- Email: [email protected]
Analysis of nuclear response in CFETR toroidal field coils with density reduction VR technique
Fusion Engineering and Design 147 (2019) 111243
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Analysis of nuclear response in CFETR toroidal field coils with density reduction VR technique
T
⁎
Peng Lua,b, Kun Xuc, Yu Zhengc,d, Xia Lic, Songlin Liuc, , Jianjun Huanga, Bin Yub a
Advanced Energy Research Center, Shenzhen University, Shenzhen 518060, PR China Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, PR China c Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui, 230031, PR China d School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, PR China b
A R T I C LE I N FO
A B S T R A C T
Keywords: CFETR TFC McCad Variance reduction Density reduction
The China Fusion Engineering Test Reactor (CFETR) has been designed as steady-state operated tokamak device. The CFETR new engineering design has been initialized corresponding to the latest core parameters (major/ minor radius is R = 7.2 m/a = 2.2 m). The nuclear analysis of CFETR was carried out to evaluate the neutron shielding capabilities and nuclear responses to toroidal field coils (TFC). The 3D neutronics model of CFETR was built with the support of McCad tool to convert the CAD model automatically. An extended variance reduction (VR) technique of combined MAGIC GVR with density reduction method has been involved to generate suitable weight windows to enhance the efficiency of particle transport. Highly detailed neutron and photon map has been obtained which meet the requirements for Monte Carlo nuclear analyses. The global neutron flux distribution of 3D CFETR with Pf = 200 MW to 1.5 GW was obtained to evaluate its shielding performance. The nuclear responses to TFC such as the nuclear heating and fast neutron fluence have been evaluated. Initial results show the shielding of current divertor design is not sufficient and the optimizing work has been done. The final results satisfy the referred ITER design limit and it can provide the support for the future more detailed design of divertor and other shielding systems.
1. Introduction Nuclear fusion has many advantages in comparison with fossil fuels and fission energy: it is carbon free, there is no production of long-lived radioactive waste, and deuterium and lithium are abundant on Earth. Many decades ago, the scientists already started to build fusion device to explore a smooth way for attaining plasma from nuclear fusion. So far, the ITER (International Thermonuclear Experimental Reactor), which is already under construction in Cadarache France, should be the most expected device for its aim to produce 500 MW of fusion power running at long pulses of 400 s. The China Fusion Engineering Test Reactor (CFETR) in turn goes further than ITER not only achieving the long-pulse operation but also with mission to breed the tritium and cycle the tritium in self-sustained state. Some data on the conceptual design of CFETR has been released in recent years [1]. The newest physical design of CFETR has been fixed and the engineering design has been initialized in 2018 [2]. Based on the lessons from the previous design, its size increased to R = 7.2 m and its fusion power (Pf)
⁎
capability became more flexible at 200 MW, 500 MW, 1 GW and 1.5 GW in one machine. This makes the machine more versatile but also more challenging in terms of its engineering design. The nuclear analysis, in the meantime, tries to follow the progress of CFETR design. The important nuclear responses such as neutron flux and nuclear heating will be needed for the evaluation of irradiation shielding, heat removal, etc. The superconducting performance of TFC strongly depends on the operation temperature and heat removal capability of helium coolant in the center of coil. Thus the fast neutron fluence (neutron energy > 0.1 MeV) and nuclear heating exposed on TFC should be limited. In this paper, the nuclear heating and fast neutron fluence at TFC case, conductor and insulator has been analyzed. As the design of CFETR has followed the ITER, many technologies will be taken as reference. For example, according to ITER design limits [3], the fast neutron fluence in magnet conductor should not exceed 1 × 1019 n/cm2 and in insulator 2 × 1018 n/cm2. Meanwhile, the nuclear heating density in magnet steel case should not exceed 6 × 10−4 W/cm3 and in magnet conductor 3 × 10−4 W/cm3 in case of
Corresponding author. E-mail address: [email protected] (S. Liu).
https://doi.org/10.1016/j.fusengdes.2019.111243 Received 25 January 2019; Received in revised form 27 May 2019; Accepted 20 June 2019 0920-3796/ © 2019 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
concepts which are both under research. In this work, the water cooled ceramic breeding (WCCB) blankets were investigated. The previous research progress of WCCB has been reported [9–13]. The updated design [14] has adopted a cooling tube assembly (CTA) composed of dual-wall pressurized tube (DWT) concept for cooling function instead of conventional cooling plate (CP). This is much easier to be manufactured than CP. While, in order to generate the neutronics model, the CTA geometry has been simplified by modifying the tube to plate but mixing with part of breeding zone material, shown in Fig. 2. The WCCB blankets choose Li2TiO3 and Be12Ti as tritium breeder and neutron multiplier, the RAFM steel, i.e. CLAM or CLF-1 [15–17] as structure material. The first wall (FW) is protected by 2 mm thick tungsten. It’s also known as plasma facing component (PFC). The FW is mixture of coolant water and structure material CLAM steel. Other components such as back plate (BP), back supporting structure (BSS), radial-poloidal stiffening plate (SP), side wall (SW), cover are also mixture of water and steel and minor fraction of helium gas. The material composition of components is shown in Table 1.
overheating in superconductor. The initial evaluation of irradiation effect to TFC in CFETR will be conducted by referring to ITER design limit. To serve the nuclear analysis of CFETR, a 3D neutronics model has been built based on engineering CAD model. This has been done with an open source code McCad to convert the CAD model to neutronics model [4]. McCad is developed by KIT/INR as visualization interface and automatical conversion software. With the help of McCad, it becomes easier and quicker to establish the neutronics model when compared with conventional error-prone and tedious way. The nuclear analysis of CFETR has been conducted by using of MCNP particle transport code [5]. To implement the CFETR nuclear analysis with MCNP, a sophisticated variance reduction (VR) technique was applied to speed up the computation due to its large size and complex geometry. The global variance reduction (GVR) MAGIC [6] method is chosen and implemented. This comes from the fact that the MAGIC is indeed a user-friendly and easy-operated method. No other supporting software was needed, only the MC code, here namely MCNP. The MAGIC method iterates the particle flux calculation to obtain the weight windows to facilitate the particle transport. It usually needs several iterated steps to obtain the final convergent results. In this paper, the authors present a new implementation of MAGIC but combining with density reduction method for global flux calculation of CFETR. Some attractive work have been reported in implementation of density reduction method [7,8]. The extended method first decreases the mass density of problem geometry in order to run quickly to produce seed weight windows. Then increase the density gradually up to original one and run with support of previous generated weight windows. This is also iterated step but can finally obtain suitable results in a quick way. The extended method has been successfully applied on CFETR for global neutron and photon transport and accurate results have been obtained. More details are discussed below.
3. Methodology 3.1. Combined MAGIC GVR with density reduction Due to the large size and complex geometry of fusion device like CFETR, the Monte Carlo particle simulation will always consume a lot of computer power and time even run with parallel model. Consequently, accurate result could hardly be obtained unless a VR technique is used. In this paper, the authors employ the MAGIC method but combining with density reduction. The detailed workflow is as follows: i First, setup two sets of mesh covering all the geometry in order to tally the neutron and photon (N&P) flux. The mass density of all material in CFETR is reduced to very low level as 0.2 times original one. By doing so, a well converged global N&P flux can be obtained relatively quickly. ii Then increase the mass density to 0.5 times. Reproduce the weight windows for next iterated step by using the N&P flux in the first calculation, but improve the gradient of weight windows among adjacent mesh voxel following the formula:
2. Neutronics model The initial CAD model of CFETR includes the main components: blanket, divertor, toroidal field coil (TFC), poloidal field coil (PFC), central solenoid (CS), vacuum vessel (VV), thermal shielding (TS), port plug, cryostat, bio-shield. While the original CAD geometry should be simplified to remove unimportant structures such as holes, chamfers etc. Otherwise it’s difficult to be converted by using of McCad tool. The whole model was divided into 16 segments in toroidal direction (Fig. 1). Only one segment has been converted to neutronics model. One segment includes 18 outboard blanket (OB) modules: 6 blankets in poloidal and 3 in toroidal, 12 inboard blanket (IB) modules: 6 in poloidal and 2 in toroidal respectively. The water cooled and helium cooled blankets are two candidate
ϕ wi = ⎜⎛ i ⎟⎞ ϕ ⎝ max ⎠
n
(1)
where n is expanding factor and n > 1, ϕi is neutron or photon flux in mesh voxel i, ϕmax is max flux in the whole mesh. This time, n is set to greater than 1, but in the shielding zone the expanding factor n can be larger. Perform the particle transport with the support of generated
Fig. 1. One of 16 sectors of CFETR (left and center) and the converted neutronics model prepared using McCad tool (right). 2
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
Fig. 2. Simplified CTA geometry for generating the neutronics model.
was implemented. The mesh size to tally the N&P flux is set as rectangular mesh of 20 × 20 × 20 cm. The length of CFETR at X, Y and Z direction is about 2200 cm, 860 cm and 4300 cm respectively. Thus totally the number of mesh voxel is about 8 × 105. Consider the huge number of mesh voxels, computation speed and limit of computer storage capability, only a coarse two energy groups are set to separate the neutrons in tally cells: that is thermal neutrons (< 0.1 MeV) and fast neutrons (> 0.1 MeV). More energy groups setting is possible only with strong support of computer power. The three iteration calculation (shown in Fig. 3), first two for the generation of weight windows and last the regular particle transport, were simulated with 140 computer cores. The calculation for step i) is fast when very low density is set and totally ˜1.5 × 104 minutes of CPU time is consumed to get accurate results: within more than 90.6% of mesh voxel the relative error (RE) is less than 5%. Next calculation for step ii), increase the mass density to 0.5 times original one, process the weight windows by using of N&P flux results. The expanding factor n is set to 1.5 for most area but increased 1.7 at middle and down port plug, 1.9 at central solenoid, 2 at upper port and bio-shield (Fig. 3(a)). These expanding factors are decided through some trial calculations, i.e. adjusting the expanding factors to generate weight windows and run quickly (with small number of histories) in order to make the particles uniformly distributed into the geometry. With support of prepared weight windows, launch the particle transport. It consumes about ˜2 × 104 minutes of CPU time and the resulting flux has acceptable precision: within more than 80.8% of mesh voxel the RE is less than 5%. At last time the regular calculation for step iii), the setting of expanding factor n to process the weight windows is shown in Fig. 3(c). It consumes ˜1 × 105 minutes of CPU time: within more than 82.4% of mesh voxel the RE is less than 5%, 95.3% the RE is less than 10% and more than 99.9% is non-zero tally results. The final neutron flux distribution and RE map can be seen in Fig. 3(e), (f). This RE map demonstrates the computational precision that satisfies the requirement of nuclear analysis. Most main components of blanket, divertor, VV, TS, TF and PF coil have fine accuracy. But only part of CS and bio-shielding have high relative error beyond 10%. Most likely this can be improved when needed by manually adjusting the corresponding weight windows and taking more computer time. These weight windows, on the other hand, can also be used in future for repeated calculation of CFETR even within minor modification of geometry.
Table 1 Material composition of CFETR system and components (unit: vol% specified if wt%).
Blanket
Divertor
VV
Components
Material
PFC FW BZ CTA
100% Tungsten 14.55% H2O, 85.45% CLAM steel 14.4% Li2TiO3, 65.6% Be12Ti, 20% He 12.412% H2O, 45.763% CLAM steel, 6.023% Li2TiO3, 27.437% Be12Ti, 8.365% He 53.55% H2O, 46.12% CLAM steel, 1.65% He 11.06% H2O, 87.29% CLAM steel, 1.65% He 14.97% H2O, 85.03% CLAM steel 29.09% H2O, 70.91% CLAM steel 2.18% H2O, 96.23% CLAM steel, 0.0159% He 75% SS316 L, 25% H2O (150 °C, 5 MPa) 71.05% W, 6.41% oxygen free copper (OFC), 8.11% CuZrCr, 14.43% H2O SS316 L(N)-IG SS316 L(N)-IG Borated water, 1.32 wt% B and enriched in 10-B to 95% Borated steel, 1.2 wt% Boron and enriched in 10-B to 95% 50% H2O, 50% CLAM steel SS316LN Nb3Sn SS316LN NbTi SS304/SS304L Concrete
BP BSS rpSP SW cover Cassette First Wall
shell rib Inner shielding
TS Port TF, CS PF
plug case conductor case conductor
Cryostat Bio-shield
weight windows and produce the mesh tally of assumed density of problem.
• Finally, increase the mass density to original one. Repeat the second
step to prepare the weight windows. Still the expanding factor n can be adjusted by user but actually need some rule of thumb. Then launch the particle transport to get real flux results.
The processing of weight windows and setting of expanding factor at specified location has been realized with developed Python script. This method has been successfully applied on CFETR for N&P transport.
3.2. N&P transport With the support of combined VR method, the N&P transport can be carried for global analysis. The Fendl-2.1 nuclear cross section library 3
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
Fig. 3. (a): neutron flux of assumed mass density as 0.2 times original one and the expanding factor setting to prepare the weight windows; (b): relative error of figure (a) neutron flux; (c): neutron flux of assumed mass density as 0.5 times original one, calculated with support of previous weight windows, and the expanding factor setting; (d): relative error of figure (c) neutron flux; (e): final results of 200 MW fusion power neutron flux (n/cm2/s) and relative error (100%).
example, Between the 3rd and 4th blanket, the neutron flux behind BSS at gap position is about 2 times larger than other zone. The 6th and 7th blankets are thinner than other blankets as the thickness in radial direction is 50.7 cm and 70.0 cm respectively. Thus the neutron flux behind BSS is nearly one order of magnitude higher than other blankets (e.g. 3rd blanket). It has weaker shielding performance according to current design. Some optimization work will be carried out in future. The neutron flux distribution of divertor is shown in Fig. 4 right down figure. Highest neutron flux reaches about 3.1e+14 n/cm2/s. The divertor design so far cannot meet the shielding requirements due to the exhaust channel where neutrons can leak (Fig. 4). This also can be detected in Fig. 5 where the TFC conductor has hot spot in nuclear heating density below divertor zone. On the other hand, the joint between divertor and blanket also needs improvement in shielding performance. That’s why two spots in nuclear heating density of TFC have been identified. To decrease the neutron irradiation damage to in-vessel components as well as superconductor coils, the shielding design of divertor and blanket has been optimized. Following is the detail about the nuclear analysis of TFC.
4. Results 4.1. Global neutron flux distribution The CFETR neutron flux results have been visualized with Paraview post-processing code by converting the tally results to VTK format [18]. Fig. 4 left figure shows the neutron flux of CFETR with Pf = 1.5 GW. Highest neutron flux reaches about 4.7e+14 n/cm2/s at center of plasma. Outside bio-shield, the neutron flux decrease more than 10 orders of magnitude. Starting from the right bottom, the blankets are labeled from number 1 to the 11 in counterclockwise. The neutron flux distribution of blanket is shown in Fig. 4 right top figure. Highest neutron flux reaches about 4.5e+14 n/cm2/s in outboard blanket at equatorial plane and lowest about 6.3e+10 n/cm2/s at BSS of 8th blanket. It decreases more than 3 orders of magnitude due to shielding performance of coolant water in blanket. There is 2 cm gap between adjacent blankets both in toroidal and poloidal direction. Thus it results in penetration of neutrons through these gaps and increases the irradiation damage to the components behind blanket such as VV and TS. For
4
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
Fig. 4. Left: y = 0 section; right top: neutron flux of WCCB blanket; right down: neutron flux of divertor.
For one piece of TFC, it is segmented to 48 parts and the labeled number is shown in Fig. 7. The nuclear heating of TF case, conductor and insulator in one piece of TFC when Pf = 200 MW can be seen in Fig. 8. The total nuclear heating of TFC in whole reactor is about 4.2 kW when Pf = 200 MW and 31.7 kW when Pf = 1.5 GW (Table 2). The TFC steel case contribute about 63.7% to total nuclear heating, insulator negligible 0.3% and conductor 36.0%. The ITER design limits the total nuclear heating deposited on TFC to 14 kW considering the heat removal capability. For CFETR, in other words, must be scaled with a factor because of the different neutron intensity and operation scenario compared with ITER. The allowable total nuclear heating deposited on CFETR TFC should be proposed in future by the engineering design group. The nuclear heat density distribution and fast neutron fluence in TFC poloidal direction is shown in Fig. 9. Benefiting from the optimized engineering design of divertor and blanket, it has more reliable shielding performance. The highest nuclear heating density at TFC case and conductor reaches 5.60 × 10−5 and 1.89 × 10−5 W/cm3 respectively with Pf = 200 MW at 4th segment, but not exceed the ITER design limit even when Pf = 1.5 GW (Table 3). The neutron fluence of TF conductor and insulator with Pf = 200 MW and 1.5 GW has been calculated for 10 full power years (FPY) of operation. And the highest neutron fluence of TF conductor and insulator reaches 2.01 × 1017 and 1.98 × 1017 respectively when Pf = 200 MW. They are still not beyond the design limit when Pf = 1.5 GW. However, the nuclear heating density and fast neutron fluence at TF superconductor are averaged over the 48 segments and they could be several factors lower than the peak nuclear responses. After the releasing of detailed TFC engineering design, such as the arrangement and turns of superconductor coil, the nuclear analysis will be updated to compare the peak nuclear responses. The results show the optimizing work did decrease the neutron damage to TFC by adding shielding blocks at bottom of divertor and connection between divertor and outboard blanket. However, this is somehow still a makeshift solution as this work is only conducted from the point view of nuclear analysis. Furthermore, the choice of shielding material, for now is 50% water and 50% CLAM steel, is possible to be substituted by investigating WC, B4C and other well neutron shielding performance material if the allocated space is not sufficient and the block volume should be reduced. A comprehensive study should be conducted in future to consider not only the nuclear responses but also the allowed allocated space to shielding block, the mechanical analysis and other engineering simulations. However, information provided in this paper is useful for further updates of the design.
Fig. 5. Nuclear heating density (W/cm3) in TFC conductor when Pf = 1.5 GW.
4.2. Irradiation effect to TFC Since the neutrons leak from divertor and increase the damage to VV and superconductor coils additional shielding was added to two places. The optimized structure of divertor and blanket is shown in Fig. 6 (as circled in red). First is the connection part between divertor and outboard blanket. A 50 cm long shielding block was stretched out from the manifold and BSS of bottom outboard blanket in order to prevent the neutrons leaking from the gap. It was filled with 50% water and 50% CLAM steel. Initial calculation shows it indeed decrease the neutron flux to an accepted level. The second change is at the bottom of divertor. A shielding block was added to the VV and was also filled with 50% water and 50% CLAM steel. To decide the required thickness of the second shielding block, a parameter study has been carried out by change the block thickness from 25 cm, 35 cm and 45 cm. Result shows 35 cm thickness of shielding block can meet the design limit. Following are the analysis according to this optimization. 5
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
Fig. 6. Left: original design; right: shielding blocks to the bottom of divertor and gap between divertor and blanket.
Fig. 7. Segment number of TFC.
5. Conclusion
This work has been started by constructing a 3-D neutronics model with support of McCad automatic conversion tool. This model includes the main components of WCCB, divertor, VV, TS, TFC, PFC, CS, Cryostat and bio-shielding. For particle transport calculation, the MCNP code was employed with support of FENDL-2.1 nuclear cross section library. To accelerate the particle transport, a combined density reduction with MAGIC GVR method was used. The calculation shows this VR method has high efficiency and the final results show sufficient precision for nuclear analyses. Initial results show the shielding of divertor is not sufficient and
The latest CFETR design has been released with major radius of machine as R = 7.2 m. Other systems such as WCCB, as one of two candidate blanket concepts, also updated following the tritium breeding and neutron shielding requirements of CFETR. The nuclear analysis has been initialized to evaluate its global shielding performance. To guarantee the safe work condition of TFC, the nuclear heating and fast neutron fluence parameters have been evaluated and judged referred to ITER design limit. 6
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
cause high irradiation damage and heating to TFC. An optimizing work has been finished by adding shielding blocks at two identified neutron pathways causing hot spots on TFC. With a parameter study, the two shielding blocks were decided as one of 35 cm thickness block at bottom of divertor and 50 cm long block stretched out from blanket BSS and manifold. These two shielding blocks were all filled with mixture of 50% water and 50% CLAM steel. The optimized results show the total nuclear heating to TFC in whole reactor is about 4.2 kW when Pf = 200 MW and 31.7 kW when Pf = 1.5 GW. The nuclear heating density at TFC case and conductor and accumulated neutron fluence in 10 FPY at TFC conductor and insulator did not exceed the referred ITER design limit. The presented optimizations will provide guidance for more detailed design of CFETR divertor and blanket as well as other related shielding systems.
Declarations of interest Fig. 8. Total nuclear heating (W) in one piece of TFC when Pf = 200 MW.
None.
Table 2 TFC total nuclear heating of 200 MW and 1.5 GW of fusion power.
Pf = 200 MW, Nuclear Heating [W] Pf = 1.5 GW, Nuclear Heating [W]
Acknowledgments
TF case
TF insulator
TF conductor
Total
2.69E+03
1.40E+01
1.52E+03
4.22E+03
2.02E+04
1.05E+02
1.14E+04
3.17E+04
The authors wish to acknowledge the financial support of National Key R&D Program of China [grant number 2017YFE0300501], [grant number 2017YFE0300502], and the Chinese National Natural Science Foundation [grant number 11775256].
Fig. 9. Left top: nuclear heating density of TF case; left down: fast neutron fluence of TF conductor accumulated in 10 FPY; right top: nuclear heating density of TF conductor; right down: fast neutron fluence of TF insulator accumulated in 10 FPY. 7
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
Table 3 Nuclear responses of TFC and referred ITER design limit. Nuclear Responses
Fast neutron fluence in magnet conductor (n/cm2) (10 FPY)
Fast neutron fluence in insulator (n/cm2) (10 FPY)
Nuclear heating density in magnet steel case (W/cm3)
Nuclear heating density in magnet conductor (W/cm3)
ITER Design Limit Pf = 200 MW(Maxmium) Pf = 1.5 GW (Maxmium)
1 × 1019 2.01 × 1017 1.51 × 1018
2 × 1018 1.98 × 1017 1.49 × 1018
6 × 10−4 5.60 × 10−5 4.20 × 10−4
3 × 10−4 1.89 × 10−5 1.43 × 10−4
References
(2017) 865–870. [10] L. Chen, et al., A DEM-based heat transfer model for the evaluation of effective thermal conductivity of packed beds filled with stagnant fluid: thermal contact theory and numerical simulation, Int. J. Heat Mass Transf. 132 (2019) 331–346. [11] K.C. Jiang, et al., Preliminary analysis on DNB in the first wall of WCCB blanket for CFETR, IEEE Trans. Plasma Sci. 46 (6) (2018) 2318–2323. [12] X.K. Zhang, et al., Updated neutronics analyses of a water cooled ceramic breeder blanket for the CFETR, Plasma Sci. Technol. 19 (11) (2017). [13] X.B. Ma, et al., Electromagnetic force evaluation on the water cooled ceramic breeder blanket for CFETR, Fusion Eng. Des. 131 (2018) 21–28. [14] S. Liu, et al., Updated design of water-cooled breeder blanket for CFETR, Fusion Eng. Des. (2019). [15] L. Peng, et al., Preliminary analysis of irradiation effects on CLAM after low dose neutron irradiation, J. Nucl. Mater. 386-88 (2009) 312–314. [16] H.E. Ge, et al., Tensile properties of CLAM steel irradiated up to 20.1 dpa in STIP-V, J. Nucl. Mater. 468 (2016) 240–245. [17] P.H. Wang, et al., Technical issues for the fabrication of a CN-HCCB-TBM based on RAFM steel CLF-1, Plasma Sci. Technol. 15 (2) (2013) 133–136. [18] Y.F. Qiu, et al., Integrated approach for fusion multi-physics coupled analyses based on hybrid CAD and mesh geometries, Fusion Eng. Des. 96-97 (2015) 159–164.
[1] Y.X. Wan, et al., Overview of the present progress and activities on the CFETR, Nucl. Fusion 57 (10) (2017). [2] J. Li, Progresses and activities of CFETR, Presented in SOFT (2018). [3] ITER Magnet Design Description Document Part 1, (2009) ITER D 2NPLKM, version 1.8, September. [4] L. Lu, et al., Improved algorithms and advanced features of the CAD to MC conversion tool McCad, Fusion Eng. Des. 89 (9-10) (2014) 1885–1888. [5] MCNP, A General Monte Carlo N-Particle Transport Code, Version 5, Volume I: Overview and Theory, X-5 Monte Carlo Team, 2003 April 24 (Revised 2/1/2008). [6] A. Davis, et al., Comparison of global variance reduction techniques for Monte Carlo radiation transport simulations of ITER, Fusion Eng. Des. 86 (9-11) (2011) 2698–2700. [7] T.E. Booth, MCNP Variance Reduction Examples, Los Alamos National Laboratory, 2004 LA-UR-12-25907. [8] K. Kondo, et al., Neutronic analysis for the IFMIF target and test cell using a new CAD-based geometry model, Fusion Eng. Des. 87 (7-8) (2012) 983–988. [9] S. Liu, et al., Conceptual design of the water cooled ceramic breeder blanket for CFETR based on pressurized water cooled reactor technology, Fusion Eng. Des. 124
8
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Analysis of nuclear response in CFETR toroidal field coils with density reduction VR technique
T
⁎
Peng Lua,b, Kun Xuc, Yu Zhengc,d, Xia Lic, Songlin Liuc, , Jianjun Huanga, Bin Yub a
Advanced Energy Research Center, Shenzhen University, Shenzhen 518060, PR China Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, PR China c Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui, 230031, PR China d School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, PR China b
A R T I C LE I N FO
A B S T R A C T
Keywords: CFETR TFC McCad Variance reduction Density reduction
The China Fusion Engineering Test Reactor (CFETR) has been designed as steady-state operated tokamak device. The CFETR new engineering design has been initialized corresponding to the latest core parameters (major/ minor radius is R = 7.2 m/a = 2.2 m). The nuclear analysis of CFETR was carried out to evaluate the neutron shielding capabilities and nuclear responses to toroidal field coils (TFC). The 3D neutronics model of CFETR was built with the support of McCad tool to convert the CAD model automatically. An extended variance reduction (VR) technique of combined MAGIC GVR with density reduction method has been involved to generate suitable weight windows to enhance the efficiency of particle transport. Highly detailed neutron and photon map has been obtained which meet the requirements for Monte Carlo nuclear analyses. The global neutron flux distribution of 3D CFETR with Pf = 200 MW to 1.5 GW was obtained to evaluate its shielding performance. The nuclear responses to TFC such as the nuclear heating and fast neutron fluence have been evaluated. Initial results show the shielding of current divertor design is not sufficient and the optimizing work has been done. The final results satisfy the referred ITER design limit and it can provide the support for the future more detailed design of divertor and other shielding systems.
1. Introduction Nuclear fusion has many advantages in comparison with fossil fuels and fission energy: it is carbon free, there is no production of long-lived radioactive waste, and deuterium and lithium are abundant on Earth. Many decades ago, the scientists already started to build fusion device to explore a smooth way for attaining plasma from nuclear fusion. So far, the ITER (International Thermonuclear Experimental Reactor), which is already under construction in Cadarache France, should be the most expected device for its aim to produce 500 MW of fusion power running at long pulses of 400 s. The China Fusion Engineering Test Reactor (CFETR) in turn goes further than ITER not only achieving the long-pulse operation but also with mission to breed the tritium and cycle the tritium in self-sustained state. Some data on the conceptual design of CFETR has been released in recent years [1]. The newest physical design of CFETR has been fixed and the engineering design has been initialized in 2018 [2]. Based on the lessons from the previous design, its size increased to R = 7.2 m and its fusion power (Pf)
⁎
capability became more flexible at 200 MW, 500 MW, 1 GW and 1.5 GW in one machine. This makes the machine more versatile but also more challenging in terms of its engineering design. The nuclear analysis, in the meantime, tries to follow the progress of CFETR design. The important nuclear responses such as neutron flux and nuclear heating will be needed for the evaluation of irradiation shielding, heat removal, etc. The superconducting performance of TFC strongly depends on the operation temperature and heat removal capability of helium coolant in the center of coil. Thus the fast neutron fluence (neutron energy > 0.1 MeV) and nuclear heating exposed on TFC should be limited. In this paper, the nuclear heating and fast neutron fluence at TFC case, conductor and insulator has been analyzed. As the design of CFETR has followed the ITER, many technologies will be taken as reference. For example, according to ITER design limits [3], the fast neutron fluence in magnet conductor should not exceed 1 × 1019 n/cm2 and in insulator 2 × 1018 n/cm2. Meanwhile, the nuclear heating density in magnet steel case should not exceed 6 × 10−4 W/cm3 and in magnet conductor 3 × 10−4 W/cm3 in case of
Corresponding author. E-mail address: [email protected] (S. Liu).
https://doi.org/10.1016/j.fusengdes.2019.111243 Received 25 January 2019; Received in revised form 27 May 2019; Accepted 20 June 2019 0920-3796/ © 2019 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
concepts which are both under research. In this work, the water cooled ceramic breeding (WCCB) blankets were investigated. The previous research progress of WCCB has been reported [9–13]. The updated design [14] has adopted a cooling tube assembly (CTA) composed of dual-wall pressurized tube (DWT) concept for cooling function instead of conventional cooling plate (CP). This is much easier to be manufactured than CP. While, in order to generate the neutronics model, the CTA geometry has been simplified by modifying the tube to plate but mixing with part of breeding zone material, shown in Fig. 2. The WCCB blankets choose Li2TiO3 and Be12Ti as tritium breeder and neutron multiplier, the RAFM steel, i.e. CLAM or CLF-1 [15–17] as structure material. The first wall (FW) is protected by 2 mm thick tungsten. It’s also known as plasma facing component (PFC). The FW is mixture of coolant water and structure material CLAM steel. Other components such as back plate (BP), back supporting structure (BSS), radial-poloidal stiffening plate (SP), side wall (SW), cover are also mixture of water and steel and minor fraction of helium gas. The material composition of components is shown in Table 1.
overheating in superconductor. The initial evaluation of irradiation effect to TFC in CFETR will be conducted by referring to ITER design limit. To serve the nuclear analysis of CFETR, a 3D neutronics model has been built based on engineering CAD model. This has been done with an open source code McCad to convert the CAD model to neutronics model [4]. McCad is developed by KIT/INR as visualization interface and automatical conversion software. With the help of McCad, it becomes easier and quicker to establish the neutronics model when compared with conventional error-prone and tedious way. The nuclear analysis of CFETR has been conducted by using of MCNP particle transport code [5]. To implement the CFETR nuclear analysis with MCNP, a sophisticated variance reduction (VR) technique was applied to speed up the computation due to its large size and complex geometry. The global variance reduction (GVR) MAGIC [6] method is chosen and implemented. This comes from the fact that the MAGIC is indeed a user-friendly and easy-operated method. No other supporting software was needed, only the MC code, here namely MCNP. The MAGIC method iterates the particle flux calculation to obtain the weight windows to facilitate the particle transport. It usually needs several iterated steps to obtain the final convergent results. In this paper, the authors present a new implementation of MAGIC but combining with density reduction method for global flux calculation of CFETR. Some attractive work have been reported in implementation of density reduction method [7,8]. The extended method first decreases the mass density of problem geometry in order to run quickly to produce seed weight windows. Then increase the density gradually up to original one and run with support of previous generated weight windows. This is also iterated step but can finally obtain suitable results in a quick way. The extended method has been successfully applied on CFETR for global neutron and photon transport and accurate results have been obtained. More details are discussed below.
3. Methodology 3.1. Combined MAGIC GVR with density reduction Due to the large size and complex geometry of fusion device like CFETR, the Monte Carlo particle simulation will always consume a lot of computer power and time even run with parallel model. Consequently, accurate result could hardly be obtained unless a VR technique is used. In this paper, the authors employ the MAGIC method but combining with density reduction. The detailed workflow is as follows: i First, setup two sets of mesh covering all the geometry in order to tally the neutron and photon (N&P) flux. The mass density of all material in CFETR is reduced to very low level as 0.2 times original one. By doing so, a well converged global N&P flux can be obtained relatively quickly. ii Then increase the mass density to 0.5 times. Reproduce the weight windows for next iterated step by using the N&P flux in the first calculation, but improve the gradient of weight windows among adjacent mesh voxel following the formula:
2. Neutronics model The initial CAD model of CFETR includes the main components: blanket, divertor, toroidal field coil (TFC), poloidal field coil (PFC), central solenoid (CS), vacuum vessel (VV), thermal shielding (TS), port plug, cryostat, bio-shield. While the original CAD geometry should be simplified to remove unimportant structures such as holes, chamfers etc. Otherwise it’s difficult to be converted by using of McCad tool. The whole model was divided into 16 segments in toroidal direction (Fig. 1). Only one segment has been converted to neutronics model. One segment includes 18 outboard blanket (OB) modules: 6 blankets in poloidal and 3 in toroidal, 12 inboard blanket (IB) modules: 6 in poloidal and 2 in toroidal respectively. The water cooled and helium cooled blankets are two candidate
ϕ wi = ⎜⎛ i ⎟⎞ ϕ ⎝ max ⎠
n
(1)
where n is expanding factor and n > 1, ϕi is neutron or photon flux in mesh voxel i, ϕmax is max flux in the whole mesh. This time, n is set to greater than 1, but in the shielding zone the expanding factor n can be larger. Perform the particle transport with the support of generated
Fig. 1. One of 16 sectors of CFETR (left and center) and the converted neutronics model prepared using McCad tool (right). 2
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
Fig. 2. Simplified CTA geometry for generating the neutronics model.
was implemented. The mesh size to tally the N&P flux is set as rectangular mesh of 20 × 20 × 20 cm. The length of CFETR at X, Y and Z direction is about 2200 cm, 860 cm and 4300 cm respectively. Thus totally the number of mesh voxel is about 8 × 105. Consider the huge number of mesh voxels, computation speed and limit of computer storage capability, only a coarse two energy groups are set to separate the neutrons in tally cells: that is thermal neutrons (< 0.1 MeV) and fast neutrons (> 0.1 MeV). More energy groups setting is possible only with strong support of computer power. The three iteration calculation (shown in Fig. 3), first two for the generation of weight windows and last the regular particle transport, were simulated with 140 computer cores. The calculation for step i) is fast when very low density is set and totally ˜1.5 × 104 minutes of CPU time is consumed to get accurate results: within more than 90.6% of mesh voxel the relative error (RE) is less than 5%. Next calculation for step ii), increase the mass density to 0.5 times original one, process the weight windows by using of N&P flux results. The expanding factor n is set to 1.5 for most area but increased 1.7 at middle and down port plug, 1.9 at central solenoid, 2 at upper port and bio-shield (Fig. 3(a)). These expanding factors are decided through some trial calculations, i.e. adjusting the expanding factors to generate weight windows and run quickly (with small number of histories) in order to make the particles uniformly distributed into the geometry. With support of prepared weight windows, launch the particle transport. It consumes about ˜2 × 104 minutes of CPU time and the resulting flux has acceptable precision: within more than 80.8% of mesh voxel the RE is less than 5%. At last time the regular calculation for step iii), the setting of expanding factor n to process the weight windows is shown in Fig. 3(c). It consumes ˜1 × 105 minutes of CPU time: within more than 82.4% of mesh voxel the RE is less than 5%, 95.3% the RE is less than 10% and more than 99.9% is non-zero tally results. The final neutron flux distribution and RE map can be seen in Fig. 3(e), (f). This RE map demonstrates the computational precision that satisfies the requirement of nuclear analysis. Most main components of blanket, divertor, VV, TS, TF and PF coil have fine accuracy. But only part of CS and bio-shielding have high relative error beyond 10%. Most likely this can be improved when needed by manually adjusting the corresponding weight windows and taking more computer time. These weight windows, on the other hand, can also be used in future for repeated calculation of CFETR even within minor modification of geometry.
Table 1 Material composition of CFETR system and components (unit: vol% specified if wt%).
Blanket
Divertor
VV
Components
Material
PFC FW BZ CTA
100% Tungsten 14.55% H2O, 85.45% CLAM steel 14.4% Li2TiO3, 65.6% Be12Ti, 20% He 12.412% H2O, 45.763% CLAM steel, 6.023% Li2TiO3, 27.437% Be12Ti, 8.365% He 53.55% H2O, 46.12% CLAM steel, 1.65% He 11.06% H2O, 87.29% CLAM steel, 1.65% He 14.97% H2O, 85.03% CLAM steel 29.09% H2O, 70.91% CLAM steel 2.18% H2O, 96.23% CLAM steel, 0.0159% He 75% SS316 L, 25% H2O (150 °C, 5 MPa) 71.05% W, 6.41% oxygen free copper (OFC), 8.11% CuZrCr, 14.43% H2O SS316 L(N)-IG SS316 L(N)-IG Borated water, 1.32 wt% B and enriched in 10-B to 95% Borated steel, 1.2 wt% Boron and enriched in 10-B to 95% 50% H2O, 50% CLAM steel SS316LN Nb3Sn SS316LN NbTi SS304/SS304L Concrete
BP BSS rpSP SW cover Cassette First Wall
shell rib Inner shielding
TS Port TF, CS PF
plug case conductor case conductor
Cryostat Bio-shield
weight windows and produce the mesh tally of assumed density of problem.
• Finally, increase the mass density to original one. Repeat the second
step to prepare the weight windows. Still the expanding factor n can be adjusted by user but actually need some rule of thumb. Then launch the particle transport to get real flux results.
The processing of weight windows and setting of expanding factor at specified location has been realized with developed Python script. This method has been successfully applied on CFETR for N&P transport.
3.2. N&P transport With the support of combined VR method, the N&P transport can be carried for global analysis. The Fendl-2.1 nuclear cross section library 3
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
Fig. 3. (a): neutron flux of assumed mass density as 0.2 times original one and the expanding factor setting to prepare the weight windows; (b): relative error of figure (a) neutron flux; (c): neutron flux of assumed mass density as 0.5 times original one, calculated with support of previous weight windows, and the expanding factor setting; (d): relative error of figure (c) neutron flux; (e): final results of 200 MW fusion power neutron flux (n/cm2/s) and relative error (100%).
example, Between the 3rd and 4th blanket, the neutron flux behind BSS at gap position is about 2 times larger than other zone. The 6th and 7th blankets are thinner than other blankets as the thickness in radial direction is 50.7 cm and 70.0 cm respectively. Thus the neutron flux behind BSS is nearly one order of magnitude higher than other blankets (e.g. 3rd blanket). It has weaker shielding performance according to current design. Some optimization work will be carried out in future. The neutron flux distribution of divertor is shown in Fig. 4 right down figure. Highest neutron flux reaches about 3.1e+14 n/cm2/s. The divertor design so far cannot meet the shielding requirements due to the exhaust channel where neutrons can leak (Fig. 4). This also can be detected in Fig. 5 where the TFC conductor has hot spot in nuclear heating density below divertor zone. On the other hand, the joint between divertor and blanket also needs improvement in shielding performance. That’s why two spots in nuclear heating density of TFC have been identified. To decrease the neutron irradiation damage to in-vessel components as well as superconductor coils, the shielding design of divertor and blanket has been optimized. Following is the detail about the nuclear analysis of TFC.
4. Results 4.1. Global neutron flux distribution The CFETR neutron flux results have been visualized with Paraview post-processing code by converting the tally results to VTK format [18]. Fig. 4 left figure shows the neutron flux of CFETR with Pf = 1.5 GW. Highest neutron flux reaches about 4.7e+14 n/cm2/s at center of plasma. Outside bio-shield, the neutron flux decrease more than 10 orders of magnitude. Starting from the right bottom, the blankets are labeled from number 1 to the 11 in counterclockwise. The neutron flux distribution of blanket is shown in Fig. 4 right top figure. Highest neutron flux reaches about 4.5e+14 n/cm2/s in outboard blanket at equatorial plane and lowest about 6.3e+10 n/cm2/s at BSS of 8th blanket. It decreases more than 3 orders of magnitude due to shielding performance of coolant water in blanket. There is 2 cm gap between adjacent blankets both in toroidal and poloidal direction. Thus it results in penetration of neutrons through these gaps and increases the irradiation damage to the components behind blanket such as VV and TS. For
4
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
Fig. 4. Left: y = 0 section; right top: neutron flux of WCCB blanket; right down: neutron flux of divertor.
For one piece of TFC, it is segmented to 48 parts and the labeled number is shown in Fig. 7. The nuclear heating of TF case, conductor and insulator in one piece of TFC when Pf = 200 MW can be seen in Fig. 8. The total nuclear heating of TFC in whole reactor is about 4.2 kW when Pf = 200 MW and 31.7 kW when Pf = 1.5 GW (Table 2). The TFC steel case contribute about 63.7% to total nuclear heating, insulator negligible 0.3% and conductor 36.0%. The ITER design limits the total nuclear heating deposited on TFC to 14 kW considering the heat removal capability. For CFETR, in other words, must be scaled with a factor because of the different neutron intensity and operation scenario compared with ITER. The allowable total nuclear heating deposited on CFETR TFC should be proposed in future by the engineering design group. The nuclear heat density distribution and fast neutron fluence in TFC poloidal direction is shown in Fig. 9. Benefiting from the optimized engineering design of divertor and blanket, it has more reliable shielding performance. The highest nuclear heating density at TFC case and conductor reaches 5.60 × 10−5 and 1.89 × 10−5 W/cm3 respectively with Pf = 200 MW at 4th segment, but not exceed the ITER design limit even when Pf = 1.5 GW (Table 3). The neutron fluence of TF conductor and insulator with Pf = 200 MW and 1.5 GW has been calculated for 10 full power years (FPY) of operation. And the highest neutron fluence of TF conductor and insulator reaches 2.01 × 1017 and 1.98 × 1017 respectively when Pf = 200 MW. They are still not beyond the design limit when Pf = 1.5 GW. However, the nuclear heating density and fast neutron fluence at TF superconductor are averaged over the 48 segments and they could be several factors lower than the peak nuclear responses. After the releasing of detailed TFC engineering design, such as the arrangement and turns of superconductor coil, the nuclear analysis will be updated to compare the peak nuclear responses. The results show the optimizing work did decrease the neutron damage to TFC by adding shielding blocks at bottom of divertor and connection between divertor and outboard blanket. However, this is somehow still a makeshift solution as this work is only conducted from the point view of nuclear analysis. Furthermore, the choice of shielding material, for now is 50% water and 50% CLAM steel, is possible to be substituted by investigating WC, B4C and other well neutron shielding performance material if the allocated space is not sufficient and the block volume should be reduced. A comprehensive study should be conducted in future to consider not only the nuclear responses but also the allowed allocated space to shielding block, the mechanical analysis and other engineering simulations. However, information provided in this paper is useful for further updates of the design.
Fig. 5. Nuclear heating density (W/cm3) in TFC conductor when Pf = 1.5 GW.
4.2. Irradiation effect to TFC Since the neutrons leak from divertor and increase the damage to VV and superconductor coils additional shielding was added to two places. The optimized structure of divertor and blanket is shown in Fig. 6 (as circled in red). First is the connection part between divertor and outboard blanket. A 50 cm long shielding block was stretched out from the manifold and BSS of bottom outboard blanket in order to prevent the neutrons leaking from the gap. It was filled with 50% water and 50% CLAM steel. Initial calculation shows it indeed decrease the neutron flux to an accepted level. The second change is at the bottom of divertor. A shielding block was added to the VV and was also filled with 50% water and 50% CLAM steel. To decide the required thickness of the second shielding block, a parameter study has been carried out by change the block thickness from 25 cm, 35 cm and 45 cm. Result shows 35 cm thickness of shielding block can meet the design limit. Following are the analysis according to this optimization. 5
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
Fig. 6. Left: original design; right: shielding blocks to the bottom of divertor and gap between divertor and blanket.
Fig. 7. Segment number of TFC.
5. Conclusion
This work has been started by constructing a 3-D neutronics model with support of McCad automatic conversion tool. This model includes the main components of WCCB, divertor, VV, TS, TFC, PFC, CS, Cryostat and bio-shielding. For particle transport calculation, the MCNP code was employed with support of FENDL-2.1 nuclear cross section library. To accelerate the particle transport, a combined density reduction with MAGIC GVR method was used. The calculation shows this VR method has high efficiency and the final results show sufficient precision for nuclear analyses. Initial results show the shielding of divertor is not sufficient and
The latest CFETR design has been released with major radius of machine as R = 7.2 m. Other systems such as WCCB, as one of two candidate blanket concepts, also updated following the tritium breeding and neutron shielding requirements of CFETR. The nuclear analysis has been initialized to evaluate its global shielding performance. To guarantee the safe work condition of TFC, the nuclear heating and fast neutron fluence parameters have been evaluated and judged referred to ITER design limit. 6
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
cause high irradiation damage and heating to TFC. An optimizing work has been finished by adding shielding blocks at two identified neutron pathways causing hot spots on TFC. With a parameter study, the two shielding blocks were decided as one of 35 cm thickness block at bottom of divertor and 50 cm long block stretched out from blanket BSS and manifold. These two shielding blocks were all filled with mixture of 50% water and 50% CLAM steel. The optimized results show the total nuclear heating to TFC in whole reactor is about 4.2 kW when Pf = 200 MW and 31.7 kW when Pf = 1.5 GW. The nuclear heating density at TFC case and conductor and accumulated neutron fluence in 10 FPY at TFC conductor and insulator did not exceed the referred ITER design limit. The presented optimizations will provide guidance for more detailed design of CFETR divertor and blanket as well as other related shielding systems.
Declarations of interest Fig. 8. Total nuclear heating (W) in one piece of TFC when Pf = 200 MW.
None.
Table 2 TFC total nuclear heating of 200 MW and 1.5 GW of fusion power.
Pf = 200 MW, Nuclear Heating [W] Pf = 1.5 GW, Nuclear Heating [W]
Acknowledgments
TF case
TF insulator
TF conductor
Total
2.69E+03
1.40E+01
1.52E+03
4.22E+03
2.02E+04
1.05E+02
1.14E+04
3.17E+04
The authors wish to acknowledge the financial support of National Key R&D Program of China [grant number 2017YFE0300501], [grant number 2017YFE0300502], and the Chinese National Natural Science Foundation [grant number 11775256].
Fig. 9. Left top: nuclear heating density of TF case; left down: fast neutron fluence of TF conductor accumulated in 10 FPY; right top: nuclear heating density of TF conductor; right down: fast neutron fluence of TF insulator accumulated in 10 FPY. 7
Fusion Engineering and Design 147 (2019) 111243
P. Lu, et al.
Table 3 Nuclear responses of TFC and referred ITER design limit. Nuclear Responses
Fast neutron fluence in magnet conductor (n/cm2) (10 FPY)
Fast neutron fluence in insulator (n/cm2) (10 FPY)
Nuclear heating density in magnet steel case (W/cm3)
Nuclear heating density in magnet conductor (W/cm3)
ITER Design Limit Pf = 200 MW(Maxmium) Pf = 1.5 GW (Maxmium)
1 × 1019 2.01 × 1017 1.51 × 1018
2 × 1018 1.98 × 1017 1.49 × 1018
6 × 10−4 5.60 × 10−5 4.20 × 10−4
3 × 10−4 1.89 × 10−5 1.43 × 10−4
References
(2017) 865–870. [10] L. Chen, et al., A DEM-based heat transfer model for the evaluation of effective thermal conductivity of packed beds filled with stagnant fluid: thermal contact theory and numerical simulation, Int. J. Heat Mass Transf. 132 (2019) 331–346. [11] K.C. Jiang, et al., Preliminary analysis on DNB in the first wall of WCCB blanket for CFETR, IEEE Trans. Plasma Sci. 46 (6) (2018) 2318–2323. [12] X.K. Zhang, et al., Updated neutronics analyses of a water cooled ceramic breeder blanket for the CFETR, Plasma Sci. Technol. 19 (11) (2017). [13] X.B. Ma, et al., Electromagnetic force evaluation on the water cooled ceramic breeder blanket for CFETR, Fusion Eng. Des. 131 (2018) 21–28. [14] S. Liu, et al., Updated design of water-cooled breeder blanket for CFETR, Fusion Eng. Des. (2019). [15] L. Peng, et al., Preliminary analysis of irradiation effects on CLAM after low dose neutron irradiation, J. Nucl. Mater. 386-88 (2009) 312–314. [16] H.E. Ge, et al., Tensile properties of CLAM steel irradiated up to 20.1 dpa in STIP-V, J. Nucl. Mater. 468 (2016) 240–245. [17] P.H. Wang, et al., Technical issues for the fabrication of a CN-HCCB-TBM based on RAFM steel CLF-1, Plasma Sci. Technol. 15 (2) (2013) 133–136. [18] Y.F. Qiu, et al., Integrated approach for fusion multi-physics coupled analyses based on hybrid CAD and mesh geometries, Fusion Eng. Des. 96-97 (2015) 159–164.
[1] Y.X. Wan, et al., Overview of the present progress and activities on the CFETR, Nucl. Fusion 57 (10) (2017). [2] J. Li, Progresses and activities of CFETR, Presented in SOFT (2018). [3] ITER Magnet Design Description Document Part 1, (2009) ITER D 2NPLKM, version 1.8, September. [4] L. Lu, et al., Improved algorithms and advanced features of the CAD to MC conversion tool McCad, Fusion Eng. Des. 89 (9-10) (2014) 1885–1888. [5] MCNP, A General Monte Carlo N-Particle Transport Code, Version 5, Volume I: Overview and Theory, X-5 Monte Carlo Team, 2003 April 24 (Revised 2/1/2008). [6] A. Davis, et al., Comparison of global variance reduction techniques for Monte Carlo radiation transport simulations of ITER, Fusion Eng. Des. 86 (9-11) (2011) 2698–2700. [7] T.E. Booth, MCNP Variance Reduction Examples, Los Alamos National Laboratory, 2004 LA-UR-12-25907. [8] K. Kondo, et al., Neutronic analysis for the IFMIF target and test cell using a new CAD-based geometry model, Fusion Eng. Des. 87 (7-8) (2012) 983–988. [9] S. Liu, et al., Conceptual design of the water cooled ceramic breeder blanket for CFETR based on pressurized water cooled reactor technology, Fusion Eng. Des. 124
8