches the values characteristic of fast reactors. This is especially true as the water–fuel ratio decreases and for heavy water. Admixing light water is accompanied, depending on the radiation time, by softening of their spectrum and a decrease in the neutron flux density. This is what determines changes in the reaction rates, the content of bred isotopes, and the numbers of nuclear fission and radiative capture events observed from the data of Tables 5–9. If water is lost at the beginning of irradiation, the reactivity of the cell decreases and is characterized by values K∞ = 0.69 for the standard cell and K∞ = 0.98 for a cell with a reduced water volume. Probably, the real water–fuel ratio will be characterized by intermediate values of K∞ and the starting loading of 233U. Maintenance of the criticality of the cell by par tially replacing heavy water with light water is accom panied by largescale breeding of the isotope sum 233U + 233Pa + 235U at the beginning of the irradiation and its decrease during further irradiation. The lower the amount of water in the cell, the longer their breed ing is maintained. The burnup as a result of the nuclear

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Table 9. Specific content (kg/t) of actinides in a cell with Rw = 0.7 cm and 233U–232Th fuel (K∞ = 1) as a function of the radiation time and the power output Radiation time (years) Actinides

0

10 (days)

50 (days)

0.25

0.5

1

2

Power output (MW d/kg) A

Z

0

0.352

1.75

3.216

6.432

12.86

25.705

237 236 235 234 233 233 232 232 231 228 208

93 92 92 92 91 92 90 92 91 90 82

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 7.20E+01 9.28E+02 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.16E–12 2.24E–08 7.52E–05 4.67E–02 4.27E–01 7.17E+01 9.28E+02 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.63E–08 4.79E–06 1.89E–03 2.42E–01 1.35E+00 7.10E+01 9.26E+02 5.49E–05 1.56E–03 6.92E–09 5.50E–12

2.42E–07 2.99E–05 6.41E–03 4.54E–01 1.68E+00 7.10E+01 9.24E+02 3.88E–04 8.77E–03 2.15E–07 2.10E–09

4.49E–06 2.33E–04 2.50E–02 9.17E–01 1.81E+00 7.14E+01 9.19E+02 9.37E–04 1.61E–02 8.91E–07 1.79E–08

3.14E–05 1.75E–03 9.17E–02 1.81E+00 1.77E+00 7.24E+01 9.10E+02 2.78E–03 3.13E–02 4.89E–06 2.09E–07

3.94E–04 1.19E–02 3.10E–01 3.45E+00 1.69E+00 7.38E+01 8.94E+02 8.82E–03 5.88E–02 2.86E–05 2.52E–06

10

12

13

Radiation time (years) Actinides

3

4

6

8 Power output (MW d/kg)

A

Z

38.537

51.357

76.963

102.542

128.076

153.573

166.327

237 236 235 234 233 233 232 232 231 228 208

93 92 92 92 91 92 90 92 91 90 82

1.66E–03 3.45E–02 6.03E–01 4.94E+00 1.62E+00 7.45E+01 8.78E+02 5.08E–02 1.38E–01 4.28E–04 1.23E–04

4.51E–03 7.18E–02 9.46E–01 6.31E+00 1.55E+00 7.45E+01 8.62E+02 7.63E–02 1.64E–01 8.07E–04 3.23E–04

1.77E–02 1.94E–01 1.73E+00 8.72E+00 1.40E+00 7.29E+01 8.34E+02 1.27E–01 1.96E–01 1.80E–03 1.17E–03

4.53E–02 3.82E–01 2.57E+00 1.07E+01 1.30E+00 6.96E+01 8.07E+02 1.71E–01 2.11E–01 2.92E–03 2.72E–03

9.16E–02 6.32E–01 3.44E+00 1.24E+01 1.16E+00 6.39E+01 7.83E+02 2.07E–01 2.12E–01 3.97E–03 5.01E–03

1.58E–01 9.40E–01 4.27E+00 1.38E+01 1.06E+00 5.60E+01 7.61E+02 2.35E–01 2.01E–01 4.88E–03 7.94E–03

2.00E–01 1.12E+00 4.66E+00 1.43E+01 1.11E+00 5.20E+01 7.51E+02 2.45E–01 1.95E–01 5.26E–03 9.62E–03

fission reaction increases with the selfbreeding con tinued. A relatively low breeding rate of 236U and heavier transuranium elements in the thorium–uranium fuel, which makes handling of radioactive waste simpler, attracts attention. The content of the bred 232U isotope determines the radiation characteristics of uranium and thorium separated from the irradiated fuel. The content of the 228Th isotope determines the radiation characteristics of thorium separated from the irradiated fuel. During the cooling of the irradiated fuel, 232U decays into 228Th thus increasing the radioactivity of the irradiated thorium.

Consequently, we see that utilization of the tho rium–uranium fuel, heavy water diluted with light water in PWRs, and a closed thorium–uranium fuel cycle provides solutions to the main problems of the modern nuclear power industry. The feasibility of self breeding of the 233U and 235U isotopes and the practi cability of closing the fuel cycle transfers nuclear power engineering from the class of technologies with exhaustible fuel resources to the class of technologies with renewable fuel resources. Deep burnup of 232Th during the fission of 233U and 235U nuclei quantita tively decreases the actinide component in radioactive waste, which makes management of this waste funda mentally simpler. The absence of the normally used

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Flux density, n cm−2 s−1 1015

1285

5

3 2

4

1014

1013 1

1012

1011 −3 10

10−2

10−1

100

101 Years

Fig. 4. Energy dependence of the neutron flux density on the radiation time in a cell with Rw = 0.85 cm: (1) thermal group, (2) second group, (3) third group, (4) fourth group, and (5) total.

Flux density, n cm−2 s−1 1015

5

3

2

4 1014

1013

1012 1 1011 −3 10

10−2

10−1

100

101

102 Years

Fig. 5. Energy dependence of the neutron flux density on the radiation time in a cell with Rw = 0.7 cm: (1) thermal group, (2) second group, (3) third group, (4) fourth group, and (5) total.

reactivity margin, the increased role of the Doppler effect, and delay in breeding of 233U at the stage of decay of 233Pa make the reactor control easier and enhance its safe operation. The physical and chemical properties of the thorium–uranium fuel are more preferable in the nuclear power industry than the sim ilar properties of the uranium–plutonium fuel. A rela tively high content of the radiologically hazardous PHYSICS OF ATOMIC NUCLEI

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232U

isotopes in the bred uranium is an engineering barrier to use of the reactor 233U fuel to manufacture nuclear explosive devices.

CONCLUSIONS The main conclusion is that calculations and theo retical investigations have demonstrated a possibility

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of breeding the 233U + 235U isotopes in thorium–ura nium (232Th–233U) oxide fuel in the VVER pressurized water reactors. Such a possibility is ensured by the neutron nuclear properties of 233U and 232Th and a unique capacity of the water used as the moderator and the coolant of changing the energy distribution of the neutrons by varying its composition in the course of reactor operation. Use of D2O at the initial criticality ensures an increased content of 233U in the fuel and a decreased neutron capture by water and heavy element nuclei, including 233U itself, particularly at a decreased water–fuel ratio. In the case of continuous burnup of 233U and its delayed breeding due to the decay of 233Pa, the criticality can be ensured by continuously diluting heavy water with light water. The calculations show that, at a decreased water– fuel ratio, dilution of heavy water with light water at a level of ~20% proves to be sufficient to maintain the criticality of the PWR cell for about eight years at a specific power of 211 W/cm. Transition from the cell to the real reactor will affect the numerical values but will not change the main conclusions. On the basis of the abovestated information, an application for an invention has been filed.

ACKNOWLEDGMENTS We are grateful to V.F. Kolesov for fruitful discus sions of the results and Yu.V. Frolova for her assistance in performing the numerical computations. REFERENCES 1. L. B. Freeman, B. R. Beadoin, R. Frederickson, et al., Nucl. Sci. Eng. 102, 341 (1989). 2. G. V. Kiselev and V. N. Konev, Phys. Usp. 50, 1259 (2007). 3. T. S. Belanova, A. V. Ignatyuk, A. B. Pashchenko, and V. I. Plyaskin, Radiative Capture of Neutrons (Energoat omizdat, Moscow, 1986) [in Russian]. 4. V. E. Marshalkin, V. M. Povyshev, A. K. Zhitnik, and A. B. Ronzhin, Vopr. At. Nauki Tekh., Teor. Prikl. Fiz., No. 1, 11 (2001). 5. Calculation of the Isotopic Composition, Cross Sections and Fluxes for a Typical PWRCell Loaded mith (PU Th) O2Fuel, as a Function of the Fuel Burnup, Report (IAEA, 1996).

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