Corresponding author: Sergey V. Bedenko (bedenko@tpu.ru)

Academic editor: Yury Kazansky

A computational study has been performed for various options of the thorium reactor core loading. Neutronic studies of fuel have been conducted, its isotopic composition has been calculated, and the alpha emitters and the sources of neutron and photon radiation in the microencapsulated nuclear fuel have been analyzed. The studies had the purpose of developing the methodology used to estimate the radiation characteristics of nuclear fuel with a complex inner structure. Emphasis is placed on calculating the quantitative and spectral composition of the neutrons formed as the result of (a, n) reactions on small- and average-mass nuclei. The ratio of the quantity of the neutrons resulting from the (a, n) reactions to the quantity of the neutrons formed as the result of spontaneous fission has been calculated for fuel with heterogeneous and homogeneous arrangements of fissionable and structural elements. The developed tools will make it possible to estimate the neutron radiation dose, to revise the traditional fresh and spent fuel handling procedures, and to estimate, using the Rossi alpha method, the neutron multiplication factor in deeply subcritical systems. The neutron yield and spectrum were calculated using an analytical model and verified codes such as WIMS-D5B, ORIGEN-APP, SOURCES-4C and SRIM-2013.

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Emphasis in the study is placed on calculating the neutron component of the dispersed nuclear fuel’s radiation characteristics. Neutrons are formed in nuclear fuel due to spontaneous and induced fissions, and as a result of (a, n) reactions on small- and average-mass nuclei (_{sf}_{sf}_{an} formed as a result of (a, n) reactions to the quantity of the neutrons resulting from spontaneous (_{sf}_{f}_{eff}

The purpose of the study is to develop the methodology to calculate the quantitative and spectral compositions of the neutron radiation source with a heterogeneous arrangement of fissionable and structural elements in nuclear fuel. Such studies are conducted with the use of verified codes and dedicated programs. It often turns out during numerical modeling of radiation fields and in development of new procedures and regulations for the _{2}, (U,Pu)O_{2}) for LWR-type reactors, while the use of ORIGEN-S may lead to incorrect results in the event of other reactor types and for fuel other than of the standard type (

The nuclear reactor considered in (_{2} composition used as nuclear fuel. The (a, n) reaction can run in the nuclear fuel of such reactor not only on ^{17,18}O isotopes but also on ^{13}С and ^{29,30}Si contained in the microfuel (Ti_{3}SiC_{2}) and fuel pellet (SiC) coatings. The rated neutron spectrum c_{an}(^{13}С and ^{29,30}Si is much higher than the (a, n) neutron spectrum on ^{17,18}O (^{13}С carbon in the pellet matrix may reach 62.5 %.

For unirradiated dispersed nuclear fuel, c_{an}(_{an}(_{a}(_{a}(^{232}Th,^{239,240,241}Pu) are distributed uniformly within the kernel and create spherically symmetrical radiation.

The irradiated fuel kernel represents a mixture of unburnt Pu and Th isotopes, minor actinides, oxygen, and fission fragments. The initial functions _{a}(_{an}(_{an}(

The energy distribution of neutrons c_{an}(_{an}(_{НM}_{FP}_{a}(

Three types of fuel pellets designated 0817, 1017 and 1200 were used in (_{inf}^{239}Pu and ^{232}Th and on the quantity of the ^{241}Pu and ^{233}U formed. When a fuel pellet of the type 0817 is used, ^{239}Pu burns out rapidly and ^{233}U and ^{241}Pu do not have enough time to accumulate in such quantity as required for maintaining the steady-state fission reaction. Therefore, after 1500 days of operation, the quantity of ^{239}Pu and ^{239}Pu left in the reactor is too small and r_{inf}^{233}U and ^{241}Pu and to longer operation of the reactor. We shall note that the burn-up of ^{239}Pu is practically the same for the pellets of the types 0817 and 1017 amounting to 96 and 97% respectively. Therefore, the option with a fuel pellet of the type 1200 is the best one in terms of lifetime and the involvement of ^{232}Th in the fuel cycle, but an increase in the dispersed phase fraction in such pellet (w_{fuel}^{239}Pu. The analysis of results in (^{239}Pu requires the selection of a fuel pellet of the type 1017 (Fig.

Fuel pellet of the type 1017 (a) and a 2D computational model of the equivalent cell (b).

Further neutronic experiments were conducted in WIMS-D5B, a versatile code for calculating the cell of different reactor types. The WIMS code uses a 69-group system of constants based on the evaluated nuclear database, ENDF/B-VII.0, which makes it possible to calculate fast and thermal neutron reactors.

The geometry module of the WIMS code is not capable to create cells of a hexagonal shape, so the hexagonal НGTRU cell (_{eff}

Computational studies were performed for 30 reactor core loading options differing in composition. The content of heavy metal in the pellet kernels (%) for all of the calculated options is as follows: Pu – 50, ^{232}Th – 50. The isotopic composition of Pu (%): 238 – 0, 239 – 94, 240 – 5.4; 241 – 0.6; 242 – 0. The results of the studies are shown in Fig. _{fuel}^{239}Pu will decrease.

Duration of operation as a function of fraction of dispersed phase.

We shall note that the overall nature of the dependence _{fuel}_{fuel}_{eff}

Thus, we have selected a fuel pellet of the type 1017 with the dispersed phase content of 17 % (see Fig. _{fuel}^{239}Pu burns up to 84.5%, ^{240}Pu to 36.9%, and ^{232}Th to 9.68%.

Irradiated microfuel represents a complex mixture of isotopes, so the functions _{a}(_{an}(_{an}(_{0},

_{0},

where _{0} = l_{t}_{t}

As of the time of the irradiation start, l_{t}_{1} = 1/S_{t}_{1} = 1/0.309 = 3.24 cm, _{01} = 93, and l_{t}_{2} = 1/0.313 = 3.19 cm, _{02} = 91 as of the irradiation cycle end. The average-weighted value of the neutron free path l_{t}_{n}(_{0}, that is, all materials of the fuel pellet (graphite matrix, kernel and coatings) can see one and the same spectrum. The diagram of the dependence of _{0}, _{0} is presented in Fig. _{0}, _{01 and}_{02} (l_{t}_{01.02}, 0)/_{01.02}, 175) = 1.26) and differs greatly from _{04}, _{t}_{t}_{03,04,}_{t}_{t}

Probability density of the neutron interactions within the kernel: 1 − _{01} = 91; 2 – _{02} = 93.

We shall assume that heavy isotopes in the kernel burn out uniformly (_{0}, _{FP}

where

The average energy of excitation for a light-weight fragment (_{1} = 90) is equal to about 10 MeV, and that of a heavy-weight fragment (_{2} = 140) is equal to about 8 MeV. The path length of light-weight fragments in the kernel material as of the end of irradiation will be 4 to 7 μm (_{1} = l/

Spatial distribution of fission fragments within the kernel: 1 – _{1} = 0.023; 2 – _{2} = 1.

The computational studies performed have helped to formulate the following assumptions.

1. The irradiated kernel is a homogeneous mixture of heavy isotopes, fission fragments, and oxygen.

2. The sources of alpha particles, alpha particles as such and fission fragments are distributed uniformly and homogeneously in the kernel.

3. Each source creates isotropic and spherically symmetrical radiation.

4. The functions χ_{an}(_{an}(_{a}(_{a}(

The subject of the study is the HGTRU microfuel and fuel pellet. The configuration of the kernel, the coatings and the fuel pellet is shown in Fig. _{a}(

The fraction of the radiation

where m = 1/l_{0} is the absorption coefficient; and l_{0} is the average particle path.

Relation (2) is valid with any m_{0})_{0} for the particles (neutrons, gamma-quanta) the path of which is described by an exponential distribution. In the event of μ_{0}<<_{0}/(4_{0} <<

^{–1} – 0.0625(l/^{3}, l <<

If the full number of the alpha particles formed in the kernel at the time of the decay is equal to _{a0}, and _{a}(_{a0}(1 − _{a}(_{a}(_{a0}∙_{a}(

The differential energy spectrum of the alpha particles escaping from the kernel surface for a unit of time at a solid angle of 4p is connected with _{a}(

Spectrum of alpha particles escaping from the kernel surface at a solid angle of 4p (1 – irradiated fuel; 2 – unirradiated fuel).

where l_{a}(_{a}(

The path 1/ l_{a}(_{i}_{a}_{i}_{a}(_{i}_{a}_{i}_{a}_{i}_{a}_{i}

Fig. _{a0} in the kernel in an unirradiated fuel pellet (w_{fuel}^{5} a/s/kernel; 99.9% of the alpha particles result from the decay of the ^{239,240}Pu isotopes; the average energy of the alpha particle spectrum is <_{a}> = Sd_{i}_{i}_{a}(5.15) = 7.11%.

For an irradiated fuel pellet, _{a0} = 3.08∙10^{7} a/s/kernel; 99.06 % of the alpha particles result from the decay of the ^{242,244}Сm isotopes; <_{a}> = 5.93 MeV; and _{a}(5.93) = 7.94%. The calculation has shown that the alpha particles formed in unirradiated and irradiated fuel pellet kernels (see Fig. _{a}(

The subject of the study is a hexagonal fuel block of the HGTRU reactor plant (^{–3} m) and seven large-diameter channels (∅24×10^{–3} m) for the coolant. The flat-to-flat dimension of the fuel block is 0.207 m and its height is 0.80 m.

Fig. ^{–3} m and the height is 0.8 m. The fuel channel is filled with pellets of the type 1017.

Energy spectrum of the neutron source: 1 – integral yield of neutrons; 2 – yield of neutrons from spontaneous fission and the (α, n) reaction on ^{17,18}O [(Th,Pu)O_{2}]; 3 – yield of neutrons from to the (α, n) reaction on ^{17,18}O; 4 – yield of neutrons from the (α, n) reaction on^{13}С (RuS).

The integral yield of neutrons _{S} = (_{an}(^{17,18}O,^{13}С) +_{sf}_{fuel}^{3} neutr./s/basis. The contribution of neutrons from the (a, n) reactions on ^{17,18}O of the oxide fuel ceramics is _{an}(^{17,18}O)/_{S} = 41.1% (Fig. ^{13}С is _{an}(^{13}С)/_{S} = 1.18% (Fig. _{an}(^{17,18}O,^{13}С)/_{sf}_{an}(^{17,18}O,^{13}С) = 2.98∙10^{1} neutr./s/cm^{3}. For a homogeneous fuel pellet of a VVER-1000 reactor (fresh UO_{2} with an enrichment of 4.4%), the similar ratio is equal to _{an}(^{17,18}O)/_{sf}_{an}(^{17,18}O) = 1.011∙10^{–3} neutr./s/cm^{3}.

The yield of neutrons _{an} from the (a, n) reactions (see Fig. _{an}(^{18,17}O nuclei of the oxide fuel ceramics during the interaction of the alpha particles resulting from the decay of the ^{239,240,241}Pu and ^{232}Th isotopes. For a homogeneous pellet, _{an} also defines the shape of _{an}(_{an}(_{an}(^{1/2}]^{−1}∙exp[−(^{2}/2^{2}]. For an irradiated heterogeneous pellet, the total yield of neutrons can be approximated by the spectral Watt function c_{sf}^{1/2}, since _{an}/_{sf}_{an} = 8.26∙10^{1} neutr./s/cm^{3} (w_{fuel}

The spectrum of the source of photons resulting from the decay of the ^{239,240,241}Pu and ^{232}Th isotopes was prepared in the Origen-Arp code in a group form and is presented in Fig.

Energy spectrum of the photon source.

The integral yield of photons for w_{fuel}^{10} gamma-quantum/s/basis. Over 99.01 % of photons are formed in the energy region of 10 to 30 keV. The energy spectra of the radiation sources (see Figs

The fuel block investigated in this paper is a subcritical multiplying system with a complex inner structure. The (a,n) reaction in the fuel block of such reactor needs to be considered not only on the oxygen nuclei of the (Th,Pu)O_{2} composition but also on the carbon nuclei contained in the first coating of dispersed microencapsulated fuel. Procedures have been developed to calculate the quantitative and spectral compositions of the neutron radiation from this fuel which made it possible to determine the ratio of the quantity of the neutrons _{an} from the (a, n) reactions to the similar quantity _{sf}

The tools developed as part of the study will make it possible to estimate the neutron radiation dose from the fuel under investigation, to revise the traditional procedures for handling fresh and irradiated fuel, and to estimate the neutron multiplication factor in the НGTRU fuel block using the Rossi alpha method.

The work has been supported by the Russian Scientific Fund. Grant No. 18-19-00136, dated 18.04.2018.

* Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2018, n. 3, pp. 75–87.