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Design of a photoneutron source based on 10 MeV electrons of radiotherapy linac
Annals of Nuclear Energy 63 (2014) 69–74
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Design of a photoneutron source based on 10 MeV electrons of radiotherapy linac M. Tatari ⇑, A.H. Ranjbar Faculty of Physics, Shahid Bahonar University of Kerman, Kerman 7616914111, Iran
a r t i c l e
i n f o
Article history: Received 9 February 2013 Received in revised form 13 June 2013 Accepted 19 July 2013
Keywords: Photoneutron source Heavy water Tungsten Jet impingement MATLAB code
a b s t r a c t The optimization of a compact, economical and simple photoneutron production, by using the tungsten as bremsstrahlung production target and heavy water serving as the dual purpose of photoneutron production and heat exchange medium, has been studied. The Monte Carlo code MCNPX has been used to optimize the targets geometry and reflectors geometry to increase the photoneutron yield as the highest possible rate. The process of bremsstrahlung production extremely heats up the tungsten target, making it necessary to be cooled down to below 350 K. The MATLAB code and jet impingement cooling method were used to obtain the temperature of tungsten target versus the electron current and also the velocity of heavy water coolant. The jet impingement cooling method was used to control the temperature of tungsten target versus the electron current and the jet velocity. Results showed that for the temperature of 350 K, the radius of tungsten was obtained to be 15.7 cm in accordance with the maximum electron current for 10 MeV electrons. Applying the optimized dimensions of the targets and a beryllium layer of 50 cm thick as a reflector and c-contamination converter, the neutron yield was found to be 1.25 1011 n/mA/s for 10 MeV electrons. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Researches on photoneutron production based on electron accelerators have been ongoing since 1950 (Barber and George, 1959; Berger and Seltzer, 1970; Seltzer and Berger, 1973) and vastly progressed in recent years. The so-called phenomenon has many applications in science, medicine and industry, such as Neutron Activation Analysis (NAA) (Oprea et al., 2011), Boron Neutron Capture Therapy (BNCT) (Nigg et al., 1997), detection of explosives, narcotics, and alcoholic beverages (Jones, 2003; Yang et al., 2007). There are several preferred aspects for photoneutron sources using accelerators rather than radioactive sources such as the high neutron intensity production (many orders of magnitude), the possibility of switching off without any need for shielding, and their low gamma ray contamination. Several studies have been conducted on neutron production using linear electron accelerator (linac) for radiography, tomography and BNCT (Rahmani and Shahriari, 2010; Huang et al., 2006; Auditore et al., 2005). They have introduced hybrid photoneutron target BeD2 + W as a proper target for BNCT since it has a high photoneutron cross section and low threshold energy for photoneutron production (Rahmani and Shahriari, 2010). Numerous calculations and measurements have been carried out on angular distributions, energy and flux of photoneutrons
⇑ Corresponding author. Tel./fax: +98 3413222034. E-mail address: [email protected] (M. Tatari). 0306-4549/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2013.07.025
produced by microtron and betatron (Chakhlov et al., 1999; Jallu et al., 1999; Eshwarappa et al., 2005; Patil et al., 2010). A good agreement between measurements and MCNPX simulations has been found for neutrons that produced by sending 510 MeV electrons on different optimized targets (Quintieri et al., 2012). A few works have been carried out onto the measurement of photoneutron yield from heavy water (Coceva et al., 1988; Golovkov et al., 1989; Vasina et al., 1989). Dale and Gahl used from the MCNP code for modeling a photoneutron yield based on 10 MeV electron linac in a heavy water target and they compared the MCNP model with the experimental results (Dale and Gahl, 2001). The optimized converters, when fitted to the head of the linear electron accelerators, make the possibility use of them as a source of neutrons. In the process of photoneutron production the geometry and properties of the electron impinging target and the photon impinging target can greatly affect the neutron production flux. In particular, the photon-energy threshold required to overcome the binding energy of neutrons in photoneutron target and photoneutron cross sections are of high importance. 2D(c, n)1H and 9 Be(c, n)8Be reactions have the lowest threshold energies for photoneutron production and their cross sections have obtained by numerous researchers (Mobley and Laubenstein, 1950; Jakobson, 1961; Guth and Mullin, 1949). On the other hand, the majority of the energy of the incoming electrons is converted into heat in photon production target and the target temperature quickly rise up and hence greatly affects its properties. To prevent the target oxidization and its collapse, it must
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be cooled down to temperatures less than 350 K. Various methods of cooling such as water-cooled targets (Korenev, 2004; Auslender et al., 2004), circular liquid lead (Altstadt et al., 2007) have been introduced. In recent years the use of impinging fluid jets for removing heat in the target has been proposed (Kim and Kim, 2009) in which the coolant is directed toward a nozzle and injected onto the target container. The MCNPX Monte Carlo Code was used to design a cylindrical container consisting of tungsten as the bremsstrahlung production target and D2O as the photoneutron production target. Furthermore, to remove the huge amount of electron beam power converted to heat in the target and reach a more feasible photoneutron source, the jet impingement cooling method was used. In this method D2O was employed as the coolant liquid and a numerical code in the MATLAB programming software was implemented. However, the proposed neutron source is relatively inexpensive, compact enough to be used in hospitals and the design promises to produce enough neutron flux for short treatment times.
2. Source design 2.1. The e–c converter The materials with high atomic numbers are suitable for the production of bremsstrahlung photons (Knoll, 2000). Because of high atomic number of tungsten and its physical properties, it was selected as a target material for photon production. For maximum bremsstrahlung production in a tungsten as an e–c converter, the Monte Carlo code MCNPX was used to optimize the dimensions of a disc target. In SDEF card a small disk has been used as an monoenergetic electron source (10 MeV). Photon yields have been calculated by F1 tally. The LINAC beam parameters that have been considered in calculations are as follows: Output beam energy: 10 MeV. Output beam current: 50 mA. Pulse repetition rate: 300 Hz. Pulse duration: 3.6 ls. Average beam power: 540 W. In Fig. 1, variation of photon yield as a function of target thickness was shown, using tungsten radius of 1 cm. This figure shows a maximum photon yield at target thickness of 0.15 cm. Similarly, Fig. 2 shows the variation of photon yield as a function of the radius of target at the optimum thickness. This figure shows a photon yield saturation at a disc radius of 1.5 cm. The obtained optimum thickness of the electron target (0.15 cm) is less than the electron
Fig. 1. Photon yield in a cylindrical target of tungsten as a function of its thickness.
Fig. 2. Photon yield in tungsten target (disk) as a function of disk radius.
ranges (0.32 cm) in the target. This difference is attributed to the optimum dimensions of the tungsten target for maximum bremsstrahlung production at its front face. Hence some of the electrons will escape from the tungsten target and enter the D2O target. Fig. 3 shows the bremsstrahlung spectrum produced by 10 MeV electrons with the optimized dimensions obtained for the tungsten e–c converter. 2.2. The c–n converter To produce photoneutrons, a gamma ray photon with an energy of at least the binding energy of the neutrons to the c–n converter is required to make the reactions energetically possible. Applying the conservation laws of energy and linear momentum, neutron energy is obtained to be (Knoll, 2000):
En ðhÞ ffi
MðEc þ Q Þ Ec ½ð2mMÞðm þ MÞðEc þ Q Þ0:5 þ cos h mþM ðm MÞ2
ð1Þ
where Q = Q-value of the photoneutron reaction (MeV). h = angle between gamma photon and neutron direction. Ec = gamma energy (assumed 931 MeV). M = mass of recoil nucleus c2. m = mass of neutron c2. The threshold energy of photon reaction for light nuclei is greater than that of heavy nuclei. For light nuclei is given to be
Fig. 3. Bremsstrahlung spectrum produced by the optimized dimensions at the front surface of the tungsten target.
M. Tatari, A.H. Ranjbar / Annals of Nuclear Energy 63 (2014) 69–74
71
Fig. 5. Photoneutron cross section of D.
Fig. 4. Schematic of the D2O-based neutron source: (1) tungsten target, (2) D2O target and (3) reflector; (a) schematic view and (b) MCNP simulation.
8–19 MeV and for heavy nuclei it is said to be 6–8 MeV. But there are two exceptions: Beryllium (A = 4 with Ec,th = 1.666 MeV) and Deuterium (A = 2 with Ec,th=2.226 MeV) which their photoneutron cross section are low and they are used when the photon energy is low (Patil et al., 2010). Photoneutron cross section of Deuterium and Beryllium are shown in Figs. 5 and 6, respectively IAEA-TECDOC-Draftno.3 (2000). Their photoneutron cross sections are of the order of milibar from their threshold energy to 10 MeV. The photoneutron cross section of Deuterium is about 2.3 mbar ns for 10 MeV photon energy and for Beryllium is approximately 1.3 mbar ns. A cylindrical heavy water target was considered for photoneutron production as shown in Fig. 4. The dimensions of the neutron production target was optimized in a similar way as for the tungsten target. In MCNPX calculations photoneutron yields have been calculated by F1 tally. The results are presented in Figs. 7 and 8. These figures show that the optimal thickness of the D2O target is 9 cm, while the optimal radius is 32 cm. Fig. 9 presents a spectrum of the photoneutrons at the D2O target surface which posses an angular distribution. The simulations show that photoneutron yield in the forward direction (b = 0°) is higher than other directions and increasing the b angle (the angle between the direction of the incident electrons and the produced photoneutrons), leads to a decrease in the neutron yield. Considering that surrounding the neutron source by a proper c–n converter and/or a reflector could increase the neutron flux (Auditore et al., 2005; Allen and Beynon, 1995), we have optimized the thickness of a beryllium layer and a few reflectors, with a
Fig. 6. Photoneutron cross section of Be.
Fig. 7. Photoneutron production as a function of heavy water thicknesses.
conical head for collimating the neutrons, as shown in Fig. 4. The reflector material must have a low neutron absorption cross-section and a high neutron scattering cross-section, while the c–n converter surrounding material must have a low neutron absorption cross-section and with a low c–n threshold energy at the
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Fig. 8. Photoneutron production as a function of cylindrical heavy water container radius.
that the photoneurton yield increases with increasing the thickness of materials, but surrounding the photoneutron source by a layer of beryllium increases the neutron fluence several times higher than graphite and lead reflectors. the reason of higher photoneutron fluence of the beryllium layer is that beryllium can act as a reflector and also c-contamination converter (Patil et al., 2012). When the energy of the contamination photons is greater than 1.666 MeV (threshold energy of beryllium c–n), photoneutron production occurs. It can also be seen that the number of photoneutrons increases with an increasing beryllium thickness of up to 50 cm after which it remains almost constant. Choosing this configuration with the optimum thickness of the beryllium, the photoneutron spectra at the aperture was obtained and are shown in Fig. 11. The total photoneutron yield at the aperture and their average energy are 1.25 1011 n/mA/s and 0.16 MeV, respectively. According to calculations, the total photon contamination yield at the aperture is 2.78 1014 photon/mA/s with the average energy of 1.60 MeV. Coceva et al. have calculated the total neutron yield from 10 MeV electron accelerator and heavy water as photoneutron converter to be 1011 n/s/mA (Coceva et al., 1988). Eshwarappa et al. have used tantalum as e–c converter and beryllium as c–n irradiated by 8.75 MeV electron accelerator and found it to be 3.14 104 neutron/photon (Eshwarappa et al., 2005) in this study it was found to be 4.49 104 neutron/photon for 10 MeV electrons. Generally, comparing the neutron yield obtained by the above researchers and even others with our findings, it could be concluded that their neutron fluence or flux is either less than or around our result with some exceptions, implying that our proposed design is simple, more economical, and more practical, as the heat transfer process has been fully investigated. 2.3. Cooling the photon target
Fig. 9. Photoneutron spectrum obtained by the optimized dimensions of D2O target.
c-contamination energies. Graphite and lead and beryllium were chosen as the reflecting materials in a conical shape for practical applications. The neutron fluence at the exit (8 cm) of the conical applicator and 28 cm away from the D2O surface as a function of the thickness of reflectors is shown in Fig. 10. The results shown
Fig. 10. Photoneutron yield in reflectors as a function of thickness. The symbols are: j, Beryllium; w, Graphite; N, Lead.
Tungsten metal is stable in dry and humid air only at moderate temperatures and it starts to oxidize at about 400 °C. The oxide layer is not dense and does not offer any protection against further oxidation. Above 700 °C the oxidation rate increases rapidly, and above 900 °C, sublimation of the oxide takes place, resulting in catastrophic oxidation of the metal. Any moisture content of the air enhances the volatility of the oxide. Although tungsten is the metal with the highest melting point, its sensitivity toward oxidation is a big disadvantage. Therefore, all high temperature applications are limited to a protective atmosphere or vacuum. Bulk tungsten does not react with water but will be oxidized by water vapor at elevated temperature (e.g., at 600 °C) (Lassner and Schubert, 1999).
Fig. 11. Photoneutron spectrum obtained by the optimized target of W + D2O when 50 cm beryllium is surrounding the targets.
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The MCNPX simulation was also used for evaluating the heat generated by the incident electrons in the tungsten target using tally F6. It showed that the energy deposited is equal to 0.347764 MeV/(g e) for 10 MeV incident electrons. For 1 mA of 10 MeV incident electrons and after a few seconds, the temperature of the target reaches its melting point. Thus, in order to employ high electron currents a feasible cooling liquid and method should be used. We have chosen the heavy water that acts as a dual purpose medium (as the neutron production target and also coolant medium). To prevent the evaporation of this liquid medium and oxidation of the tungsten, the temperature of tungsten must remain below the boiling point of heavy water. However, for thermal management of such a high temperature target the impinging fluid jet is the most effective and proper technique that could remove a huge amount of the heat produced in the electron target. To prevent the evaporation of this liquid medium and oxidation of the tungsten, the temperature of tungsten must remain below the boiling point of heavy water. Hence, for thermal management of such a high temperature target a proper technique that can remove a huge amount of the heat produced in the electron-c target must be used. The impingement cooling method is one of the most effective alternatives to increase the heat transfer rates across a high temperature target. In this method, with an appropriately configured distribution nozzle array, and the freedom to tailor the jet flow to the local cooling requirements, a high heat transfer coefficient can be attained. In order to prevent oxidation of the tungsten, a temperature limitation for the tungsten must be considered. Considering this limitation, the peak heat flux on the target can be calculated. In order to estimate the temperature, conservation equation of energy is derived for the target as below:
q00tungstenwall ðpR2 þ 2pRLÞ þ q00jet ðpR2 Þ þ q00tungstenambient ðpR2 Þ ¼ q_ ðpR2 LÞ
ð2Þ
where q00 = convective heat flux (W/m2); q_ = rate of energy generation per unit volume (W/m3); R = radius of tungsten (m); L = thickness of tungsten (m).
Velocity of heavy water (m/s)
Imax (mA) for Ee = 10 MeV
1 3 5 7 9
2.16 4.49 6.31 7.90 9.34
where h is the convective heat transfer coefficient (W/m2 K). Nusselt number is a dimensionless number that determines the ratio of convection to pure conduction heat transfer as below (Incropera and DeWitt, 1981):
Nu ¼
hD kf
ð4Þ
where kf is thermal conductivity of the fluid (W/m K). A larger Nusselt number corresponds to more active convection with turbulent flow. In order to simulate the heat transfer between the jet and tungsten a jet Nusselt number is used, as follows (Bejan and Kraus, 2003): 2 NU D ¼ 41 þ
H=D pffiffiffi 0:6= f
!3 30:05 ( pffiffiffi 5 f
pffiffiffi 1 2:2 f
)
pffiffiffi ReD0:667 Pr0:42 1 þ 0:2½ðH=DÞ 6 f
ð5Þ
where Re, Pr and H/D are the jet Reynolds number, Prandtl number and ratio of tungsten height to diameter of jet respectively and f is impinging area ratio and calculated according to this equation:
f ¼ 0:785nD2 =A
ð6Þ
n is number of jets and A is surface area of tungsten. Also, the convective heat transfer between the tungsten surface and ambient can be calculated as follows:
q00tungstenambient ¼ hðT tungsten T ambient Þ
ð7Þ
The net rate radiation heat transfer between the ground surface and the collector roof is given by:
The convective heat transfer between the tungsten surface and the jet can be calculated as follows:
q00Jet ¼ hðT tungsten T Jet Þ
Table 1 The maximum electron current at various jet velocities of heavy water. The temperature limitation was assumed to be 350 K and the radius of the tungsten target was 15.7 cm.
ð3Þ
q00tungstenwall ¼ er T 4tungsten T 4wall
ð8Þ
where e and r (5.67 108 W/m2 K4) are the emissivity and Stefan–Boltzmann constant, respectively. To estimate temperature of the tungsten for any heat flux on the target, conservation equation of the energy is numerically solved using a computer program implemented in MATLAB programming software. A parametric study to determine the appropriate radii corresponding to a range of electron currents for different values of jet velocity is performed, considering a temperature limitation of 350 K and a jet with 2 cm in diameter. Fig. 12 illustrates the radius of tungsten versus electron currents at a jet velocity of 3 m/s. It can be observed that the appropriate radius of tungsten in accordance with the maximum current of electrons is 15.7 cm. The numerical results for the maximum electron current for various values of the jet velocity are shown in Table 1. 3. Conclusion
Fig. 12. Radius of tungsten target versus incident electron current. The temperature limitation was assumed to be 350 K and the jet velocity was 3 m/s.
A photoneutron source consisting of a tungsten target as e–c converter, heavy water acting as both c–n converter and heat transfer liquid and also a beryllium layer as a reflector and c-contamination-n converter surrounding the targets has been developed using 10 MeV electron accelerator. The MCNPX Monte Carlo code was used to optimize the dimensions of the targets. A
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maximum photon yield was obtained at a cylindrical tungsten target with 0.15 cm and 1.5 cm in thickness and radius, respectively. Employing these optimum dimensions, the optimum thickness of the neutron production target, D2O, was obtained to be 9 cm, while its optimum radius was obtained to be 32 cm. Among graphite, lead and beryllium as the neutron reflectors that surrounding the photoneutron source, beryllium with a 50 cm thickness provided a higher neutron flux. Using the optimized values of the targets, the neutron fluence at the aperture of the reflector was 1.25 1011 n/mA/s with an average energy of 0.16 MeV. Jet impingement cooling method was employed to deploy high electron currents as a means of producing higher neutron fluxes. To prevent the oxidization and melting of the tungsten target and evaporation of the heavy water a temperature limit of 350 K was considered in all studying processes. A computer simulation program was implemented for determining the appropriate radii corresponding to a range of electron currents for different values of jet velocities. Based on the results, the appropriate radius of tungsten in accordance with a maximum electron current of 4.50 mA at a jet velocity of 3 m/s was obtained to be 15.7 cm. The proposed design together with the optimized parameters and dimensions promises a compact neutron source to be used for radiotherapy and BNCT applications. References Allen, D.A., Beynon, T.D., 1995. A design study for an accelerator-based epithermal neutron beam for BNCT. Phys. Med. Biol. 40, 807–821. Altstadt, E., Beckert, C., Freiesleben, H., Galindo, V., Grosse, E., Junghans, A., Klug, J., Naumann, B., Schneider, S., Schlenk, R., Wagner, A., Weiss, F.P., 2007. A photoneutron source for time-of-flight measurements at the radiation source ELBE. Ann. Nucl. Energy 34 (12), 36–50. Auditore, L., Barna, R., Pasquale, D.D., Italiano, A., Trifiro, A., Trimarchi, M., 2005. Study of a 5 MeV electron linac based neutron source. Nucl. Instrum. Methods B 229 (1), 137–143. Auslender, V., Bukin, A., Voronin, L., Kokin, E., Korobeinikov, M., Krainov, G., Lukin, A., Radchenko, V., Sidorov, A., Tkachenko, V., 2004. Bremsstrahlung converters for powerful industrial electron accelerators. Radiat. Phys. Chem. 71 (12), 297– 299 (13th International Meeting on Radiation Processing (IMRP-2003)). Barber, W.C., George, W.D., 1959. Neutron yields from targets bombarded by electrons. Phys. Rev. 116 (6), 1551–1559. Bejan, A., Kraus, A., 2003. Heat Transfer Handbook Number J., vol. 1. Wiley. Berger, M.J., Seltzer, S.M., 1970. Bremsstrahlung and photoneutrons from thick tungsten and tantalum targets. Phys. Rev. C 2 (2), 621–631. Chakhlov, V., Bell, Z., Golovkov, V., Shtein, M., 1999. Photoneutron source based on a compact 10 MeV betatron. Nucl. Instrum. Methods A 422 (13), 5–9. Coceva, C., Cupini, E., Fioni, G., 1988. Characteristics of pulsed neutron sources obtained with a low-energy electron accelerato, nuclear data for science and technology. In: Igarasi, S. (Ed.), Proceedings of the International Conference Mito, 1988, JAERI, Saikon, pp. 363–366. Dale, G.E., Gahl, J.M., 2001. Modeling the neutron yield of a therapeutic thermal neutron source driven with a repetitively pulsed electron linac. Pulsed Power Plasma Sci. 2, 1154–1157. Eshwarappa, K., Ganesh, Siddappa, K., Kashyap, Y., Sinha, A., Sarkar, P., Godwal, B., 2005. Estimation of photoneutron yield from beryllium target irradiated by
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Design of a photoneutron source based on 10 MeV electrons of radiotherapy linac M. Tatari ⇑, A.H. Ranjbar Faculty of Physics, Shahid Bahonar University of Kerman, Kerman 7616914111, Iran
a r t i c l e
i n f o
Article history: Received 9 February 2013 Received in revised form 13 June 2013 Accepted 19 July 2013
Keywords: Photoneutron source Heavy water Tungsten Jet impingement MATLAB code
a b s t r a c t The optimization of a compact, economical and simple photoneutron production, by using the tungsten as bremsstrahlung production target and heavy water serving as the dual purpose of photoneutron production and heat exchange medium, has been studied. The Monte Carlo code MCNPX has been used to optimize the targets geometry and reflectors geometry to increase the photoneutron yield as the highest possible rate. The process of bremsstrahlung production extremely heats up the tungsten target, making it necessary to be cooled down to below 350 K. The MATLAB code and jet impingement cooling method were used to obtain the temperature of tungsten target versus the electron current and also the velocity of heavy water coolant. The jet impingement cooling method was used to control the temperature of tungsten target versus the electron current and the jet velocity. Results showed that for the temperature of 350 K, the radius of tungsten was obtained to be 15.7 cm in accordance with the maximum electron current for 10 MeV electrons. Applying the optimized dimensions of the targets and a beryllium layer of 50 cm thick as a reflector and c-contamination converter, the neutron yield was found to be 1.25 1011 n/mA/s for 10 MeV electrons. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Researches on photoneutron production based on electron accelerators have been ongoing since 1950 (Barber and George, 1959; Berger and Seltzer, 1970; Seltzer and Berger, 1973) and vastly progressed in recent years. The so-called phenomenon has many applications in science, medicine and industry, such as Neutron Activation Analysis (NAA) (Oprea et al., 2011), Boron Neutron Capture Therapy (BNCT) (Nigg et al., 1997), detection of explosives, narcotics, and alcoholic beverages (Jones, 2003; Yang et al., 2007). There are several preferred aspects for photoneutron sources using accelerators rather than radioactive sources such as the high neutron intensity production (many orders of magnitude), the possibility of switching off without any need for shielding, and their low gamma ray contamination. Several studies have been conducted on neutron production using linear electron accelerator (linac) for radiography, tomography and BNCT (Rahmani and Shahriari, 2010; Huang et al., 2006; Auditore et al., 2005). They have introduced hybrid photoneutron target BeD2 + W as a proper target for BNCT since it has a high photoneutron cross section and low threshold energy for photoneutron production (Rahmani and Shahriari, 2010). Numerous calculations and measurements have been carried out on angular distributions, energy and flux of photoneutrons
⇑ Corresponding author. Tel./fax: +98 3413222034. E-mail address: [email protected] (M. Tatari). 0306-4549/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2013.07.025
produced by microtron and betatron (Chakhlov et al., 1999; Jallu et al., 1999; Eshwarappa et al., 2005; Patil et al., 2010). A good agreement between measurements and MCNPX simulations has been found for neutrons that produced by sending 510 MeV electrons on different optimized targets (Quintieri et al., 2012). A few works have been carried out onto the measurement of photoneutron yield from heavy water (Coceva et al., 1988; Golovkov et al., 1989; Vasina et al., 1989). Dale and Gahl used from the MCNP code for modeling a photoneutron yield based on 10 MeV electron linac in a heavy water target and they compared the MCNP model with the experimental results (Dale and Gahl, 2001). The optimized converters, when fitted to the head of the linear electron accelerators, make the possibility use of them as a source of neutrons. In the process of photoneutron production the geometry and properties of the electron impinging target and the photon impinging target can greatly affect the neutron production flux. In particular, the photon-energy threshold required to overcome the binding energy of neutrons in photoneutron target and photoneutron cross sections are of high importance. 2D(c, n)1H and 9 Be(c, n)8Be reactions have the lowest threshold energies for photoneutron production and their cross sections have obtained by numerous researchers (Mobley and Laubenstein, 1950; Jakobson, 1961; Guth and Mullin, 1949). On the other hand, the majority of the energy of the incoming electrons is converted into heat in photon production target and the target temperature quickly rise up and hence greatly affects its properties. To prevent the target oxidization and its collapse, it must
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be cooled down to temperatures less than 350 K. Various methods of cooling such as water-cooled targets (Korenev, 2004; Auslender et al., 2004), circular liquid lead (Altstadt et al., 2007) have been introduced. In recent years the use of impinging fluid jets for removing heat in the target has been proposed (Kim and Kim, 2009) in which the coolant is directed toward a nozzle and injected onto the target container. The MCNPX Monte Carlo Code was used to design a cylindrical container consisting of tungsten as the bremsstrahlung production target and D2O as the photoneutron production target. Furthermore, to remove the huge amount of electron beam power converted to heat in the target and reach a more feasible photoneutron source, the jet impingement cooling method was used. In this method D2O was employed as the coolant liquid and a numerical code in the MATLAB programming software was implemented. However, the proposed neutron source is relatively inexpensive, compact enough to be used in hospitals and the design promises to produce enough neutron flux for short treatment times.
2. Source design 2.1. The e–c converter The materials with high atomic numbers are suitable for the production of bremsstrahlung photons (Knoll, 2000). Because of high atomic number of tungsten and its physical properties, it was selected as a target material for photon production. For maximum bremsstrahlung production in a tungsten as an e–c converter, the Monte Carlo code MCNPX was used to optimize the dimensions of a disc target. In SDEF card a small disk has been used as an monoenergetic electron source (10 MeV). Photon yields have been calculated by F1 tally. The LINAC beam parameters that have been considered in calculations are as follows: Output beam energy: 10 MeV. Output beam current: 50 mA. Pulse repetition rate: 300 Hz. Pulse duration: 3.6 ls. Average beam power: 540 W. In Fig. 1, variation of photon yield as a function of target thickness was shown, using tungsten radius of 1 cm. This figure shows a maximum photon yield at target thickness of 0.15 cm. Similarly, Fig. 2 shows the variation of photon yield as a function of the radius of target at the optimum thickness. This figure shows a photon yield saturation at a disc radius of 1.5 cm. The obtained optimum thickness of the electron target (0.15 cm) is less than the electron
Fig. 1. Photon yield in a cylindrical target of tungsten as a function of its thickness.
Fig. 2. Photon yield in tungsten target (disk) as a function of disk radius.
ranges (0.32 cm) in the target. This difference is attributed to the optimum dimensions of the tungsten target for maximum bremsstrahlung production at its front face. Hence some of the electrons will escape from the tungsten target and enter the D2O target. Fig. 3 shows the bremsstrahlung spectrum produced by 10 MeV electrons with the optimized dimensions obtained for the tungsten e–c converter. 2.2. The c–n converter To produce photoneutrons, a gamma ray photon with an energy of at least the binding energy of the neutrons to the c–n converter is required to make the reactions energetically possible. Applying the conservation laws of energy and linear momentum, neutron energy is obtained to be (Knoll, 2000):
En ðhÞ ffi
MðEc þ Q Þ Ec ½ð2mMÞðm þ MÞðEc þ Q Þ0:5 þ cos h mþM ðm MÞ2
ð1Þ
where Q = Q-value of the photoneutron reaction (MeV). h = angle between gamma photon and neutron direction. Ec = gamma energy (assumed 931 MeV). M = mass of recoil nucleus c2. m = mass of neutron c2. The threshold energy of photon reaction for light nuclei is greater than that of heavy nuclei. For light nuclei is given to be
Fig. 3. Bremsstrahlung spectrum produced by the optimized dimensions at the front surface of the tungsten target.
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Fig. 5. Photoneutron cross section of D.
Fig. 4. Schematic of the D2O-based neutron source: (1) tungsten target, (2) D2O target and (3) reflector; (a) schematic view and (b) MCNP simulation.
8–19 MeV and for heavy nuclei it is said to be 6–8 MeV. But there are two exceptions: Beryllium (A = 4 with Ec,th = 1.666 MeV) and Deuterium (A = 2 with Ec,th=2.226 MeV) which their photoneutron cross section are low and they are used when the photon energy is low (Patil et al., 2010). Photoneutron cross section of Deuterium and Beryllium are shown in Figs. 5 and 6, respectively IAEA-TECDOC-Draftno.3 (2000). Their photoneutron cross sections are of the order of milibar from their threshold energy to 10 MeV. The photoneutron cross section of Deuterium is about 2.3 mbar ns for 10 MeV photon energy and for Beryllium is approximately 1.3 mbar ns. A cylindrical heavy water target was considered for photoneutron production as shown in Fig. 4. The dimensions of the neutron production target was optimized in a similar way as for the tungsten target. In MCNPX calculations photoneutron yields have been calculated by F1 tally. The results are presented in Figs. 7 and 8. These figures show that the optimal thickness of the D2O target is 9 cm, while the optimal radius is 32 cm. Fig. 9 presents a spectrum of the photoneutrons at the D2O target surface which posses an angular distribution. The simulations show that photoneutron yield in the forward direction (b = 0°) is higher than other directions and increasing the b angle (the angle between the direction of the incident electrons and the produced photoneutrons), leads to a decrease in the neutron yield. Considering that surrounding the neutron source by a proper c–n converter and/or a reflector could increase the neutron flux (Auditore et al., 2005; Allen and Beynon, 1995), we have optimized the thickness of a beryllium layer and a few reflectors, with a
Fig. 6. Photoneutron cross section of Be.
Fig. 7. Photoneutron production as a function of heavy water thicknesses.
conical head for collimating the neutrons, as shown in Fig. 4. The reflector material must have a low neutron absorption cross-section and a high neutron scattering cross-section, while the c–n converter surrounding material must have a low neutron absorption cross-section and with a low c–n threshold energy at the
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Fig. 8. Photoneutron production as a function of cylindrical heavy water container radius.
that the photoneurton yield increases with increasing the thickness of materials, but surrounding the photoneutron source by a layer of beryllium increases the neutron fluence several times higher than graphite and lead reflectors. the reason of higher photoneutron fluence of the beryllium layer is that beryllium can act as a reflector and also c-contamination converter (Patil et al., 2012). When the energy of the contamination photons is greater than 1.666 MeV (threshold energy of beryllium c–n), photoneutron production occurs. It can also be seen that the number of photoneutrons increases with an increasing beryllium thickness of up to 50 cm after which it remains almost constant. Choosing this configuration with the optimum thickness of the beryllium, the photoneutron spectra at the aperture was obtained and are shown in Fig. 11. The total photoneutron yield at the aperture and their average energy are 1.25 1011 n/mA/s and 0.16 MeV, respectively. According to calculations, the total photon contamination yield at the aperture is 2.78 1014 photon/mA/s with the average energy of 1.60 MeV. Coceva et al. have calculated the total neutron yield from 10 MeV electron accelerator and heavy water as photoneutron converter to be 1011 n/s/mA (Coceva et al., 1988). Eshwarappa et al. have used tantalum as e–c converter and beryllium as c–n irradiated by 8.75 MeV electron accelerator and found it to be 3.14 104 neutron/photon (Eshwarappa et al., 2005) in this study it was found to be 4.49 104 neutron/photon for 10 MeV electrons. Generally, comparing the neutron yield obtained by the above researchers and even others with our findings, it could be concluded that their neutron fluence or flux is either less than or around our result with some exceptions, implying that our proposed design is simple, more economical, and more practical, as the heat transfer process has been fully investigated. 2.3. Cooling the photon target
Fig. 9. Photoneutron spectrum obtained by the optimized dimensions of D2O target.
c-contamination energies. Graphite and lead and beryllium were chosen as the reflecting materials in a conical shape for practical applications. The neutron fluence at the exit (8 cm) of the conical applicator and 28 cm away from the D2O surface as a function of the thickness of reflectors is shown in Fig. 10. The results shown
Fig. 10. Photoneutron yield in reflectors as a function of thickness. The symbols are: j, Beryllium; w, Graphite; N, Lead.
Tungsten metal is stable in dry and humid air only at moderate temperatures and it starts to oxidize at about 400 °C. The oxide layer is not dense and does not offer any protection against further oxidation. Above 700 °C the oxidation rate increases rapidly, and above 900 °C, sublimation of the oxide takes place, resulting in catastrophic oxidation of the metal. Any moisture content of the air enhances the volatility of the oxide. Although tungsten is the metal with the highest melting point, its sensitivity toward oxidation is a big disadvantage. Therefore, all high temperature applications are limited to a protective atmosphere or vacuum. Bulk tungsten does not react with water but will be oxidized by water vapor at elevated temperature (e.g., at 600 °C) (Lassner and Schubert, 1999).
Fig. 11. Photoneutron spectrum obtained by the optimized target of W + D2O when 50 cm beryllium is surrounding the targets.
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The MCNPX simulation was also used for evaluating the heat generated by the incident electrons in the tungsten target using tally F6. It showed that the energy deposited is equal to 0.347764 MeV/(g e) for 10 MeV incident electrons. For 1 mA of 10 MeV incident electrons and after a few seconds, the temperature of the target reaches its melting point. Thus, in order to employ high electron currents a feasible cooling liquid and method should be used. We have chosen the heavy water that acts as a dual purpose medium (as the neutron production target and also coolant medium). To prevent the evaporation of this liquid medium and oxidation of the tungsten, the temperature of tungsten must remain below the boiling point of heavy water. However, for thermal management of such a high temperature target the impinging fluid jet is the most effective and proper technique that could remove a huge amount of the heat produced in the electron target. To prevent the evaporation of this liquid medium and oxidation of the tungsten, the temperature of tungsten must remain below the boiling point of heavy water. Hence, for thermal management of such a high temperature target a proper technique that can remove a huge amount of the heat produced in the electron-c target must be used. The impingement cooling method is one of the most effective alternatives to increase the heat transfer rates across a high temperature target. In this method, with an appropriately configured distribution nozzle array, and the freedom to tailor the jet flow to the local cooling requirements, a high heat transfer coefficient can be attained. In order to prevent oxidation of the tungsten, a temperature limitation for the tungsten must be considered. Considering this limitation, the peak heat flux on the target can be calculated. In order to estimate the temperature, conservation equation of energy is derived for the target as below:
q00tungstenwall ðpR2 þ 2pRLÞ þ q00jet ðpR2 Þ þ q00tungstenambient ðpR2 Þ ¼ q_ ðpR2 LÞ
ð2Þ
where q00 = convective heat flux (W/m2); q_ = rate of energy generation per unit volume (W/m3); R = radius of tungsten (m); L = thickness of tungsten (m).
Velocity of heavy water (m/s)
Imax (mA) for Ee = 10 MeV
1 3 5 7 9
2.16 4.49 6.31 7.90 9.34
where h is the convective heat transfer coefficient (W/m2 K). Nusselt number is a dimensionless number that determines the ratio of convection to pure conduction heat transfer as below (Incropera and DeWitt, 1981):
Nu ¼
hD kf
ð4Þ
where kf is thermal conductivity of the fluid (W/m K). A larger Nusselt number corresponds to more active convection with turbulent flow. In order to simulate the heat transfer between the jet and tungsten a jet Nusselt number is used, as follows (Bejan and Kraus, 2003): 2 NU D ¼ 41 þ
H=D pffiffiffi 0:6= f
!3 30:05 ( pffiffiffi 5 f
pffiffiffi 1 2:2 f
)
pffiffiffi ReD0:667 Pr0:42 1 þ 0:2½ðH=DÞ 6 f
ð5Þ
where Re, Pr and H/D are the jet Reynolds number, Prandtl number and ratio of tungsten height to diameter of jet respectively and f is impinging area ratio and calculated according to this equation:
f ¼ 0:785nD2 =A
ð6Þ
n is number of jets and A is surface area of tungsten. Also, the convective heat transfer between the tungsten surface and ambient can be calculated as follows:
q00tungstenambient ¼ hðT tungsten T ambient Þ
ð7Þ
The net rate radiation heat transfer between the ground surface and the collector roof is given by:
The convective heat transfer between the tungsten surface and the jet can be calculated as follows:
q00Jet ¼ hðT tungsten T Jet Þ
Table 1 The maximum electron current at various jet velocities of heavy water. The temperature limitation was assumed to be 350 K and the radius of the tungsten target was 15.7 cm.
ð3Þ
q00tungstenwall ¼ er T 4tungsten T 4wall
ð8Þ
where e and r (5.67 108 W/m2 K4) are the emissivity and Stefan–Boltzmann constant, respectively. To estimate temperature of the tungsten for any heat flux on the target, conservation equation of the energy is numerically solved using a computer program implemented in MATLAB programming software. A parametric study to determine the appropriate radii corresponding to a range of electron currents for different values of jet velocity is performed, considering a temperature limitation of 350 K and a jet with 2 cm in diameter. Fig. 12 illustrates the radius of tungsten versus electron currents at a jet velocity of 3 m/s. It can be observed that the appropriate radius of tungsten in accordance with the maximum current of electrons is 15.7 cm. The numerical results for the maximum electron current for various values of the jet velocity are shown in Table 1. 3. Conclusion
Fig. 12. Radius of tungsten target versus incident electron current. The temperature limitation was assumed to be 350 K and the jet velocity was 3 m/s.
A photoneutron source consisting of a tungsten target as e–c converter, heavy water acting as both c–n converter and heat transfer liquid and also a beryllium layer as a reflector and c-contamination-n converter surrounding the targets has been developed using 10 MeV electron accelerator. The MCNPX Monte Carlo code was used to optimize the dimensions of the targets. A
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maximum photon yield was obtained at a cylindrical tungsten target with 0.15 cm and 1.5 cm in thickness and radius, respectively. Employing these optimum dimensions, the optimum thickness of the neutron production target, D2O, was obtained to be 9 cm, while its optimum radius was obtained to be 32 cm. Among graphite, lead and beryllium as the neutron reflectors that surrounding the photoneutron source, beryllium with a 50 cm thickness provided a higher neutron flux. Using the optimized values of the targets, the neutron fluence at the aperture of the reflector was 1.25 1011 n/mA/s with an average energy of 0.16 MeV. Jet impingement cooling method was employed to deploy high electron currents as a means of producing higher neutron fluxes. To prevent the oxidization and melting of the tungsten target and evaporation of the heavy water a temperature limit of 350 K was considered in all studying processes. A computer simulation program was implemented for determining the appropriate radii corresponding to a range of electron currents for different values of jet velocities. Based on the results, the appropriate radius of tungsten in accordance with a maximum electron current of 4.50 mA at a jet velocity of 3 m/s was obtained to be 15.7 cm. The proposed design together with the optimized parameters and dimensions promises a compact neutron source to be used for radiotherapy and BNCT applications. References Allen, D.A., Beynon, T.D., 1995. A design study for an accelerator-based epithermal neutron beam for BNCT. Phys. Med. Biol. 40, 807–821. Altstadt, E., Beckert, C., Freiesleben, H., Galindo, V., Grosse, E., Junghans, A., Klug, J., Naumann, B., Schneider, S., Schlenk, R., Wagner, A., Weiss, F.P., 2007. A photoneutron source for time-of-flight measurements at the radiation source ELBE. Ann. Nucl. Energy 34 (12), 36–50. Auditore, L., Barna, R., Pasquale, D.D., Italiano, A., Trifiro, A., Trimarchi, M., 2005. Study of a 5 MeV electron linac based neutron source. Nucl. Instrum. Methods B 229 (1), 137–143. Auslender, V., Bukin, A., Voronin, L., Kokin, E., Korobeinikov, M., Krainov, G., Lukin, A., Radchenko, V., Sidorov, A., Tkachenko, V., 2004. Bremsstrahlung converters for powerful industrial electron accelerators. Radiat. Phys. Chem. 71 (12), 297– 299 (13th International Meeting on Radiation Processing (IMRP-2003)). Barber, W.C., George, W.D., 1959. Neutron yields from targets bombarded by electrons. Phys. Rev. 116 (6), 1551–1559. Bejan, A., Kraus, A., 2003. Heat Transfer Handbook Number J., vol. 1. Wiley. Berger, M.J., Seltzer, S.M., 1970. Bremsstrahlung and photoneutrons from thick tungsten and tantalum targets. Phys. Rev. C 2 (2), 621–631. Chakhlov, V., Bell, Z., Golovkov, V., Shtein, M., 1999. Photoneutron source based on a compact 10 MeV betatron. Nucl. Instrum. Methods A 422 (13), 5–9. Coceva, C., Cupini, E., Fioni, G., 1988. Characteristics of pulsed neutron sources obtained with a low-energy electron accelerato, nuclear data for science and technology. In: Igarasi, S. (Ed.), Proceedings of the International Conference Mito, 1988, JAERI, Saikon, pp. 363–366. Dale, G.E., Gahl, J.M., 2001. Modeling the neutron yield of a therapeutic thermal neutron source driven with a repetitively pulsed electron linac. Pulsed Power Plasma Sci. 2, 1154–1157. Eshwarappa, K., Ganesh, Siddappa, K., Kashyap, Y., Sinha, A., Sarkar, P., Godwal, B., 2005. Estimation of photoneutron yield from beryllium target irradiated by
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