Neutronic Evaluation of a Power Plant Conceptual Study considering Different Modelings

1 FTP/P7-25 Neutronic Evaluation of a Power Plant Conceptual Study considering Different Modelings C.E. Velasquez 1,2), C. Pereira 1,2), M.A. Veloso 1,2), A.L.Costa 1,2) 1) Nuclear Engineering Department (DEN), Universidade Federal de Minas Gerais (UFMG), Brazil 2) Rede Nacional de Fusão (FINEP/CNPq) E-mail contact of main author: claubia@nuclear.ufmg.br Abstract. Three different models of Power Plant Conceptual Study (PPCS) were evaluated using MCNP. One of the geometries was made considering the intersection of cylinders and tori, another one with cylinders and planes and the last one just with tori. The walls along the radial axis were located at the same distance and all were filled with the same order of materials. The geometries have symmetry and then the reactor could be divided into four perpendicular parts from the top view of the reactor. In this way, it was possible to follow the flux along different trajectories. The detectors were located starting from the first wall until the last one and surrounding each wall. In addition, it was obtained the flux over each volume that surrounds the vacuum chamber. The reaction rates over the materials of the plasma facing components were obtained to evaluate the differences related to the neutron cross section of each material used. The results give information about the behavior of each modeling, from the point of view of neutron flux and neutron interactions. 1. Introduction The R&D of materials for nuclear fusion especially for the first wall (FW) becomes important in the last years. The FW would have to withstand extremely conditions as a high neutron flux, high temperatures, thermal stress, radiation induce swelling, erosion due to sputtering. Besides, the high neutron flux produces different types of reactions depending on neutron cross sections of each material used. The main first wall materials studied nowadays by nuclear fusion devices as JET [1] and ASDEX-Upgrade [2] are Beryllium and Tungsten as the main component. To simulate the neutron interactions with matter produced by D-T nuclear fusion, Monte Carlo programs, in particular the MCNP, are the preferred tools. At DEN, using MCNP, the neutron flux and the interaction frequency along the radial axis are evaluated for various materials used to build the first wall. W alloy and beryllium, and the combination of both were studied [3]. Nevertheless, the MCNP code results are very sensible to the modeling used and it can induce errors in the evaluation, and in the time execution. The aim of this work is to study, evaluate and compare the influence of the high neutron flux over three different modeling representing the same nuclear fusion device. The differences between these modelings are the geometrical surfaces used to represent them and tallies used in the MCNP code. It will be evaluated the reaction rate mainly in the FW and along the different walls, the neutron flux along the walls, and the best PPCS modeled. The best PPCS modeled it will be obtained by evaluating the lowest convergence error and the lowest computing time spent to perform the simulations. 2. Methodology Using Monte Carlo N-Particle (MCNP) [4], three different Tokamak models were simulated, maintaining some basic parameters from the ITER design such as: the vacuum chamber volume, the fusion neutron source and the major and minus radius of the plasma. The neutron

2 FTP/P7-25 flux and the reaction rates were obtained over different volumes; FW, divertor and along the different device walls. The point detector was placed between the outside plasma region and before the first wall at 828cm from the center. To simulate this point detector was used just a quarter part of each model (see FIG. 5). The three geometries were compared under the same conditions. The simulations were execute in a cluster of three CPUs making a PVM parallel working network with the following features: the processors are Intel (R) Core (TM) 2 Quad CPU Q9300 2.5GHz, speed 2.497MHz. The history cutoff was performed with 12 cores working in parallel and for the SSW/SSR card; it was performed just with 1 core. 2.1. Geometric Models The geometrical changes between these three models are the surfaces chosen to represent the Tokamak. It was used three surfaces: planes, cylinders and tori. The model 1 is made with the intersection of cylinders and tori (see FIG.1), the model 2 with cylinders and planes (see FIG.2.), and the model 3 just with tori (see FIG.3.). The walls along the radial axis are located at the same distance and all of them were filled with the same order of materials. The major radius R is 6.21m and the minus radius a is 2m. The material for the outboard first wall was beryllium, for the inboard first wall and divertor was tungsten alloy W1.1TiC. FIG. 1.Cylinders and Tori; FIG.2.Cylinders and Planes; FIG.3. Tori The principal Tokamak components were modeled based on the following sequence from the plasma to the Bioshield: First Wall,, Shield Block, Vessel (VV) wall, VV Filling, VV wall, Vessel Thermal Shield VVTS, Toroidal Field Coil (TFC) Wall Box, TFC Superconductor and insulator, TFC Wall Box, Cryostat and Bioshield (see FIG.4). Each color from the picture represents a different material. The three models from a top view look like concentric circles (see FIG.5). 2.2. The PPCS Design Parameters For the simulation of the three PPCS models was used a D T Tokamak fusion neutron source which was simulated in a torus shape with the radius shown in Table I. The energy distribution for the fusion neutron source is described by a Gaussian fusion energy spectrum that obeys (see Eq. 1) where a is the width in MeV and b is the average energy in MeV. p(e) = C exp[-((e-b)/a) 2 ] (1) The parameters of the emission spectrum were adjusted automatically by MCNP through the choice of a standard source for D T fusion. The plasma temperature, the neutron source strength showed (see Table I). Most of the parameters used are based on the ITER design.

3 FTP/P7-25 TABLE I: PLASMA PARAMETERS. [5] Parameters Value Major radius, R (m) 6.21 Minus radius, a (m) 2 Neutron source (neutrons/s) 14.4x10 19 Plasma temperature (kev) 10 Type of plasma D-T Volume Plasma Chamber (m 3 ) 837 FIG.4. Principal Components FIG.5. Top View from the Tokamak 2.3. Materials Most of materials used for the simulation are based on the ITER guidelines and the article in fusion engineering and design [6, 7]. The FW materials, studied in a previous paper [3], were S65-Be and the W-1.1TiC [8] in the outboard and inboard position, respectively. The heat Sink is an alloy of cupper CuCrZr-IG and the Shield Block is stainless steel. The VV is composed by three walls,, SS304B7, 60 %; water,40 % and the last one. The material of the VVTS is stainless steel SS304L. The TF coils were assumed to be 45 % Nb3Sn+50 % Incoloy 908+5 % Al2O3. Due to the CS composition complexity, this module s composition was assumed to be 27 % Nb3Sn+30 % Incoloy 908+30 % SS316+10 % resins+3 % Al2O3. To simplify the model, the small details of the CS composition were not considered. The composition of the filling material of the CS and and TF coils was assumed to be 45 % Nb3Sn+50 % Incoloy 908+5 % Al2O3. The Bio shield is concrete. [9-11] 3. Results 3.1. Neutron Flux Along the Different PPCS Modelings The neutron flux was measured with a point detector tally (see FIG. 6) in the scrape-off layer between the edge of the plasma zone and before the first wall. The measures were performed using the history cutoff (NPS) and the SSW/SSR card. The figure 6 below show that the results from both forms of execution followed the same pattern, but the SSW/SSR card had a higher neutron flux for the majority of the neutron energy spectrum. To appreciate the differences in the neutron energy spectrum, it was executed with different numbers of

4 FTP/P7-25 histories (see Fig. 7). The main differences between them are located around 0.5 to 5eV of energy, assuming as a reference the one with NPS= histories due to is the one with less calculation relative error. Neutron Flux (neutrons.cm -2 s -1 ) 10 15 NPS SSW/SSR Neutron Flux (neutrons.cm -2.s -1 ) 10 15 NPS 1e5 NPS 2e5 NPS 5e5 NPS 1e6 NPS 5e6 NPS 1e7 10-8 10-6 10-4 10 2 FIG. 6 Neutron flux comparison between the history cutoff NPS and SSW/SSR 10-8 10-6 10-4 10 2 FIG. 7 Differences of neutrons energy spectrum for the same model but increasing the NPS In addition, the neutron energy spectra along the different walls from the FW to TFC for the different PPCS models were evaluated. According to the results (see FIG. 8 a, b and c), there is no large differences between each model until the VVTS wall. a) b) c) 105 101 Divertor 100 Inner FW Outer FW Shield block 10-3 10-4 10-5 VV VV VV Wall filling Wall 10-6 VVTS 10-7 TFC 10-8 Model 1 Neutron Flux (neutrons.cm -2.s -1 ) 105 101 Divertor 100 Inner FW Outer FW Shield block 10-3 10-4 VV filling 10-5 10-6 VVTS 10-7 TFC 10-8 Model 2 Neutron Flux (neutrons.cm -2 s -1 ) 105 101 Divertor Inner FW Outer FW Shield block 10-3 10-4 VV filling 10-5 10-6 VVTS 10-7 TFC 10-8 Model 3 Neutron Flux (neutrons.cm -2 s -1 ) Divertor Inner FW Outer FW Shield block VV filling VVTS TFC FIG.8 Neutron energy spectrum along the walls a) Model 1 b) Model 2 c) Model 3 MCNP fusion source has a Gaussian distribution of neutrons. For three models, the neutron measured carry 14.1MeV passing through the divertor volume is about the 8% of the total amount of neutrons. In contrast, the neutron measured carry 14.1MeV over the ARIES-DB [8] divertor surface is 13%. The difference is about 5%, this could be because of the fact that the neutrons have already suffered different types of attenuation reactions over the divertor volume and the neutrons over the ARIES-DB surface not yet. 3.2. Reaction Rates in the Firs Wall The different neutron reaction rates occurring in the first wall are presented for the S65-Be (see FIG.8) and W1.1TIC (see FIG.9). As expected, the elastic scattering and radiative capture occur from thermal to the fast region. Nevertheless, inelastic scattering, neutron production and charged particles production (proton, alpha, Tritium, etc.) have high

5 FTP/P7-25 probability to occur up to 10MeV [12, 13]. In the beryllium, there are an important production rate of neutrons, alpha and tritium up to 10 MeV. Reaction Rate (reactions/s) S65-Be n,n n,n' n,y (n,2n)&(n,3n) n,p n,n'p n,alpha n,d n,n'alpha n,t n,he-3 10-8 10-7 10-6 10-5 10-4 10-3 10 1 Fig. 8 FW S65-Be Reaction Rate For the tungsten, the more probable interactions are elastic and inelastic scattering and radiative capture. Due to the high probability of the nucleus to be left in an excited stated, it will contribute to the material activation during the operation and after the shutdown, increasing damage material and high doses probabilities. The elastic scattering and radiative capture have probability to occur over all the spectrum and the inelastic scattering occur with higher probability than radiative capture up to 1MeV. Reaction Rate (reactions/s) W1.1TiC n,n n,n' n,y (n,2n)&(n,3n) n,p n,n'p n,alpha n,d n,n'alpha n,t n,he-3 10-8 10-7 10-6 10-5 10-4 10-3 10 1 Fig.9 FW S65-Be Reaction Rate The reaction rates comparison from both materials S65-Be and W1.1TiC are showed below (see FIG. 10). According to the results, the beryllium has a high reaction rate for neutrons production that could induce transmutation in a reasonable proportion. These reactions are tritium (~ interaction/s) and alpha (~ interaction/s) production. Comparing the results for both materials (see Fig. 10), the tungsten has high reactions rates for (n,γ), (n,2n), (n,p) and (n,np) than beryllium [14].

6 FTP/P7-25 Outer (S-65 Be) First Wall Inner (W1.1TiC) n,p n,n'p n,alpha n,d n,n'alpha n,t n,he-3 Reaction Rate (reactions/s) n,n n,n' n,y (n,2n)&(n,3n) 102 101 Toroidal Field Coil Wall Box Toroidal Field Coil Superconductor and Insulator Toroidal Field Coil Wall Box Vessel Thermal Shield 10-3 Vessel Wall 10-4 Vessel Filling Vessel Wall Shield Block Outer First Wall Divertor Inner First Wall 10-5 10-6 10-7 10-8 10 4 10 3 s a W-1.1TiC W-1.1TiC Be CuCrZr-IG SS304B7, 60 %; water,40 % SS304L 45 % Nb3Sn+ 5 % Al2O3+ 50 %Incoloy908 FIG.10 Reaction Rate for the plasma facing components FIG.11 Ʃ s /Ʃ a indicates the number of collision suffered before the neutron being absorbed The number of collision suffered before the neutron being absorbed (see FIG.11) was compared. Hence, there are two important conclusions: in the S65-Be material, neutrons with energies between 10-4 MeV and 1MeV pass through the beryllium suffering more scattering collision (~10 4 ) before being absorbed than others materials; in the tungsten, neutrons with energies up to 10 MeV have more scattering collisions before being absorbed than beryllium and the others materials. This means that the tungsten will absorb less neutrons than the beryllium and it would be a good property to withstand the higher neutron flux with energy up to 10MeV. 4. Computational Time Versus Error 4.1. History Cutoff and the SSW/SSR Card The history cutoff and the SSW/SSR card analysis indicates which of them spent less computational time with the lowest relative error and if the error was under the reliability limits (see FIG. 6 & 12). Besides, the SSW/SSR card had less the relative error from the MCNP at lower number of histories than using the history cut-off. Nevertheless, for the same relative error, the history cut-off spent less computational time than SSW/SSR. 10 2 NPS SSW/SSR NPS SSW/SSR Relative Error (%) 10 1 Computational Time (s) 10 4 10 3 10-8 10-6 10-4 10 2 Energy (Mev) FIG.12 the error for the SSW/SSR at 828 cm (see FIG. 6) of distance from the centre 10 2 2.0x 4.0x 6.0x 8.0x 1.0x Number of Histories (NPS) FIG. 13 the computational time versus the number of histories

7 FTP/P7-25 There is no differences between the neutron flux in the modeling (see FIG.7) and the error decreased for all case using histories (see FIG. 14). Relative Error (%) 10 2 10 1 NPS=1E5 NPS=2E5 NPS=5E5 NPS=1E6 NPS=5E6 NPS=1E7 10-8 10-7 10-6 10-5 10-4 10-3 10 1 10 2 Relative Error (%) 10 2 10 1 Model 1 Model 2 Model 3 D I- FWO- FW HS BS VAC VV- WVV- FVV- W VVTS VAC TFC- W TFC TFC- W Walls along the device FIG. 14 the increasing of the number of histories FIG. 15 the error comparison from the figure 8 for the different walls Along the device reduce the error in the neutron energy spectrum The maximum relative error recommended by the MCNP manual for the flux over a volume is about 10%. These three models were run with histories (see FIG.15), showing which one from the three models obtain the less error, being the first one the model 3 followed by the model 2 and then model 1. The difference in the computational time did not differ too much between each model for the same number of histories (Model 1=208min, Model 2=206min and Model 3=204min). 5. Conclusions The comparison based on the relative error (see FIG.15), indicates that the most suitable model is the 3 and then the 2. The model 3 could be more useful to perform studies about the neutron flux in different parts of the device. Moreover, the model 2 would be better for futures studies of transmutation driven systems. The different number of histories cutoff executed (from to ) shows that the shapes of the neutron fluxes have little differences. Following the studied of the materials, the tungsten has a higher neutron cross section for radiative capture and inelastic collision reactions than beryllium, this could induce neutron activation in W. In addition, for high energies, the tungsten needs more scattering collisions before being absorbed than beryllium (see FIG.11), being a good material to suffer high irradiation of fast neutron. On the other hand, in the range from 10-4 MeV to 1MeV, the beryllium is appropriated because the neutron suffer more scattering collision before being absorbed. The use of the SSW/SSR card is not worth due to it spends too much time to be executed and the error is just reduced a bit lower than the execution by the history cut-off. Therefore, it is much better to increase the number of histories than use the SSW/SSR card. 6. References [1] M.J. Rubel, et al., Beryllium plasma-facing components for the ITER-Like Wall Project at JET, J. Phys.: Conf. Ser. 100, (2008). [2] R. Neu, et al., Operational conditions in a W-clad tokamak, Journal of Nuclear Materials 367 370, (2007), pp.1497 1502 [3] C. Velasquez, et al., Axial Neutron Flux Evaluation in a Tokamak System: a Possible Transmutation Blanket Position for a Fusion Fission Transmutation System, Brazilian Journal of Physics 42/3-4 (2012), pp. 237-247

8 FTP/P7-25 [4] X-5 Monte Carlo Team, MCNP A General Monte Carlo N-Particle Transport Code, Version 5, Volume II: User s Guide, University of California, Los Alamos National Laboratory. (2003). [5] W.M. Stacey, Tokamak D T fusion neutron source requirements for closing the nuclear fuel cycle, Nucl. Fusion 47 (2007) 217-221 [6] R. Pampin, Tungsten transmutation and resonance self-shielding in PPCS models for the study of sigma-phase formation, UKAEA FUS 525, EURATOM/UKAEA Fusion, (2005) [7] M. Kaufmann, R. Neu, Tungsten as first wall material in fusion devices. Fusion Eng. Des. 82, (2007) 521 527. [8] A.Robinson, et. al, W-Based Alloys for Advanced Divertor Designs: Detailed Activation and Radiation Damage Analyses, Fusion Technology Institute, University of Wisconsin, UWFDM-1378 [9] A. Araujo, C. Pereira, M.A.F. Veloso, A.L. Costa, Flux and dose rate evaluation of iter system using MCNP5. Braz. J. Phys. 40 (2009) 58 62. [10] ITER-Final Design Report: http://www.naka.jaea.go.jp/iter/fdr/ (2001) [11] D.L. Aldama, A. Trkov, FENDL-2.1 Update of an evaluated nuclear data library for fusion applications, Summary documentation (2004) [12] A. K. Suri, et al., Materials Issues in Fusion Reactors, J. Physics, Conference Series 208 (2010) 012001 [13] T. A. Tomberlin, Beryllium A Unique Material In Nuclear Applications, 36th International SAMPE Technical Conference, Nov. (2004) [14] V. Avrigeanu, et al., Sensitivity of Activation Cross Sections of Tungsten to Nuclear Reaction Mechanisms, AIP Conf. Proc. 769 (2005),pp. 1501-1504.