Comparative Simulation Study of Direct and Indirect Target Production of 99Mo with Linear Accelerator at SAMEER

When high energy electron beam falls on a high Z target it generates bremsstrahlung photons which can be used to produce ⁹⁹Mo from 100Mo using photo-neutron (γ, n) reaction. Two different approaches are studied to carry out photo-neutron reaction. First, a converter target approach in which photons are generated in a high Z target of tungsten using (e,γ) reaction and then (γ, n) reaction in ¹⁰⁰Mo for ⁹⁹Mo production. Second, a direct target approach wherein 30 MeV electrons hit directly onto ¹⁰⁰Mo target to carry out both (e, γ) and (γ,n) reactions in the ¹⁰⁰Mo target itself. GEANT4 simulation gives photons and neutrons fluxes and their angular distributions from both the approaches, which are then used to calculate activity of ⁹⁹Mo. The study shows that for very thin ¹⁰⁰Mo target of about 0.1 radiation length converter target shows better activity whereas, for any thickness beyond it the direct target approach is found to be more efficient. For 30 MeV and 10 kW beam falling on ¹⁰⁰Mo target with 1.4 radiation length, direct target approach is found to be more efficient. Therefore, after improvising the geometry of ¹⁰⁰Mo target in the case of direct target method an increased specific activity is obtained through GEANT4 simulation.

Keywords: Electron Linac; Activity; Bremsstrahlung; Photo-Neutrons; GEANT4; Nuclear Medicine; GDR (Giant Dipole Resonance)

After realizing the demand of 99Mo in nuclear diagnostics, various efforts are made worldwide to produce 99Mo using green technology. Therefore, development of a 30 MeV high current electron linac is undertaken at SAMEER for radio-isotope production. 99mTc is a widely used radioactive tracer isotope in Nuclear Medicine. 99Mo decays with a half-life of 65.976 hours to the meta-stable state of Technetium-99 (99mTc). It further decays to ground state of Technetium-99 (99gTc) by isomeric transition with a half-life of 6.0067 hours emitting a 0.1427 MeV gamma ray [1]. The emanating gamma ray energy of about 142.7 keV is convenient for detection. 99mTc, due to its short half-life, is ideal for diagnostics in nuclear imaging and 50% of total 99mTc dose is found to be excreted by the body within 1.8 days [2,3]. 99Mo has a half-life of 65.976 hours which is enough to transport it as 99mTc generator to faraway locations. These advantages have accelerated the extensive use of 99mTc in medical scans. Today production of 99Mo depends entirely on reactor-based technology using Highly Enriched Uranium (HEU) [4]. There are five reactors in the world HFR (High Flux Reactor) in Netherlands, BR-2 (Belgian Reactor) in Belgium, NRU (National Research Universal) reactor in Canada, OSIRIS in France, SAFARI-1 (South Africa Fundamental Atomic Research Installation) in South Africa where preparation of 99Mo is usually done. Out of these NRU, Canada has been permanently shut down in March, 2018 creating huge difference in demand to supply ratio of 99Mo [5]. HFR and BR-2 are expected to expire in 2024 and 2026 respectively [6]. This will give rise to differences in demand to supply ratio of 99Mo. In India, there are almost 280 nuclear imaging facilities operational as of 2018 based on AERB (Atomic Energy Regulatory Board) data. 99Mo generators are supplied from BRIT (Board of Radiation & Ion Technology) and also from other countries like Israel, Turkey, and UK etc. The strength of the generator decides the cost, which can vary from INR 27,000 to INR 70,000. Treatment cost depends on the dose administered to the patients, which can range from 2 mCi to 20 mCi depending on the type of scan. Today, over 70% of nuclear medical procedures include the use of 99mTc [7]. Due to its wide use in nuclear medicine, it is important to find environment friendly and cost effective ways to produce 99Mo [8]. Apart from neutron induced fission of 235U, various other reaction channels using neutrons, protons, electrons/photons are possible to produce 99Mo or 99mTc directly when they are bombarded on 235U, 238U, 98Mo and 100Mo targets [9-11]. One of the reaction channels is 98Mo (n,γ) 99Mo, where thermal and epithermal neutrons provide highest reaction cross-section but still few hundred times lesser than the thermal neutron induced fission reaction cross-section of 235U. Proposals for 98Mo (n, γ) 99Mo reaction include the use ADSR (Accelerator Driven Sub critical Reactors) to carry out neutron capture or fission of 98Mo or 235U, respectively [12]. Another reaction channel is 100Mo (p, 2n) 99mTc, which produces 99mTc directly but due to the short half-life of 99mTc it has to be produced and utilized locally. There are also proposals of using electron accelerator to produce 99Mo by means of photo-neutron reaction of 100Mo. T. Ruth in his report proposed the use of accelerators as one of the most effective future ideas for producing 99Mo [13]. The photons required for 100Mo to 99Mo conversion can be obtained from electron accelerators as bremsstrahlung photons. This is expected to give higher specific activity than neutron capture of 98Mo [10]. According to various references and studies carried out for production of 99Mo, specific activity of 99Mo is found to vary depending upon method of production and target used [14-16]. Currently, Canadian Isotope Innovations Corporation’s (CIIC’s) has proposed the use of linac for the production of 99Mo via 100Mo(γ,n)99Mo reaction to produce about 1,100 Ci/week of 99Mo. NorthStar, Wisconsin, is also looking forward to produce 99Mo through photo-neutron reaction and is expected to bring the technology in the market by the end of 2019 [17]. In a patent published by Diamond et al. the electron linac based technology for producing 99Mo has been studied thoroughly [18].

At SAMEER, looking at various efforts made worldwide to produce 99Mo using green technology, a project to study accelerator based production of 99Mo using 30 MeV high beam power electron linac is undertaken. A prototype of the 30 MeV electron linac is to be developed in two stages. In first stage, a 15 MeV 3-5 kW linac will be developed followed by an upgraded 30 MeV-10 kW beam power linac. 99Mo will be produced via photo neutron reaction using enrich 100Mo target. Cross-section of (γ, n) reaction peaks at photon energy 14-15 MeV up to 0.15 barns. 30 MeV electron linac is expected to produce enough photon flux of energies up to 30 MeV which is used for 99Mo production through 100Mo (γ, n) 99Mo reaction. In this paper, first SAMEER linac parameters are described and in section II, GEANT4 simulations for beam energy optimization is explained. Later, section III describes direct and indirect target approaches with target optimization and activity calculations.

SAMEER has designed, developed and successfully tested side coupled; standing wave structure operating at π/2 mode with an operation frequency of ~ 3 GHz. Linac with 15 MeV energy is successfully tested as a prototype development [19]. Therefore, to achieve 30 MeV, two 15 MeV linacs in series operation is proposed. Schematic of the layout is shown in Figure 1. The main parameters of the linac are given in Table 1.

In the proposed design, a 60 kV DC triode gun is the source of electrons with pulse mode operation followed by diagnostic area for current and emittance measurement. First linac is comprised of 3 and ½ buncher cavities and remaining cavities are fixed length accelerating cavities. Second linac is comprised of only fixed length accelerating cavities. Two independent klystrons provide RF power to the linac and they are synched by a master signal from the RF driver’s control unit. Exit end of the second linac is connected to a very thin (150 µm) low atomic number (Z) material window. Electrons after gaining 30 MeV energy falls on a high Z material target like tungsten and produce bremsstrahlung radiation in all directions. Photons in the forward direction are collimated and fall on enriched molybdenum target for (γ, n) reaction. A very high duty operation of linac is expected to get the desired beam power. The target used is retractable type, wherein low and high Z target is inserted in the beam path for bremsstrahlung generation or for beam dump. One more port with low Z material window is designed for direct irradiation of Mo targets. The targets are water cooled and thermal design is done using ANSYS software [20].

GEANT4 (Geometry and Tracking) simulating tool is used to design the target and estimate 99Mo activity [21]. It is a MonteCarlo based simulation tool which takes source particles as individual events. Simulations with 20 million events are found to be statistically sufficient without loading the computer processor and RAM. A 30 MeV pencil electron beam source and W/99Mo targets surrounded by detectors are kept in a box of vacuum for GEANT4 simulations. A simplistic spherical photon and neutron detector is designed to find out photon and neutron fluxes as well as their angular distributions. Validation of the GEANT4 code is done using standard data available in references and experimental results from SAMEER’s 6 MeV linac. The reaction under study is the 100Mo(γ,n)99Mo reaction, where photons and neutrons are used in estimating the production of 99Mo. Hence, the most important data for validation is of photon flux and neutron flux generated by the code. In Figure 2 a photon flux angular distribution graph from Berger-Seltzer is reproduced using the initial parameters mentioned in the reference [22].

The graph shows similar pattern to the reference graph. It has a strong forward direction peak and sharp dip at 90° angle from beam direction. This dip is observed due to practically infinite target thickness in X and Y plane whereas the beam is incident in Z direction. The forward direction peak obtained from GEANT4 is slightly lower than what is given in the reference and a difference of 11.80%, 13.40% and 9.03% is observed for tungsten target of thickness 0.5, 1.0 and 2.0 r.l. respectively. This discrepancy matches with the mentioned difference of up to 25% for angular distribution maxima in forward direction due to normalization between experimental and computed data [23]. GEANT4 simulation data is also compared with an experimental result from SAMEER’s 6 MeV electron linac. This comparison is shown in Figure 3.

During experiment 6 MeV electron beam is bombarded on a 1.5 mm thick tungsten target with 2.5 mm thick copper backing. The photon beam is collimated in a small angle of 12 °. The measurement is done on Radiation Field Analyzer (RFA). The plot shows less than 10% difference between experimental values and GEANT4 data in Figure 3. Similarly, validation of neutron flux data is done by comparing values given in reference paper of Barber and George [24]. For the given initial condition of 1 radiation length (r.l.) of 100Mo target and 34.3 MeV electron beam energy, neutron flux coming out of 100Mo using GEANT4 is 10.7315x10-4 n/e which is comparable with the interpolated value of 12x10-4 n/e [24].

Bremsstrahlung photons coming from (e, γ) reaction in a high Z target is used to carry out 100Mo(γ,n)99Mo reaction. The bremsstrahlung photons are of continuous energies starting from 0 up to electron beam energy. Depending upon the required energy of photons, first, optimization of electron beam energy of the linac is done. Tungsten (Z=74) is considered as electron to photon converter target. Bremsstrahlung flux spectra are obtained as given in Figure 4 with energy variation of electron beam energy.

As seen in Figure 4, when one increases the electron beam energy from 15 MeV to 70 MeV, the total photon flux and the end point energy of bremsstrahlung increases, which is expected from a typical bremsstrahlung pattern. But it is also observed that increasing electron beam energy does not appreciably increase the number of effective bremsstrahlung photons (12-17 MeV) under the GDR curve and mostly the photon flux of higher energy increases. Hence, a 30 MeV electron beam seems reasonable for the production of 99Mo by 100Mo (γ, n) 99Mo reaction. Further increase in the energy of electron will provide more number of photons of higher energy that can lead to production of other isotopes by (γ, 2n) (γ, 3n) and (γ, pn) reactions [25].

After deciding on electron beam energy and validating GEANT4 codes, two approaches to carry out 100Mo (γ,n)99Mo reaction are studied as shown in Figure 5

(A) Converter target approach: In this approach, a converter target is kept before Mo target to produce photon flux required for 100Mo(γ,n) 99Mo reaction. Tungsten being high Z material and high melting point is suitable for electron to photon conversion.

(B) Direct Target approach: In this approach, electron beam hit directly on to 100Mo target. Mo target has sufficient bremsstrahlung conversion efficiency because of its relatively high atomic number, Z=42. It is expected that the bremsstrahlung photons produced locally are utilized at the same 100Mo target to give 99Mo

After beam energy optimization, geometry of converter target is optimized. The optimization is done to obtain maximum effective photon flux. Using GEANT4, thickness of tungsten is varied between 0.1 and 5 r.l. and plotted along with GDR curve obtained from Beil H, et al. see Figure 6.

The thickness of target at which maximum area under the GDR curve is obtained is best suited for electron photon conversion. It is observed that for very thin targets many electrons come out of the target without interacting completely thus producing less photon flux. As target thickness increases, photon flux also increases but soon saturates after few r.l. thick targets. When thickness is increased to 1.5 r.l. the effective photon flux is found to have decreased in the region of GDR curve and for 5 r.l. the photon flux under GDR curve is further reduced. This happens because of self-absorption of photons inside tungsten target. Hence increasing the thickness of target beyond a particular value is found to decrease the photon flux. An optimized thickness of converter target is one where there is maximum electron interaction and minimum self absorption. For further optimization, flux weighted average reaction cross-section (σa) is calculated for various thickness of tungsten [26]. σa gives reaction cross section weighted over photon flux and directly relates photon flux generation to 99Mo production probability. Flux weighted average reaction cross-section is given by following equation

In Figure 7 Thickness of tungsten target is plotted against flux weighted average reaction cross- section (σa) for 100Mo(γ,n)99Mo reaction. Maximum reaction cross-section is obtained for tungsten target of thickness 0.8 r.l. Hence, tungsten of 0.8 r.l. thickness is decided to produce photons required for photo-neutron reaction.

Activity Calculation:Calculation of Activity, A is done using Eq. (2)

Where, Ie represents current in units of number of electrons. λ, t, V, ω, ρ, Na and M are decay constant of 99Mo, irradiation time, volume, mass fraction, density, Avogadro’s number and molar mass of 100Mo target, respectively [27]. Integral term is the area under the GDR curve for 100Mo (γ,n) 99Mo reaction and photon flux obtained from GEANT4 (shaded region in Figure 8).

Using the cross-section curve and GEANT4 output, our geometric parameters give activity of 0.951 Ci/mA/day/g (35.18 GBq/ mA/day/g) of 99Mo. With 97% enriched Mo activity calculated is 0.923 Ci/mA/day/g (35.151 GBq/mA/day/g). There is very slight change in the activity calculated using 97% enriched Mo. Therefore, depending on the per gram cost of enriched Mo, its design will be fixed. Figure 9 shows change in specific activity with irradiation time.

In converter target design, 100Mo is kept at some distance from tungsten target. Due to this experimental arrangement the photons coming in forward 30° cone angle will fall on 100Mo. Figure 10 shows the decrease in photon flux intensity when only 30° forward cone angle is used.

This photon collimation reduces specific activity by 55% and it comes down to 0.428 mCi/μA/day/g (15.836 GBq/mA/day/g). But collimation of photon flux is important to reduce residual radioactivity and also to decrease shielding requirements in other directions.

Activity Calculation using Neutron Flux coming out of 100Mo:Photon flux information is used in Eq. (2) to calculate activity of 99Mo, whereas another method of activity calculation uses value of neutron flux from 100Mo. This method gives direct estimate of 99Mo production since number of neutrons coming out of 100Mo are directly proportional to number of photo-neutron reactions taking place. Therefore, an estimate of (γ, xn) reaction taking place inside 100Mo target can be done by counting the neutrons coming out of 100Mo. In converter target method neutron flux is found to increase when 100Mo is added after tungsten. It implies that the photons coming out of tungsten interact with 100Mo and produce photo-neutrons. An apparent increase in neutron flux when 100Mo is added after tungsten is visible in Figure 11.

To make precise estimate of neutron flux, an electron beam hitting two targets (100Mo kept after W) and a neutron detector around 100Mo is simulated in GEANT4. A schematic of converter target method with neutron detector is given in Figure 12.

The position of neutron detector is such that it detects the neutrons coming out of 100Mo from all the directions and neutrons coming from tungsten in forward 48 º direction as well. The isotropic nature of neutron flux makes it possible to estimate the flux of neutron coming from tungsten in 48º forward cone angle. This flux is then subtracted from the total neutron flux detected in the neutron detector. By using aforementioned geometric set up shown in fig 12 and isotropic nature of neutron flux distribution, the number of neutrons coming from 100Mo is found to be 3.37x1012 for 1mA beam current. This neutron flux is a result of all photo-neutron reactions like (γ, 1n) (γ, 2n) and (γ, 3n) out of which the only relevant reaction for 99Mo production is (γ, 1n). The reaction cross-sections for (γ, 1n) (γ, 2n) and (γ, 3n) reactions alongside the photon flux obtained from tungsten target using GEANT4 simulations is given in Figure 13.

By calculating the area under the GDR curve for three (γ, xn) reactions and photon flux curve, it is found that about 55% of total neutron flux comes from (γ, 1n) whereas the rest of the neutrons come from other (γ, xn) reaction channels [28]. As mentioned in the TRIUMF report the neutrons coming from the (γ, 1n) reaction give direct estimation of the production of 99Mo. Therefore, Activity using neutron flux can be obtained as follows [29].

where, N_Mo is the neutron flux coming out of ¹⁰⁰Mo

Activity Calculation:In direct target approach, the photons for (γ, n) reaction are produced inside 100Mo target and utilized there itself; therefore it is practically impossible to determine exact count of photons produced and their energies in order to calculate the activity with the help of GDR curve and Equation 2. Hence, for direct target approach neutrons flux coming out of 100Mo target is used to estimate the activity. An electron beam of 30 MeV is hit on 100Mo target and neutron flux is found using GEANT4 simulations. Neutron flux is used in Eq. 3 to estimate the photo-neutron reactions leading to the production of 99Mo.

Target Thickness Optimization:Activity calculations for different thicknesses of ¹⁰⁰Mo target is done as shown in Figure 14

It shows that for thicknesses above 1-2 radiation length of Mo target there is no appreciable increase in the activity. 100Mo is an expensive material so increasing its thickness beyond an appreciable length is not cost effective. It can be seen from Figure 15 that increasing 100Mo thickness beyond 1.4 radiation length decreases the overall specific activity. Hence 1.4 r.l. is a reasonable enough thickness for 99Mo production.

Radius Optimization:For comparison of the two approaches viz converter target and direct target, it is important to keep dimension and composition of 100Mo same while calculating activity. In the case of converter target approach, the photons are produced in tungsten and utilized in 100Mo. The geometry and positions of both tungsten and 100Mo is such that if the radius of 100Mo is reduced lesser photons will fall onto it hence reducing the activity. In the case of direct target approach, the photons are produced and utilized in 100Mo itself. Angular distribution of photon flux suggests that most of the photons from 30 MeV electron beam are generated in forward direction. Hence, radius of 12.5 mm is not entirely useful for direct target approach. The radius of cylindrical 100Mo target can be reduced in order to reduce overall mass of 100Mo without drastically affecting the activity. Figure 16 compares the increase in mass of 100Mo and its activity as a function of increasing radius. It can be seen from the plot that above 4 mm of radius (6.88 grams) the increase in activity is not appreciable; suggesting that further increase in radius of 100Mo is not effective in 99Mo production.

Activity calculation is done using the simulation code GEANT4 and ROOT. For our system namely 30 MeV electron linac with average beam power of 8-10 kW and 100Mo, activity estimate by converter target method is 0.246 Ci/g (9.102 GBq/g) and by direct target method 0.588 Ci/g (21.756 GBq/g) which is based on GEANT4 simulation code. By improvising direct target geometry, it is found that mass specific activity increases more than 7 times. Hence reducing radius of 100Mo target in the case of direct target method gives 4.146 Ci/g (153.402 GBq/g) of activity for 6.88 grams of 100Mo, which is within the suggested range of specific activity by T. Ruth [30].

Activity obtained through direct target method and converter target method is compared in Figure 17 to decide more effective way of 99Mo production. The comparison shows that the activity from direct target is consistently more than the activity from converter target method for 100Mo for thickness above 0.2 radiation length. Geometry of direct target approach facilitates production and complete utilization of photons in all 4 π direction, which increases the overall activity, but cooling of Mo target becomes very crucial in this approach. Since, the same target is used for radiochemistry later on therefore; design of mounting of 100Mo for irradiation is very challenging. In converter target method entire beam energy is lost due to absorption in W target therefore cooling mechanism is provided only to W target. For such a high intensity beam a very important parameter is thermal power which could be dissipated on target or converter. Therefore, resolving this cooling problem is a difficult task. Two important factors which needs more consideration are as follows:

(a) The target material is usually Mo powder, pressed under very high pressure and melted under micro powder metallurgy. That target material has a very bad thermal conductivity so that the thermal power inside the target is transmitted to target container with low efficiency. So, it needs a special cooling method even using cryogenic methods

(b) Decreasing the beam diameter by decreasing the distance between converter (W) and target (100Mo) is a good option for decreasing the mass of target material, but it increases the power density on target. And calculation of optimal distance to compromise the cooling parameters and target material mass is urgently needed.

Lastly, it is observed that for very thin molybdenum targets converter target assembly is more effective, this is because in direct target approach, thin 100Mo target does not stop the electron beam completely. Thus, decreasing the overall available bremsstrahlung photons.

To validate the calculation of activity, data of various references are compared. For converter target method same input parameters as mentioned in the Diamond are used for comparison. Calculations done using Equation 2 and GEANT4 simulation produce activity of 33.16 Ci (1226.92 GBq) for 67.26 grams of 100Mo sample. This is found to be at least 4 times lesser than the activity mentioned by Diamond, et al. [18]. In case of direct target method calculations are done for 100Mo of thicknesses 1, 2, and 3r.l. The activities obtained from Equation (3) and GEANT4 simulations for the aforementioned thicknesses are 32.74 Ci/ 26.09 Ci/ 20.12 Ci (1211.38 GBq/965.33 GBq/744.44 GBq), respectively. These values can be compared with the results presented by Tsechanski A [23]. The variation in the activity values is large in most of the references either in converter target method or direct target method. There is no experimental data available to verify the final activity obtained after irradiation. Therefore, a good linac experimental setup to quantify the activity with any beam parameters is important.

It is concluded that for very thin molybdenum targets (~ 0.1 radiation length) converter target assembly is more effective in producing 99Mo via photo neutron reaction, whereas for any thickness beyond 0.1 radiation length direct target method provides much higher specific activity.

The author would like to thank Dr. S. V. Suryanarayan and Dr. R. Thomas of Nuclear Physics Division, BARC for their immense help. Author would also like to thank MeitY for supporting the High Energy linac activity for radio-isotope production under grant-in-aid.