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Study of an optimal configuration of a transmutation reactor based on a low-aspect-ratio tokamak Bong Guen Hong a,∗ , Hoseok Kim b a b
Department of Quantum System Engineering, Chonbuk National University, 567 Baekje-daero, Jeonju, Jeonbuk 54896, Republic of Korea Department of Applied Plasma Engineering, Chonbuk National University, 567 Baekje-daero, Jeonju, Jeonbuk 54896, Republic of Korea
h i g h l i g h t s • Optimum configuration of a transmutation reactor based on a low aspect ratio tokamak was found. • Inboard and outboard radial build are determined by plasma physics, engineering and neutronics constraints. • Radial build and equilibrium fuel cycle play a major role in determining the transmutation characteristics.
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Article history: Received 20 January 2016 Received in revised form 13 April 2016 Accepted 22 May 2016 Available online xxx Keywords: Tokamak neutron source Transmutation reactor Low aspect ratio tokamak Systems analysis
a b s t r a c t We determine the optimal configuration of a transmutation reactor based on a low-aspect-ratio tokamak. For self-consistent determination of the radial build of the reactor components, we couple a tokamak systems analysis with a radiation transport calculation. The inboard radial build of the reactor components is obtained from plasma physics and engineering constraints, while outboard radial builds are mainly determined by constraints on neutron multiplication, the tritium-breeding ratio, and the power density. We show that the breeding blanket model has an effect on the radial build of a transmutation blanket. A burn cycle has to be determined to keep the fast neutron fluence plasma-facing material below its radiation damage limit. We show that the radial build of the transmutation reactor components and the equilibrium fuel cycle play a major role in determining the transmutation characteristics. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The concept of a transmutation reactor using a 14-MeV fusion neutron source has been investigated [1–3] as a potential method for destroying nuclear waste in spent nuclear fuels. Transmutation reactors based on a tokamak neutron source need to destroy as much nuclear waste as possible while minimizing the overall size of the reactor from an economic viewpoint. A low-aspectratio (LAR) tokamak [4] offers a viable option for a fusion neutron source because it allows not only a large natural elongated plasma shape, which is favorable for transmutation reactors, but also a high plasma beta, which leads to a high-performance compact reactor. Each component of a tokamak reactor must satisfy all physics and engineering constraints. The shielding requirement plays an important role in determining the inboard radial build, and the tritium-breeding requirement has a large effect in determining the
∗ Corresponding author. E-mail address: [email protected] (B.G. Hong).
outboard radial build in a LAR tokamak reactor. For a transmutation reactor, the requirements for neutron multiplication and power density also need to be considered in determining the radial build. The transmutation and tritium-breeding capability need to be maximized, while limiting the neutron multiplication factor keff to less than 1.0 because a sub-critical reactor is preferred from the viewpoint of reactor safety, and limiting the power density to less than 100 MW/m3 to maintain cooling capability. Self-consistent determination of the radial build of the reactor components thus requires a radiation transport calculation coupled with a tokamak systems analysis [5]. In a LAR tokamak, tritium self-sufficiency can be satisfied using only an outboard tritium breeding blanket and appropriate selection of inboard shield material [6]. Also, in a transmutation reactor based on a LAR tokamak, the nuclear waste, i.e. transuranic actinides (TRUs: Pu and minor actinides Np, Am, Cm, etc.), and the tritium breeder can be located in the outboard blanket. By locating the tritium-breeding blanket after the transmutation blanket, we expect not only tritium self-sufficiency, as abundant thermal neutrons produced by fission of the TRUs contribute to the breed-
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ing of tritium, but also that neutrons reflected/produced from the tritium-breeding blanket will contribute to the transmutation of the nuclear waste. Thus, it is necessary to investigate the effect of different tritium-breeding blanket models on the outboard radial build of a transmutation reactor. Effective transmutation of nuclear waste requires an equilibrium fuel cycle. Potential radiation damage to the reactor components limits the achievable residence time of nuclear waste. Thus radiation damage due to neutrons from both fusion and fission on the blanket structure has to be considered in evaluating transmutation performance. In Section 2, we describe how we couple our radiation transport calculations with the tokamak systems analysis. We present the optimal configuration of a transmutation reactor based on a LAR tokamak and its transmutation characteristics in Section 3. In Section 4, we summarize our findings.
2. Coupled systems analysis Tokamak systems analysis, which has been used in concept definition studies of various tokamak reactors [5], determines the optimum radial build of a transmutation reactor. For the radiation transport and burn-up calculations, we use the one-dimensional radiation transport code BISON-C [7] with a 42 neutron group crosssection library based on JENDL-3.3. For the estimation of the local tritium breeding ratio (TBR), we use the JENDL dosimetry file [8]. The BISON-C code solves the one-dimensional radiation transport equation to obtain the neutron flux and then solves the nuclide burn-up equations using the obtained flux. We note that the onedimensional radiation transport calculation is adequate for scoping studies, and thus it is also enough in a coupled analysis with the zero-dimensional tokamak systems code to identify the key characteristics of a transmutation reactor. To couple the tokamak systems code with the one-dimensional radiation transport code, BISON-C, we develop an interface module. Starting from the initial estimate for the design parameters, we calculate the plasma physics and the engineering constraints, as well as the radial build of the reactor components, in the systems analysis. From these, the interface module adjusts the meshes to be appropriate for the radiation transport analysis. With the new meshes, we perform the radiation transport and burn-up analyses and calculate the neutron flux, keff , and various quantities. The interface module calculates the TBR, the power density and the shielding parameters. We then recalculate the radial builds, plasma physics, and engineering parameters in the systems analysis. This procedure continues until we find reactor parameters that satisfy all the plasma physics and engineering constraints. Fig. 1 shows a calculation procedure for the coupled systems analysis. A cross sectional view in a R-Z plane of the LAR tokamak is shown in Fig. 2 with an equatorial radial build. For the radiation transport analysis, we model the transmutation reactor using one-dimensional cylindrical geometry. The material composition of the reactor components is listed in Table 1. We determine the radial build of the components using the plasma physics and engineering constraints, which have to be satisfied simultaneously by each component of the reactor. The LAR tokamak allows an elongated, high beta plasma, which improves magnetohydrodynamic (MHD) performance and confinement. In this study, we use the expressions of plasma performance for the LAR tokamak, including maximum elongation, minimum safety factor, and maximum N , derived in Refs. [9–11]. The superconducting magnet and vacuum vessel designs were constrained to use International Thermonuclear Experimental Reactor (ITER) technology [12,13]. We use ferritic-martensitic stainless steel (FMS) as the fast wall and as the structural material of the blankets.
Fig. 1. Calculation procedure for the coupled analysis.
Fig. 2. A cross sectional view of the LAR tokamak and an equatorial radial build.
The radial build of the shield is determined by the TF coil protection requirement against nuclear heating and the radiation damage induced by neutrons from both fusion and fission. The constraints, which assume a design lifetime for the transmutation reactor of 40 years with 75% availability, are keeping fast neutron fluence to the superconductor below 1023 n m−2 for Nb3 Sn, displacement damage to the Cu stabilizer below 5 × 10−4 dpa, and dose to the insulators of less than 109 rad for organic insulators.
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Table 1 Material composition of the transmutation reactor. Component
Materials (Volume%)
Space Toroidal field coil Vacuum vessel Shield First wall Scrape-off layer Plasma Scrape-off layer First wall Transmutation blanket Breeding blanket High temp. shield Low temp. shield Vacuum vessel Toroidal field coil
– Nb3 Sn, Cu, Epoxy, SUS316, L. He Borated steel (60), H2 O (40) WC (80), H2 O (20) FMS (60), H2 O (40) – D, T – FMS (60), H2 O (40) TRU (5), FMS (15), He (75), SiC (5) He (7), PbLi (90), FMS (3) WC (60), H2 O (40) WC (80), H2 O (20) Borated steel (60), H2 O (40) Nb3 Sn, Cu, Epoxy, SUS316, L. He
Table 2 Composition of TRUs in the spent fuel of 1 GWe KSNP. Nuclide
Mass (%)
Np237 Pu238 Pu239 Pu240 Pu241 Pu242 Am241 Am243 Cm244 Cm245
6.88 2.18 45.65 22.03 1.22 7.35 12.31 2.18 0.15 0.05
The transmutation blanket and tritium breeding blanket are located only in the outboard blanket. The transmutation blanket (BL1) is loaded with the TRUs from the spent fuel of 1 GWe Korea Standard Nuclear Power plant (KSNP), and the tritiumbreeding blanket (BL2) is placed after the transmutation blanket to use the neutrons produced by the fission of the TRUs for tritium self-sufficiency and the neutrons reflected from and produced in the tritium-breeding blanket for the transmutation of the nuclear waste. Table 2 shows the nuclide composition of the TRUs contained in the spent fuel of 1 GWe KSNP. The radial build of the blankets should maximize the TBR (>1.35) and transmutation rate and keep the power density and neutron multiplication within their limiting values which are set to be 0.95 and 100 MW/m3 , respectively. In the transmutation blanket, we use FMS as a structural material and He as a coolant. For the tritium-breeding blanket, we use He-cooled lithium lead (HCLL) with natural Li and FMS as the structural material. The TRU fuel is assumed to take a form of a TRISO (TRi-ISOtropic) particle coated with SiC. We also investigate using a He-cooled solid breeder (HCSB) as the tritium-breeding blanket to learn how the tritium blanket model affects the outboard radial build of the transmutation reactor. The typical set of variables and constraints used in the coupled systems analysis is summarized in Table 3. The first four constraints determine the plasma performance, i.e., the electron temperature, electron density, heating and current drive power, and major radius. With the major radius determined by the plasma performance, the engineering constraints determine the radial build of the reactor systems. The tritium breeding requirement, transmutation blanket requirements, shielding requirements, TF coil equation, TF coil critical current density limit, TF coil case stress limit, ripple limit, and radial build constraint determine the thickness of the tritium breeding blanket, thickness of the transmutation blanket, thickness of the shield, thickness of the TF coil, TF coil current density, thickness of the TF coil case, position of the outboard TF coil, and bore radius of the TF coil, respectively.
Fig. 3. Dependence of the minimum major radius and neutron wall loading on the fusion power.
3. Optimal radial build of a transmutation reactor based on a LAR tokamak 3.1. Inboard radial build We investigate the radial build of a transmutation reactor for an aspect ratio, A, in the range of 1.5–2.0 and a fusion power in the range of 100–300 MW. The plasma performance is assumed to produce the required fusion power with the maximum plasma performance for a LAR tokamak, i.e., a safety factor of qa = qa ,min , normalized plasma beta of N = N,max , a confinement enhancement factor of H = 1.2, and plasma density of n = nG , where nG is the Greenwald density limit. The plasma physics and engineering constraints determine the inboard radial build of the reactor components. Among them, the constraints on the radiation shielding of the TF coil and the maximum magnetic field at the TF coil play a key role in determining the minimum major radius. Fig. 3 shows the dependence of the minimum major radius and the neutron wall loading on the fusion power when A = 1.5 and 2.0. The minimum major radius R0 increases as the fusion power increases, and is large when A is small. With the TRUs loaded in the transmutation blanket, the required inboard shield thickness increases compared to the case with no TRUs loaded because the neutrons from the fission of the TRUs have to be shielded. Neutron wall loading increases as the fusion power increases, and it is large when A is large. It is less than 1.0 MW/m2 for A in the range of 1.5–2.0 and fusion power in the range of 100–300 MW. The shield thickness is large when the aspect ratio and fusion power are large because of large neutron wall loading. 3.2. Outboard radial build and transmutation characteristics We determined the outboard radial build of the transmutation reactor components to limit the maximum neutron multiplication (keff ) to below 0.95, to limit the maximum power density to below 100 MW/m3 , and to satisfy the tritium self-sufficiency of TBR > 1.35 with an assumed blanket coverage factor of 80% in the one-dimensional model. Requirements for the neutron multiplication and power density determine the radial thickness of the transmutation blanket, BL1 . When A = 1.5, BL1 = 0.2 m, 0.23 m, and 0.28 m with fusion power of 100 MW, 200 MW and 300 MW, respectively. When A = 2.0, BL1 increases to 0.26 m, 0.36 m, and 0.43 m due to increased neutron wall loading, with a fusion power of 100, 200, and 300 MW, respectively. To transmute nuclear waste effectively, an equilibrium fuel cycle that which transmutes TRUs in batches needs to be developed. A reference fuel cycle consists of five burn cycles. The transmutation
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Table 3 Set of variables and constraints in the systems analysis. Constraint
Variable
Plasma physics (1) Beta limit, N < N,max (2) Density limit, ne < nGreenwald (3) Power balance equation, Pcon + Prad = POH + Paux + P␣ (4) Fusion power, Pfusion = desired power Engineering (5) Tritium breeding requirement, TBR > 1.35 (6) Transmutation blanket requirements, keff < 0.95 power density <100 MW/m3 (7) Shielding requirements for TF coil fast neutron fluence < 1023 n m−2 displacement damage < 5 × 10−4 dpa dose to the insulators <109 rad (8) TF coil equation, Bmax × RTFi = R0 × BT (9) TF coil current density limit, JTF < 2.8 × 108 A m−2 (10) TF coil case stress limit, TFcase < 550 MPa (11) Ripple limit, ␦ripple < 0.1% (12) Radial build
(1) Electron temperature, Te (2) Electron density, ne (3) Auxiliary heating power, Paux (4) Major radius, R0 (5) Thickness of breeding blanket, BL2 (6) Thickness of transmutation blanket, BL1 (7) Thickness of shield, shld (8) Thickness of TF coil, TF (9) TF coil current density, JTF (10) TF coil case thickness, TFcase (11) Bore radius of TF coil, Rbore (12) Outer TF coil location, RTFo
Table 4 Equilibrium fuel cycle analysis for A = 1.5 and 2.0. Aspect ratio
A = 1.5
Burn cycle (day) 100 MW
300 6.05 848 13 3000 0.6 0.2 0.2 6.34 1335 19 4750 0.9 0.23 0.2 6.68 1773 23 6350 1.1 0.28 0.21
200 MW
300 MW
Fig. 4. Variation of keff as TRUs burn: (a) No fuel cycle and (b) fuel cycle with a burn cycle of 300 days.
blanket is divided into 5 batches so that each batch has a same volume. The fuel is loaded at outmost batch and shuffled to inner batch after each burn cycle. After the fifth burn cycle, the equilibrium is reached and the batch of depleted fuel is removed. Depending on the burn-up of the nuclear waste, it can be deposited in a highlevel-waste repository or reprocessed to remove fission products and recover TRUs to be recycled again in the transmutation reactor. The radiation damage limit of the plasma-facing material of the blanket determines the achievable residence time of the nuclear waste. Depending on the accumulated fast neutron fluence, the plasma-facing material has to be replaced several times during the reactor’s lifetime. The radiation damage limit of FMS is assumed to be 3.0 × 1027 n m−2 . Fig. 4(a) shows the variation in keff as the TRUs burn up for cases with A = 1.5 and 2.0, and a fusion power of 100 MW and 300 MW. In this case, the fusion powers are kept constant, i.e., at their maximum capacity. The keff decreases as the TRUs burn up, and the decrease rate becomes larger with larger A and larger fusion
Height (m) Trans. rate (kg/y) Burn-up (%) Power (MW) Fast fluence @FW (1027 n m−2 ) BL1 (m) BL2 (m) Height (m) Trans. rate (kg/y) Burn-up (%) Power (MW) Fast fluence @FW (1027 n m−2 ) BL1 (m) BL2 (m) Height (m) Trans. rate (kg/y) Burn-up (%) Power (MW) Fast fluence @FW (1027 n m−2 ) BL1 (m) BL2 (m)
A = 2.0 600 647 20 2300 1.0
972 27 3480 1.4
1294 33 4600 1.8
300 3.30 573 19 2040 0.9 0.26 0.2 3.53 911 26 3300 1.3 0.36 0.3 3.68 1175 31 4270 2.2 0.43 0.4
600 – –
630 37 2300 2.7
802 43 3000 3.2
power due to large neutron wall loading. The total power produced from the fusion and the fission reactions and the amount of transmuted nuclear waste are proportional to Pfusion × keff /(1 − keff ), where Pfusion is the fusion power. They decrease as the TRUs burn, and their decrease rate gets larger. To transmute a large amount of nuclear waste, keff needs to be high and its decrease rate needs to be small during the burn-up period. Fig. 4(b) shows the variation in keff when the equilibrium fuel cycle with five burn cycles (300 days each) is reached for the cases with A = 1.5 and 2.0. In this case, the total power is kept constant and thus the fusion power has to increase as the TRUs burn up to compensate for the consumption of fusion neutrons up to the maximum fusion power of 100 MW or 300 MW. The variation in keff during 1500 days is much smaller than the cases shown in Fig. 4(a) because of the equilibrium fuel cycle. In Table 4, we compare the transmutation performance when the fusion power capacity is 100 MW, 200 MW and 300 MW for the cases with A = 1.5 and 2.0, and the burn cycle of 300 days and 600 days. The reactor height is assumed to be × a (where is the elongation and a is the minor radius), and the total power is kept constant. The total power and the transmutation performance are obtained based on the assumption that the power distribution is uniform along the reactor height, and thus they correspond to the maximum value at the equatorial region. The burn cycle is deter-
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Table 5 Radial build of a transmutation reactor with A = 1.5. Fusion power (MW) Component (m)
100
200
300
Space Toroidal field coil Vacuum vessel Shield First wall Scrape-off layer Plasma Scrape-off layer First wall Trans. blanket Breeding blanket High temp. shield Low temp. shield Vacuum vessel Toroidal field coil
0.10 0.28 0.43 0.83 0.85 0.95 4.72 4.82 4.84 5.05 5.26 5.56 6.16 6.31 6.61
0.10 0.32 0.47 0.89 0.91 1.01 5.04 5.14 5.16 5.38 5.59 5.89 6.49 6.64 7.01
0.10 0.34 0.49 0.92 0.94 1.04 5.22 5.32 5.34 5.62 5.83 6.13 6.73 6.88 7.29
Table 6 Radial build of a transmutation reactor with A = 2.0.
Fig. 5. Neutron spectra when A = 1.5 and fusion power = 100 MW: (a) HCLL blanket and (b) HCSB blanket.
mined by the requirement on the total power and the fast neutron fluence over five cycle residence times. When the fusion power is 100 MW, the total power larger than 2000 MW can be produced for the burn cycle of 600 days with A = 1.5, but the total power larger than 2000 MW can not be produced for the burn cycle of 600 days with A = 2.0. The fast neutron fluence over five cycle residence times increases with the fusion power, the burn cycle and the aspect ratio A. When the fusion power is 300 MW and A = 2.0, the fast neutron fluence over five cycle residence times is larger than the radiation damage limit of the first wall. The fast wall has to be replaced at the time of the shuffling before the radiation damage limit of FMS is reached. During the transmutation, Pu239, Pu240, Am241, Pu242 and Np237, which constitute a majority of TRU decrease but actinides such as Pu238, Pu241, Am243, Am242, Am244 and Cm245 increase since they are produced from the neutron absorption of the other actinides and they are difficult to transmute. The transmutation rate is larger with a larger fusion power, a smaller aspect ratio, and a shorter burn cycle. However, the burn-up fraction increases with a larger fusion power, a larger aspect ratio, and a longer burn cycle. When A = 1.5, a transmutation reactor with 300 MW of fusion power capacity can produce a total power of 6350 MW and support about 7 pressurized water reactors (PWRs) of 1.0 GWe capacity with a burn cycle of 300 days. With a burn cycle of 600 days, the reactor can produce a total power of 4600 MW and supports about 5 PWRs. When A = 2.0, a transmutation reactor with 300 MW of fusion power can produce a total power of 4270 MW and support about 4 PWRs with a burn cycle of 300 days. With a burn cycle of 600 days, the reactor can produce a total power of 3000 MW and supports about 3 PWRs. Here, we assumed that the TRUs from 1 PWR of 1 GWe capacity are approximately 250 kg/y. As the TRUs burn up, the TBR decreases due to the burn-up of Li6. To satisfy the TBR requirement of TBR > 1.35 during the burn-up
Fusion power (MW) Component (m)
100
200
300
Space Toroidal field coil Vacuum vessel Shield First wall Scrape-off layer Plasma Scrape-off layer First wall Trans. blanket Breeding blanket High temp. shield Low temp. shield Vacuum vessel Toroidal field coil
0.10 0.39 0.54 1.07 1.09 1.19 3.58 3.68 3.70 3.96 4.17 4.47 5.07 5.22 5.71
0.10 0.45 0.60 1.16 1.18 1.28 3.83 3.93 3.95 4.31 4.62 4.92 5.52 5.67 6.28
0.10 0.49 0.64 1.21 1.23 1.33 4.00 4.10 4.12 4.55 4.96 5.26 5.86 6.01 6.67
period, the radial thickness of the tritium-breeding blanket, BL2 , increases with the fusion power due to increased neutron wall loading. When A = 1.5, BL2 increases slightly with the fusion power. But when A = 2.0, BL2 = 0.2, 0.3, and 0.4 m with the fusion power of 100, 200, and 300 MW, respectively. Fig. 5 shows the neutron spectra at the end of the fifth burn cycle in the transmutation blanket and the tritium-breeding blanket for A = 1.5 with the fusion power = 100 MW. Cases with the HCLL blanket (a) and the HCSB blanket (b) are shown. The flux in the tritium-breeding blanket is larger with than without the TRUs, indicating a contribution from the fission of the TRUs. The fast (>0.1 MeV) neutron fluxes in the transmutation blanket and the tritium-breeding blanket with the HCLL blanket are higher than those with the HCSB blanket, which we attribute to the fast neutrons produced from the (n, 2n) reaction in Pb in the HCLL blanket. These neutrons contribute to the transmutation of the TRUs in the transmutation blanket, and we find the radial thickness of the transmutation blanket to be smaller than that with the HCSB blanket (BL1 = 0.23 m). The neutron flux with the lower energy in the HCSB blanket is higher than that in the HCLL blanket because the neutrons from the fusion reaction and the fission of the TRUs slowed down without being absorbed in the Pb. It resulted in smaller radial thickness of the tritium-breeding blanket (BL2 = 0.18 m) for the HCSB blanket due to the high tritium breeding cross section of Li-6 from the low neutron energy. Thus, the outboard radial build of the components of the transmutation reactor are closely related to one another. Tables 5 and 6 summarize the radial builds of the transmutation reactor for the cases with the HCLL blanket and fusion power of 100, 200, and 300 MW when A = 1.5 and 2.0, respectively.
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4. Conclusion
References
We determined the optimum radial build of a transmutation reactor based on a LAR tokamak neutron source with fusion power in the range of 100–300 MW through coupled analysis of the tokamak systems and the radiation transport. The radial build of the reactor components is self-consistently determined by the constraints on the plasma physics performance, tokamak engineering, and neutron performance. We investigate the transmutation characteristics when the transmutation reactor produces a constant total power. The transmutation rate is larger with a larger fusion power, a smaller aspect ratio, and a shorter burn cycle. However, the burn-up fraction increases with larger fusion power, a larger aspect ratio, and a longer burn cycle. We showed that the radial build of the transmutation reactor components and the equilibrium fuel cycle play major roles in determining the transmutation characteristics.
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Acknowledgments This paper was supported by research funds from Chonbuk National University in 2015 and by the research facilities at the Plasma Application Institute of Chonbuk National University. This work was also supported by a National Research Foundation of Korea (NRF) grant under contract nos. 2015R1D1A3A01019752 and 2013M1A7A1A01043740.
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Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Study of an optimal configuration of a transmutation reactor based on a low-aspect-ratio tokamak Bong Guen Hong a,∗ , Hoseok Kim b a b
Department of Quantum System Engineering, Chonbuk National University, 567 Baekje-daero, Jeonju, Jeonbuk 54896, Republic of Korea Department of Applied Plasma Engineering, Chonbuk National University, 567 Baekje-daero, Jeonju, Jeonbuk 54896, Republic of Korea
h i g h l i g h t s • Optimum configuration of a transmutation reactor based on a low aspect ratio tokamak was found. • Inboard and outboard radial build are determined by plasma physics, engineering and neutronics constraints. • Radial build and equilibrium fuel cycle play a major role in determining the transmutation characteristics.
a r t i c l e
i n f o
Article history: Received 20 January 2016 Received in revised form 13 April 2016 Accepted 22 May 2016 Available online xxx Keywords: Tokamak neutron source Transmutation reactor Low aspect ratio tokamak Systems analysis
a b s t r a c t We determine the optimal configuration of a transmutation reactor based on a low-aspect-ratio tokamak. For self-consistent determination of the radial build of the reactor components, we couple a tokamak systems analysis with a radiation transport calculation. The inboard radial build of the reactor components is obtained from plasma physics and engineering constraints, while outboard radial builds are mainly determined by constraints on neutron multiplication, the tritium-breeding ratio, and the power density. We show that the breeding blanket model has an effect on the radial build of a transmutation blanket. A burn cycle has to be determined to keep the fast neutron fluence plasma-facing material below its radiation damage limit. We show that the radial build of the transmutation reactor components and the equilibrium fuel cycle play a major role in determining the transmutation characteristics. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The concept of a transmutation reactor using a 14-MeV fusion neutron source has been investigated [1–3] as a potential method for destroying nuclear waste in spent nuclear fuels. Transmutation reactors based on a tokamak neutron source need to destroy as much nuclear waste as possible while minimizing the overall size of the reactor from an economic viewpoint. A low-aspectratio (LAR) tokamak [4] offers a viable option for a fusion neutron source because it allows not only a large natural elongated plasma shape, which is favorable for transmutation reactors, but also a high plasma beta, which leads to a high-performance compact reactor. Each component of a tokamak reactor must satisfy all physics and engineering constraints. The shielding requirement plays an important role in determining the inboard radial build, and the tritium-breeding requirement has a large effect in determining the
∗ Corresponding author. E-mail address: [email protected] (B.G. Hong).
outboard radial build in a LAR tokamak reactor. For a transmutation reactor, the requirements for neutron multiplication and power density also need to be considered in determining the radial build. The transmutation and tritium-breeding capability need to be maximized, while limiting the neutron multiplication factor keff to less than 1.0 because a sub-critical reactor is preferred from the viewpoint of reactor safety, and limiting the power density to less than 100 MW/m3 to maintain cooling capability. Self-consistent determination of the radial build of the reactor components thus requires a radiation transport calculation coupled with a tokamak systems analysis [5]. In a LAR tokamak, tritium self-sufficiency can be satisfied using only an outboard tritium breeding blanket and appropriate selection of inboard shield material [6]. Also, in a transmutation reactor based on a LAR tokamak, the nuclear waste, i.e. transuranic actinides (TRUs: Pu and minor actinides Np, Am, Cm, etc.), and the tritium breeder can be located in the outboard blanket. By locating the tritium-breeding blanket after the transmutation blanket, we expect not only tritium self-sufficiency, as abundant thermal neutrons produced by fission of the TRUs contribute to the breed-
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ing of tritium, but also that neutrons reflected/produced from the tritium-breeding blanket will contribute to the transmutation of the nuclear waste. Thus, it is necessary to investigate the effect of different tritium-breeding blanket models on the outboard radial build of a transmutation reactor. Effective transmutation of nuclear waste requires an equilibrium fuel cycle. Potential radiation damage to the reactor components limits the achievable residence time of nuclear waste. Thus radiation damage due to neutrons from both fusion and fission on the blanket structure has to be considered in evaluating transmutation performance. In Section 2, we describe how we couple our radiation transport calculations with the tokamak systems analysis. We present the optimal configuration of a transmutation reactor based on a LAR tokamak and its transmutation characteristics in Section 3. In Section 4, we summarize our findings.
2. Coupled systems analysis Tokamak systems analysis, which has been used in concept definition studies of various tokamak reactors [5], determines the optimum radial build of a transmutation reactor. For the radiation transport and burn-up calculations, we use the one-dimensional radiation transport code BISON-C [7] with a 42 neutron group crosssection library based on JENDL-3.3. For the estimation of the local tritium breeding ratio (TBR), we use the JENDL dosimetry file [8]. The BISON-C code solves the one-dimensional radiation transport equation to obtain the neutron flux and then solves the nuclide burn-up equations using the obtained flux. We note that the onedimensional radiation transport calculation is adequate for scoping studies, and thus it is also enough in a coupled analysis with the zero-dimensional tokamak systems code to identify the key characteristics of a transmutation reactor. To couple the tokamak systems code with the one-dimensional radiation transport code, BISON-C, we develop an interface module. Starting from the initial estimate for the design parameters, we calculate the plasma physics and the engineering constraints, as well as the radial build of the reactor components, in the systems analysis. From these, the interface module adjusts the meshes to be appropriate for the radiation transport analysis. With the new meshes, we perform the radiation transport and burn-up analyses and calculate the neutron flux, keff , and various quantities. The interface module calculates the TBR, the power density and the shielding parameters. We then recalculate the radial builds, plasma physics, and engineering parameters in the systems analysis. This procedure continues until we find reactor parameters that satisfy all the plasma physics and engineering constraints. Fig. 1 shows a calculation procedure for the coupled systems analysis. A cross sectional view in a R-Z plane of the LAR tokamak is shown in Fig. 2 with an equatorial radial build. For the radiation transport analysis, we model the transmutation reactor using one-dimensional cylindrical geometry. The material composition of the reactor components is listed in Table 1. We determine the radial build of the components using the plasma physics and engineering constraints, which have to be satisfied simultaneously by each component of the reactor. The LAR tokamak allows an elongated, high beta plasma, which improves magnetohydrodynamic (MHD) performance and confinement. In this study, we use the expressions of plasma performance for the LAR tokamak, including maximum elongation, minimum safety factor, and maximum N , derived in Refs. [9–11]. The superconducting magnet and vacuum vessel designs were constrained to use International Thermonuclear Experimental Reactor (ITER) technology [12,13]. We use ferritic-martensitic stainless steel (FMS) as the fast wall and as the structural material of the blankets.
Fig. 1. Calculation procedure for the coupled analysis.
Fig. 2. A cross sectional view of the LAR tokamak and an equatorial radial build.
The radial build of the shield is determined by the TF coil protection requirement against nuclear heating and the radiation damage induced by neutrons from both fusion and fission. The constraints, which assume a design lifetime for the transmutation reactor of 40 years with 75% availability, are keeping fast neutron fluence to the superconductor below 1023 n m−2 for Nb3 Sn, displacement damage to the Cu stabilizer below 5 × 10−4 dpa, and dose to the insulators of less than 109 rad for organic insulators.
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Table 1 Material composition of the transmutation reactor. Component
Materials (Volume%)
Space Toroidal field coil Vacuum vessel Shield First wall Scrape-off layer Plasma Scrape-off layer First wall Transmutation blanket Breeding blanket High temp. shield Low temp. shield Vacuum vessel Toroidal field coil
– Nb3 Sn, Cu, Epoxy, SUS316, L. He Borated steel (60), H2 O (40) WC (80), H2 O (20) FMS (60), H2 O (40) – D, T – FMS (60), H2 O (40) TRU (5), FMS (15), He (75), SiC (5) He (7), PbLi (90), FMS (3) WC (60), H2 O (40) WC (80), H2 O (20) Borated steel (60), H2 O (40) Nb3 Sn, Cu, Epoxy, SUS316, L. He
Table 2 Composition of TRUs in the spent fuel of 1 GWe KSNP. Nuclide
Mass (%)
Np237 Pu238 Pu239 Pu240 Pu241 Pu242 Am241 Am243 Cm244 Cm245
6.88 2.18 45.65 22.03 1.22 7.35 12.31 2.18 0.15 0.05
The transmutation blanket and tritium breeding blanket are located only in the outboard blanket. The transmutation blanket (BL1) is loaded with the TRUs from the spent fuel of 1 GWe Korea Standard Nuclear Power plant (KSNP), and the tritiumbreeding blanket (BL2) is placed after the transmutation blanket to use the neutrons produced by the fission of the TRUs for tritium self-sufficiency and the neutrons reflected from and produced in the tritium-breeding blanket for the transmutation of the nuclear waste. Table 2 shows the nuclide composition of the TRUs contained in the spent fuel of 1 GWe KSNP. The radial build of the blankets should maximize the TBR (>1.35) and transmutation rate and keep the power density and neutron multiplication within their limiting values which are set to be 0.95 and 100 MW/m3 , respectively. In the transmutation blanket, we use FMS as a structural material and He as a coolant. For the tritium-breeding blanket, we use He-cooled lithium lead (HCLL) with natural Li and FMS as the structural material. The TRU fuel is assumed to take a form of a TRISO (TRi-ISOtropic) particle coated with SiC. We also investigate using a He-cooled solid breeder (HCSB) as the tritium-breeding blanket to learn how the tritium blanket model affects the outboard radial build of the transmutation reactor. The typical set of variables and constraints used in the coupled systems analysis is summarized in Table 3. The first four constraints determine the plasma performance, i.e., the electron temperature, electron density, heating and current drive power, and major radius. With the major radius determined by the plasma performance, the engineering constraints determine the radial build of the reactor systems. The tritium breeding requirement, transmutation blanket requirements, shielding requirements, TF coil equation, TF coil critical current density limit, TF coil case stress limit, ripple limit, and radial build constraint determine the thickness of the tritium breeding blanket, thickness of the transmutation blanket, thickness of the shield, thickness of the TF coil, TF coil current density, thickness of the TF coil case, position of the outboard TF coil, and bore radius of the TF coil, respectively.
Fig. 3. Dependence of the minimum major radius and neutron wall loading on the fusion power.
3. Optimal radial build of a transmutation reactor based on a LAR tokamak 3.1. Inboard radial build We investigate the radial build of a transmutation reactor for an aspect ratio, A, in the range of 1.5–2.0 and a fusion power in the range of 100–300 MW. The plasma performance is assumed to produce the required fusion power with the maximum plasma performance for a LAR tokamak, i.e., a safety factor of qa = qa ,min , normalized plasma beta of N = N,max , a confinement enhancement factor of H = 1.2, and plasma density of n = nG , where nG is the Greenwald density limit. The plasma physics and engineering constraints determine the inboard radial build of the reactor components. Among them, the constraints on the radiation shielding of the TF coil and the maximum magnetic field at the TF coil play a key role in determining the minimum major radius. Fig. 3 shows the dependence of the minimum major radius and the neutron wall loading on the fusion power when A = 1.5 and 2.0. The minimum major radius R0 increases as the fusion power increases, and is large when A is small. With the TRUs loaded in the transmutation blanket, the required inboard shield thickness increases compared to the case with no TRUs loaded because the neutrons from the fission of the TRUs have to be shielded. Neutron wall loading increases as the fusion power increases, and it is large when A is large. It is less than 1.0 MW/m2 for A in the range of 1.5–2.0 and fusion power in the range of 100–300 MW. The shield thickness is large when the aspect ratio and fusion power are large because of large neutron wall loading. 3.2. Outboard radial build and transmutation characteristics We determined the outboard radial build of the transmutation reactor components to limit the maximum neutron multiplication (keff ) to below 0.95, to limit the maximum power density to below 100 MW/m3 , and to satisfy the tritium self-sufficiency of TBR > 1.35 with an assumed blanket coverage factor of 80% in the one-dimensional model. Requirements for the neutron multiplication and power density determine the radial thickness of the transmutation blanket, BL1 . When A = 1.5, BL1 = 0.2 m, 0.23 m, and 0.28 m with fusion power of 100 MW, 200 MW and 300 MW, respectively. When A = 2.0, BL1 increases to 0.26 m, 0.36 m, and 0.43 m due to increased neutron wall loading, with a fusion power of 100, 200, and 300 MW, respectively. To transmute nuclear waste effectively, an equilibrium fuel cycle that which transmutes TRUs in batches needs to be developed. A reference fuel cycle consists of five burn cycles. The transmutation
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Table 3 Set of variables and constraints in the systems analysis. Constraint
Variable
Plasma physics (1) Beta limit, N < N,max (2) Density limit, ne < nGreenwald (3) Power balance equation, Pcon + Prad = POH + Paux + P␣ (4) Fusion power, Pfusion = desired power Engineering (5) Tritium breeding requirement, TBR > 1.35 (6) Transmutation blanket requirements, keff < 0.95 power density <100 MW/m3 (7) Shielding requirements for TF coil fast neutron fluence < 1023 n m−2 displacement damage < 5 × 10−4 dpa dose to the insulators <109 rad (8) TF coil equation, Bmax × RTFi = R0 × BT (9) TF coil current density limit, JTF < 2.8 × 108 A m−2 (10) TF coil case stress limit, TFcase < 550 MPa (11) Ripple limit, ␦ripple < 0.1% (12) Radial build
(1) Electron temperature, Te (2) Electron density, ne (3) Auxiliary heating power, Paux (4) Major radius, R0 (5) Thickness of breeding blanket, BL2 (6) Thickness of transmutation blanket, BL1 (7) Thickness of shield, shld (8) Thickness of TF coil, TF (9) TF coil current density, JTF (10) TF coil case thickness, TFcase (11) Bore radius of TF coil, Rbore (12) Outer TF coil location, RTFo
Table 4 Equilibrium fuel cycle analysis for A = 1.5 and 2.0. Aspect ratio
A = 1.5
Burn cycle (day) 100 MW
300 6.05 848 13 3000 0.6 0.2 0.2 6.34 1335 19 4750 0.9 0.23 0.2 6.68 1773 23 6350 1.1 0.28 0.21
200 MW
300 MW
Fig. 4. Variation of keff as TRUs burn: (a) No fuel cycle and (b) fuel cycle with a burn cycle of 300 days.
blanket is divided into 5 batches so that each batch has a same volume. The fuel is loaded at outmost batch and shuffled to inner batch after each burn cycle. After the fifth burn cycle, the equilibrium is reached and the batch of depleted fuel is removed. Depending on the burn-up of the nuclear waste, it can be deposited in a highlevel-waste repository or reprocessed to remove fission products and recover TRUs to be recycled again in the transmutation reactor. The radiation damage limit of the plasma-facing material of the blanket determines the achievable residence time of the nuclear waste. Depending on the accumulated fast neutron fluence, the plasma-facing material has to be replaced several times during the reactor’s lifetime. The radiation damage limit of FMS is assumed to be 3.0 × 1027 n m−2 . Fig. 4(a) shows the variation in keff as the TRUs burn up for cases with A = 1.5 and 2.0, and a fusion power of 100 MW and 300 MW. In this case, the fusion powers are kept constant, i.e., at their maximum capacity. The keff decreases as the TRUs burn up, and the decrease rate becomes larger with larger A and larger fusion
Height (m) Trans. rate (kg/y) Burn-up (%) Power (MW) Fast fluence @FW (1027 n m−2 ) BL1 (m) BL2 (m) Height (m) Trans. rate (kg/y) Burn-up (%) Power (MW) Fast fluence @FW (1027 n m−2 ) BL1 (m) BL2 (m) Height (m) Trans. rate (kg/y) Burn-up (%) Power (MW) Fast fluence @FW (1027 n m−2 ) BL1 (m) BL2 (m)
A = 2.0 600 647 20 2300 1.0
972 27 3480 1.4
1294 33 4600 1.8
300 3.30 573 19 2040 0.9 0.26 0.2 3.53 911 26 3300 1.3 0.36 0.3 3.68 1175 31 4270 2.2 0.43 0.4
600 – –
630 37 2300 2.7
802 43 3000 3.2
power due to large neutron wall loading. The total power produced from the fusion and the fission reactions and the amount of transmuted nuclear waste are proportional to Pfusion × keff /(1 − keff ), where Pfusion is the fusion power. They decrease as the TRUs burn, and their decrease rate gets larger. To transmute a large amount of nuclear waste, keff needs to be high and its decrease rate needs to be small during the burn-up period. Fig. 4(b) shows the variation in keff when the equilibrium fuel cycle with five burn cycles (300 days each) is reached for the cases with A = 1.5 and 2.0. In this case, the total power is kept constant and thus the fusion power has to increase as the TRUs burn up to compensate for the consumption of fusion neutrons up to the maximum fusion power of 100 MW or 300 MW. The variation in keff during 1500 days is much smaller than the cases shown in Fig. 4(a) because of the equilibrium fuel cycle. In Table 4, we compare the transmutation performance when the fusion power capacity is 100 MW, 200 MW and 300 MW for the cases with A = 1.5 and 2.0, and the burn cycle of 300 days and 600 days. The reactor height is assumed to be × a (where is the elongation and a is the minor radius), and the total power is kept constant. The total power and the transmutation performance are obtained based on the assumption that the power distribution is uniform along the reactor height, and thus they correspond to the maximum value at the equatorial region. The burn cycle is deter-
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Table 5 Radial build of a transmutation reactor with A = 1.5. Fusion power (MW) Component (m)
100
200
300
Space Toroidal field coil Vacuum vessel Shield First wall Scrape-off layer Plasma Scrape-off layer First wall Trans. blanket Breeding blanket High temp. shield Low temp. shield Vacuum vessel Toroidal field coil
0.10 0.28 0.43 0.83 0.85 0.95 4.72 4.82 4.84 5.05 5.26 5.56 6.16 6.31 6.61
0.10 0.32 0.47 0.89 0.91 1.01 5.04 5.14 5.16 5.38 5.59 5.89 6.49 6.64 7.01
0.10 0.34 0.49 0.92 0.94 1.04 5.22 5.32 5.34 5.62 5.83 6.13 6.73 6.88 7.29
Table 6 Radial build of a transmutation reactor with A = 2.0.
Fig. 5. Neutron spectra when A = 1.5 and fusion power = 100 MW: (a) HCLL blanket and (b) HCSB blanket.
mined by the requirement on the total power and the fast neutron fluence over five cycle residence times. When the fusion power is 100 MW, the total power larger than 2000 MW can be produced for the burn cycle of 600 days with A = 1.5, but the total power larger than 2000 MW can not be produced for the burn cycle of 600 days with A = 2.0. The fast neutron fluence over five cycle residence times increases with the fusion power, the burn cycle and the aspect ratio A. When the fusion power is 300 MW and A = 2.0, the fast neutron fluence over five cycle residence times is larger than the radiation damage limit of the first wall. The fast wall has to be replaced at the time of the shuffling before the radiation damage limit of FMS is reached. During the transmutation, Pu239, Pu240, Am241, Pu242 and Np237, which constitute a majority of TRU decrease but actinides such as Pu238, Pu241, Am243, Am242, Am244 and Cm245 increase since they are produced from the neutron absorption of the other actinides and they are difficult to transmute. The transmutation rate is larger with a larger fusion power, a smaller aspect ratio, and a shorter burn cycle. However, the burn-up fraction increases with a larger fusion power, a larger aspect ratio, and a longer burn cycle. When A = 1.5, a transmutation reactor with 300 MW of fusion power capacity can produce a total power of 6350 MW and support about 7 pressurized water reactors (PWRs) of 1.0 GWe capacity with a burn cycle of 300 days. With a burn cycle of 600 days, the reactor can produce a total power of 4600 MW and supports about 5 PWRs. When A = 2.0, a transmutation reactor with 300 MW of fusion power can produce a total power of 4270 MW and support about 4 PWRs with a burn cycle of 300 days. With a burn cycle of 600 days, the reactor can produce a total power of 3000 MW and supports about 3 PWRs. Here, we assumed that the TRUs from 1 PWR of 1 GWe capacity are approximately 250 kg/y. As the TRUs burn up, the TBR decreases due to the burn-up of Li6. To satisfy the TBR requirement of TBR > 1.35 during the burn-up
Fusion power (MW) Component (m)
100
200
300
Space Toroidal field coil Vacuum vessel Shield First wall Scrape-off layer Plasma Scrape-off layer First wall Trans. blanket Breeding blanket High temp. shield Low temp. shield Vacuum vessel Toroidal field coil
0.10 0.39 0.54 1.07 1.09 1.19 3.58 3.68 3.70 3.96 4.17 4.47 5.07 5.22 5.71
0.10 0.45 0.60 1.16 1.18 1.28 3.83 3.93 3.95 4.31 4.62 4.92 5.52 5.67 6.28
0.10 0.49 0.64 1.21 1.23 1.33 4.00 4.10 4.12 4.55 4.96 5.26 5.86 6.01 6.67
period, the radial thickness of the tritium-breeding blanket, BL2 , increases with the fusion power due to increased neutron wall loading. When A = 1.5, BL2 increases slightly with the fusion power. But when A = 2.0, BL2 = 0.2, 0.3, and 0.4 m with the fusion power of 100, 200, and 300 MW, respectively. Fig. 5 shows the neutron spectra at the end of the fifth burn cycle in the transmutation blanket and the tritium-breeding blanket for A = 1.5 with the fusion power = 100 MW. Cases with the HCLL blanket (a) and the HCSB blanket (b) are shown. The flux in the tritium-breeding blanket is larger with than without the TRUs, indicating a contribution from the fission of the TRUs. The fast (>0.1 MeV) neutron fluxes in the transmutation blanket and the tritium-breeding blanket with the HCLL blanket are higher than those with the HCSB blanket, which we attribute to the fast neutrons produced from the (n, 2n) reaction in Pb in the HCLL blanket. These neutrons contribute to the transmutation of the TRUs in the transmutation blanket, and we find the radial thickness of the transmutation blanket to be smaller than that with the HCSB blanket (BL1 = 0.23 m). The neutron flux with the lower energy in the HCSB blanket is higher than that in the HCLL blanket because the neutrons from the fusion reaction and the fission of the TRUs slowed down without being absorbed in the Pb. It resulted in smaller radial thickness of the tritium-breeding blanket (BL2 = 0.18 m) for the HCSB blanket due to the high tritium breeding cross section of Li-6 from the low neutron energy. Thus, the outboard radial build of the components of the transmutation reactor are closely related to one another. Tables 5 and 6 summarize the radial builds of the transmutation reactor for the cases with the HCLL blanket and fusion power of 100, 200, and 300 MW when A = 1.5 and 2.0, respectively.
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4. Conclusion
References
We determined the optimum radial build of a transmutation reactor based on a LAR tokamak neutron source with fusion power in the range of 100–300 MW through coupled analysis of the tokamak systems and the radiation transport. The radial build of the reactor components is self-consistently determined by the constraints on the plasma physics performance, tokamak engineering, and neutron performance. We investigate the transmutation characteristics when the transmutation reactor produces a constant total power. The transmutation rate is larger with a larger fusion power, a smaller aspect ratio, and a shorter burn cycle. However, the burn-up fraction increases with larger fusion power, a larger aspect ratio, and a longer burn cycle. We showed that the radial build of the transmutation reactor components and the equilibrium fuel cycle play major roles in determining the transmutation characteristics.
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Acknowledgments This paper was supported by research funds from Chonbuk National University in 2015 and by the research facilities at the Plasma Application Institute of Chonbuk National University. This work was also supported by a National Research Foundation of Korea (NRF) grant under contract nos. 2015R1D1A3A01019752 and 2013M1A7A1A01043740.
Please cite this article in press as: B.G. Hong, H. Kim, Study of an optimal configuration of a transmutation reactor based on a low-aspectratio tokamak, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.05.039