Radioisotope production at the IFMIF-DONES facility

The International Fusion Materials Irradiation Facility Demo Oriented NEutron Source (IFMIFDONES) is a single-sited novel Research Infrastructure for testing, validation and qualification of the materials to be used in a fusion reactor. Recently, IFMIF-DONES has been declared of interest by ESFRI (European Strategy Forum on Research Infrastructures) and its European host city would be Granada (Spain). In spite the first and most important application of IFMIF-DONES related to fusion technology, the unprecedented neutron flux available could be exploited without modifying the routine operation of IFMIF-DONES. Thus, it is already planned an experimental hall for a complementary program with neutrons. Also, a complementary program on the use of the deuteron beam could help IFMIF-DONES to be more sustainable. In the present work, we study radioisotope production with deuterons of 177Lu. The results show the viability of IFMIF-DONES for such production in terms of the needs of a territory of small-medium size. Also the study suggests that new nuclear data at higher deuteron energies are mandatory for an accurate study in this field.


Introduction
IFMIF will be an installation for irradiation tests that will simulate the conditions inside a fusion reactor in terms of neutron fluence and neutron energy [1]. In Europe, during the last decades the so-called European Fusion Program has been developed, coordinated between the different European countries and Euratom. In order to reproduce the same hard radiation conditions inside a fusion reactor, it is necessary to build a specific neutron source based on the nuclear reaction that occurs between deuterium and lithium nuclei. The need to build a first fusion reactor, 'early DEMO', has imposed some urgency in the construction of a neutron irradiation plant. It was decided, in the European framework, the design and construction of a plant that was able to generated that level of damage. At the proposal of the National Fusion Laboratory it was decided that it will be DONES (DEMO-Oriented Neutron Source), which basically consists of a simplification of IFMIF. The IFMIF project will consist of two accelerators, however, DONES will consist of a single accelerator in an attempt to achieve this urgency.
Thanks to great efforts many good news have arrived in the last years. For instance, Granada is the european city host the construction of the IFMIF-DONES, and the facility has been recently selected as a key infrastructure in energy by the European Strategy Forum on Research Infrastructures (ESFRI) [2].
The main technological challenges of the installation are the accelerator and the lithium target. The planned accelerator to be included in IFMIF-DONES will accelerate * e-mail: jpraena@ugr.es with a current of 125 mA deuterons up to 40 MeV, which means that it must handle 5 MW power. The deuteron beams will strike a liquid lithium target that needs to circulate at high speed, 15 m/s, to extract the high incident power. IFMIF-DONES will reach a neutron flux of 10 18 m −2 s −1 with a broad peak at 14 MeV. In the Figure 1 we can see a scheme of IFMIF-DONES [3]. The materials most exposed in the reactors will be irradiated in the high flux module and in the other two test cells less exposed materials will be irradiated; but the question now is about the possible applications of IFMIF-DONES, beyond the study of materials. The White Paper included a preliminary report on a complementary scientific program at IFMIF-DONES [4]. The main part of the report is the compilation of scientific cases for a final Complementary Program ordered by scientific domain: applications of medical interest, nuclear physics and radioactive ion beam installations, basic physics studies and industrial application of neutrons. However, there was not studies regarding the production of radioisotopes with deuterons. In this article, we perform a preliminary study on the possible use of IFMIF-DONES for producing medical radioisotopes. We have taken advantage of our theoretical study on the production of radioisotopes with a deuteron accelerator of low energy (3 MeV) and high current (10 mA) [5].
Specifically, for the present work, the study of 177 Lu will be of interest to us. This radioisotope has a half-life equal to 6.6465 d [6], that is, it can be produced and transported without drastically reducing its activity. IFMIF-DONES offers the possibility of generating this radioisotope through two production routes, see Figure 2. The first reaction is the direct route (green) and the second is the indirect route (grey). According to the tabulated data of the IAEA [7], the average emission energies of electrons are in the range from 40 to 150 keV. This range makes the radioisotope suitable for therapeutic use. On the other hand, during the disintegration the gamma radiation causes it to be detected with imaging techniques. For these reasons, 177 Lu is used at present for theranostic (therapy and diagnosis) [8]. Among others, 177 Lu is widely used as a radiopharmaceutical to treat gastroenteropancreatic neuroendocrine tumors [9][10] [11]. Currently, the 177 Lu is only produced in nuclear reactors with two possible reactions [12]. The first is the neutron capture on 176 Lu, 176 Lu(n,γ) 177(m+g) Lu with enriched samples, where the products are the same as the direct route with deuterons. The second is the neutron capture on 176 Yb(n,γ) 177 Yb with enriched samples, where the products are the same as the indirect route with deuterons, thus, 177 Yb decays to 177g Lu with no production of the undesirable long-live metastable state. Lutetium is excreted through the urine which must be treated as a nuclear waste for a long time when the metastable state is produced [8]. In case of deuteron production at IFMIF-DONES the metastable state would be negligible produced in comparison with nuclear reactors.
In this work, as a first attemp to design a realistic setup for estimating the radioisotope production with deuterons at IFMIF-DONES, it has been considered a simple model for the calculation of the temperature of the target. The target consists of an ytterbium sample deposited onto a copper backing cooled by flowing water. The optimal thick-ness of the sample will be studied with the boundary condition that the temperature must be below the melting point of ytterbium and copper. The current of the deuteron beam will be 1/100 the maximum current for designing issues. It will be shown that in order to continue more accurate studies in the radioisotope production, it is mandatory to new data above 20 MeV on the reaction 176 Yb+d.

Materials and method
The accelerator of IFMIF-DONES open two production routes for the Lu, which should be studied. In order to not melt the target the optimal thickness of Yb will be calculated as well as the dissipated power. Then, the lutetium production rate and the activity of the lutetium will be studied.
The production of lutetium, through the direct route, is obtained from the differential equation: where N 177 Lu is the number of nuclei produced, R 177 Lu is the rate of production and λ 177 Lu is the decay constant. The production rate is given by: Therefore, the number of nucleus produced remains: For the indirect route, the differential equation must consider the time of disintegration of the ytterbium. In this way, the differential equation to solve is: The difference with the direct route production rate is also in the cross-section. Therefore, the number of nucleus produced remains: From here we must solve the two integrals that appear in expressions (3) and (5) [13]. Then, we will calculate the activity of lutetium.

Stopping power
The stopping power is given by the semi-empirical expression developed by Ziegler and Andersen. This expression was developed for protons, and is given by [14]: (6) where β = v c , E is the energy of the incident beam and all the values of the different A are particular constants of the ytterbium. Taking into account that the stopping power depends on the energy and speed of the incident particle, the relationship between the expression for the stopping power of protons and deuterons is: where m p y m d are the mass of the proton and deuteron. The same expressions are used by the SRIM code (Stopping and Range of Ions in Matter) [15]. We will use SRIM for a double check of the energy losses by the deuterons in ytterbium.
On the other hand, the setting for the fit of the direct route is (red line): where a=(-54±5) mb y b=(4.4±0.3)10 −3 mb/keV [17]. Figure 3 shows the fits performed up to 40 MeV for both cross-sections based on the method of our work [5].

Target working principle and thermal analysis
When a beam of energetic charged particles strikes a target a part of the energy is transferred due to the stopping of charged particles. That transfer increases the temperature of the target with the possibility to melt it. To avoid this, a cooling system should be used. In this work, the target structure is composed by 3 sections. The first one is the ytterbium foil, which is attached to the second section,  [17]. Circle red points corresponds to experimental values of the direct route 1776 Yb(d,n) 177(m+g) Lu, Hermanne et al. [16] The lines correspond to the used fit following Arias de Saavedra et al. [5]. the backing. The second section is then in touch or immersed in the third one, the cooling fluid. Figure 4 show schematically the concept of the target.
The thicknesses of the foil and the backing are key parameters because determine the power sustained in each section. This power must be dissipated keeping the temperatures well below the melting points of Yb and Cu. The dissipation is due to conduction, along the target, and to convection, due to the fluid in contact with the backing. Assuming stationary conditions, the heat dissipated by the fluid is: where h is the convection loss coefficient. The convection loss coefficient is related with the Nusselt number by means of the thermal conductivity coefficient and the dimensions of the considered target. Thus, the convection loss coefficient can be calculated as [18]: where k f is the coefficient of thermal conductivity of the fluid, r is the radius of the target (1 cm), we have considered the same radius for the deuteron beam, ρ is the density of the water, µ is the dynamic viscosity of the fluid and c p is the specific heat at constant fluid pressure. On the other hand, the incident heat flow is: where k is the coefficient of thermal conductivity of the target-support system and l is the thickness. Therefore, the expression of the incident heat is: considering l << r and the conservation of energy, q beam =q f luid =q, we have the following expression: where h t is:

Activity and specific activity
The activity of the lutetium sample is given by the expression: where N 177 Lu (t) is the number of generated nucleus of 177 Lu, which is obtained by adding the result of the expressions 3 and 5. On the other hand, the produced mass of lutetium is given by the expression: 176.94 g 6.022 · 10 23 (17) Finally, having the activity and mass of lutetium after irradiation, we can calculate the specific activity.

Results
Once we have analyzed all the variables, we can start to make the corresponding calculations. First, we calculate the energy loss by deuterons in ytterbium. From here, we can calculate the temperature reached by the target, which will be the boundary condition. In the following calculations we have considered a copper backing of 0.7 mm in thickness. The deuterons are stopped in the water or in a second target, which could produce another radioisotope or also 177 Lu. This option will be developed in forthcoming studies. The cooling water circulates at 5 m/s with a temperature of 20 • C. Table 1 shows the average energy lost in Yb, the temperature of the Yb foil and temperature of the Cu backing for 40 MeV deuterons at 125 mA for different ytterbium thicknesses (l Yb ).

∆E MeV l Yb (mm) T Yb (K)
T Cu (K) 9.020 1.000 622 · 10 3 518 · 10 3 4.305 0.500 273 · 10 3 247 · 10 3 0.833 0.100 49 · 10 3 47 · 10 3 0.414 0.050 24 · 10 3 23.8 · 10 3 0.083 0.010 15 · 10 3 14.9 · 10 3 The melting temperature of ytterbium is T Yb = 1096 K and for copper is T Cu = 1358 K. Then, the production of lutetium for an intensity of I= 125 mA is unfeasible. Therefore, the limitations in the deuteron current imposed by the temperatures are remarkable. For a future complementary program on the production of radioisotopes with deuterons, the reduction of the intensity of the incident beam should be considered. Thus, considering the same model, for an intensity I= 1.25 mA, neither the ytterbium foil nor the copper backing are melt, if the Yb thickness is less than l Yb = 200 µm.
One of the aims of the present work is to compare the analytical model for radioisotope production with deuterons to the current production at nuclear reactors by means of neutron capture reactions. In case of nuclear reactors, the chemical form of the Yb sample is Yb 2 O 3 with a maximum possible enrichment of 97% [19]. In the following, we calculate the production rates, mass and activity of 97% enriched Yb 2 O 3 and ytterbium samples. The melting point of Yb 2 O 3 is higher than natural ytterbium, while the thermal conductivity is lower [20]. Nevertheless, our calculations have kept as boundary condition the temperature of the foils, either oxide or natural, well below their melting points. In the following results, we have considered 40 MeV deuteron energy, I= 1.25 mA deuteron current, Yb thickness of 150 µm, Cu backing thickness of 0.7 mm, and temperature and velocity of water 20 • C and 5 m/s, respectively.  The higher production rate obtained for the 196 Yb 2 O 3 is due to its higher density than the natural ytterbium. With the same parameters, we have calculated the mass produced by lutetium after irradiation, in Figure 5 the results are shown as a function of time, up to 24 hours of irradiation. Figure 6 shows the results obtained for the generated lutetium activity.

Discussion
The specific activity obtained after 24 h at IFMIF-DONES is 0.119 GBq/mg for the 196 Yb 2 O 3 sample, and 0.076 GBq/mg for the 196 Yb sample. We can compare these values to the specific activity produced in nuclear reactors with 196 Yb 2 O 3 sample after an irradiation of 72 h, which is 2.96 TBq/mg [19]. Although the specific activity is lower, the production at IFMIF-DONES would have a considerable impact in a regional health system as Granada (Spain). Conventionally a patient needs four dosis during a treatment. Each dose has a price of 14 kEuros per dose and an activity of 7.4 GBq per dose [21]. Therefore, in case of 24 h of irradiation at IFMIF-DONES of a 196 Yb 2 O 3 sample as considered in the present work, the produced With the same idea, we have studied with the same model other radioisotopes of interest in diagnosis and therapy that could be produced at IFMIF-DONES facility. The thicknesses of each reaction was selected to keep the temperature well below the melting point of the corresponding element and the Cu backing. The rest of parameters are the same of the present study on 177 Lu. The idea behind is the same, to provide a preliminary study of their production for motivating a possible discussion on a radioisotope complementary program. Table 3 shows a resume of the results considering the same parameters as  Table 3. Activity (GBq) and mass (mg) of the radioisotope produced in each reaction. The considered enrichment is 100 % except for Zn, Tm and Rh, which is natural abundance.
Finally, it is important to mention in the framework of the 2019 International Conference On Nuclear Data, that there are a need of experimental data for the lutetium production and for many reactions considered in Table  3. Briefly, there is no data above 25 MeV for the 64 Ni(d,2n)

Conclusions
We have studied the production of radioisotopes with 40 MeV deuterons at IFMIF-DONES. Specifically, for 177 Lu at present used in diagnosis and imaging of cancers, two reactions has been analyzed: the indirect route 176 Yb(d,p) 177 Yb→ 177 Lu, and the direct route 1776 Yb(d,n) 177(m+g) Lu. A cooling system has been studied with an analytical model. In order to avoid the melting of the target, the current should be decreased to 1.25 mA. The produced 177 Lu in 24 h could have a significant impact in the health system at regional level. The nuclear data needs on deuteron-induced reactions for calculating the possible production at IFMIF-DONES have been shown. Our next step will be to perform a study with Solidworks using a real target. Also, the possibility to multiple irradiation with the same deuteron beam will be studied as well as the production of impurities.