1. Introduction

Radioisotopes have become a fundamental part of medical diagnostic procedures, especially for cancers and cardiovascular diseases. In combination with monitoring devices which record the gamma rays emitted from within, they can study the dynamic processes taking place in various parts of the body. In therapy, the uses of radioisotopes are relatively few, but still important. Cancerous growths are sensitive to damage by radiation. Therefore, some cancerous growths can be controlled or eliminated by irradiating the area containing the growth [1]. The growing use of radioisotopes for the treatment of several cancers has prompted the investigation of further alternative production routes to satisfy the demand for medical isotopes [2]. Currently there are many approaches to producing these isotopes, for example, Targeted Alpha Therapy uses ²²⁵Ac and ²¹³Bi, which are considered the most important alpha emitting isotopes. These two radioisotopes are obtained by producing ²²⁹Th in a reactor [3, 4]. Oak Ridge National Laboratory and the High Flux Isotope Reactor are the main suppliers of high-purity ²²⁵Ac from the decay of existing ²²⁹Th stocks. Approximately 26 GBq of ²²⁵Ac have been produced annually from the ²²⁹Th stock, typically in six campaigns per year [5]. The evaluation of accelerator routes, including the production of ²²⁵Ac via the ²²⁶Ra (p, 2n) and ²²⁶Ra (γ, n) nuclear reactions have also gained momentum. Another production approach using a high-energy accelerator has been investigated as well, employing intense 100, 200, or 800 MeV proton beams and natural thorium targets for the large-scale production of the therapy isotopes ^223,225Ra, ^225,227Ac, and ²²⁷Th [2].

Herein, we investigate the ADS reactor approach, which has attracted considerable attention for isotope production/transmutation, as shown in Fig. 1. ADS is a subcritical reactor and it can play an important role in the transmutation process of heavy elements and isotope production [6, 7]. This type of reactor was essentially designed for safely transmuting radioactive waste into stable elements or elements with relatively short-lived radioactivity, while producing useful power [8-12]. ADS possesses some advantages because the accelerator provides further neutrons through the interaction of accelerated particles with a target mostly located at the center of core, in addition to the neutrons coming from fission. Therefore, it is expected to be more efficient from the viewpoint of burnup characteristics than critical reactors [6, 13, 14]. Since ADS reactors are not required to maintain criticality, it is possible to increase burnup, i.e., to extract more energy from a given mass of fuel and more neutron flux in the core, where the neutron intensity is an important factor in transmutation processes and isotope production [15, 16].

Figure 1Full-screen View

(Color online) Accelerator-Driven System (ADS) concept [17].

The transmutation of ²²⁶Ra to ²²⁹Th through neutron irradiation requires three neutron captures and two β^- decays through a number of pathways [5], and the dominant production pathway is via:

This study aims to investigate the feasibility of ²²⁹Th production via transmutation of ²²⁶Ra in an ADS reactor to provide ²²⁵Ac and ²¹³Bi at the end according to the decay scheme based on ²²⁹Th. The ADS reactor model has two regions, i.e., an outer zone, which has a thermal neutron spectrum in which ²²⁶Ra is irradiated, and an inner zone, whose fast spectrum serves as a radioactive waste incinerator. Isotope formation from the irradiation of ²²⁶Ra is calculated using MCNPX and CINDER’90 for solving the time-dependent Bateman equations [18].

2. ADS Core Description and Model

The current ADS reactor model comprises a subcritical core with two regions (zones), as shown in Fig. 2a. The fast spectrum zone surrounds the central tube, which is contained in a tank made of stainless steel. The fast zone is filled with fuel elements, but made up of plutonium, americium, and curium samples (Pu, Am, and Cm)O₂ within MgO, with a density of 6.077 g/cm³ [19]. The sample was put together for investigating high-level radioactive waste transmutation; this study has been conducted already with the same model of two zones and will be submitted for publication soon. The inner zone is surrounded by thermal spectrum zone comprising shortened fuel pins, with 4% enriched uranium (a more detailed description of the core is given in Table 1). The main geometrical and material characteristics of this model are based on the previous investigations performed at the Institute for Safety Problems of Nuclear Power Plants (NPPs) and the Institute for Nuclear Research, Kyiv, Ukraine [20, 21].

Figure 2.Full-screen View

(Color online) Horizontal cross-section view of MCNPX model for the two-zone ADS core (a) Vertical cross-section view of the MCNPX model for the two-zone ADS core (b).

The high-intensity neutron generator will be used as a driver for the subcritical reactor [22]. For the source definition of external neutron source in ADS, charged particles (deuterons) move from the top to the bottom of the central tube of the system and finally hit the titanium target saturated with tritium. The fusion of a deuterium and tritium nucleus (D-T nuclear reaction) results in the formation of a ⁴He nucleus and a neutron with a kinetic energy of approximately 14 MeV. For the purpose of simplicity and normalization in the MCNPX model, a point isotropic source with neutron energy of 14 MeV has been identified in the input file.

3. Results and Discussions

3.1. ²²⁶Ra Target position characteristics

Calculations for the current model were performed using the MCNPX 2.7 transport code with the ENDF/B-VII.0 data library [23]. The initial subcriticality was fixed at 0.97±0.0006. One kg of ²²⁶Ra target was irradiated at different positions in the outer zone, and this was repeated for 16 time steps, which is representative of four years of operation. To select the typical position for production of ²²⁹Th using a thermal neutron flux of about 2.0 x 10¹⁴ n/cm².s, the neutron spectrum was calculated at six different distances from the center of the core, i.e., at 21, 27, 33, 39, 45, and 51 cm (referred to in Fig. 3 as TP1, TP2, TP3, TP4, TP5, TP6, respectively).

Figure 3.Full-screen View

(Color online) Neutron spectra at selected target positions (TP) in the outer zone.

The neutron flux changes with the target position (TP) as observed in Fig. 3, especially in the region of the hard spectrum, in which the presence of fast neutrons increases whenever we approach the inner zone. Although there is no large difference in the thermal and epithermal regions with the target position, we can see a slight difference in neutron flux at TP3.

To further assess the typical TP selection, we also calculated ²²⁹Th yields in units of activity at the same six TPs with time using the depletion input card tally (BURN). BURN calculates the changes in isotope concentration over time based on the CINDER'90 package in combination with MCNPX. Fig. 4 shows that ²²⁹Th yields vary with the target position, with a typical value of 0.63 GBq/g of ²²⁶Ra after 2.5 years at TP3, which is 33 cm away from the core center (as illustrated in the model view in Fig.2b). Based on this analysis, the optimal irradiation position for the production of ²²⁹Th would be at TP3. This preference for TP3 is due to a relatively high neutron flux in the range of epithermal energy, where the ${}_{}{}^{226}Ra[n,\gamma ]$ reaction is more likely to take place; therefore, the production of ²²⁹Th is expected to be greater at TP3. It is worth mentioning that the maximum yields for TP5 and TP6 are at 3 and 3.5 years with activity values corresponding to 0.61 and 0.60 GBq/g, respectively; after this time the activity begins to decrease. This means that the neutron energy becomes more thermalized at TP3 with time, which makes the neutron absorption reaction less likely.

Figure 4.Full-screen View

(Color online) Numerical calculation of ²²⁹Th production at different TPs over 4 years of irradiation using a neutron flux of 2 × 10¹⁴ n/cm².s.

3.2. Evaluation of the production of ²²⁹Th, ^228Th, and ²²⁷Ac in the ADS model

After selecting a typical target irradiation position in the outer zone, we fixed the position and changed the neutron flux used for irradiation of the ²²⁶Ra target to evaluate the behavior of the yields of ²²⁷Ac, ²²⁸Th, and ²²⁹Th from ²²⁶Ra with neutron flux. These calculations are aimed at estimating the increasing rate of the desired isotope and the expected time to achieve the maximum production amount as a function of flux.

Depending on the dominant formation pathway for ²²⁹Th, we expected that ²²⁷Ac and ²²⁸Th would be coproduced with ²²⁹Th. The yields for those isotopes as a function of irradiation time and at four different values of neutron fluxes (ϕ= 2.0 × 10¹⁴, 3.42 × 10¹⁴, 4.6 × 10¹⁴, and 6.84 × 10¹⁴ n.cm^-2.s^-1) are shown in Figs. 5a, b, c, and d, respectively. The results correspond to the route behavior and production rate is sensitive to the neutron flux. The peaks of mass yield shift to the left of the time scale (i.e., to shorter time) with an increase in the neutron flux, particularly for ²²⁸Th and ²²⁹Th formation, wherein the first cycle contains a relatively large amount of ²²⁷Ac than the other two isotopes. The ²²⁷Ac yields produced through quick decay of ${}^{227}Ra(t_{1/2}=42.2,{\beta }^{-})$ in turn is formed from the ${}^{226}Ra[n,\gamma ]$ reaction. Subsequently, the amount of ²²⁷Ac decreases with a dramatic increase in ²²⁸Th yield through the most likely reaction: ${}_{}{}^{227}Ac[n,\gamma ]{}_{}{}^{228}\mathrm{Ac}(t_{1/2}=6.15h,{\beta }^{-}){}_{}{}^{228}Th$, which, in turn, transmutes to ²²⁹Th by neutron capture.

Figure 5:Full-screen View

(Color online) The yields of ²²⁷Ac, ²²⁸Th, and ²²⁹Th, as a function of time and neutron flux.

Table 2 shows the maximum production mass of ²²⁹Th as a function of time and flux. The irradiation time decreases from 2.5 years at a neutron flux equal to 2.0 × 10¹⁴ to less than one year when the neutron flux increases to 6.84 × 10¹⁴ and the ²²⁹Th yield increases by ̴13%. These calculations are useful when considering the economic feasibility, or the cost of producing ²²⁹Th when increasing the neutron flux in the core.

Table 2.Full-screen View

The optimal irradiation time for maximum yield of ²²⁹Th at different values of neutron flux.

Neutron flux (n/cm2.s)	Irradiation time (Days)	229Th yield (g)
2.00 E+14	9.00E+02	86.48
3.42E+14	6.60E+02	92.83
4.56E+14	4.80E+02	96.71
6.84E+14	3.00E+02	99.1

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We compared our method of calculating ²²⁹Th yields (from 1 kg of ²²⁶Ra irradiation at a neutron flux of 4.6 × 10¹⁴ n/cm².s for four years in ADS using the two zones model), with that from a previous study [4] in which the production of ²²⁹Th was conducted in a critical core with the same amount of ²²⁶Ra target (1 kg) irradiated using a neutron flux of 4.7 × 10¹⁴ n/cm².s. The results are shown in Fig. 6. Our ADS calculations indicate rapidly increasing ²²⁹Th yields during the first operation cycle up to 1.33 years of irradiation, before a decrease in yield at 1.5 years. The maximum amount of ²²⁹Th yield was 96.71 g from 1 kg ²²⁶Ra. In contrast, the production of ²²⁹Th in the critical core was relatively slow, reaching a maximum yield of 72.75 g from 1 kg ²²⁶Ra after 3.2 years.

Figure 6.Full-screen View

(Color online) ²²⁹Th yields in the ADS core vs in a critical reactor.

This behavior of ADS with two zones can be attributed to the availability of two types of neutron spectrum, which allows for fast neutrons from the inner zone to penetrate the membrane to the outer zone, leading to significant numbers of epithermal neutrons in the outer zone near the membrane. Once those neutrons have been slowed down, they have a high probability of being captured by ²²⁶Ra. This model of neutrons penetrating a membrane cannot be used when we consider a critical core with two zones, because in this case there is no role for a membrane in addition to the two zones; the idea is to have two types of neutron spectrum inside the core. As mentioned before, the main aim of the ADS with two zones is to benefit from the fast zone for high-level waste transmutation and the thermal zone for long-lived fission product transmutation, in addition to isotope production.

4. Conclusion

The production of ²²⁹Th through irradiation of ²²⁶Ra was investigated numerically in a proposed ADS model with fast and thermal spectrum zones. We compared the results obtained using the proposed model with those obtained using a critical reactor.

Based on calculations, the two-zone ADS model can produce ²²⁹Th from ²²⁶Ra transmutation in addition to serving as a radioactive waste incinerator. The proposed model shows greater efficiency for producing ²²⁹Th than critical reactor (25%) in less time (58%), using the same initial amount of ²²⁶Ra and same neutron flux. Furthermore, the proposed model can produce a significant amount of ²²⁸Th, which is coproduced with ²²⁹Th during the irradiation of ²²⁶Ra. This is based on the fact that the fast neutrons from the inner zone penetrate the stainless steel membrane and move to the outer zone, thereby changing the neutron spectrum surrounding the inner zone. The presence of two types of neutron spectra in the core is useful for ²²⁶Ra transmutation and increases ²²⁹Th yields.

These results provide a strong basis to discuss and evaluate the needs for future research into the feasibility of producing ²²⁹Th in a different ADS model with one zone. They also allow for a comparison between calculations and available experimental results.