Gas-cooled thorium reactor at various fuel loadings and its modification by a plasma source of extra neutrons

Gas-cooled thorium reactor at various fuel loadings and its modification by a plasma source of extra neutrons 1 first-author 2 corresp Corresponding author, bedenko@tpu.ru Corresponding author, bedenko@tpu.ru bedenko@tpu.ru 3 2 2 1 2 Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia National Research Tomsk Polytechnic University, Tomsk 634050, Russia National Research Tomsk Polytechnic University, Tomsk 634050, Russia Russian Federal Nuclear Center–Zababakhin Institute of Applied Physics, Snezhinsk 456770, Russia Russian Federal Nuclear Center–Zababakhin Institute of Applied Physics, Snezhinsk 456770, Russia This work presents the results of computer simulation of neutronic processes in a high-temperature gas-cooled thorium reactor for 30 different options of core loading. To guarantee stable and long-term reactor operation (7–10 years), the quantity of fuel compact dispersion phase and starting fuel composition was selected. It is demonstrated that it is possible in principle to substitute the near-axial recirculation zone of the reactor core by a long magnetic trap with a high-temperature plasma column for generating thermonuclear neutrons. The distribution of neutron yield along the length of the plasma source is also presented. Such a thorium reactor, with a near-axial source of extra neutrons, can be applied for researching thermophysical and neutronic characteristics of dispersion thorium fuel to improve its properties. The results of the work are of great interest from the perspective of future advancement of the thermonuclear power industry, by means of creation of a hybrid installation based on a thorium reactor with a long plasma column as a source of additional neutrons. Low-power thorium reactor Thorium hybrid reactor Nuclear fuel evolution 1 Introduction 1 The study of the physics of low-power high-temperature gas-cooled thorium reactor units (HGTRU) (Tomsk Polytechnic University (TPU), Tomsk) was started three years ago [ 1 1 - 3 3 1-3 ] and its authors have already chosen the most appropriate core configuration and nuclear fuel material composition. The authors have stated [ 1 1 ] that the reactor being studied is capable of operating for no less than 3000 effective days at a power of 60 MWth. Reactors of this type [ 1 1 - 18 18 1-18 ] are considered ideal sources of energy and heat for supplying power to distant regions of the country, and do not require large reservoirs or rivers. In case of bringing such reactors [ 1 1 , 2 2 , 8 8 - 18 18 8-18 ] to a commercially competitive level, they are intended to en sure the power industry basis of such Russian regions. These reactors have several advantages in comparison with other types: high reliability, high efficiency (up to 50%), possibility to use fuel of different types and compositions, short period of construction and equipment delivery, low cost (in comparison with the thermal light-water reactors (LWR) generally used and the BN-type (BN-600, -800) sodium-cooled fast breeder reactor), and simplified management of spent fuel. A special feature of the reactor studied in this work [ 1 1 , 2 2 ] is that it is able to produce heat, electricity, and hydrogen simultaneously, and its core can easily be modified for solving another task [ 19 19 ]. In addition, the reactor power can be adjusted according to regional energy needs. At present, a series of experiments is being carried out at TPU for the purpose of studying the physical properties of new-generation nuclear fuel for HGTRU. Dispersion fuel, which is being developed at TPU, is also a new-generation fuel. It is a fuel material with advanced mechanical, thermophysical, and neutronic properties. As the reactor core has not previously been studied with this fuel in neutronic experiments, it was necessary to create an installation to carry out the required experiments. A special facility intended for studying the neutronic properties of the dispersion (Th,Pu)O 2 fuel was suggested in the capacity of such installation by the employee group of Budker Institute of Nuclear Physics of SB RAS (Novosibirsk, Russia) [ 19 19 ]. This facility is an assembly of fuel blocks, the axial part of which is substituted by a long magnetic trap [ 20 20 , 21 21 ] with high-temperature plasma providing generation of thermonuclear neutrons. The results of computer simulation of neutronic processes in the core of the HGTRU for 30 different loading options are presented in the paper. To ensure stable reactor operation, the fraction of the dispersion phase and the composition of the starting fissionable nuclide were chosen. The possibility to modify the axial part of the core was investigated in accordance with the concept suggested in the works [ 19 19 ]. From the perspective of advancement in the field of fundamental knowledge, the purpose of these researches is to expand and to deepen understanding of the possibilities that are opening up due to the development of thermonuclear energy technologies of the future. From the perspective of solutions to important applied tasks, it can be said that the results will form the basis of organizing the stable operation of HGTRU in a long-term operating cycle (no less than 7 years), with a high burn-up degree of both the thorium and plutonium components of the fuel. 2 Numerical investigation 1 2.1 Computational model of the basic core configuration 2 The core of the HTGRU (red colored area in Fig. 1 Fig. 1 , see [ 1 1 ]) consists of fuel blocks in the configuration of graphite hexagons. The core is surrounded by two rows of graphite hexagons of the same configuration, but without holes for fuel (white colored area in Fig. 1 Fig. 1 ). On the top and bottom the core is also closed with graphite blocks, but here they are laid in just one row. Schematic drawings of the fuel block and its cross-section are presented in Fig. 2 Fig. 2 . One can see that there are cylindrical channels along the length of the block. The fuel block contains 76 channels of small diameter for fuel pellets (indicated in red) and seven channels of large diameter for helium flows (indicated in blue). The width of the graphite fuel block is 0.207 m, and its height is 0.8 m. The width of the graphite block enclosing the core at both the top and bottom is also 0.207 m, but its height is 0.3 m. Microencapsulated fuel (microfuel) for a fuel pellet of HGTRU ( Fig. 3 Fig. 3 , [ 1 1 ]) is a spherical fuel kernel of fissionable material (Th; Pu)O 2 with a diameter of 350 μm, covered successively by layers of pyrolytic carbon (PyC) and Ti 3 SiC 2 . These fuel kernels are dispersed into a graphite matrix of cylindrical fuel pellets ( Fig. 3 Fig. 3 ), which are placed in the fuel block. At the first stage of research presented in the works [ 1 1 - 3 3 1-3 ], three types of fuel pellets with reference designations 0817, 1017, and 1200 were used. The diameters of these fuel pellet types were different: 8.17× <math id="M1"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> , 10.17× <math id="M2"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> , and 12.00× <math id="M3"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> m, respectively. The heights of the fuel pellets (20× <math id="M4"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> m) and thicknesses of the external SiC layer (0.3× <math id="M5"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> m) were equal for all types. The percentage of heavy metal content in all types of fuel pellets were (%): Pu–50, 232 Th–50; and the isotopic compositions of Pu were (wt%) [ 1 1 ]: 238 – 0, 239 – 94, 240 – 5.4, 241 – 0.6, 242 – 0. In the work [ 1 1 ] it is shown that an increase in fuel pellet diameter leads to a decrease in the initial excess of reactivity ρ inf ( ρ inf = ( <math id="M6"><mrow><msub><mi>k</mi><mrow><mtext>inf</mtext></mrow></msub></mrow></math> - 1)/ <math id="M7"><mrow><msub><mi>k</mi><mrow><mtext>inf</mtext></mrow></msub></mrow></math> ) (providing the size dimensions of the reactor fuel block are unchanged). It should be noted that the reactor operation time depends on the initial quantity of Pu, Th in the loaded fuel and accumulated isotopes 241 Pu and 233 U. When a fuel pellet of the type 0817 is used, the isotope 239 Pu burns up quickly and the secondary fuel ( 241 Pu and 233 U) does not manage to accumulate in quantities sufficient for stable and long-term operation of the reactor. Therefore, after 1250 days of reactor operation, there is too little 239 Pu left in the core (less than 2 %), and ρ inf sharply falls to 0. When the fuel pellets of the types 1017 (d ρ inf /d t ≈ 0.011 %/days) and 1200 (d ρ inf /d t ≈ 0.007 %/days) are used, it results in the accumulation of 233 U, 241 Pu in the middle of the fuel cycle, prolonging the core life with steadier reactor operation. It should be noted that for pellets of the type 0817, 1017, and 1200, the burn-up of 239 Pu ( η ( 239 Pu) = ( <math id="M8"><mi>N</mi></math> ( <math id="M9"><mrow><msub><mi>t</mi><mrow><mtext>beginning</mtext></mrow></msub></mrow></math> ) - <math id="M10"><mi>N</mi></math> ( <math id="M11"><mrow><msub><mi>t</mi><mrow/></msub><mi>e</mi><mi>n</mi><mi>d</mi></mrow></math> ))/ <math id="M12"><mi>N</mi></math> ( <math id="M13"><mrow><msub><mi>t</mi><mrow><mtext>beginning</mtext></mrow></msub></mrow></math> )) is 95.5, 96.6 and 92.7%, respectively [ 1 1 ]. This means that loading the core with type 1200 fuel pellets is the most appropriate for achieving maximum fuel core lifetime. Further calculations showed ( Fig. 4 Fig. 4 ) that an increase in the dispersed phase fraction ω f ( ω f = <math id="M14"><mrow><msub><mi>V</mi><mrow/></msub><mi>m</mi><mi>i</mi><mi>c</mi><mi>r</mi><mi>o</mi><mi>f</mi><mi>u</mi><mi>e</mi><mi>l</mi></mrow></math> × <math id="M15"><mi>N</mi></math> / <math id="M16"><mrow><msub><mi>V</mi><mrow/></msub><mi>m</mi><mi>a</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>x</mi></mrow></math> ) of the type 1200 fuel pellet results in a decrease in η ( 239 Pu). Consequently, to provide better burn-up of 239 Pu in the (Th,Pu)-fuel cycle, the type 1017 fuel pellet has to be chosen. Computations were performed for the unit cell of the infinite regular lattice ( <math id="M17"><mrow><msub><mi>k</mi><mrow/></msub><mi>i</mi><mi>n</mi><mi>f</mi></mrow></math> ) in the program WIMS-D5B; the fuel part of the cell was homogenized. The computational model of the cell unit is presented in [ 1 1 ]; the homogenization process is described in the works [ 1 1 , 22 22 ]. WIMS-D5B (Nuclear Energy Agency) is a universal program for computing cells of different reactor types. The WIMS code uses a 69-group system of constants on the basis of the evaluated nuclear database ENDF/B-VII.0 (the basic library has been compiled with 14 fast groups, 13 resonance groups, and 42 thermal groups), which allows computing in reactors of fast and thermal neutrons. In WIMS, the accuracy of the computed functionals is set by the step equal to 10 days. To assess poisoning in the reactor by xenon, the first 2 days are computed separately. 2.2 Neutronic computations for different core-loading configurations 2 At the second stage of the performed computer calculations, the cylindrical reactor cell that is an equivalent of the Wigner–Seitz system is studied. The fuel part of the cell is homogenized; computations are also performed in the program WIMS-D5B. To determine the effective K-factor ( k eff ), an axial and radial geometrical parameter ( B ) is introduced. It is computed considering the transition from the actual core size to the equivalent Wigner–Seitz system. "White mirror" is used as a boundary condition on the side surface of the cell, and "translation symmetry" is used on the cell faces. The computation results of 30 core-loading options with type 1017 fuel pellets are presented in Fig. 5 Fig. 5 . The results of the computer simulation show that the increase in ω f after reaching a level of 17–18% does not lead to any noticeable increase in the reactor fuel campaign T (days) ( Fig. 5(b) Fig. 5(b) ). The increase in ω f also has no effect on the spectrum ϕ Vn ( E ) of the reactor under study ( Fig. 6 Fig. 6 ). It should be noted that it is not possible with existing technologies to synthesize a fuel compact in which ω f is more than 37.5%. Therefore, for further research we chose the type 1017 fuel pellet at ω f = 18%. The 2221 spheres of the microfuel are used in the type 1017 fuel pellets with the dispersed phase fraction at the chosen ω f = 18%. The fuel mass in this pellet is equal to 0.519 × <math id="M18"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> kg (Th, Pu)O 2 , the full core loading = 600.6 kg, 232Th = 246.24 kg, and 239Pu = 231.47 kg. According to the results obtained in WIMS, the reactor with this type of fuel pellets is capable of operating for 3110 effective days at the power P = 60 MWth. The neutron flux density in the core ϕ Vn ( E ) is 8.14× <math id="M19"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>13</mn></mrow></msup></mrow></math> n cm^-2 s^-1. There are 9.41% of the neutrons with energy <math id="M20"><mrow><msub><mi>E</mi><mtext>n</mtext></msub></mrow></math> up to 4 eV, 35.57% of neutrons with <math id="M21"><mrow><msub><mi>E</mi><mtext>n</mtext></msub></mrow></math> from 4 eV up to 183.2 keV, and 55.02% of neutrons with <math id="M22"><mrow><msub><mi>E</mi><mtext>n</mtext></msub></mrow></math> from 183.2 keV to 10.5 MeV ( Fig. 5 Fig. 5 ). In these conditions, ( k eff ) is 1.24, ρ initial 19.35%, and (d ρ /dt) ≈ 6.2 × <math id="M23"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> %/days. The burn-up of 239 Pu is 81.3% ( η = <math id="M24"><mi>N</mi></math> (0) – <math id="M25"><mi>N</mi></math> (3110))/ <math id="M26"><mi>N</mi></math> (0)), and the burn-up of 232 Th is 9.66%. The computation results of fuel isotopic composition evolution N ( t ) are presented in Fig. 7 Fig. 7 and in Table 1 Table 1 . 1 1 Nuclide 1 1 Beginning of life 1 1 Medium of life 1 1 End of life 1 1 239 Pu 1 1 47 % 1 1 26.54 % 1 1 8.81 % 1 1 240 Pu 1 1 2.5 % 1 1 2.84 % 1 1 2.35 % 1 1 241 Pu 1 1 0.5 % 1 1 5.39 % 1 1 6.33 % 1 1 242 Pu 1 1 - 1 1 0.42 % 1 1 1.26 % 1 1 232 Th 1 1 50 % 1 1 47.82 % 1 1 45.17 % 1 1 232 U 1 1 - 1 1 0.00 % 1 1 9.63E-04 % 1 1 233 U 1 1 - 1 1 1.66 % 1 1 2.70 % 1 1 234 U 1 1 - 1 1 0.09 % 1 1 0.28 % 1 1 235 U 1 1 - 1 1 0.01 % 1 1 0.07 % 1 1 242 Cm 1 1 - 1 1 0.00 % 1 1 0.13 % 1 1 244 Cm 1 1 - 1 1 0.00 % 1 1 0.20 % 1 1 Burn-out 1 1 0 1 1 145.5 1 1 304 1 1 (GWt×d/tHM) 1 1 1 1 1 1 1 1 t (days) 1 1 0 1 1 1500 1 1 3130 Additionally, the dependence of concentration changes of isotopes ^231,233Pa on time 231,233 N( t ) were derived, and concentrations of 149 Sm and 135 Xe were analyzed. The data on ^231,233Pa, 233 U, 149 Sm, and 135 Xe concentrations allow the evaluation of the required intensity <math id="M27"><mrow><msub><mi>I</mi><mtext>n</mtext></msub></mrow></math> ( t ) of neutron emission from a thermonuclear reaction in a plasma column. By varying the percentage of D-T reactions in comparison with D-D reactions in the plasma column, one can change <math id="M28"><mrow><msub><mi>I</mi><mtext>n</mtext></msub></mrow></math> within the range <math id="M29"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>13</mn></mrow></msup></mrow></math> n cm^-1 s^-1 to 2 × <math id="M30"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>14</mn></mrow></msup></mrow></math> n cm^-1 s^-1. That should provide the condition <math id="M31"><mrow><msub><mi>k</mi><mrow/></msub><mi>e</mi><mi>f</mi><mi>f</mi></mrow></math> = constant during both the first days of operation of the facility and the whole fuel irradiation cycle. The neutronic computation performed in WIMS-D5B was repeated in the program MCU5TPU [ 23 23 ]. The results of these computations are presented in Fig. 8 Fig. 8 . The code MCU5TPU was developed at the National Research Center Kurchatov Institute (Russia), and is used for simulation of particle transfer by the Monte-Carlo method in any reactor. MCU uses its own nuclear data bank, MCUDB50 [ 23 23 ]. If one creates a large initial reactivity excess ρ initial (as demonstrated in Fig. 8 Fig. 8 ) then a burnable absorber can compensate for this excess. For example, to compensate for the large ρ initial in the LWR and BN-type reactors, Gd_2O_3, Er_2O_3, and B_4C are used. In this case, daughter nuclides formed as a result of radiation capture reactions on 157 Gd, 167 Er, and 10 B do not have a significant impact regarding further neutronic processes in the core. In solving the task of choosing the appropriate burnable absorber, it is of interest to search for nuclides, the daughter nuclides of which can have a favorable effect on the development of a self-supporting chain reaction. The authors of the works [ 24 24 , 25 25 ] suggested using PaO_2 as a burnable absorber. A peculiar feature of isotope 231 Pa is that its transmutation leads to the formation of 232 U and 233 U, and isotope 233 U is a fissionable material. This means that isotope 231 Pa performs the functions of a burnable absorber and a source of a new fissionable material. However, 231 Pa production in the amounts required for implementation of the concept suggested in the work [ 24 24 ] is rather challenging. That said, 231 Pa can be effectively used in small amounts as a burnable absorber, for example, in a high-temperature reactor core. In the work [ 25 25 ] it is suggested to use 240 Pu as a burnable material. In our case ( Fig. 7 Fig. 7 ), the presence of 240 Pu in the fuel composition results in significant accumulation of 241 Pu, which can be well fissioned by epithermal neutrons, and its nuclear concentration 241 N( t ) exceeds the nuclear concentration of 233 U by more than 2.5 times across the whole fuel campaign. The computation showed that 241 Pu and 233 U specify the dependence type of <math id="M32"><mrow><msub><mi>k</mi><mrow/></msub><mi>e</mi><mi>f</mi><mi>f</mi></mrow></math> ( t ) and provide steady reactor operation for 8.5 years. The proposed usage of 231 Pa becomes appropriate if we compare the dependency of absorption cross-sections abs ( E ) on the neutron energy E for traditional neutron absorbers with the dependency for 231 Pa ( Fig. 9 Fig. 9 and Table 2 Table 2 ). It is seen in Fig. 9 Fig. 9 (ENDF/B-VII.I) that the neutron-absorption cross-section on the nuclei of 157 Gd, 167 Er, and 10 B for the neutron energy range 0.3-10 6 eV are on a level close to the absorption cross-section of the nuclei of 231 Pa. 1 1 Nuclide 1 1 abs ( E average ) barn 1 1 231 Pa 1 1 0.742 1 1 10 B 1 1 0.656 1 1 167 Er 1 1 0.186 1 1 157 Gd 1 1 0.188 1 1 240 Pu 1 1 0.143 If one examines Fig. 6(b) Fig. 6(b) , one can come to the conclusion that about 91% of neutrons in the core of the reactor have an energy more than 4 eV. The average value ( E average ) on the neutron energy spectrum shown in Fig. 6(a) Fig. 6(a) is 5.539 × <math id="M33"><mrow><msup><mrow><mn>10</mn></mrow><mn>5</mn></msup></mrow></math> eV. The absorption cross-sections abs ( E average ) of the nuclei of absorbers and 231 Pa are presented in Table 2 Table 2 for abs ( E average ). It can be seen that 231 Pa is likely to be a substitute for 10 B and some other traditional absorbers. The influence of 10 B on the neutronic properties of a reactor core with epithermal and fast neutron spectrum was analyzed by the authors in [ 1 1 ]. In the loading option discussed above ( Fig. 8 Fig. 8 ), the initial reactivity excess is compensated for by the isotope 240 Pu. Its content (wt%) in the fuel increased from 5.4% up to 9%; the content of 239 Pu decreased by 3.6%, correspondingly. The use of 240 Pu in HTGRU does not lead to any undesired increase of reactivity in the middle of the fuel cycle, as it happens in the core of the pressurized water reactor (PWR) [ 26 26 ]. Using 240 Pu, ρ initial was reduced from 19.35% to 11.51%, and (d ρ /d t ) decreased by a factor of 1.51. According to the concept suggested by the authors in the work [ 19 19 ], the core of HGTRU, the axial part of which is substituted by a long magnetic trap with high-temperature plasma, starts up from the subcritical state ( <math id="M34"><mrow><msub><mi>k</mi><mrow/></msub><mi>e</mi><mi>f</mi><mi>f</mi></mrow></math> = 0.95). To transfer the core into the subcritical state, it is enough to cover the surfaces of fuel pellets with a 13 μm thick layer of ZrB_2. 2.3 Computational model of the axial zone of the core; specific neutron yield of fusion plasma source 2 Currently, two types of neutron source for continuous operation in a fission–fusion hybrid energy system seem to be the most promising. The first type is an accelerator-driven system (ADS). This type is the most studied [ 30 30 , 31 31 ]. In this work, we focus our studies on the second type – a neutron source based on fusion plasma in a long magnetic trap. The schematic drawing of the facility intended to study nuclei fuel properties in the operation of such a plasma neutron source is presented in Fig. 10 Fig. 10 [ 19 19 ]. The axial zone of the reactor core is substituted for a cylindrical vacuum chamber that contains high-temperature plasma generating high-energy neutrons by D-D and/or D-T fusion reactions. To inject heating neutral beams into the plasma, a special chamber is attached to this cylindrical chamber. A magnetic field in these two adjoined vacuum chambers containing the plasma provides heat isolation of this plasma from the chamber walls in a radial direction. Heat isolation of the plasma along the magnetic field lines is provided by the multimirror sections of the magnetic field, which are adjacent to the ends of the two adjoined chambers of high-temperature plasma. The chamber for fusion neutron generation in the axial zone of the core has the required length of 3 m. The total length of the two adjoined chambers of high-temperature plasma is approximately 7 m. The total length of the whole facility is about 12 m. Distribution of the magnetic field induction along the axis of the two adjoined chambers with high-energy ions (the length is approximately 7 m) was chosen in the paper [ 20 20 ] from considerations of the maximum neutron yield in the core plasma region upon the condition of good homogeneity of radial neutron flow. The choice of plasma parameters in the long magnetic trap was made according to the provided computation results. The results of the calculation [ 20 20 ] for the distribution along the textitz-axis of the specific neutron yield per linear centimeter of the plasma column in the case of D-D reaction is plotted in Fig. 11 Fig. 11 . A red bar located on the interval of z -coordinates from 200 cm to 500 cm marks the part of the column that is situated inside the reactor core. One can see in Fig. 11 Fig. 11 that for the distribution of magnetic field and plasma column parameters chosen in [ 20 20 ], the specific neutron yield changed insignificantly in the plasma column part that was placed in the core. Nevertheless, non-homogeneity of plasma distribution along the z -axis may be taken into consideration in our simulations. As examples of the possibility to analyze various plasma distributions along the z -axis, the specific neutron yields of plasma neutron sources with cylindrical and conical shapes of the plasma column were analyzed. In numerical simulation, it was considered that the plasma column is a volume source of monoenergetic neutrons with isotropic velocity distribution at the point of their origination. In accordance with the results of the paper [ 20 20 ], injection of a 100 MW deuterium beam will produce high-energy sloshing ions with density up to 1.5 × <math id="M35"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>14</mn></mrow></msup></mrow></math> cm -3 . In this case, the specific emission of neutrons from a volume unit due to the D-D reaction is 1.76 × <math id="M36"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>12</mn></mrow></msup></mrow></math> n cm^-3 s^-1 in the core region, and the specific neutron yield rate is 6.00 × <math id="M37"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>13</mn></mrow></msup></mrow></math> n cm^-1 s^-1. The power of 2.45 MeV neutrons will be about 20 kW in the whole device and about 6 kW inside the core region. Two options are suggested to increase the neutron yield. The first is to add tritium and produce plasma with the percentage 50% D and 50% T isotopes. The simple estimation for this condition shows that neutrons with power of 14.1 MeV will generate up to 2.5–3 MW in the whole device and up to 0.8–0.9 MW inside the core region. If the injection power of neutral beams is reduced 10 times down to 10 MW, the power of D-T neutrons will decrease by approximately two orders of magnitude and will have values close to the basic D-D scenario. The second option is to improve plasma confinement by multimirror plugs, while the basic calculation assumes ordinary mirror configuration. This option could increase the neutron yield by several times, but its applicability is still contingent on experimental proofs. We calculated a spatial neutron flux distribution ϕ Zn ( z ) over the z -axis for the external surface of the copper winding of the plasma neutron source for both cases: 50% T with 50% D, and 100 % D at the same specific neutron yield 6.00 × <math id="M38"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>13</mn></mrow></msup></mrow></math> n cm^-1 s^-1. The neutron flux distributions for cylindrical and conical shapes of the plasma column were analyzed. The diameter of the cylindrical plasma column was 17 cm. For the conical column shape, its diameter decreased from 17 cm down to 13 cm over a length of 300 cm. As one can see in Fig. 10 Fig. 10 , a copper winding covers the external surface of the vacuum chamber. This copper winding has thickness 5 cm and is divided from the plasma column by the vacuum chamber wall, of thickness 4 mm. Considering the thickness of the winding, the external surface of the plasma neutron source has a diameter that varies from 22 cm to 18 cm for the conical plasma column shape. This diameter is 22 cm for the cylindrical shape. The neutron flux ϕ Sn ( E ) on the external surface of the copper winding was generated by usage of the program in the energy group structure ABBN-78 (of 28 energy neutron groups). Spatial neutron flux distribution ϕ n ( z ) with respect to the z -axis of the facility and its radius y was obtained by placing a computational grid with a size of 1000 by 1000 cells along the height z ( ϕ Zn ( z )) and radius y ( ϕ Yn ( z )) of the model. The presented results were obtained in simulations performed using the programs MCNP5 (ENDF/B-VII.0) [ 27 27 ], Serpent 1.1.7 (ENDF/B-VII.0) [ 28 28 ], and PRIZMA (ENDF/B-VII.I) [ 29 29 ]. The study using the program PRIZMA was performed at the Zababakhin All-Russian Scientific Research Institute of Technical Physics (http://www.vniitf.ru/o-vniitf). The classic Monte-Carlo method was used to solve the task in the frame of the MCNP, Serpent, and PRIZMA applications. In the simulations, we considered the influence of copper coils on the propagation of the neutron fluxes in the volume of the stand. In accordance with the results of detailed computer simulations and the information about usage of copper conductors in fission reactors, we concluded that our magnetic field coils could be operated without being destroyed during the operation cycle of our fission–fusion stand. 3 CALCULATION DATA AND DISCUSSION 1 The calculation data of the neutron flux density distribution ϕ Zn ( z ) on the external surface of the plasma neutron source for cylindrical (blue and green) and tapered (conic) plasma (red) are presented in Fig. 12 Fig. 12 for both cases: 50% T with 50%D, and 100% D. For these calculations, we applied the computation model and program code in the frame of usage of MCNP5. We used three different codes to calculate the data of the neutron flux normalized spectrum ϕ Sn ( E ) (the fraction of neutrons escaping in the direction of the core from 1 cm 2 of the facility side surface per second) on the external surface of the facility. As one can see in Fig. 13(a) Fig. 13(a) , these three codes give almost identical results. The maximum discrepancy between MCNP5 and Serpent 1.1.7 is observed in the 26th energy group (that is, for neutrons in the energy range <math id="M39"><mrow><msub><mi>E</mi><mtext>n</mtext></msub></mrow></math> from 6.5 to 10.5 MeV) and is -6.42 %. The maximum discrepancy between MCNP5 and PRIZMA is +3.35 % (the 26th energy group). The discrepancy in the calculation data is conditioned by the use of the nuclear data from libraries of different revision and by the peculiarities of their preparation. It can be seen in Fig. 11 Fig. 11 that ϕ Zn ( z ) greatly depends on the plasma column shape, but ϕ Sn ( E ) differs significantly only in the 28th group ( Fig. 13(b) Fig. 13(b) ) in the energy range of <math id="M40"><mrow><msub><mi>E</mi><mtext>n</mtext></msub></mrow></math> from 14.0 to 14.5 MeV. Therefore, to determine the power distribution of D-T neutrons it is possible not to consider plasma non-homogeneity and neutron flux in the radial direction. The calculation data performed in Serpent ( Fig. 14 Fig. 14 ) showed that the probability density of neutron interactions of ( n, xn ) type was at a maximum in steel constructional elements and in inner layers of the copper solenoid ( Fig. 14 Fig. 14 , red color). In the peripheral layers of the copper winding, the ( n , 2 n )-reaction is almost absent ( Fig. 14 Fig. 14 , blue color). If, however, the layer of BeO is placed on the external surface of the solenoid, D-T neutrons from the 23rd to 28th groups (neutrons with <math id="M41"><mrow><msub><mi>E</mi><mtext>n</mtext></msub></mrow></math> from 2.5 to 14.5 MeV) contribute to the production of neutrons in the channel of ( n , 2 n ) reactions on nuclei of isotope 9 Be. In a fixed-source MCNP problem, the net multiplication M is defined to be unity plus the gain <math id="M42"><mrow><msub><mi>G</mi><mrow/></msub><mi>f</mi></mrow></math> in neutrons from fission, plus the gain <math id="M43"><mrow><msub><mi>G</mi><mi>x</mi></msub></mrow></math> from no fission multiplicative reactions. As the multiplication M in the facility is conditioned mainly by ( n , 2 n ) reactions, in the case of D-T plasma M = 1 + <math id="M44"><mrow><msub><mi>G</mi><mrow><mi>n</mi><mn>,2</mn><mi>n</mi></mrow></msub></mrow></math> . In the facility with D-T plasma of cylindrical and conical shape, M is equal to 1.2742 and 1.2728 (MCNP5), respectively. In addition, the contribution of ( n , 2 n )-reactions to multiplication is 21.3%. In the case of D-D plasma, M is 1.000 (MCNP5). The total escape of D-D neutrons from the facility is 80.4%, while neutron escape from the side and end surfaces are 66.5 ( ϕ Zn = 6.67 × <math id="M45"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>12</mn></mrow></msup></mrow></math> n cm^-2 s^-1 and 13.9% ( ϕ Yn = 1.39 × <math id="M46"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>13</mn></mrow></msup></mrow></math> n cm^-2 s^-1), respectively. The total escape of D-T neutrons from the facility is 98.5%, of which neutron escape from the sides and end surface is 83.6 ( ϕ Zn = 8.39× <math id="M47"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>12</mn></mrow></msup></mrow></math> n cm^-2 s^-1) and 14.9% ( ϕ Yn = 1.49 × <math id="M48"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>13</mn></mrow></msup></mrow></math> n cm^-2 s^-1), respectively. It should also be mentioned that thorium in the first row of the assembly transmutes into 231 Pa under the influence of D-T neutrons from the 26th, 27th, and 28th groups due to ( n , xn )-reactions. Therefore, the core provides extra neutrons and fissionable isotope 233 U. To compare the neutron spectrum ϕ Sn ( E ) ( Fig. 13 Fig. 13 ) with the spectrum ϕ Vn ( E ) ( Fig. 6 Fig. 6 ) correctly, ϕ Sn ( E ) was derived in the energy group structure WIMS69 (WIMS-D5B), and an additional neutron group with energy from 10.5 to 14.5 MeV ( Fig. 14 Fig. 14 ) was used. The neutron flux distribution functions <math id="M49"><mrow><msub><mrow/><mtext>n</mtext></msub><mo stretchy="false">(</mo><msub><mi>E</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true"><mrow><msubsup><mo>∫</mo><mn>0</mn><mrow><mi>E</mi><mi>i</mi></mrow></msubsup></mrow></mstyle><msub><mi>ϕ</mi><mtext>n</mtext></msub><mo stretchy="false">(</mo><mi>E</mi><mo stretchy="false">)</mo><mtext>d</mtext><mi>E</mi><mo>/</mo><mstyle displaystyle="true"><mrow><msubsup><mo>∫</mo><mn>0</mn><mi>∞</mi></msubsup></mrow></mstyle><msub><mi>ϕ</mi><mtext>n</mtext></msub><mo stretchy="false">(</mo><mi>E</mi><mo stretchy="false">)</mo><mtext>d</mtext><mi>E</mi></mrow></math> presented in Fig. 15 Fig. 15 were derived in the same energy group structure as the functions ϕ Vn ( E ) ( Fig. 15 Fig. 15 , curve 1) and ϕ Sn ( E ) ( Fig. 15 Fig. 15 , curve 2). In accordance calculations, neutrons escaping from the side surface of the facility ( Fig. 16 Fig. 16 , curve 2) can be divided into four main group with different energy <math id="M50"><mrow><msub><mi>E</mi><mtext>n</mtext></msub></mrow></math> . The percentages of these groups of neutrons are as follows: 2.03% – <math id="M51"><mrow><msub><mi>E</mi><mtext>n</mtext></msub></mrow></math> from zero to 4 eV (thermal neutrons), 30.19% – <math id="M52"><mrow><msub><mi>E</mi><mtext>n</mtext></msub></mrow></math> from 4 eV to 183 keV (epithermal neutrons), 50.11% – <math id="M53"><mrow><msub><mi>E</mi><mtext>n</mtext></msub></mrow></math> from 183 keV to 10.5 MeV, and 17.69% – <math id="M54"><mrow><msub><mi>E</mi><mtext>n</mtext></msub></mrow></math> from 10.5 to 14.5 MeV (fast neutrons). In the reactor core ( Fig. 16 Fig. 16 , curve 1) there are 9.41% thermal neutrons, 35.57% epithermal, and 55.02% fast neutrons. For the data presented in Fig. 15 Fig. 15 , the specific neutron yield is I n = 6.0 × <math id="M55"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>13</mn></mrow></msup></mrow></math> n cm^-1 s^-1 ( Fig. 11 Fig. 11 ). To achieve the possibility of exactly correct usage of neutron emissions from the plasma source for studying neutronic and thermal-physical properties of thorium–plutonium fuel in the core of HGTRU, we have to achieve a specific neutron yield on the level I n = 1.8 × <math id="M56"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>14</mn></mrow></msup></mrow></math> n cm^-1 s^-1 ( Fig. 15 Fig. 15 , curve 3). This is three times large than the 6.0 × <math id="M57"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>13</mn></mrow></msup></mrow></math> n cm^-1 s^-1 ( Fig. 15 Fig. 15 , curve 2) that was already achieved in simulation for the D-D plasma column. This increase in neutron yield will be realized in the case of replacing a certain quantity of deuterium with tritium in the plasma column, without changing any other parameters of the plasma. In the case of the 50% T with 50% D in the plasma column with other plasma parameters unchanged, the specific neutron yield has to be 25 times greater. 4 CONCLUSION 1 Computer simulation of neutronic processes in the core of a high-temperature gas-cooled thorium reactor for 30 different options of core loadings was performed in the frame of our work. The quantity of fuel compact dispersion phase and the composition of fissionable nuclides were examined. Production of extra neutrons by the means of thermonuclear reactions occurring in high-temperature plasma and of ( n , xn )-type reactions was analyzed. The possibility of applying a plasma D-T source of neutrons to modify the near-axial region of the HGTRU core was demonstrated. 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DOI: 10.1016/j.nme.2016.04.012 http://doi.org/10.1016/j.nme.2016.04.012 (2016) IFMIF, the European-Japanese efforts under the Broader Approach agreement towards a Li(d,xn) neutron source: Current status and future options The authors thank Dr. S. Sinitsky for the schematic design of the copper winding in the region of the reactor core. 10.1007/s41365-019-0707-y This work was supported by Russian Science Foundation Fundamental Research (No. 19-29- 02005 mk). 2019-05-13 2019-07-25 2019-07-28 2019-11-20 2019-12-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2019 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-019-0707-y http://dx.doi.org/10.1007/s41365-019-0707-y . 2019 Nuclear Science and Techniques 12 30