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Possibility of tritium self-sufficiency in low aspect ratio tokamak reactor with the outboard blanket only
Fusion Engineering and Design 81 (2006) 2779–2784
Possibility of tritium self-sufficiency in low aspect ratio tokamak reactor with the outboard blanket only T. Hayashi ∗ , K. Tobita, S. Nishio, S. Sato, T. Nishitani, M. Yamauchi Naka Fusion Institute, Japan Atomic Energy Agency, 801 Mukouyama, Naka, Ibaraki 311-0193, Japan Available online 17 August 2006
Abstract The possibility of tritium self-sufficiency in a low aspect ratio (low-A) tokamak reactor with the outboard blanket only has been studied to simplify the inboard structure located in a high magnetic field. The tritium breeding ratio (TBR) of the outboard blanket increases by applying a neutron multiplier such as lead and beryllium to the inboard reflector. The effect in local TBR of a 40 cm thick inboard reflector of lead is about 40% that of the inboard breeding blanket. The local TBR of a reactor with both the lead inboard reflector and outboard blanket using a Li2 O breeder and a beryllium multiplier can be larger than 1.35 for aspect ratios less than 2.9. The local TBR of 1.35 satisfies the net TBR requirement of 1.05 where there is 78% coverage of the breeding zone over the total plasma-facing surface area. The result indicates there is a design solution achieving tritium self-sufficiency even in a low-A tokamak reactor with the outboard breeding blanket only, using an appropriate inboard reflector. Be12 Ti and Li2 TiO3 are recommended from the viewpoint of safety. In the combination, the aspect ratio is required to be less than 1.35 to achieve local TBR of 1.35. © 2006 Elsevier B.V. All rights reserved. Keywords: Tritium breeding ratio; Blanket; Reflector; Lead; Beryllium; Aspect ratio
1. Introduction In a tokamak reactor, the tritium breeding ratio (TBR) in a blanket is required to be more than unity [1–4]. One of the most critical issues in the reactor design is blanket structural robustness against electromagnetic (EM) forces acting during plasma disruptions. In particular, care in the design of the breeding ∗ Corresponding author. Tel.: +81 29 270 7431; fax: +81 29 270 7449. E-mail address: [email protected] (T. Hayashi).
0920-3796/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2006.07.045
blanket on the inboard side is necessary to overcome higher EM forces created by the high magnetic field. Therefore it is desirable to simplify the inboard structure to improve the reliability and safety. Many design studies of fusion reactors characterized by low aspect ratio (A) and low toroidal field have been reported [5–10]. In the tokamak with the outboard blanket only, a low-A reactor has the advantage that it can achieve a larger TBR than a conventional-A reactor, because the area of the outboard wall is larger. The coverage of the breeding zone over plasma facing area strongly depends on the designs of the divertor, ports
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and blankets. Assuming that the coverage of the breeding zone is 78%, local TBR above 1.35 is required to achieve net TBR of 1.05. In this case, the other 22% is flexibly and efficiently allocated to the other plasma-facing components. For example, the coverage of divertor, ports and non-breeding area of blanket such as headers and ribs may be 6%, 2% and 14%, respectively. This paper describes the possibility of tritium self-sufficiency in low-A tokamak reactors with the outboard blanket only, an inboard neutron reflector being installed instead of an inboard breeding blanket. Neutron transport calculations have been performed to evaluate the local TBR and to assess the prospect of a fusion plant without an inboard breeding blanket.
2. Calculation method Table 1 shows the one-dimensional calculation model. The plasma major and minor radii were 5.77 and 2.1 m, respectively, and its aspect ratio corresponded to 2.75. When the thickness of the inboard reflector or blanket was increased from 0 to 40 cm, that of the inboard shield was decreased from 90 to 50 cm to maintain constant major radius and aspect ratio. The inboard side of toroidal field (TF) coils and/or center solenoid (CS) can be placed in the inboard space of 225 cm
width. Each region in Table 1, such as the breeding blanket and reflector, was assumed to be homogeneous. The thickness of the outboard blanket is 90 cm. The blanket was assumed to consist of supercritical water (SCW) as a coolant, solid breeder pebbles (Li2 O or Li2 TiO3 ), neutron multiplier pebbles (Be or Be12 Ti) and low activation ferritic steel, F82H. These materials were selected based on design studies for a solid blanket system for DEMO reactors [1,3,4]. Packing fractions of the breeder and multiplier are, respectively, 0.51 and 0.80. From the point of view of safety, an important issue for water-cooled components using beryllium is the beryllium-steam reaction in the case of a loss-of-coolant accident (LOCA). The combination of Be12 Ti multiplier and Li2 TiO3 breeder is recommended over that of Be and Li2 O from the viewpoint of safety [1,3,11,12]. The calculations were carried out with the onedimensional transport code, ANISN [13], and a transport group constant set of FUSION-40 [14], which consists of 42 neutron groups and 21 ␥-ray groups based on JENDL-3.1 [15]. For the estimation of the local TBR, we have used the JENDL dosimetry file. We conducted the sensitivity analyses by changing the type and thickness of the inboard reflector, the volume ratio of the neutron multiplier to the tritium breeder, the enrichment factor of the 6 Li as the lithium isotope, and the aspect ratio of the tokamak reactor.
Table 1 One-dimensional calculation model for sensitivity analyses Region
Material
Thickness (cm)
Inboard space VV Shield Back plate
Void F82H F82H (70%), water (30%) F82H
225 10 90–50 15
Reflector or blanket
Various materials such as lead (70%) F82H (50%), SCW (50%) Void Plasma Void F82H (50%), SCW (50%)
0–40
Li2 O or Li2 TiO3 , Be or Be12 Ti, SCW (16.8%), F82H (14.4%) F82H F82H (70%), water (30%) F82H
90
First wall Gap (SOL) Plasma Gap (SOL) First wall Outboard blanket
Back plate Shield VV
1.6 25 420 10 1.6
15 55 10
3. Results and discussion 3.1. Effect of inboard reflector Fig. 1 shows the dependence of the local TBR on the thickness of various inboard reflectors. In the calculations, the 90% 6 Li enriched Li2 O breeder, the Be multiplier and the optimum volume ratio of these materials described in Section 3.2 were used. The local TBR is higher for lead, intermediate for beryllium, and lower for tungsten. It is notable that, only in the case of lead does the local TBR increase with the thickness of the inboard reflector, TBR being larger than 1.35 when thickness is over 20 cm. Fig. 2(a) and (b) show neutron fluxes for various materials at positions in the 40 cm thick inboard reflector, the first wall and part of the scrape-off layer (SOL): (a) showing the total neutron flux and (b) showing the
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low energy neutron flux (E < 0.1 MeV). Because the 6 Li(n,t)4 He cross-section is very large in the lower neutron energy region [16], the low energy neutrons can increase the TBR. In Fig. 2(b), low energy neutron fluxes in the inboard SOL of lead and beryllium are higher than those in conventional reflectors such as F82H and tungsten, because lead and beryllium work as neutron multipliers. Therefore, the local TBR of the outboard blanket was increased by the low energy neutrons produced in the inboard material as shown in Figs. 1 and 2(b). 3.2. Dependency on the ratio of the multiplier to the breeder Fig. 1. Dependence of local TBR on the thickness of inboard reflector for various materials.
Fig. 2. Change of neutron fluxes in the inboard reflector comprising various materials: (a) total neutron flux and (b) low energy neutron flux (E < 0.1 MeV).
Fig. 3(a) and (b) show the dependency of local TBR on the volume ratio of the neutron multiplier to the tritium breeder: (a) for various combinations of the multiplier (Be or Be12 Ti) with the 90% 6 Li enriched
Fig. 3. Dependence of local TBR on the volume ratio of the multiplier to the breeder: (a) for various combinations of the multiplier (Be or Be12 Ti) with 90% 6 Li enriched breeder (Li2 O or Li2 TiO3 ) and (b) for various 6 Li enrichments of Li2 O with Be multiplier.
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breeder (Li2 O or Li2 TiO3 ), (b) for various 6 Li enrichments of Li2 O with the Be multiplier. The volume ratios of SCW and F82H were kept constant in order to evaluate only the effect of mixture ratio of multiplier and breeder. A 40 cm thick lead inboard reflector was used for the calculations. In Fig. 3(a), the local TBR for the combination of Li2 O and Be is significantly larger than that of the other combinations including Li2 O, Li2 TiO3 , Be and Be12 Ti. In addition, the optimum volume ratios vary according to the combination of the breeder and multiplier. The optimum volume ratios for the combinations of Be/Li2 O and Be12 Ti/Li2 TiO3 are 4.5 and 1.8, respectively. This indicates that the selection of the optimum combination and also the optimum volume ratio of the breeder and multiplier are necessary to attain the larger TBR. As the 6 Li enrichment rises in Fig. 3(b), both the local TBR and optimum volume ratio of the multiplier to the breeder increase. The optimum ratios for the 6 Li enrichment of 30% and 90% are, respectively, 2.4 and 4.5. These results show that the higher 6 Li enrichment can reduce the optimum amount of lithium, and can increase the TBR if more multiplier is used. Only in the case of Be and 90% 6 Li enriched Li2 O is the local TBR slightly larger than 1.35 in Fig. 3(a) and (b) at the appropriate volume ratio.
3.3. Dependency on the aspect ratio Fig. 4(a) and (b) show dependencies of the local TBR on the aspect ratio for (a) beryllium multiplier and 90% 6 Li enriched Li2 O breeder, (b) Be12 Ti multiplier and 90% 6 Li enriched Li2 TiO3 breeder. The aspect ratios were varied by changing the major radius, keeping a fixed minor radius. In the calculations for the aspect ratio less than 1.75, the inboard structures such as the vacuum vessel and shield were expediently removed. Moreover, we have also evaluated the local TBR for a reactor with both outboard and 40 cm thick inboard breeding blankets to compare with a reactor with the outboard blanket only. In the calculations for the 40 cm thick inboard reflector of lead (black triangle in Fig. 4(a) and (b)), the local TBR decreases with the aspect ratio because of the reduction of the area ratio of the outboard breeding region to the total plasma facing area. This indicates that, in the tokamak with the outboard blanket only, a low-A reactor has the advantage in achieving large TBR over a conventional-A reactor. For the combination of Be and Li2 O shown in Fig. 4(a), the local TBR is larger than 1.35 where aspect ratios are less than 2.9, which satisfies the net TBR requirement of 1.05 when there is 78% coverage of the breeding zone
Fig. 4. Dependencies of local TBR on the aspect ratio for (a) beryllium multiplier and 90% 6 Li enriched Li2 O breeder, (b) Be12 Ti and 90% 6 Li enriched Li TiO . The total local TBR (white circle) is sum of the local inboard TBR (white rhombus) and the local outboard TBR (white 2 3 block). The black triangle is the local outboard TBR of the reactor with a 40 cm thick inboard reflector of lead.
T. Hayashi et al. / Fusion Engineering and Design 81 (2006) 2779–2784
over the total plasma-facing surface area. The minimum aspect ratio of a tokamak reactor strongly depends on the neutron shielding space between plasma and inboard TF coils to protect them against fast neutron irradiation. The reasonable aspect ratio of the present low-A reactor design is around 2.5, and the local TBR increases up to 1.38 at this aspect ratio. For Be12 Ti and Li2 TiO3 in Fig. 4(b), the aspect ratio is required to be less than 1.35 to achieve a local TBR of 1.35. In the calculations for the reactor with both the inboard and outboard blankets shown in Fig. 4(a) and (b), the total local TBR (white circle), which is sum of the local TBRs of inboard (white rhombus) and outboard (white block) blankets, is almost constant for all aspect ratios because the local inboard TBR compensates for the reduction of the local outboard TBR. The total local TBR with inboard and outboard blankets for the combinations of Li2 O/Be and Li2 TiO3 /Be12 Ti are more than 1.55 and 1.35, respectively. On the other hand, the difference between the local outboard TBR in the reactor with the inboard reflector of lead (black triangle) and that in the reactor with the inboard pebble blanket (white block) is the effect of the inboard reflector. In Fig. 4(a) and (b), this difference is about 40% of the local inboard TBR (white rhombus) for aspect ratios from 2 to 4, but it is more than 40% for A < 2.
4. Conclusion Neutron transport calculations were carried out to evaluate the local TBR in a low aspect ratio tokamak reactor with an outboard breeding blanket only. The main results are summarized below: (1) The local TBR of the outboard blanket increases by applying a neutron multiplier such as lead or beryllium to the inboard reflector. The effect on the local TBR of a 40 cm thick inboard reflector of lead is about 40% that of the inboard breeding blanket. (2) The local TBR with the lead inboard reflector can be larger than 1.35 when the aspect ratio is less than 2.9, which satisfies the net TBR requirement of 1.05 where there is 78% coverage of the breeding zone over the total plasma facing area.
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This indicates there is a solution for tritium selfsufficiency in a low-A tokamak reactor using the outboard breeding blanket only when the appropriate inboard reflector and outboard blanket are adopted. (3) Be12 Ti and Li2 TiO3 are recommended from the viewpoint of safety. For the combination with the lead inboard reflector, the aspect ratio is required to be less than 1.35 to achieve the local TBR of 1.35.
References [1] M. Enoeda, Y. Kosaku, T. Hatano, T. Kuroda, N. Miki, T. Honma, et al., Design and technology development of solid breeder blanket cooled by supercritical water in Japan, Nucl. Fusion 43 (2003) 1837–1844. [2] S. Sato, T. Nishitani, Impact of armor materials on tritium breeding ratio in the fusion reactor blanket, J. Nucl. Mater. 313–316 (2003) 690–695. [3] K. Tsuchiya, H. Kawamura, T. Takayama, S. Kato, Control of particle size and density of Li2 TiO3 pebbles fabricated by indirect wet processes, J. Nucl. Mater. 345 (2005) 239– 244. [4] Y. Yanagi, S. Sato, M. Enoeda, T. Hatano, S. Kikuchi, T. Kuroda, et al., Nuclear and thermal analyses of supercritical-watercooled solid breeder blanket for fusion DEMO reactor, J. Nucl. Sci. Technol. 38 (2001) 1014–1018. [5] K. Tobita, S. Nishio, M. Enoeda, M. Sato, T. Isono, S. Sakurai, et al., Design study of fusion DEMO plant at JAERI, in: Proceedings of the Seventh ISFNT (International Symposium on Fusion and Nuclear Technology), Tokyo, Fusion Eng. Des. 81 (2006) 1151–1158. [6] T. Hayashi, K. Tobita, S. Nishio, K. Ikeda, Y. Nakamori, S. Orimo, Neutronics assessment of advanced shield materials using metal hydride and borohydride for fusion reactors, in: Proceedings of the Seventh ISFNT, Tokyo, Fusion Eng. Des. 81 (2006) 1285–1290. [7] K. Tobita, S. Nishio, S. Konishi, S. Jatsukawa, Waste management for JAERI fusion reactors, J. Nucl. Mater. 329–333 (2004) 1610–1614. [8] T. Nishitani, M. Yamauchi, S. Nishio, M. Wada, Neutronics design of the low aspect ratio tokamak reactor VECTOR, in: Proceedings of the Seventh ISFNT, Tokyo, Fusion Eng. Des. 81 (2006) 1245–1249. [9] M. Yamauchi, T. Nishitani, S. Nishio, Neutron shielding and blanket neutronics study on low aspect ratio tokamak reactor, IEEJ Trans. Fundam. Mater. 125 (11) (2005) 943–946. [10] L.A. El-Guebaly, ARIES Team, ARIES-ST nuclear analysis and shield design, Fusion Eng. Des. 65 (2003) 263–284. [11] K. Munakata, H. Kawamura, M. Uchida, Study on reactivity of titanium beryllide with water vapor, in: Proceedings of the Sixth IEA International Workshop on Beryllium Technology
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for Fusion, JAERI-Conference 2004–006, Miyazaki, 2004, pp. 210–215. [12] Y. Sato, M. Uchida, H. Kawamura, High Temperature Oxidation Behavior of Titanium Beryllide in Air, JAERI-Conference 2004–006, 2004, pp. 203–209. [13] W.W. Engle Jr., A User’s Manual for ANISN, A OneDimensional Discrete Ordinates Transport Code with Anisotropic Scattering, Oak Ridge Report K-1693, 1967.
[14] K. Maki, K. Kosako, Y. Seki, H. Kawasaki, Nuclear Group Constant Set FUSION-J3 for Fusion Reactor Nuclear Calculations Based on JENDL-3, JAERI-M 91-072, 1991. [15] K. Shibata, T. Nakagawa, T. Asami, T. Fukahori, T. Narita, S. Chiba, Japanese Evaluated Nuclear Data Library, Version-3, JENDL-3, JAERI 1319, 1990. [16] http://www.nndc.bnl.gov/exfor/endf00.htm.
Possibility of tritium self-sufficiency in low aspect ratio tokamak reactor with the outboard blanket only T. Hayashi ∗ , K. Tobita, S. Nishio, S. Sato, T. Nishitani, M. Yamauchi Naka Fusion Institute, Japan Atomic Energy Agency, 801 Mukouyama, Naka, Ibaraki 311-0193, Japan Available online 17 August 2006
Abstract The possibility of tritium self-sufficiency in a low aspect ratio (low-A) tokamak reactor with the outboard blanket only has been studied to simplify the inboard structure located in a high magnetic field. The tritium breeding ratio (TBR) of the outboard blanket increases by applying a neutron multiplier such as lead and beryllium to the inboard reflector. The effect in local TBR of a 40 cm thick inboard reflector of lead is about 40% that of the inboard breeding blanket. The local TBR of a reactor with both the lead inboard reflector and outboard blanket using a Li2 O breeder and a beryllium multiplier can be larger than 1.35 for aspect ratios less than 2.9. The local TBR of 1.35 satisfies the net TBR requirement of 1.05 where there is 78% coverage of the breeding zone over the total plasma-facing surface area. The result indicates there is a design solution achieving tritium self-sufficiency even in a low-A tokamak reactor with the outboard breeding blanket only, using an appropriate inboard reflector. Be12 Ti and Li2 TiO3 are recommended from the viewpoint of safety. In the combination, the aspect ratio is required to be less than 1.35 to achieve local TBR of 1.35. © 2006 Elsevier B.V. All rights reserved. Keywords: Tritium breeding ratio; Blanket; Reflector; Lead; Beryllium; Aspect ratio
1. Introduction In a tokamak reactor, the tritium breeding ratio (TBR) in a blanket is required to be more than unity [1–4]. One of the most critical issues in the reactor design is blanket structural robustness against electromagnetic (EM) forces acting during plasma disruptions. In particular, care in the design of the breeding ∗ Corresponding author. Tel.: +81 29 270 7431; fax: +81 29 270 7449. E-mail address: [email protected] (T. Hayashi).
0920-3796/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2006.07.045
blanket on the inboard side is necessary to overcome higher EM forces created by the high magnetic field. Therefore it is desirable to simplify the inboard structure to improve the reliability and safety. Many design studies of fusion reactors characterized by low aspect ratio (A) and low toroidal field have been reported [5–10]. In the tokamak with the outboard blanket only, a low-A reactor has the advantage that it can achieve a larger TBR than a conventional-A reactor, because the area of the outboard wall is larger. The coverage of the breeding zone over plasma facing area strongly depends on the designs of the divertor, ports
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and blankets. Assuming that the coverage of the breeding zone is 78%, local TBR above 1.35 is required to achieve net TBR of 1.05. In this case, the other 22% is flexibly and efficiently allocated to the other plasma-facing components. For example, the coverage of divertor, ports and non-breeding area of blanket such as headers and ribs may be 6%, 2% and 14%, respectively. This paper describes the possibility of tritium self-sufficiency in low-A tokamak reactors with the outboard blanket only, an inboard neutron reflector being installed instead of an inboard breeding blanket. Neutron transport calculations have been performed to evaluate the local TBR and to assess the prospect of a fusion plant without an inboard breeding blanket.
2. Calculation method Table 1 shows the one-dimensional calculation model. The plasma major and minor radii were 5.77 and 2.1 m, respectively, and its aspect ratio corresponded to 2.75. When the thickness of the inboard reflector or blanket was increased from 0 to 40 cm, that of the inboard shield was decreased from 90 to 50 cm to maintain constant major radius and aspect ratio. The inboard side of toroidal field (TF) coils and/or center solenoid (CS) can be placed in the inboard space of 225 cm
width. Each region in Table 1, such as the breeding blanket and reflector, was assumed to be homogeneous. The thickness of the outboard blanket is 90 cm. The blanket was assumed to consist of supercritical water (SCW) as a coolant, solid breeder pebbles (Li2 O or Li2 TiO3 ), neutron multiplier pebbles (Be or Be12 Ti) and low activation ferritic steel, F82H. These materials were selected based on design studies for a solid blanket system for DEMO reactors [1,3,4]. Packing fractions of the breeder and multiplier are, respectively, 0.51 and 0.80. From the point of view of safety, an important issue for water-cooled components using beryllium is the beryllium-steam reaction in the case of a loss-of-coolant accident (LOCA). The combination of Be12 Ti multiplier and Li2 TiO3 breeder is recommended over that of Be and Li2 O from the viewpoint of safety [1,3,11,12]. The calculations were carried out with the onedimensional transport code, ANISN [13], and a transport group constant set of FUSION-40 [14], which consists of 42 neutron groups and 21 ␥-ray groups based on JENDL-3.1 [15]. For the estimation of the local TBR, we have used the JENDL dosimetry file. We conducted the sensitivity analyses by changing the type and thickness of the inboard reflector, the volume ratio of the neutron multiplier to the tritium breeder, the enrichment factor of the 6 Li as the lithium isotope, and the aspect ratio of the tokamak reactor.
Table 1 One-dimensional calculation model for sensitivity analyses Region
Material
Thickness (cm)
Inboard space VV Shield Back plate
Void F82H F82H (70%), water (30%) F82H
225 10 90–50 15
Reflector or blanket
Various materials such as lead (70%) F82H (50%), SCW (50%) Void Plasma Void F82H (50%), SCW (50%)
0–40
Li2 O or Li2 TiO3 , Be or Be12 Ti, SCW (16.8%), F82H (14.4%) F82H F82H (70%), water (30%) F82H
90
First wall Gap (SOL) Plasma Gap (SOL) First wall Outboard blanket
Back plate Shield VV
1.6 25 420 10 1.6
15 55 10
3. Results and discussion 3.1. Effect of inboard reflector Fig. 1 shows the dependence of the local TBR on the thickness of various inboard reflectors. In the calculations, the 90% 6 Li enriched Li2 O breeder, the Be multiplier and the optimum volume ratio of these materials described in Section 3.2 were used. The local TBR is higher for lead, intermediate for beryllium, and lower for tungsten. It is notable that, only in the case of lead does the local TBR increase with the thickness of the inboard reflector, TBR being larger than 1.35 when thickness is over 20 cm. Fig. 2(a) and (b) show neutron fluxes for various materials at positions in the 40 cm thick inboard reflector, the first wall and part of the scrape-off layer (SOL): (a) showing the total neutron flux and (b) showing the
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low energy neutron flux (E < 0.1 MeV). Because the 6 Li(n,t)4 He cross-section is very large in the lower neutron energy region [16], the low energy neutrons can increase the TBR. In Fig. 2(b), low energy neutron fluxes in the inboard SOL of lead and beryllium are higher than those in conventional reflectors such as F82H and tungsten, because lead and beryllium work as neutron multipliers. Therefore, the local TBR of the outboard blanket was increased by the low energy neutrons produced in the inboard material as shown in Figs. 1 and 2(b). 3.2. Dependency on the ratio of the multiplier to the breeder Fig. 1. Dependence of local TBR on the thickness of inboard reflector for various materials.
Fig. 2. Change of neutron fluxes in the inboard reflector comprising various materials: (a) total neutron flux and (b) low energy neutron flux (E < 0.1 MeV).
Fig. 3(a) and (b) show the dependency of local TBR on the volume ratio of the neutron multiplier to the tritium breeder: (a) for various combinations of the multiplier (Be or Be12 Ti) with the 90% 6 Li enriched
Fig. 3. Dependence of local TBR on the volume ratio of the multiplier to the breeder: (a) for various combinations of the multiplier (Be or Be12 Ti) with 90% 6 Li enriched breeder (Li2 O or Li2 TiO3 ) and (b) for various 6 Li enrichments of Li2 O with Be multiplier.
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breeder (Li2 O or Li2 TiO3 ), (b) for various 6 Li enrichments of Li2 O with the Be multiplier. The volume ratios of SCW and F82H were kept constant in order to evaluate only the effect of mixture ratio of multiplier and breeder. A 40 cm thick lead inboard reflector was used for the calculations. In Fig. 3(a), the local TBR for the combination of Li2 O and Be is significantly larger than that of the other combinations including Li2 O, Li2 TiO3 , Be and Be12 Ti. In addition, the optimum volume ratios vary according to the combination of the breeder and multiplier. The optimum volume ratios for the combinations of Be/Li2 O and Be12 Ti/Li2 TiO3 are 4.5 and 1.8, respectively. This indicates that the selection of the optimum combination and also the optimum volume ratio of the breeder and multiplier are necessary to attain the larger TBR. As the 6 Li enrichment rises in Fig. 3(b), both the local TBR and optimum volume ratio of the multiplier to the breeder increase. The optimum ratios for the 6 Li enrichment of 30% and 90% are, respectively, 2.4 and 4.5. These results show that the higher 6 Li enrichment can reduce the optimum amount of lithium, and can increase the TBR if more multiplier is used. Only in the case of Be and 90% 6 Li enriched Li2 O is the local TBR slightly larger than 1.35 in Fig. 3(a) and (b) at the appropriate volume ratio.
3.3. Dependency on the aspect ratio Fig. 4(a) and (b) show dependencies of the local TBR on the aspect ratio for (a) beryllium multiplier and 90% 6 Li enriched Li2 O breeder, (b) Be12 Ti multiplier and 90% 6 Li enriched Li2 TiO3 breeder. The aspect ratios were varied by changing the major radius, keeping a fixed minor radius. In the calculations for the aspect ratio less than 1.75, the inboard structures such as the vacuum vessel and shield were expediently removed. Moreover, we have also evaluated the local TBR for a reactor with both outboard and 40 cm thick inboard breeding blankets to compare with a reactor with the outboard blanket only. In the calculations for the 40 cm thick inboard reflector of lead (black triangle in Fig. 4(a) and (b)), the local TBR decreases with the aspect ratio because of the reduction of the area ratio of the outboard breeding region to the total plasma facing area. This indicates that, in the tokamak with the outboard blanket only, a low-A reactor has the advantage in achieving large TBR over a conventional-A reactor. For the combination of Be and Li2 O shown in Fig. 4(a), the local TBR is larger than 1.35 where aspect ratios are less than 2.9, which satisfies the net TBR requirement of 1.05 when there is 78% coverage of the breeding zone
Fig. 4. Dependencies of local TBR on the aspect ratio for (a) beryllium multiplier and 90% 6 Li enriched Li2 O breeder, (b) Be12 Ti and 90% 6 Li enriched Li TiO . The total local TBR (white circle) is sum of the local inboard TBR (white rhombus) and the local outboard TBR (white 2 3 block). The black triangle is the local outboard TBR of the reactor with a 40 cm thick inboard reflector of lead.
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over the total plasma-facing surface area. The minimum aspect ratio of a tokamak reactor strongly depends on the neutron shielding space between plasma and inboard TF coils to protect them against fast neutron irradiation. The reasonable aspect ratio of the present low-A reactor design is around 2.5, and the local TBR increases up to 1.38 at this aspect ratio. For Be12 Ti and Li2 TiO3 in Fig. 4(b), the aspect ratio is required to be less than 1.35 to achieve a local TBR of 1.35. In the calculations for the reactor with both the inboard and outboard blankets shown in Fig. 4(a) and (b), the total local TBR (white circle), which is sum of the local TBRs of inboard (white rhombus) and outboard (white block) blankets, is almost constant for all aspect ratios because the local inboard TBR compensates for the reduction of the local outboard TBR. The total local TBR with inboard and outboard blankets for the combinations of Li2 O/Be and Li2 TiO3 /Be12 Ti are more than 1.55 and 1.35, respectively. On the other hand, the difference between the local outboard TBR in the reactor with the inboard reflector of lead (black triangle) and that in the reactor with the inboard pebble blanket (white block) is the effect of the inboard reflector. In Fig. 4(a) and (b), this difference is about 40% of the local inboard TBR (white rhombus) for aspect ratios from 2 to 4, but it is more than 40% for A < 2.
4. Conclusion Neutron transport calculations were carried out to evaluate the local TBR in a low aspect ratio tokamak reactor with an outboard breeding blanket only. The main results are summarized below: (1) The local TBR of the outboard blanket increases by applying a neutron multiplier such as lead or beryllium to the inboard reflector. The effect on the local TBR of a 40 cm thick inboard reflector of lead is about 40% that of the inboard breeding blanket. (2) The local TBR with the lead inboard reflector can be larger than 1.35 when the aspect ratio is less than 2.9, which satisfies the net TBR requirement of 1.05 where there is 78% coverage of the breeding zone over the total plasma facing area.
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This indicates there is a solution for tritium selfsufficiency in a low-A tokamak reactor using the outboard breeding blanket only when the appropriate inboard reflector and outboard blanket are adopted. (3) Be12 Ti and Li2 TiO3 are recommended from the viewpoint of safety. For the combination with the lead inboard reflector, the aspect ratio is required to be less than 1.35 to achieve the local TBR of 1.35.
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