2.1 Computational model of the basic core configuration

The core of the HTGRU (red colored area in Fig. 1, see [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). On the top and bottom the core is also closed with graphite blocks, but here they are laid in just one row.

Fig. 1.Full-screen View

(Color online) Schematic of the cross-section of a reactor core model.

Schematic drawings of the fuel block and its cross-section are presented in 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.

Fig. 2.Full-screen View

(Color online) Schematics of the core fuel block (a) and its cross-section (b).

Microencapsulated fuel (microfuel) for a fuel pellet of HGTRU (Fig. 3, [1]) is a spherical fuel kernel of fissionable material (Th; Pu)O₂ with a diameter of 350 μm, covered successively by layers of pyrolytic carbon (PyC) and Ti₃SiC₂. These fuel kernels are dispersed into a graphite matrix of cylindrical fuel pellets (Fig. 3), which are placed in the fuel block.

Fig. 3.Full-screen View

(Color online) Microencapsulated fuel and fuel pellet of the type 1017.

At the first stage of research presented in the works [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×${10}^{-3}$, 10.17×${10}^{-3}$, and 12.00×${10}^{-3}$m, respectively. The heights of the fuel pellets (20×${10}^{-3}$ m) and thicknesses of the external SiC layer (0.3×${10}^{-3}$ m) were equal for all types. The percentage of heavy metal content in all types of fuel pellets were (%): Pu–50, ²³²Th–50; and the isotopic compositions of Pu were (wt%) [1]: 238 – 0, 239 – 94, 240 – 5.4, 241 – 0.6, 242 – 0.

In the work [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 = ($k_{\text{inf}}$ - 1)/$k_{\text{inf}}$) (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 ²⁴¹Pu and ²³³U.

When a fuel pellet of the type 0817 is used, the isotope ²³⁹Pu burns up quickly and the secondary fuel (²⁴¹Pu and ²³³U) 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 ²³⁹Pu left in the core (less than 2 %), and ρ_inf sharply falls to 0. When the fuel pellets of the types 1017 (dρ_inf/dt ≈ 0.011 %/days) and 1200 (dρ_inf/dt ≈ 0.007 %/days) are used, it results in the accumulation of ²³³U, ²⁴¹Pu 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 ²³⁹Pu (η(²³⁹Pu) = ($N$ ($t_{\text{beginning}}$) - $N$ ($t_{}end$))/$N$($t_{\text{beginning}}$)) is 95.5, 96.6 and 92.7%, respectively [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) that an increase in the dispersed phase fraction ω_f (ω_f = $V_{}microfuel$×$N$/$V_{}matrix$) of the type 1200 fuel pellet results in a decrease in η(²³⁹Pu). Consequently, to provide better burn-up of ²³⁹Pu in the (Th,Pu)-fuel cycle, the type 1017 fuel pellet has to be chosen.

Fig. 4.Full-screen View

(Color online) Neutronic properties of the reactor cell unit for two types of fuel pellet: 1 – type 1017; 2 – type 1200.

Computations were performed for the unit cell of the infinite regular lattice ($k_{}inf$) in the program WIMS-D5B; the fuel part of the cell was homogenized. The computational model of the cell unit is presented in [1]; the homogenization process is described in the works [1, 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

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.Full-screen View

Neutronic properties of the equivalent system: (a) –dependence of η(²³⁹Pu) on ω_f, (b) – dependence of irradiation time T on ω_f.

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)). The increase in ω_f also has no effect on the spectrum ϕ_Vn(E) of the reactor under study (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%.

Fig. 6.Full-screen View

The neutron spectrum in the reactor core: (a) – normalized spectrum of the neutron flux; (b) – integral distribution function of the neutrons over energy in the flux.

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 × ${10}^{-3}$ kg (Th, Pu)O₂, 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 ϕVn(E) is 8.14×${10}^{13}$ n cm^-2 s^-1. There are 9.41% of the neutrons with energy $E_{\text{n}}$ up to 4 eV, 35.57% of neutrons with $E_{\text{n}}$ from 4 eV up to 183.2 keV, and 55.02% of neutrons with $E_{\text{n}}$ from 183.2 keV to 10.5 MeV (Fig. 5). In these conditions, (k_eff) is 1.24, ρ_initial 19.35%, and (dρ/dt) ≈ 6.2 × ${10}^{-3}$%/days. The burn-up of ²³⁹Pu is 81.3% (η = $N$ (0) – $N$(3110))/$N$(0)), and the burn-up of ²³²Th is 9.66%. The computation results of fuel isotopic composition evolution N(t) are presented in Fig. 7 and in Table 1.

Fig. 7.Full-screen View

(Color online) Concentration evolution of the main minor actinides in HGTRU with time due to fuel burn-up.

Additionally, the dependence of concentration changes of isotopes ^231,233Pa on time ^231,233N(t) were derived, and concentrations of ¹⁴⁹Sm and ¹³⁵Xe were analyzed. The data on ^231,233Pa, ²³³U, ¹⁴⁹Sm, and ¹³⁵Xe concentrations allow the evaluation of the required intensity $I_{\text{n}}$ (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 $I_{\text{n}}$ within the range ${10}^{13}$ n cm^-1 s^-1 to 2 × ${10}^{14}$ n cm^-1 s^-1. That should provide the condition $k_{}eff$ = 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]. The results of these computations are presented in 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].

Fig. 8.Full-screen View

(Color online) Dependence of k_eff on the core operation time t in case of large initial reactivity excess.

If one creates a large initial reactivity excess ρ_initial (as demonstrated in 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 ¹⁵⁷Gd, ¹⁶⁷Er, and ¹⁰B 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, 25] suggested using PaO_2 as a burnable absorber. A peculiar feature of isotope ²³¹Pa is that its transmutation leads to the formation of ²³²U and ²³³U, and isotope ²³³U is a fissionable material. This means that isotope ²³¹Pa performs the functions of a burnable absorber and a source of a new fissionable material. However, ²³¹Pa production in the amounts required for implementation of the concept suggested in the work [24] is rather challenging. That said, ²³¹Pa can be effectively used in small amounts as a burnable absorber, for example, in a high-temperature reactor core.

In the work [25] it is suggested to use ²⁴⁰Pu as a burnable material. In our case (Fig. 7), the presence of ²⁴⁰Pu in the fuel composition results in significant accumulation of ²⁴¹Pu, which can be well fissioned by epithermal neutrons, and its nuclear concentration ²⁴¹N(t) exceeds the nuclear concentration of ²³³U by more than 2.5 times across the whole fuel campaign. The computation showed that ²⁴¹Pu and ²³³U specify the dependence type of $k_{}eff$ (t) and provide steady reactor operation for 8.5 years.

The proposed usage of ²³¹Pa 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 ²³¹Pa (Fig. 9 and Table 2). It is seen in Fig. 9 (ENDF/B-VII.I) that the neutron-absorption cross-section on the nuclei of ¹⁵⁷Gd, ¹⁶⁷Er, and ¹⁰B for the neutron energy range 0.3-10⁶ eV are on a level close to the absorption cross-section of the nuclei of ²³¹Pa.

Fig. 9.Full-screen View

(Color online) Dependence of neutron-absorption cross-sections of various isotopes on neutron energy.

If one examines 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) is 5.539 × ${10}^5$ eV. The absorption cross-sections _abs(E_average) of the nuclei of absorbers and ²³¹Pa are presented in Table 2 for _abs(E_average). It can be seen that ²³¹Pa is likely to be a substitute for ¹⁰B and some other traditional absorbers. The influence of ¹⁰B on the neutronic properties of a reactor core with epithermal and fast neutron spectrum was analyzed by the authors in [1].

In the loading option discussed above (Fig. 8), the initial reactivity excess is compensated for by the isotope ²⁴⁰Pu. Its content (wt%) in the fuel increased from 5.4% up to 9%; the content of ²³⁹Pu decreased by 3.6%, correspondingly. The use of ²⁴⁰Pu 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]. Using ²⁴⁰Pu, ρ_initial was reduced from 19.35% to 11.51%, and (dρ/dt) decreased by a factor of 1.51. According to the concept suggested by the authors in the work [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 ($k_{}eff$ = 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

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, 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 [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.

Fig. 10.Full-screen View

(Color online) Schematic of the facility containing the plasma neutron source to study the fuel properties in long-time operation of the reactor core.

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] 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] 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. 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 that for the distribution of magnetic field and plasma column parameters chosen in [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.

Fig. 11.Full-screen View

(Color online) Distribution of the specific neutron yield per linear centimeter of the plasma column in the case of D-D fusion reactions along the z-axis (the part of the column inside the reactor core is marked by the red line).

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], injection of a 100 MW deuterium beam will produce high-energy sloshing ions with density up to 1.5 × ${10}^{14}$ cm^-3. In this case, the specific emission of neutrons from a volume unit due to the D-D reaction is 1.76 × ${10}^{12}$ n cm^-3 s^-1 in the core region, and the specific neutron yield rate is 6.00 × ${10}^{13}$ 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 × ${10}^{13}$ 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, 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], Serpent 1.1.7 (ENDF/B-VII.0) [28], and PRIZMA (ENDF/B-VII.I) [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.