ISSN 1810-5408

Nuclear Science and Technology

Volume 9, Number 2, June 2019

Published by VIETNAM ATOMIC ENERGY SOCIETY VIETNAM ATOMIC ENERGY INSTITUTE

NUCLEAR SCIENCE AND TECHNOLOGY

Volume 9, Number 2, June 2019

Editorial Board

Editor-in-chief

Tran Huu Phat (VINATOM)

Executive Editors

Vuong Huu Tan (VARANS) Tran Chi Thanh (VINATOM) Cao Đình Thanh (VINATOM) Hoang Anh Tuan (VAEA)

Editors

Nguyen Kien Cuong (VINATOM) Le Hong Khiem (IOP) Nguyen Nhi Dien (VINATOM) Dao Tien Khoa (VINATOM) Nguyen Thi Kim Dung (VINATOM) Tran Hoai Nam (Duy Tan University) Ho Manh Dung (VINATOM) Dang Duc Nhan (VINATOM) Nguyen Nam Giang (VINATOM) Nguyen Hao Quang (VINATOM) Trinh Van Giap (VINATOM) Nguyen Mong Sinh (VINATOM) Le Ngoc Ha (108 Military Central Hospital) Tran Duc Thiep (IOP) Phan Son Hai (VINATOM) Dang Quang Thieu (VINATOM) Le Huy Ham (VAAS) Le Ba Thuan (VINATOM) Nguyen Quoc Hien (VINATOM) Nguyen Trung Tinh (VARANS) Le Van Hong (VINATOM) Tran Ngoc Toan (VINATOM) Nguyen Tuan Khai (VINATOM) Duong Thanh Tung (VARANS) Pham Dinh Khang (VINATOM) Nguyen Nu Hoai Vi (VARANS)

Science Secretary Hoang Sy Than (VINATOM)

...... Copyright: ©2008 by the Vietnam Atomic Energy Society (VAES), Vietnam Atomic Energy Institute (VINATOM). Pusblished by Vietnam Atomic Energy Society, 59 Ly Thuong Kiet, Hanoi, Vietnam Tel: 84-24-39420463 Fax: 84-24-39424133 Email: [email protected] Vietnam Atomic Energy Institute, 59 Ly Thuong Kiet, Hanoi, Vietnam Tel: 84-24-39420463 Fax: 84-24-39422625 Email: [email protected] ...... Contents

On Burnup Modelling Issues Associated with VVER–440 Fuels Branislav Vrban, Štefan Čerba, Jakub Lüley, Filip Osuský,Mikuláš Vorobeľ, Vladimír Nečas…………………………………………………………………………………………………... 01

Estimation of Production in VVER-440 Reactor Core During Normal Operation Štefan Čerba, Jakub Lüley, Branislav Vrban, Filip Osuský, Vladimír Nečas…………...... 10

Processing of the multigroup cross-sections for MCNP calculations Jakub Lüley, Branislav Vrban, Štefan Čerba, Filip Osuský, Vladimír Nečas...... 17

Conceptual design of a small-pressurized water reactor using the AP1000 fuel assembly design Van Khanh Hoang, Viet Phu Tran, Van Thin Dinh, Hoai Nam Tran………………………… 25

Low-energy experiments at the S3 spectrometer S. Franchoo……………………………………………………………………………………………………….. 31

Dosimetric characteristics of 6 MV photons from TrueBeam STx medical linear accelerator: simulation and experimental data N. D. Ton, B. D. Linh, Q.T. Pham………………………………………………………………………… 37

Conceptual designing of a slow positron beam system using Simion simulation program Cao Thanh Long, Huynh Dong Phuong, Nguyen Trung Hieu, Tran Quoc Dung……….. 45

Nuclear Science and Technology, Vol.9, No. 2 (2019), pp. 01-09 On Burnup Modelling Issues Associated with VVER–440 Fuels

Branislav Vrban1,2, Štefan Čerba1, Jakub Lüley1, Filip Osuský1, Mikuláš Vorobeľ1 and Vladimír Nečas1 1Slovak University of Technology in Bratislava, Faculty of Electrical Engineering and Information Technology, Institute of Nuclear and Physical Engineering, Ilkovičova 3, 812 19 Bratislava, Slovakia, 2B&J NUCLEAR Ltd., Alžbetin Dvor 145, 900 42 Miloslavov, Slovakia Email [email protected] (Received 12 November 2019, accepted 19 November 2019)

Abstract: The paper investigates various computational modelling issues associated with VVER-440 fuel depletion, relevant to burnup credit. The SCALE system and the TRITON sequence are used for the calculations. The effects of variations in depletion parameters and used calculation methods on the isotopic vectors are investigated. The burnup behaviour of Gadolinium is quite important in actual core analysis, but its behaviour is somewhat complicated, requiring special treatment in numerical modelling and calculations. Therefore, a special part of the paper is devoted to the treatment of Gadolinium-bearing fuels. Moreover, some discussions on power normalization are also included. To assess the acquired modelling experience used to predict the VVER-440 spent fuel nuclide composition, the measured compositions of Novovoronezh NPP irradiated fuel assembly are compared to data calculated by TRITON sequence. The samples of fuel assembly with 3.6 wt. % U-235 enrichment underwent 4-cycle campaign of totally 1109 effective full power days in the core and cooling period of 1-13 years. Calculated concentrations are compared to measured values burdened with their experimental uncertainties for totally 47 nuclides. The calculated results show overall a good agreement for all nuclides, differences from measured are pointed out and discussed in the paper. Keywords: burnup, VVER 440, modelling, SCALE.

I. INTRODUCTION consideration. Slovakia has four nuclear reactors generating half of its electricity and The prediction accuracy of burnup another two under construction. This paper calculations is a critical factor in the reactor investigates and summarizes modelling issues analysis sequence. The core properties depend associated with VVER-440 fuel depletion on the actual composition of the fuel; thus, the performed by the SCALE system [1]. The characteristics of the reactor core undergo effects of variations in the depletion parameters changes during burnup. Moreover, the isotopic and used calculation methods on the isotopic composition of the spent fuel discharged from vectors are investigated. The burnup behaviour the core is a key factor in both the operations of Gadolinium, a burnable poison in nuclear and the material control activities of the deep fuel, is quite important in actual core analysis; geological repository. An accurate estimate of therefore, a special part of the paper is devoted the time-dependent radionuclide inventory in to this issue. Finally, some discussions on this material is necessary to evaluate many power normalization are also included. Other spent fuel issues, including and publications relevant to burnup modelling gamma-ray source terms for shielding analysis, issues for PWR can be found in [2,3]. To decay-heat source terms for temperature assess the ability of the SCALE system and the distribution and radiological and chemical associated nuclear data to predict the VVER- toxicity for environmental impact 440 spent fuel nuclide composition, the

©2019 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute ON BURNUP MODELLING ISSUES ASSOCIATED WITH VVER–440 FUELS measured compositions of Novovoronezh NPP triangular grid pattern. The assembly is irradiated fuel assembly are compared to data enclosed in a hexagonal wrapper with the calculated by the TRITON sequence in the last width across the flat equal to 145 mm (the 2nd part of the paper. The work done follows the generation FA). The FA and emergency reactor simplified specification of the computational control assemblies (ERC) are positioned in a benchmark based on the #2670 ISTC project hexagonal grid with a spacing of 147 mm. The [4] providing VVER-440 data for 8 samples fuel rods are in the bundle in a triangular grid cut outs of 4 fuel pins of the fuel assembly pattern with a pitch of 12.3 mm. The fuel rod (FA) No. D26135 with the average reached claddings are made of the E110 zirconium burnup 38.5 MWd/kgU. The #2670 ISTC alloy (Zr + 1% Nb), while the wrapper tubes of project has was carried out between years 2003 FA and ERC are made of the E125 zirconium and 2005. Measurements of samples cut out of alloy (Zr + 2.5% Nb). The modelled outside were performed in RIAR Dimitrovgrad, diameter of fuel rod cladding is 9.1 mm and the Russia, the final project report is publicly inside diameter is 7.75 mm. The cladding accessible [6]. The FA irradiation was done houses a fuel column assembled of during the 15 - 18 core loads in the fourth dioxide pellet. Generally, several types of power unit of Novovoronezh NPP. profiled fuel assemblies are used to maintain power peaking factors under the design limits. II. METHODS AND TECHNIQUES A Gd2O3 absorber is integrated with a mass content of 3.35% into number of FAs to aid A. VVER-440 geometry model description fuel profiling. The profiling diagrams with All the current VVER-440 fuel various initial enrichments and locations of assemblies used in Slovakia are hexagonal and fuel bundles used in self-developed 2D SCALE the fuel rods are placed in the assembly in a models are shown in Fig. 1.

a) ERC fuel part - 3.84 wt % U-235 b) FA - 4.25 wt% U-235 c) FA & ERC fuel part - 4.87 wt % U-235 Fig. 1. Profiling diagram for fuel rod bundles used in computational model

2 BRANISLAV VRBAN et al.

B. Calculation methodology modelled with temperature of 933 K and the An accurate treatment of of structural materials and water transport and depletion in VVER-440 fuel coolant is 555 K. The fuel pellet density is assemblies characterized by heterogeneous and 10.55 g/cc and the density of zirconium alloys complex design requires the use of advanced equals 6.55 g/cc. Very fine depletion steps computational tools. The depletion module (<0.5 MWd/kgHM) are used before TRITON [5], included in SCALE 6.1.3 code Gadolinium peak reactivity to track the fast system developed by ORNL, was used to poison concertation changes. After peak perform depletion simulations for two- reactivity, longer steps are used but are kept dimensional FA and ERC models. The smaller than 1 MWd/kgHM. TRITON depletion module is coupling the 2D C. Sensitivity and parametric evaluations transport code NEWT with the point depletion and decay code ORIGEN-S. The TRITON The effects of various relevant depletion lattice physics modelling approach for PWR parameters on the models keff (due to the fuel is extensively described in reflective boundary conditions identical to kinf) SCALE/TRITON primer [6]. For the sake of and isotopic changes were investigated, brevity, just the most important options used in however just the most interesting cases are our best modelling approach (BMA) and based presented. Variations of a single parameter are on SCALE/TRITON primer and our studied in each case; the remaining parameters experience for burnup calculations are shown are based on parameters used in BMA model. here. The developed models are 2D assembly  Several VVER fuel types and enrichments models with reflective boundary conditions on of U-235 are investigated in the paper. all sides, which represent infinite radial arrays of infinite length fuel assemblies. An  Since the real-life operating history of each unstructured coarse-mesh finite-difference FA or ECS varies significantly, it is acceleration approach (CMFD) is used with necessary to determine an operating history “partial-current” acceleration scheme. All that is bounding in terms of its effect on results of sensitivity and parametric reactivity, or to define a simple operating evaluations were calculated with the standard history with quantified margin that will SCALE V7-238 multigroup neutron library bound the effect of operational variations. based on ENDF/B-VII.0 evaluated data [7]. One of the most important parameters The V7-56 multigroup neutron library based on varying is the boron acid concentration. The ENDF/B-VII.1 [8] evaluated data was used in four concentrations are investigated cb={1; the case of simplified benchmark calculation. 2.56; 4; 5} g/kg. Fuel pins with burnable absorbers were  The Gadolinium-bearing (Gd) pins should depleted by constant flux option instead of be treated with special approach including constant power approach. The average specific constant flux option and consideration of power of each model is derived from the spatial depletion. The influence of both average reactor power of NPP Bohunice unit 4 approaches to integral multiplication during cycle 30 and equals to 33.05421 parameter and to isotopic are studied. kWth/kgHM. The average concentration of boron acid (H3BO3) is obtained using the same  Calculations were performed to assess the approach and reaches cb=2.56 g/kg. The fuel is effect of assumed specific power, with

3 ON BURNUP MODELLING ISSUES ASSOCIATED WITH VVER–440 FUELS

varying the specific power from the half of dissolution of the cut-out specimen including BMA power to the doubled value. control over fuel dissolution completeness, radiochemical extraction of U, Pu, Np, Am,  The moderator (also coolant) temperature Cm, Nd, Cs and Ce from fuel solution, varies significantly within the fuel axial nuclide composition measurements of the profile, therefore it is necessary to assess its extracted elements, measurement of uranium, influence on the fuel multiplication factor , neptunium, americium, and nuclide concentrations. The three water neodymium, cerium and caesium mass moderator with boric acid temperatures are fractions using isotopic dilution and investigated ={541.05 K; measurements of Np-237, Cm and Ce-144 0.7803 g/cc, 555 K, 0.7604 g/cc; 570.45 K, contents. All the results are burdened with 0.7258 g/cc}. It should be noted that the nuclide specific error range for a confidence moderator/coolant density was calculated probability of Р=0.95. These errors are with assumption of the design pressure of considered in the results section of this 12.26 MPa. paper. The radiochemical examinations of D. The simplified benchmark specific groups of nuclides were done in different and are precisely taken into account The calculation presented in the paper in the calculation model. is based on data published for samples No. 21 and 182 taken from the fuel pin No. 6 of E. Results the FA No. D26135. The axial position of sample No. 21 with a length of ~ 10 mm cut The results of different fuel types and out from fuel was approx. 1 m above the the average enrichments of U-235 are shown lower fuel pin plug. The sample No. 182 was in Fig. 2. As it can be seen, for ERC with the in the lower part of the core just approx. 10 uniform enrichment of 1.6 wt% U-235 and cm above the fuel pin plug. Our results for without integrated burnable absorbers, the sample No. 149 from pin No. 54 can be reactivity decreases monotonically with found in our previous work [9]. The data in burnup in a nearly linear fashion. In contrast, document [5] are not fully comprehensive, for fuels with Gadolinium the reactivity therefore user effect may be present in our increases as fuel burnup proceeds, reaches a approach. The spent fuel assembly was maximum at the burnup where the absorber is operated from October 1987 up to July 1991 nearly depleted (between 6 to 8 MWd/kgHM), (1369 calendar days). There were 1109 and then decreases monotonically. The effective full power days. A cooling period reactivity peak is more noticeable in the (since the end of irradiation period to the models with average enrichments of 3.84 and radiochemical analysis) made up approx. 12 4.25 wt% U-235 than in the 4.87 wt% U-235 years. Thus, the working assembly is typical case. This effect is caused by the different of the majority of fuel assemblies, which are ratio of fissile to absorbing Gd isotopes and stored in NPP storage pools. The nuclide by their opposite influence on the criticality composition of spent specimens parameters in each assembly type. Interesting was examined in the analytical and mass- finding is that the highest peak value moves to spectrometric analysis laboratories of the higher burnup for FAs with higher uranium RIAR [10]. The examination included enrichment.

4 BRANISLAV VRBAN et al.

concentration changes causes significant underestimation of the system reactivity in early burnup stages. Later the reactivity of Gd peak is systematically overestimated.

Fig. 2. Effect of assembly type It is not shown, but we can conclude that the reactivity trends of various boron acid concentrations are parallel during the whole burnup. The concentrations of important Fig. 4. Effect of deplete-by-flux option isotopes gathered during depletion with vs. spatial depletion maximal and minimal investigated boron acid concentrations are shown in Fig. 3. To find the cause, Gd isotopes depletion is shown in Fig. 5. The Gd-155 and Gd-157 have much larger thermal cross sections than U-235, thus their concentration changes significantly influence the neutron balance of the system. Gd-157 depletes more rapidly in the case when spatial concentration changes are not taken into account. This faster concentration decrease is consequence of higher effective absorption cross section yielding to lower reactivity of the system. Consequently, this concentration difference Fig. 3. Effect of boron acid concentration causes higher reactivity amplitude of Gd peak in later burnup steps. The agreement diverges mainly for Pu- 239 as a function of burnup. As mentioned To assess the effect of assumed specific above, the Gd pins should be treated with power, the fuel temperature was kept constant special approach including constant flux option in all calculation steps. Consistent with other and consideration of spatial depletion. The studies, the general trend is for reactivity to influence of both approaches to multiplication decrease with increasing specific power. With parameter and to isotopic changes is shown in respect to reactivity the use of minimum Fig. 4 and Fig. 5. It is evident from Fig. 4 that specific power seems to be conservative neglecting the depletion by constant flux modelling option. As shown in Fig. 6., the option does not lead to different results as concentrations of Pu-239 and Pu-241 decrease obtained by using BMA modelling approach. with increasing specific power, which would On the other hand, ignoring of fast spatial Gd also tend to reduce reactivity.

5 ON BURNUP MODELLING ISSUES ASSOCIATED WITH VVER–440 FUELS

cross-section for thermal . Consequently, Pu-239 concentration is sensitive to the level of system under- moderation.

The results of the simplified benchmark calculation for samples No. 21 and 182 of main and minor are mainly shown in Fig. 8 to Fig. 11. The calculated (denoted as C) and experimentally determined (E) nuclide

concentrations are presented in the form of Fig. 5. Effect of spatial depletion C/E-1 ratio. As can be seen, the highest relative for burnable poisons. deviation is in the case of U-235 and sample We assume that almost all important No. 21, where the calculation overestimates the fission products decrease with decreasing average measurement value approximately by specific power which would tend to increase 20 %. reactivity.

Fig. 7. Effect of moderator temperature Fig. 6. Effects of specific power.

The VVER-440 FAs are designed as under-moderated, therefore one can expect lower fuel multiplication properties with the higher moderator temperature. The results achieved confirm our expectations and are fully in accordance with theory. The concentrations of fissile Pu-239, see Fig. 7, are shown to rise with increasing moderator temperature. Fig. 8. Comparison of results – sample 21

Isotope Pu-239 is formed from fertile U- The resonance absorption by U-238 is 238 by absorption of a resonance and thermal enhanced by Doppler broadening with neutrons and then undergoing double decay increased fuel temperature. According to through U-239 and Np-239 isotopes. On the almost no deviation of calculated and measured other hand, Pu-239 has very high absorption values for U-238, we conclude that fuel

6 BRANISLAV VRBAN et al. temperature was modelled in appropriate way. As shown above, the concentration of Pu-239 is sensitive to the level of system under- moderation due to its very high absorption cross-section for thermal neutrons. The comparison of results shows the good agreement for Pu-239 nuclide and both samples; therefore, we assume that fuel density and system under-moderation was modelled Fig. 11. Comparison of results – sample 182. correctly. The precursor of Np-237, which precedes formation of U-232 and thus limits fuel reprocessing by Tl-208 gamma , is the U-236, of which the calculated concentration lies near to the measurement error boundary.

Fig. 9. Comparison of results – sample 182.

It is worth mentioning, that overall results of sample No. 182 are systematically closer to the measured values. The reason of this behaviour is not clear to us and should be investigated further. Fig. 12. Comparison of results – sample 21.

The minor actinides concentrations are underestimated varying on the nuclide to nuclide basics. The Am-241 concentration is slightly underestimated (approx. -4 to -10%). This deviation should be taken into account in follow-on criticality and decay heat calculations.

Fig. 10. Comparison of results – sample 21.

Contrary, the final concentration of Pu- 241 is slightly underestimated by approx. 5 to 10 %. This underestimation can influence the multiplication properties of final spent fuel configuration. In case of the neutron absorbing materials the concentration of Pu-238 is significantly overestimated, what is compensated by underestimating of Np-237. Fig. 13. Comparison of results – sample 182.

7 ON BURNUP MODELLING ISSUES ASSOCIATED WITH VVER–440 FUELS

The Fig. 10 to Fig. 15 mainly show VVER-440 reactors. The influence of results for fission products, for which most calculation approaches and parameters have calculation results lies slightly under or in the been summarized, however much more error range of measurements. effort is needed, and further calculations are planned. It was demonstrated that special care should be given to Gadolinium bearing pins. Surprisingly the constant by flux depletion option does not play a significant role in the concentration calculations. The influence of operational history to final reactivity was proven and briefly analysed. The concentration of boron acid significantly influences Pu-239 production Fig. 14. Comparison of results – sample 214 as a function of burnup. It was found out that with respect to reactivity the use of The higher discrepancies can be found minimum specific power seems to be for Cs-134 (-30 %), Sm-148 (-19 %) and Ag- conservative modelling option. The relevant 109 (80 %) nuclides. The results of Cs-137 as effect was found in the case of variations of the primary source of penetrating gamma moderator/coolant temperature. This radiation from spent fuel until 300 years of observation just supports the fact that axial discharge are satisfactory and lie under the measurement errors. depletion should be carefully considered where mainly the moderator temperature plays a vital role. In fact, all investigated parameters have little effect on fission- product worth. The most sensitive isotope in all investigated cases was Pu-239 isotope. To assess the currently developed Best Modelling Approach the comparison between the calculation results and experimental data

from Novovoronezh NPP was provided. Fig. 15. Comparison of results – sample 182 Results obtained indicate that the U-235 calculation overestimates the average III. CONCLUSIONS measurement value approximately by 20 %. The analysis of The minor actinides concentrations were in properties and nuclide compositions is a general underestimated, where in case of Am- very important stage for the nuclear fuel 241 the underestimation reached approximately cycle as well as for neutron-physical -10%. For the investigated fission products, the calculations of VVER-type reactor cores good agreement was achieved, where most and their future improvement. This paper calculation results fell into the error range of described the main results of analyses measurements. The higher discrepancies were performed to achieve a better understanding identified in the case of Cs-134 (-30 %) of the modelling issues associated with nuclide.

8 BRANISLAV VRBAN et al.

This work was based on simplified [4]. L. Markova, F. Havluj, “Simplified benchmark definition and is affected by user Benchmark Specification based on #2670 experience and chosen modelling approach. ISTC VVER PIE”, Proc. The 12th Meeting of The influence of the used cross-section library AER Working Group E, Modra, Slovakia, is questionable and will be further investigated. April 16-18, 2007.

In the case of simplified benchmark, the higher [5]. M. D. DeHart, “High-Fidelity Lattice Physics number of energy groups can bring better Capabilities of the SCALE Code System Using results mainly for the main and minor TRITON”, The American Nuclear Society and actinides, however, used 52 group library is the European Nuclear Society 2007 Int. Conf. already optimized for pressurized water on Making the Renaissance Real, Washington, reactors. Therefore, other approaches and D.C., Trans. Am. Nucl. Soc. 97, 598-600, nuclear data libraries should be studied to 2007. support the “best practices” used for VVER- [6]. B. J. Ade, “A primer for Light Water Reactor 440 burnup credit calculations. Lattice Physics Calculations”, ORNL, U.S.NRC, NUREG/CR-7041, 2012. ACKNOWLEDGEMENT [7]. M.B. Chadwick, et al., ″ENDF/B-VII.0: Next This study has been partially financially Generation Evaluated Nuclear Data Library supported by the Slovak Research Development for Nuclear Science and Technology″, Agency No. APVV-16-0288 and by the Scientific Nuclear Data Sheets, vol. 107, pp. 2931- Grant Agency of the Ministry of Education of 3060, 2006.

Slovak Republic No. VEGA 1/0863/17. [8]. M. B. Chadwick, M. Herman, P. Obložinský et al, “ENDF/B-VII.1 Nuclear Data for Science REFERENCE and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data”, [1]. ORNL, SCALE, “A Comprehensive Nuclear Data Sheets, vol. 112, no. 12, pp. Modelling and Simulation Suite for Nuclear 2887-2996, 2011. Safety Analysis and Design”, Version 6.1, ORNL/TM-2005/39, 2011. [9]. B. Vrban, et. al., “The VVER-440 Burnup Credit Computational Benchmark Used for the [2]. M.D. DeHart, ″Sensitivity and Parametric Evaluations of Significant Aspects of Burnup SCALE System Qualification”, In APCOM Credit for PWR Spent Fuel Packages″, 2018: 24th International conference on applied ORNL/TM-12973, Lockheed Martin Energy physics of condensed matter, Slovak Republic. Res. Corp., Oak Ridge Nat. Laboratory, 1996. AIP Publishing, 2018.

[3]. M.D. DeHart, ″Parametric Analysis of PWR [10]. L. J. Jardine, “Radiochemical Assays of Spent Fuel Depletion Parameters for Long Irradiated VVER-440 Fuel for Use in Spent Term Disposal Criticality Safety″, ORNL/TM- Fuel Burnup Credit Activities”, Lawrence 1999/99, Lockheed Martin Energy Res. Corp., Livermore National Laboratory, UCRL- Oak Ridge National Laboratory, 1999. TR212202, April 2005.

9 Nuclear Science and Technology, Vol.9, No. 2 (2019), pp. 10-16 Estimation of Tritium Production in VVER-440 Reactor Core During Normal Operation

Štefan Čerba1,2, Jakub Lüley1, Branislav Vrban1, Filip Osuský1, Vladimír Nečas1 1Slovak University of Technology in Bratislava, Faculty of Electrical Engineering and Information Technology, Institute of Nuclear and Physical Engineering, Ilkovičova 3, 812 19 Bratislava, Slovakia 2B&J NUCLEAR Ltd., Alžbetin Dvor 145, 900 42 Miloslavov, Slovakia Email: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] (Received 12 November 2019, accepted 19 November 2019)

Abstract: Slovakia as one of the world leading countries in the share of in electricity production and currently operates 2 nuclear power plants, each with 2 VVER-440 units. In addition to these reactors there are 2 VVER-440 units under construction and 2 units in decommissioning. The VVER-440 technology features thermal neutron spectrum, low dioxide fuel and light-water coolant, diluted boric acid and 37 emergency reactivity control assemblies with boron steel absorber. Due to the presence of 10B in the coolant/moderator which has high thermal cross-section, the absorption of neutron on these atoms may lead to tritium production. Tritium strongly contributes to the level of radioactivity of the primary coolant, therefore the NPP staff must have appropriate knowledge of its production during operation. This paper focuses on the estimation of the tritium production for a specific scenario of the operation of the 3rd unit of Mochovce NPP. For simulations the SCALE6 system is used with the detailed calculation model developed at the B&J NUCLEAR ltd. company. The calculations presented in the paper are performed using self-shielded multi-group cross-section libraries, taking into account the operation conditions of Mochovce unit 3 NPP in the first fuel campaign. Keywords: Tritium production, VVER-440, activity, criticality, SCALE system, Mochovce NPP.

I. INTRODUCTION has high isotopic exchange rate, high residence time in the environment, long half- The light-water coolant as passes life (12.3 years) and can easily leak into the through the reactor core, to remove the environment in a form of water. In addition, generated heat from fuel assemblies, gets the limits for radioactive releases allow the activated by capturing moderated neutrons. dilution of tritium (12 GBq per year), in order During normal operation numerous neutron to decrease its volumetric activity, in waste induced reactions take place, generating a waters exiting the . If variety of radioactive nuclides, such as 16N, tritium is not separated effectively from 17N, 14C or 3H. Due to the relatively long half- biosphere, it will become a part of the global life of the majority of these activation cycle. Once it is absorbed through food or products, their concentration in the primary water, it will steadily exist in human body for coolant directly influences the radiation long time and induce internal radiation exposure of personnel performing damage [1]. maintenance activities. Among all radioactive nuclides produced during reactor operation VVER reactors are the most frequently tritium (3H) is one of the most important. It built reactor types in the world. The first units

©2019 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute ŠTEFAN ČERBA et al. with predecessors of VVER-440 type reactors experience of the research team with were erected at the Novovoronesh NPP site in evaluating neutron physical characteristics of 1972 and 1973 [2]. The second step in the VVER-440 units for the Nuclear Regulatory development of VVER-440 type reactors was Authority of Slovak Republic for more than 3 the V-230 design which was mainly years [5]. constructed in the period from 1973 to 1982. The third step in VVER-440 development was II. OVERVIEW OF THE CALCULATION the V-213 reactor design. Slovakia has four METHODOLOGY nuclear reactors of this type generating half of A. The VVER-440 reactor core its electricity and two more under construction. In 1972, construction of the Jaslovské The detailed and precise 3D model of Bohunice V1 plant commenced, with two the VVER-440 V-213 reactor has been VVER-440 V-230 reactors. The first was grid developed for criticality and shielding connected in 1978, the second two years later. calculations in the KENO-VI code of the The V2 units commenced operation in 1984 SCALE6 system. The whole-core 3D model is and 1985. The Slovak NPP Mochovce with shown in Fig. 1. It consists of the reactor in- VVER-440 V-213 units 1 and 2 were put in vessel components, such as fuel assemblies operation in the summer of 1998 and the end of (including fuel rods, upper spacer grid, year 1999 due to the construction delay caused intermediate spacer grids, supporting grid, by political changes in the early 1990s. Two mixing grid, central tube and fuel endings), another units 3&4 of VVER-440 V-213 are emergency reactor control assemblies (ERC - currently under construction in Mochovce and absorber and fuel part), core basket, barrel and are planned to be put in operation in 2020 [3]. the reactor pressure vessel. The boundaries of Since the operation of the Jaslovské Bohunice the created VVER-440 whole-core model are V2 NPP and the first two units of Mochovce given by the outer surface of the dry shielding, NPP started decades ago, estimation of the the level of hot-leg piping and the basement of tritium inventory through calculation would be filtration mechanism [3]. a very challenging issue. However, the The VVER-440 fuel assemblies (FAs) rd construction of the 3 unit of Mochovce NPP are of hexagonal shape and consist of 126 provides unique opportunity to develop a new UO2 fuel pins, placed in the assembly in a methodology to numerically estimate the triangular grid pattern. The bundle of fuel production rate of tritium in its primary coolant rods in the assembly is enclosed in a and to compare the result with real experiment, hexagonal wrapper with 145 mm width across once the reactor is put into operation. the flat. The fuel assemblies and emergency This paper presents the first step of a reactor control assemblies are positioned in a complex joint long-term research activity hexagonal grid with a spacing of 147 mm. between the Slovak University of Technology The fuel rods are located in the bundle in a in Bratislava and the B&J NUCLEAR ltd. triangular grid pattern with 12.3 mm pitch. research company. This activity is based on The fuel rod cladding is made from E110 the detailed 3D model of the VVER-440 , while the wrapper tubes of reactor core developed in the state-of-the art FA and ERC are made from E125 zirconium SCALE6 [4] calculation system and the alloy [3].

11 ESTIMATION OF TRITIUM PRODUCTION IN VVER-440 REACTOR CORE …

(EFPD) without requiring the positions of the ERC assemblies to be adjusted. Compared to the ERC assemblies the boric acid ensures uniform distribution of absorber in the core, however requires time consuming dilution, if its concentration is to be decreased, and may cause positive reactivity feedback, in case of high concentration. The critical boron acid concentration was calculated using the ANDREA macro code [6]. This code, the product of Nuclear Research Institute (NRI)

REZ, has been being developed since 2005. Fig. 1. KENO 3D model of the VVER-440 V-213 The code is designed to support safety analyses reactor core of VVER type reactors [7]. The results of critical boric acid concertation are shown in Fig. 3.

Fig. 2. Equivalent sixth of the fuel loading pattern

As it was mentioned in the introduction Fig. 3. Critical boric acid concentration through the part, the analysis presented in this paper was fuel cycle carried out for the first fuel loading of Mochovce unit 3, considering a simplified As it can be seen, the critical boric acid approach. This approach assumes fresh fuel concentration of fresh fuel (0 EFPD) is 5.059 composition without burnup through the cycle g/kg. As a result of fuel burnup, the reactivity and variable critical boron acid concentration of the system decreases, so does the critical and coolant cycling. The fuel loading pattern boric acid concentration that reaches 0 g/kg at used in the present analysis is shown in Fig. 2. 266.95 EFPD. Usually, after the boric acid Due to the 60° symmetry of the core, only one concentration has reached zero, the operation sixth of the pattern is presented. The fuel of the reactor continues by withdrawing the loading pattern is based on our previous work ERC assemblies from operation position (in and consists of FA and ERC assemblies with our case 225 cm) to the upper edge of the core 2.4 % and 3.6% enrichment of 235U [2]. (250) and by decreasing the reactor power (1741 MWth in our case), core inlet B. Critical boric acid concentration temperature (268 ℃) and the pressure at the The critical boric acid concentration is a main steam collector, however these concentration that ensures critical state of the operational regimes were not considered in our reactor for the given effective full power day analysis.

12 ŠTEFAN ČERBA et al.

C. Dilution of boric acid density of the sought atoms at the given time step. Since the functions of concentrations of By operating the reactor for certain 1H, 2H and 10B, 11B atoms are relatively EFPDs the reactivity of the system decreases. complex the fuel cycle (0 – 266.95 EFPD) has To ensure criticality, the reactivity bond by been divided to 9 intervals while a simple boric acid is released by diluting its exponential fit was used for each interval. concentration. The dilution is performed by pumping out a certain amount of moderator D. Calculation of tritium inventory in and replacing it with demineralized H2O. As coolant the boric acid is diluted the concentration of The calculation of tritium inventory in 10B and 11B atoms decreases, however the the first fuel loading of Mochovce NPP unit 3 concentrations of 16O, 1H and 2H proportionally was performed in the KENO-VI module of the increase. The concentrations of 10B and 2H SCALE 6.1.3 system, based on assumption atoms in coolant are illustrated in Fig. 4 and presented in the previous chapters. SCALE6 is Fig. 5. a comprehensive modelling and simulation suite developed for nuclear safety analyses by the Reactor and Nuclear Systems Division (RNSD) of the Oak Ridge National Laboratory (ORNL). The KENO-VI is a Monte Carlo

criticality solver designed to calculate the keff and other quantities of three-dimensional systems. The KENO-VI criticality calculations were performed using 238g cross-section libraries based on ENDF/B-VII.0 [8] evaluated

data and with cell treatment using the Fig. 4. Concentration of 10B in coolant through the CENTRM/PMC sequence. fuel cycle The analysis was split into several calculation steps, while the steps represented the reactor operation between 0-5, 5-15, 15-30, 30-60, 60-100, 100-140, 140-180, 180-220 and 220-266.95 EPFD. For each time bin a stand-alone calculation was carried out with the same reactor power, ERC position, temperatures, fresh fuel composition and variable coolant isotopic composition. The

isotopic composition of isotope ( ) in Fig. 5. Concentration of 1H in coolant through the coolant was calculated using Eq. (1) and the fuel cycle dilution coefficients were derived from the exponential functions Fig. 4 and Fig. 5. The In order to use these concentrations in neutron flux was estimated to be constant the estimation of 3H inventory, the within a given calculation step. concentrations should be substituted by simple functions that accurately represent the number ( ) (1)

13 ESTIMATION OF TRITIUM PRODUCTION IN VVER-440 REACTOR CORE …

To estimate the isotopic composition of ( ) tritium, 3 production routes were considered: (6)

 Eq. (2) - (n,α) on and subsequently

(n,nα) on - 21 kbarn * 50 mbarn thermal XS

 Eq. (3) - (n,t2α) on – 0.4 barn thermal (7) ( ) ( ) ( ) XS 2 The ( ) H component can be  Eq. (4) - (n,γ) on and subsequently (n,γ)

calculated by Eq. (8) and the ( ) on – 28 barn * 40 mbarn thermal XS component of 2H and the concentrations of 10B ( ) 1 → + and H can be calculated by Eq. (1). ( ) (2)

→ ( ) (8) ( )

→ (3)

( ) ( ) In the above mentioned equations

→ → (4) represents the sum of the group-by-group flux weighted collision rate of nuclide and reaction ( ), which can be defined by Eq. Considering the abovementioned (9), where ̅̅̅(̅̅̅̅) is the volume integrated reactions and the radioactive decay of tritium average neutron flux, defined by Eq. (10). with 12.3 y. half-life, the tritium balance equation can be written as follows: ̅̅̅̅̅̅̅ ∑ ( ) ( ) (9) ( )

( )

( ) ̅̅̅(̅̅̅̅) ( ) (10) ∫ ∑

( ) (5)

( ) In each calculation step the concentration of 3H was estimated using the calculated neutron flux, weighted XS and

where ( ) , ( ) ( ) concentrations of nuclides in the coolant.

However, the concentrations of the coolant ( ) and ( ) are the time dependent changes also during a single calculation step, concentration of 3H, 2H, 3H, 7Li and 10B in the 3 thus this change has to be taken into account, unity of volume, the H decay constant , for instance by assuming constant neutron flux and are the microscopic cross- and the time integral of number densities sections of (n,α), (n,t2α) and (n,γ) reactions and through the time step. Since the coolant is the corresponding neutron flux. The time circulates with 2.5 m/s velocity, it takes dependent concentrations of 7Li and 2H can be approximately 1 s to go through the fuel core, defined by Eq. (6) and Eq. (7), where ( ) to get activated by thermal neutrons, and represents the concentration of 2H as result of additional 17 s to run through the rest of primary circle (PC) and to come back to the moderation dilution and ( ) as result of core. The activation of 3H can be calculated in (n,γ) reaction on 1H atoms.

14 ŠTEFAN ČERBA et al. two ways, by taking into account the F. Discussion circulation time ( = in-core time) and the total The number density and the activity of volume of coolant in the primary circuit or by 3 H is strongly influenced by the assumption of neglecting circulation ( = in-core + out-of- coolant circulation. The difference in the total core time) and using only the volume of 3H activity is more than 40 %. Due to moderator in the core. decreasing boron concentration saturation of E. Results the curve of 3H number density can be seen. Among all reactions 87.95 % occurred on 10B, The results of the tritium concentration 11.57 % on 2H and 0.48 % on 7Li. In CASE 1 are presented in Fig. 6, where CASE 1 the total volumetric activity of 3H reached 9.64 represents the conditions where only the in- MBq/l and in CASE 2 5.69 MBq/l. Just for core time was taken into account and CASE 2 better imagination, this activity is more than 28 the conditions where the total-time (in + out) 000 or 56 000 times higher than the was considered. The atom concentrations were international limit for 3H in drinking water [9]. achieved by multiplying the result achieved by According to document [10] published in 2018, solving Eq. (5) by the neutron source term the total released activity of tritium per one (4.523E19 n/s). The results of total and reactor unit is 2441.5 GBq. Compared to our volumetric tritium activities at the end of fuel results this value is approximately 3 times cycle (266.95 EFPD) are shown in Table I. The higher. However, considering the difference in volume of moderator for CASE 1 represents the critical boric acid concentrations, the total volume in primary circuit and for enrichment, fuel cycle length and the rough CASE 2 the volume in the core. estimation of coolant circulations, the results Table I. Tritium activity at the end of fuel cycle are acceptable. No Coolant assumption Circulation III. CONCLUSION circulation Decay const. [s-1] 2.5638E-09 In this paper the results of the first Moderator V. [m3] 242.00 12.77 approach to estimate the tritium production rate Total activity [Bq] 7.6107E11 4.4917E11 in the Slovak NPPs was presented using SCALE6, the ANDREA diffusion solver and Vol. activity [Bq/l] 9.6403E06 5.6895E06 several in-house c++ utilities. The estimation of the tritium inventory was performed assuming fresh fuel isotopic composition, reference core parameters, and various critical boric acid concentration, calculation by the ANDREA code. Three nuclear reactions were taken into account, 10B (n,α) followed by 7Li (n,nα), 10B (n,t2α) and 1H (n,γ) followed by 2H (n,γ). The change of the moderator isotopic composition was assumed by using an exponential fit through a calculation step. The Fig. 6. Concentration of 1H in coolant through the total tritium activity was assumed either by fuel cycle considering the coolant circulation time with

15 ESTIMATION OF TRITIUM PRODUCTION IN VVER-440 REACTOR CORE … the total coolant volume (reference case) or by Portorož, ISBN 978-961-6207-39-3 Slovenia, neglecting circulation and using only the September 5-8, 2016. volume of coolant in the model. In the [3]. F. Osuský, B. Vrban, Š. Čerba, J. Lüley, V., reference scenario the volumetric activity of Nečas, ″Effective dose calculation in the tritium at the end of fuel cycle reached 9.64 VVER-440 reactor maintenance area″, In 28th MBq/l. Among this activity 87.95 % was Symposium of AER on VVER Reactor Physics and Reactor Safety. Olomouc: Nuclear produced due to the 10B (n,t2α), and 11.57 % 2 Research Institute, 2018. by H (n,γ) reactions, thus in further steps it will be justified to neglect the minor tritium [4]. ORNL, SCALE, “A Comprehensive Modelling and Simulation Suite for Nuclear producing reaction on 7Li. In the following Safety Analysis and Design”, Version 6.1, steps of this research activity several ORNL/TM-2005/39, 2011.

improvements will have to be done. First of all, it will be necessary to use a more complex [5]. B. Vrban, Š. Čerba, J. Lüley, F. Osuský, V., Nečas, ″Criticality safety calculation of exponential fit of number densities for coolant VVER-440 core by SCALE system″, In 28th dilution. It will be required to better assume the Symposium of AER on VVER Reactor circulation time through the core and the Physics and Reactor Safety. Olomouc: Nuclear neutron flux that contributes to tritium Research Institute, 2018. activation. In addition, fuel burnup will also [6]. F. Havlůj, R. Vočka, J. Vysoudil, ″ANDREA have to be taken into account. After having our 2: Improved version of code for reactor core methodology improved, it will be implemented analysis″, In: Proceedings of the 22nd in the complex calculation system to optimize International conference on Nuclear the fuel loading pattern of VVER-440 reactors Engineering, Prague, Czech Republic, July 7- in Slovakia. 11, 2014.

[7]. B. Vrban, Š. Čerba, J. Lüley, V. Nečas, ACKNOWLEDGEMENT “Current Status of the WWER-440 Engineering Core Calculations at the Slovak This study has been partially financially University of Technology in Bratislava”, Proc. supported by the Slovak Research Power engineering 2018. Energy-Ecology- Development Agency No. APVV-16-0288 and Economy 2018, Tatranské Matliare, ISBN by the Scientific Grant Agency of the Ministry 978-80-89402-98-4 Slovakia, Jun 5-7, 2018.

of Education of Slovak Republic No. VEGA [8]. M.B. Chadwick, et al., ″ENDF/B-VII.0: Next 1/0863/17. Special thanks go also to B&J Generation Evaluated Nuclear Data Library for NUCLEAR ltd. Nuclear Science and Technology″, Nuclear Data Sheets, vol. 107, pp. 2931-3060, 2006.

REFERENCE [9]. Canada´s Nuclear Regulator, “Standard Guidelines for Tritium in Drinking Water”, [1]. ANS, “Nuclear criticality safety in operations Part of the Tritium Studies Project, Minister of with fissionable materials outside reactors”, Public Works and Government Services American National Standards Institute, La Canada, ISBN 978-0-662-474997-5, January Grande Park Illinois, USA, 2014. 2008.

[2]. Vrban, Š. Čerba, J. Lüley, F. Osuský, [10]. P. Bryndziar, V. Balev., “Report on monitoring “Determination of the Computational Bias in releases and readioactivy arround the Criticality Safety Validation of VVER- 440/V213”, Proc. 25th International Mochovce NPP” (in Slovak), Slovenské Conference Nuclear Energy for New Europe, elektrárne, a.s., Mochovce, May 2018.

16 Nuclear Science and Technology, Vol.9, No. 2 (2019), pp. 17-24 Processing of the multigroup cross-sections for MCNP calculations

Jakub Lüley1,2, Branislav Vrban1, Štefan Čerba1, Filip Osuský1, Vladimír Nečas1 1Slovak University of Technology in Bratislava, Faculty of Electrical Engineering and Information Technology, Institute of Nuclear and Physical Engineering, Ilkovičova 3, 812 19 Bratislava, Slovakia 2B&J NUCLEAR Ltd., Alžbetin Dvor 145, 900 42 Miloslavov, Slovakia E-mail: [email protected], [email protected], [email protected], , [email protected], [email protected] (Received 13 November 2019, accepted 19 November 2019)

Abstract: Stochastic Monte Carlo (MC) neutron transport codes are widely used in various reactor physics applications, traditionally related to criticality safety analyses, radiation shielding and validation of deterministic transport codes. The main advantage of Monte Carlo codes lies in their ability to model complex and detail geometries without the need of simplifications. Currently, one of the most accurate and developed stochastic MC code for particle transport simulation is MCNP. To achieve the best real world approximations, continuous-energy (CE) cross-section (XS) libraries are often used. These CE libraries consider the rapid changes of XS in the resonance energy range; however, computing-intensive simulations must be performed to utilize this feature. To broaden our computation abilities for industrial application and partially to allow the comparison with deterministic codes, the CE cross section library of the MCNP code is replaced by the multigroup (MG) cross-section data. This paper is devoted to the cross-section processing scheme involving modified versions of TRANSX and CRSRD codes. Following this approach, the same data may be used in deterministic and stochastic codes. Moreover, using formerly developed and upgraded cross- section processing scheme, new MG libraries may be tailored to the user specific applications. For demonstration of the proposed cross-section processing scheme, the VVER-440 benchmark devoted to fuel assembly and pip-by-pin power distribution was selected. The obtained results are compared with continues energy MCNP calculation and multigroup KENO-VI calculation. Keyword: MCNP, Multigroup calculation, VVER, criticality

I. INTRODUCTION flux, implicit sensitivity coefficients or adjoint flux and to perform cell treatment, S/U A lot of effort has been spent on the calculation can be still memory and time development of techniques to effectively expensive and special attention must be given to compute sensitivity coefficients and cross- the preparation of the covariance matrix. [1,2,3] section induced uncertainties (S/U) by Monte- Alternatively, the multigroup option is still an Carlo codes and continues-energy libraries. effective method for other applications and in MCNP6 and SCALE6.2 have currently case of cross-section adjustment, it can also implemented approaches to calculate the extend the applicability of S/U calculation. The adjoint weighted tallies, which allow both main advantage of multigroup calculation is not codes to carry out S/U analyses related to only in the reduction of the calculation time but criticality safety calculations using CE also offers to an engineer utilization of the libraries. Although, it is no necessary for CE adjoint calculations in problems where the libraries to calculate flux moments from mesh forward transport calculation is not efficient. [4]

©2019 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute PROCESSING OF THE MULTIGROUP CROSS-SECTIONS FOR MCNP CALCULATIONS

Effective use of the multigroup approach B. Computational scheme is depending on the appropriate and target The fundamental part of the problem tailored cross-section library. To achieve a oriented MG constants processing scheme is a required accuracy of the multigroup MC universal code which is able to prepare MG calculation, the problem specific cross-sections constant in various formats. In our previous have to be available. Currently, there are four analyses, the TRANSX code [11] was VVER-440 reactor units in operation and two standardly utilized. The TRANSX code is able other units are under construction in Slovakia, thus there is a clear need of improvement in to work with cross-section library in general our calculation abilities. The VVER-440 MATXS format and region-wise flux files in reactors belong to PWR family, where thermal CCCC format. It can process cross-section data scattering treatment has to be taken into with an appropriate cell treatment; infinite account during cross-section data processing. homogeneous mixture incorporating self- In many industrial applications, a validation of shielding effects by Bondarenko Method or deterministic codes requires that the MC code lump materials incorporating Dancoff utilize the same data as a deterministic code correction for several geometrical [5]. Optimized cross-section library applicable configurations (slab or cylinders in triangular to both types of calculation is therefore the or square lattice). Some modifications were basic requirement for the current neutronic made in the TRANSX source code to enhance analyses and allows us to implement various its versatility, like considering cladding within methods to the multigroup constants Dancoff correction calculation, enabling processing scheme. utilization of dummy materials, extraction of scattering matrixes for individual reactions II. THE MULTIGROUP CROSS-SECTION (elastic, inelastic and n2n) and others. The PROCESSING TRANSX code prepares problem oriented MG A. Cross-section library constants (micro or macroscopic) standardly in ISOTXS format, which can be directly used by Within this analysis the SBJ_V2019T deterministic codes PARTISN [12] or DIF3D multigroup cross-section library, which is [13]. To process MG constants for MCNP updated version of SBJ_V2018T library calculation the CRSRD [4] modules were presented in [5], was utilized as source data implemented to the TRANSX code. The file. The library is based on the ENDF/B- VII.1 evaluated data [6], includes thermal CRSRD code was designed to translate deterministic MG cross-section to the format scattering data for hydrogen in H2O based on IKE S(α,β) [7, 8] and CAB [9] models; and suitable for MCNP. is stored in MATXS format. The cross- section library was prepared in 238 group structure, the same as in SCALE6 libraries [10], where the core averaged neutron spectrum of the VVER-440 reactor was used as a weighting function. Utilization of the SBJ_V2019T library is a part of long term complex validation process of developed cross-section processing scheme. Fig. 1. Computational scheme.

18 JAKUB LÜLEY et al.

The computational scheme applied in in the 238 group calculation. In the 44 group this analysis is shown in Fig. 1. The left side is calculation, for transport correction, the Bell- devoted to the processing of the SBJ_V2019T Hansen-Sandmeier approximation was used library which is describe in [5]. The right side and 23 thermal groups were defined. In case of is aimed to the transport calculations and is CRSRD translation part, the absorption cross- described in following sections. The mid part is sections were kept with negative values, if schematically describing the data flow and the occurred, and scattering matrixes were utilized codes. In the first round the processed with the factor 2ℓ+1 to 32 equi- SBJ_V2019T library is directly used to prepare probable bins by the Maximum Entropy two sets of MG cross-sections. The first set approach. Since this process was managed by was prepared in the way that all materials were the TRANSX code with implemented modules processed as an infinitely diluted, in 238 group from CRSRD, the data flow and the formats structure and in MCNP MG format, later from the MATXS through TRANSX and denoted as 238 gH. The second set was CRSRD procedures to MCNP MG cross- prepared in the way that all structural materials section file were controlled. More information were processed as infinitely diluted, in 238 with the data flow scheme is presented in [14]. group structure and in MCNP MG format. All MCNP MG calculations were Fuel, cladding and coolant were processed validated by the MCNP calculation in CE through the cell treatment considering mode and KENO-VI [10] MG calculation cylindrical shape of lump in triangular lattice using 238 group library. In case of MCNP CE and in 238 group structure in MCNP MG calculation the cross-section data processing is format, later denoted as 238 g and in ISOTXS quite straightforward. Regarding to KENO-VI format for spectral pin calculation. In the calculation all parameters related to the cross- second round the region averaged flux spectra section data processing were selected similarly calculated for each fuel enrichment was used to as much as it was possible, like 238 group collapse MG cross-sections. The 44 group library, cell treatment, Legendre expansion, structure, same as used in SCALE6 libraries, material definition, etc. was used due to its compatibility with 238 energy group structure. The third set is later C. VVER-440 benchmark overview denoted as 44 g. All three cross-section sets The VVER-440 benchmark devoted to comprise of isotope-wise constants fuel assembly and pip-by-pin power (microscopic cross-section) and homogenized distribution was selected to demonstrate the material-wise constants (macroscopic cross- proposed cross-section data processing sections). Calculations, which utilized capabilities. Benchmark definition is based on homogenized constants are later denoted with zero power state with uniform temperature abbreviation HM as 238 gHHM, 238 gHM 543.15 K. The geometry was simplified to two- and 44 gHM respectively to the individual sets. dimensional definition with 30-degree All the TRANSX calculations were symmetry. All internal parts like core barrel, performed with the same set of input core basket and core rim called “vygorodka” parameters. Legendre polynomial expansion were included. The outer boundary of the for scattering matrixes was set to 3. Consistent- benchmark is defined by the outer edge of P approximation was used for transport reactor pressure vessel with vacuum boundary correction and 95 thermal groups were defined condition. The geometry definition is presented

19 PROCESSING OF THE MULTIGROUP CROSS-SECTIONS FOR MCNP CALCULATIONS in Fig. 2, based on the SCALE6 model. The cross-section data and software application on core is composed of three types of fuel benchmark calculation, where not only integral assemblies with enrichment 1.6, 2.4 and parameter keff is evaluated, but also local average 4.25 % and two fully inserted parameters like relative fuel assembly (FA) Emergency Reactor Control Assembly (ERC) power distribution and relative fuel pin (FP) of 6th working group. The fuel assembly with power distribution are available. Within this average enrichment 4.25 % consists from fuel paper only results of keff and FA power pins with four different enrichments where one distribution are presented and discussed. type of pin contains combination of the UO2 Geometrical and material model of the and gadolinium absorber. All fuel assemblies benchmark core was prepared for MCNP and are considered as a fresh fuel. [15] KENO-VI codes as it is described in the previous part and shown in Fig. 2. All MCNP calculations were performed by the MCNP5 1.6 version [17] with 750 mil. neutron histories within 5 000 generations. The KENO-VI calculation was performed using the version distributed within the SCALE6.1.3 system with 100 mil. neutron histories during 500 generations. Due to the relatively small difference between the results of IKE and CAB thermal Fig.2. VVER-440 benchmark geometry model [16]. scattering models (in maximum it was 63 pcm) only the results of CAB model are presented in II. RESULTS AND DISCUSSION the next chapter. All comments and conclusions presented in this paper are relevant The first type of calculation was carried and applicable for the results of IKE model. out at the level of fuel pin to obtain neutron flux spectra for cross-section collapsing. These A. Results calculations were performed by the PARTISN The results of the FP spectral code in simplified 1D geometry where the calculations are presented in Table I. Six hexagonal lattice cell was represented by the different enrichments represent three types of radius of equivalent cylinder. Due to direct FA where the last four belong to the FA with utilization of flux files (RZFLUX shown in Fig. average enrichment 4.25 %. The results of 1) and capabilities of the TRANSX code, spectral calculation carried out by PARTISN volumes were omitted in the geometry model. code are supplemented by the MCNP CE and The same geometry definition, except hexagonal KENO-VI MG calculation due to only partial to cylindrical approximation, was used also in the validation of the SBJ_V2019T library and the comparative MCNP and KENO-VI calculations. part of cross-section processing dedicated only MCNP as well as KENO-VI was run with 10 to deterministic codes. The first value mil. histories in 1000 generation and 30 presented for each code is the infinite generations were skipped. multiplication factor kinf, instead of keff, due to The main part of the research is focused on reflective boundary conditions on geometric the validation of proposed cross-section model edges. The second value in case of MC processing scheme utilizing in-house prepared codes stands for the standard deviation of kinf.

20 JAKUB LÜLEY et al.

Table I. Comparison of fuel pin (FP) calculation

FP enrichment PARTISN MCNP CE KENO-VI MG 235 % of U kinf kinf σ kinf σ 1.6 1.06290 1.07071 0.00018 1.06392 0.00015 2.4 1.18125 1.18943 0.00019 1.18228 0.00019 3.6 1.27898 1.28595 0.00020 1.27894 0.00020 4.0 1.30090 1.30790 0.00020 1.30036 0.00018

4.0+3.35Gd2O3 0.39722 0.39874 0.00008 0.39647 0.00009 4.4 1.31954 1.32602 0.00021 1.31864 0.00019

Values of keff from the MC VVER- section scheme processing and the previous 440 benchmark calculation are presented in validation. The next six values represent the Table II. The first three values can be current capabilities of the cross-section considered as a reference due to their processing scheme and possibilities of independence on the demonstrated cross- future use.

Table II. Results of keff of the VVER-440 benchmark

Computational case keff σ MCNP ref [15] 1.06827 0.00005 KENO-VI 238g [16] 1.06343 0.00006 MCNP CE 1.06478 0.00002 MCNP MG 238gHM 1.05447 0.00006 MCNP MG 44gHM 1.05498 0.00008 MCNP MG 238g 1.05161 0.00002 MCNP MG 44g 1.05015 0.00002 MCNP MG 238gH 1.08597 0.00002 MCNP MG 238g HHM 1.08831 0.00006

The relative FA power distribution Fig. 3, Fig. 4 and Fig.5 respectively. MCNP MG calculated by the KENO-VI and MCNP in CE case is represented by the calculation with 44g and MG mode with their relative change from collapsed data, since it is the most perspective the reference MCNP calculation are presented in one for application in future analyses.

Fig. 3. Relative FA power distribution of KENO-VI (left) calculation and relative change in % from MCNP reference values (right).

21 PROCESSING OF THE MULTIGROUP CROSS-SECTIONS FOR MCNP CALCULATIONS

Fig. 4. Relative FA power distribution of MCNP CE (left) calculation and relative change in % from MCNP reference values (right).

Fig. 5. Relative FA power distribution of MCNP MG 44g (left) calculation and relative change in % from MCNP reference values (right).

D. Discussion in the results presented in Table 2 was obtained at the level of reference calculations. The Comparison of the fuel pin calculation demonstrates the validity of the SBJ_V2019T relative difference between the reference MCNP library for thermal applications and the fact and KENO-VI or MCNP CE is in both cases that the whole functionality of TRANSX code more than 300 pcm. The obtained difference has has been maintained after the implementation been caused by the different nuclear evaluated of CRSRD modules. Special attention should data used during libraries processing. Reference be given to the comparison of MG calculations MCNP calculation was carried out with the (PARTISN vs. KENO-VI, see Table 1) where library processed from ENDF/B-VI data, while the relative difference in almost all cases is less the KENO-VI library is based on ENDF/B- than 100 pcm. Only for calculation of the FP VII.0 and MCNP CE library is based on consisting Gd the relative difference was ENDF/B-VII.1 data. Therefore, it is more higher, but 479 pcm is still quite reasonable suitable to compare calculated values of MCNP due to comparison of very low keff. Relative MG with KENO-VI or MCNP CE values, at difference between PARTISN and MCNP CE least at the level of keff. calculation is also acceptable because relative The relative difference between MCNP difference in average is just 570 pcm and MG and MCNP CE calculations vary from 872 PARTISN calculations systematically pcm to 2031 pcm in absolute values. The underestimated the MCNP CE calculations. closest keff was obtained for cases where the Within the criticality calculation of the homogenized macro-constants were used with VVER-440 benchmark, the first inconsistency appropriate cell treatment (44gHM and

22 JAKUB LÜLEY et al.

238gHM). Relatively comparable values were codes, which is almost done. Although, the obtained from calculation with isotope-wise first result of benchmark calculation with constants (44g and 238g). Significant complex geometry identified relevant problems difference is in the calculated standard with the cross-section interpretation, quite deviation. While the computational time of good experience with TRANSX code itself and cases with homogenized macro-constants is experience with cross-section processing for around 10 % faster than in cases with micro- deterministic codes give us opportunity to constants, the obtained standard deviation is solve this problem in near future. The achieved more than three times higher. Therefore, all reduction of computational time about 30 % is promising benefits from a utilization of promising for next applications, but significant homogenized macro-constants is vanishing in difference between 238g and 44g was not this stage of development. Generally, observed. The following analysis will be utilization of MG constants shortened the therefore focused on this phenomenon and computational time about 30 %. The worst optimal coarse group structure will be sought. results were obtained for the cases with The performance of the SBJ_V2019T library materials which were all treated as infinitely fulfilled all requirements and its applicability at diluted. least within deterministic calculations was clearly demonstrated on pin spectral In case of calculation of relative FA calculations. Next step will be the final power distribution, inconsistent results were validation on the complex set of criticality obtained. While the relative change between safety benchmarks. KENO-VI or MCNP CE values and reference MCNP values is in maximum 3.1 % for ACKNOWLEDGEMENT KENO-VI and 6.8 % for MCNP CE, the relative FA power distribution of MCNP MG This study has been partially financially calculations compared with reference MCNP is supported by the Slovak Research unacceptable. The relative change varies from - Development Agency No. APVV-16-0288 and 42 % to 17 % which is suggesting that the MG by the Scientific Grant Agency of the Ministry constants are not properly prepared. Revision of Education of Slovak Republic No. VEGA of all input files and source code of the 1/0863/17. We would like to also acknowledge TRANSX/CRSRD code did not reveal any the ongoing support of B&J NUCLEAR ltd. formal or technical problem. But collected regarding to the code development and sharing information are pointing to different necessary information. interpretation of the absorption cross-section in TRANSX and MCNP. REFERENCES

III. CONCLUSIONS [1]. B. C. Kriedrowski, F. B. Brown, “Applications of Adjoint-Based Techniques in Continuous- This paper demonstrates the first result Energy Monte Carlo Criticality Calculations”. of cross-section processing scheme aimed to Joint International Conference on preparation of the problem oriented MG cross- Supercomputing in Nuclear Applications and section constants for MCNP calculation. The Monte Carlo 2013, Paris, France, 2013. first stage of research activities involved [2]. C.J. Werner(editor), “MCNP User‟s Manual - development of the new code able to prepare Code Version 6.2”, Los Alamos National MG constants for deterministic as well as MC Laboratory, report LA-UR-17-29981, 2017.

23 PROCESSING OF THE MULTIGROUP CROSS-SECTIONS FOR MCNP CALCULATIONS

[3]. Oak Ridge National Laboratory, “SCALE [10]. SCALE: A Comprehensive Modeling and Code System: Version 6.2.2.”, ORNL/TM- Simulation Suite for Nuclear Safety Analysis 2005/39, p. 2747, 2017. and Design, ORNL/TM-2005/39, Version [4]. J. C. Wagner, E. L. Redmont II, S. P. Palmtag, 6.1.3, Oak Ridge National Laboratory, Oak J. S. Hendricks, “MCNP: Multigroup/Adjoin Ridge, Tennessee, 2011. Capabilities”, Los Alamos National [11]. R.E. MacFarlane, “TRANSX 2.15: A Code for Laboratory, 1994. Interfacing MATXS Cross-Section Libraries to [5]. Š. Čerba, B. Vrban, J. Lüley, F. Osuský, V. Nuclear Transport Codes for Fusion Systems Nečas, “Development of Multi-Group XS Analysis”, Los Alamos National Laboratory, Library for VVER-440”, Proc Int. Conf. Los Alamos, 1992. Nuclear Energy for New Europe, Portorož, [12]. R. E. Alcouffe et al., “PARTISN: A Time- Slovenia, 2018. Dependent, Parallel Neutral Particle Transport [6]. M. B. Chadwick, M. Herman, P. Obložinský, Code System,” LA-UR-08-07258, 2008. et al., “ENDF/B-VII.1 Nuclear Data for [13]. K. L. Derstine: DIF3D 10.0, Argonne National Science and Technology: Cross Sections, Laboratory, Argonne, IL, 2011. Covariances, Fission Product Yields and [14]. B. Vrban, Š. Čerba, J. Lüley, F. Osuský, V. Decay Data” in Nuclear Data Sheets, vol. Nečas, J. Haščík, Proc Int. Conf. Nuclear (112), pp. 2887-2996, 2011. Energy for New Europe, Portorož, Slovenia, [7]. Š. Čerba, J. I. M. Damian, J. Lüley, B. Vrban, 2018. V. Nečas, “Comparison of thermal scattering [15]. V. Krýsl, P. Mikoláš, D. Sprinzl and J. Švarný processing options for S(aplha,beta) cards in “„Full-Core‟ VVER-440 benchmark MCNP”, Annals of Nuclear Energy, vol. 55, extension”, Proc. of the 24th Symposium of pp. 18-22, 2013. AER, Sochi, Russia, 2014. [8]. J. Keinert, M. Mattes, E. Sartori, “JEF-1 [16]. J. Lüley, B. Vrban, Š. Čerba, F. Osuský, V. scattering law data”, JEF Report 2/JEF/DOC Nečas, J. Haščík, “Assembly homogenization 41.2. Tec. Rep., IKE Stuttgart, 1984. [9]. J. I. Márquez Damián, J. R. Granada, D. C. technique for VVER-440 reactor multi-group Malaspina, “CAB models for water: A new calculations” ", Proc Int. Conf. Nuclear Energy evaluation of the thermal neutron scattering for New Europe, Portorož, Slovenia, 2018. laws for light and heavy water in ENDF-6 [17]. LANL, „MCNP - A General N - Particle format”, Annals of Nuclear Energy, vol. 65, Transport Code“, Los Alamos National pp. 280-289, 2014. Laboratoy, Los Alamos, 2003.

24 Nuclear Science and Technology, Vol.9, No. 2 (2019), pp. 25-30 Conceptual design of a small-pressurized water reactor using the AP1000 fuel assembly design

Van Khanh Hoanga, *, Viet Phu Trana, Van Thin Dinhb, Hoai Nam Tranc aInstitute for Nuclear Science and Technology, VINATOM, 179 Hoang Quoc Viet, Hanoi, Vietnam bFaculty of , Electric Power University, 235 Hoang Quoc Viet, Hanoi, Vietnam cInstitute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh city, Vietnam *E-mail: [email protected] (Received 01 November 2019, accepted 13 November 2019)

Abstract: This paper presents the conceptual design of a 300 MWt small modular reactor (SMR) using fuel assemblies of the AP1000 reactor. Numerical calculations have been performed to evaluate a proper active core size and core loading pattern using the SRAC code system and the JENDL-4.0 data library. The analysis showed that Doppler, moderator temperature, void, and power reactivity coefficients are all negative over the core lifetime. Semi-analytical thermal hydraulics analysis reveals acceptable radial and axial fuel element temperature profiles with significant safety margin of fuel and clad surface temperature. The minimum departure from nucleate boiling ratio (MDNBR) is also calculated. The results indicate that a cycle length of 2.22 years is achievable while satisfying the operation and safety-related design criteria with sufficient margins. Keywords: small modular reactor, AP1000 reactor, neutronic analysis, thermal hydraulics analysis.

I. INTRODUCTION number of principal reactors including advanced light water reactors, heavy water In recent years, the small modular reactors, and the generation IV reactors such as reactors (SMRs), new generation reactors high temperature gas cooled reactors (HTGRs), designed with an electrical output up to 300 liquid-metal, sodium and gas-cooled fast MWe, have been received increasing attention reactors (LMFR, SFR, GFR), and molten salt within the nuclear energy community due to a reactors (MSRs). number of advantages. Because of the small size, the SMRs require less capital investment About 50 SMR designs are being under and construction time compared to traditional developed world-wide for both electrical commercialized reactors, so that financial risks generation and non-electrical application could be reduced. The SMR designs can adopt such as desalination of seawater, district most of the advanced safety features of the heating, hydrogen production and other current technologies. One of the advantages is process heat application. Among those, three that the components of the reactor system can industrial demonstration SMRs are in be fabricated at factories and transported construction including CAREM (integral modularly to the plant site for installation. It is PWR with the output of 150 – 300 MWe) in also more flexible to choose locations for the Argentina, HTR-PM (HTGR) in China and SMRs than the traditional reactors, and KLT-40S (compact PWR for a floating therefore, it would be a suitable solution for a nuclear power plant) in Russia. The integral wide range of users and applications, for pressurized water reactor (IPWR) technology instance remote areas with smaller electricity is one of the major near term SMR designs, demand. The SMRs are being developed for a of which primary components are contained

©2019 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute CONCEPTUAL DESIGN OF A SMALL-PRESSURIZED WATER REACTOR USING THE AP1000 … in the reactor vessel. CAREM is an example for three-dimensional core burnup calculation of the IPWR technology. CAREM-25, a based on the macroscopic cross-section prototype reactor with the power of 27 MWe, interpolation. In order to confirm the core is under construction. Other designs of design criteria, thermal hydraulics analysis for IPWRs are SMART (Korea), NuScale (US), the hottest channel in the core was performed mPower (US), Westinghouse SMR (US). The to establish adequate heat removal capability of IPWR of the Westinghouse Electric the design. Analytical models and equations Company is based on a partial-height 17x17 are utilized for heat conduction within the fuel fuel assembly used in the AP1000 reactor. element and convection to the coolant [7]. This reactor utilizes passive safety systems Calculations of the MDNBR have also been and proven components from the AP1000 performed for the hottest channel using plant design. All primary components empirical correlation and W-3 correlation [8]. including the steam generator and the The design process consists of two steps as pressurizer are located inside the reactor follows: vessel [3]. a) Estimation of core size: The objective of In the present work, a conceptual this step is to determine the active fuel length design of a small PWR core with thermal and the number of fuel assemblies. Neutron output of 300 MWt based on the AP1000 transport calculations have been performed fuel assembly has been presented. Neutronics for an infinite core by imposing reflective analysis has been performed to determine the boundary condition in the assembly level core height, the number of fuel assemblies model. From the mass of uranium per and core configuration. The neutronic assembly, the required number of fuel analysis has been conducted using the SRAC assemblies for the core can be determined. In code system and the JENDL-4.0 library. this determination of core size, a four-year Thermal hydraulics analysis has been core lifetime, the average discharge burnup of conducted to investigate the safety 40 GWd/t with a single batch refueling parameters of the core. Reactivity scheme and a capacity factor of 1.0 were coefficients regarding the change in assumed. temperature of fuel, coolant, etc. were also b) Determination of core loading pattern: investigated to ensure the safety feature of Once the required number assemblies are the newly designed SMR core. achieved, a symmetrical arrangement of the II. CODE AND DESIGN PROCEDURE fuel assemblies in the active core zone is proposed for the initial core configuration. The The SRAC2006 code system [4] and the core loading pattern is developed for the core JENDL-4.0 nuclear data library [5] were used design to meet the design criteria. Fuel for performing the design process of the SMR assemblies with higher U-235 enrichment are core. For the core burnup calculation process is selected with a high priority, and located in the divided into two steps. Firstly, cell burnup peripheral core locations to achieve a uniform calculation using the PIJ module was power distribution and maximum fuel conducted to produce few-group burnup utilization. Finally, the core that meets the dependent homogenized macroscopic cross- specified performance requirements is selected sections. Secondly, the COREBN [6] was used for further analysis.

26 HOANG VAN KHANH et al.

B. Estimation of core size In order to determine the active fuel length, a three-dimensional infinite core model was developed based on an assembly level model with reflective boundary condition using the SRAC code system. The model consists of an active fuel zone and two reflector zones at the top and the bottom. The AP1000 fuel assembly with the highest U- 235 enrichment, i.e., 4.95 wt.%, was selected for the active fuel zone. Reflective boundary condition was assumed for peripheral core, and extrapolated boundary condition was set at the top and the bottom. Fig. 2 shows the Fig. 1. Locations of fuel rods, guide thimbles (GT) evolution of the infinite neutron and instrumentation thimble (IT) in a fuel assembly. multiplication factor (k-inf) at the begin of cycle (BOC) and the number of assemblies III. CORE DESIGN AND loaded into the core as functions of the active PERFORMANCE ANALYSIS fuel length. It can be seen that when the A. Core parameters active fuel length is less than 190 cm, the k- inf increases rapidly with the increase of the The Robust Fuel Assembly (RFA) active fuel length. The k-inf value is nearly design is used in the AP1000 reactor. The typical fuel assembly, with 17x17 array, unchanged with the active fuel length greater contain 264 fuel rods, 24 guide thimbles, and than 190 cm. Therefore, the active fuel 1 instrumentation thimble as shown in Fig. 1 length of 190 cm was selected, and the [3]. The SMR core is designed with a number of fuel assemblies in the core was thermal output of 300 MWt. The typical determined as 45 assemblies. uranium oxide fuel rods (UO2) with 2.35, 3.40, and 4.95 wt.% U-235 enrichments are used in the current SMR [9]. The main design parameters and targets for the SMR are specified in Table 1. In the AP1000 reactor design, in order to control excess reactivity and flatten power distribution, burnable absorber rods and integral fuel burnable absorbers are also used. In this study, only fuel assemblies without burnable absorber are considered to design a new core. For the control element assemblies (CEAs), Fig. 2. Variation of infinite multiplication factor the standard 24 finger Ag-In-Cd (AIC) rod and required number of assemblies with increasing control cluster assembly is exploited. active fuel length.

27 CONCEPTUAL DESIGN OF A SMALL-PRESSURIZED WATER REACTOR USING THE AP1000 …

Table I. Main design parameters and conditions (k-eff: effective neutron multiplication factor).

Fig. 3. Core configurations of the SMR (yellow, blue, and green blocks represent fuel assembly assemblies with 4.95, 3.40 and 2.35 wt.% U-235 enrichment, respectively. White block represents water filled position). a) Core model 1 b) Core model 2 c) Core model 3 D. Analysis of temperature coefficients and been calculated. A change in temperature of control element assemblies fuel material causes a change of neutron cross- In order to investigate the feedbacks due section, which is so-called the Doppler to changes of fuel and coolant temperatures, broadening effect, resulting in a change in the temperature reactivity coefficients have reactivity. Meanwhile, a change in coolant

28 HOANG VAN KHANH et al. temperature results in the change of moderator Fig. 4 shows the map of the control element density, which leads to a change in reactivity assemblies. The CEAs are composed of of the core. For safe operation, negative values shutdown banks (S) and regulating banks of the temperature reactivity coefficients are (R) located in the outer core and the inner desirable. In the numerical analysis, the core, respectively. The reactivity temperature of fuel and/or coolant was coefficients and CEAs performance of the increased by 50K. For the isothermal selected core model (Core 3) at cold zero coefficient, both temperature of fuel and power (CZP) and hot full power (HFP) coolant were increased by 50K. states are presented in Table 3. It can see The shutdown margins of the control that all coefficients are negative during the rod assemblies were analyzed to ensure that core lifetime. The CEAs of the core have the core has sufficient control rod worth. sufficient shutdown margin.

Table II. Summary of analysis results of the different core configurations.

Fig. 4. Locations of the CEAs in the active Table III. Temperature coefficients and CEAs core zone. performance of the final core design.

29 CONCEPTUAL DESIGN OF A SMALL-PRESSURIZED WATER REACTOR USING THE AP1000 …

IV. CONCLUSIONS Status, Technical Feasibility and Economics of Small Nuclear Reactors”, June 2011. Conceptual design calculation of a 300 [3]. Jun Liao, et al.. “Preliminary LOCA Analysis MWt SMR based on the fuel assemblies of the of the Westinghouse Small Modular Reactor AP1000 reactor has been carried out. The core Using the WCOBRA/TRAC-TF2 Thermal- consists of 45 fuel assemblies with an active Hydraulics Code”, Proceedings of ICAPP'12 core height of 190 cm could operate up to 2.22 Chicago, USA, June 24-28, 2012. years without refueling. The Doppler and [4]. Keisuke Okumura, Teruhiko Kugo, Kunio moderator temperature coefficients are Kaneko and Keichiro Tsuchihashi. negative throughout the core lifetime. “SRAC2006: A Comprehensive Neutronics Maximum values of fuel, cladding and coolant Calculation Code System”, JAEA-Data/Code temperatures are within the design limits. The 2007-004, 2007. DNBR remains greater than 3.71 for the active [5]. Keiichi Shibata, et al.. “JENDL-4.0: A New core region. The analysis results represent that Library for Nuclear Science and Engineering, the final core design satisfies all the design Journal of Nuclear Science and Technology”, criteria with significant safety margins. vol. 48, No. 1, p. 1-30, 2011.

ACKNOWLEDGEMENTS [6]. Keisuke Okumura. “COREBN: A Core Burn- up Calculation Module for SRAC2006”, This research is funded by Ministry of JAEA-Data/Code 2007-003, 2007. Science and Technology (MOST) of Vietnam [7]. James J. Duderstadt Louis J. Hamilton. under grant number ĐTCB. 02/19/VKHKTHN. " Analysis", John Wiley & Sons, Inc., 1976. REFERENCES [8]. Tong L.S. “Prediction of Departure from [1]. International Atomic Energy. “Advances in Nucleate Boiling for an Axially Non-Uniform Small Modular Reactor Technology Heat Flux Distribution”. Journal of Nuclear Developments, A Supplement to: IAEA Energy, vol. 21, p. 241-248, 1967. Advanced Reactors Information System [9]. U.S. Nuclear Regulatory Commission (NRC), (ARIS)”, 2018. “Westinghouse AP1000 Design Control [2]. Organisation for Economic Co-operation and Documentation (DCD)”, Rev. 19, Chapter 4, Development, Nuclear Energy Agency. “Current Westinghouse Electric Company, 2011.

30 Nuclear Science and Technology, Vol.9, No. 2 (2019), pp. 31-36 Low-energy experiments at the S3 spectrometer

S. Franchoo IPN, 91406 Orsay, France E-mail: [email protected] (Received 08 November 2019, accepted 19 November 2019)

Abstract: With the advent of the Spiral-2 linear accelerator and the associated S3 spectrometer at the Ganil laboratory in France, new realms of intermediate-mass N=Z and very heavy nuclei will soon become available for research in nuclear structure. After their production and selection in the spectrometer, the ions of interest will be stopped in a buffer gas, neutralised, resonantly re-ionised, cooled and bunched. This will bring us in an adequate position to perform laser spectroscopy, mass measurements and decay spectroscopy of their ground and isomeric states. In this contribution we report on the ongoing commissioning of the detector set-up. Keywords: New facilities, laser spectroscopy, mass spectrometry, nuclear structure

I. INTRODUCTION above and below the Fermi energy in a single description [4]. Recent advances in nuclear theory are bringing ever heavier nuclei within reach of Experimentally, proton-induced fission ab-initio techniques. The quantum many-body at Isolde and Triumf gives access to the calculations naturally include three-nucleon neutron-rich side of the nuclear chart. The forces, emphasising their influence for instance particles diffuse out of the target as neutral in the Gamow-Teller strength of 100Sn [1]. atoms, they are ionised, extracted at low energy Large-scale shell-model calculations are and eventually post-accelerated. At NSCL and carried out in valence spaces that span Riken, fragmentation at high energy covers a complete shells and beyond, taking into broad spectrum of nuclei that are available for account correlations that previously had to be multinucleon transfer and knock-out reactions. left out. These in turn induce quadrupole In-flight spectroscopy of the emitted radiation deformation throughout the nuclear chart, relies on the development of multidetector affecting even the immediate vicinities of arrays that provide the necessary granularity doubly magic nuclei such as 78Ni [2]. The for event reconstruction. Fusion-evaporation Monte-Carlo shell model puts in place a reactions favour products rich in protons, framework for exploring the sudden quantum recoiling into a spectrometer at threshold phase transitions that are observed in exotic energies but setting aside for FLNR and S3 a isotopes. Striving to unite single-particle and range of experiments that would be difficult to collective behaviours, it stresses the role of the perform elsewhere. central and tensor forces in the shell evolution The S3 spectrometer for exotic of magic and near-magic nuclei such as radioactive ion beams is currently being zirconium, tin and mercury [3]. Reaction installed at the Ganil laboratory in France and theory increasingly embraces structure models. shall become operational in 2023. It offers By replacing both the optical and the shell- novel opportunies to investigate isotopes model potential by the nucleon self-energy, the produced in heavy-ion fusion-evaporation dispersive optical model links energy states reactions, in particular for channels with low

©2019 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute LOW-ENERGY EXPERIMENTS AT THE S3 SPECTROMETER cross sections at the proton dripline and near between the nucleus and its surrounding the upper end of the nuclear chart. An approach electrons, which is recorded by laser based on laser spectroscopy in a swiftly spectroscopy. The masses, spins and decay expanding gas jet is adopted for the detection properties of their ground states and isomeric strategy, called Radioactive Elements in a Gas levels will be constrained by complementary jet for Laser Ionisation and Spectroscopy measurements on the collected ions by means (Reglis). It shall be coupled to a mass of time-of-flight mass spectrometry and decay spectrometer that is built around a linear ion spectroscopy. trap, referred to as Piège à Ions Linéaire du B. The S3 spectrometer Ganil pour la Résolution des Isobares et la mesure de Masse (Pilgrim). A new superconducting linear accelerator has been constructed at Ganil, II. REPORT comprising 26 accelerating cavities housed in 19 cryomodules [5]. It will be able to deliver A. Physics scope stable ion beams with intensities that are ten The Reglis experiment focusses on two times larger than what is presently available. objectives, the isotopes near the N=Z line from With a mass-to-charge ratio of 3, currents of 3 Z=40 onwards and the very heavy nuclei with pµA for 40Ar, 2 pµA for 40Ca and 1 pµA for Z≥89. The first region allows to cover a broad 48Ca and 58Ni at energies up to 14.5 MeV per range of physics issues that spans from nucleon are projected. With a later upgrade of collectivity and deformation over spin-aligned the injector to a mass-to-charge ratio of 7, coupling schemes in nuclei such as 90Rh and heavy beams up to uranium will become 94Ag. Also the balance between isoscalar and available. isovector pairing interactions in 98In and the These primary beams will make it evolution of single-particle structures in 99In possible to study fusion-evaporation reactions and 101Sn attracts much interest. We shall shed with cross sections down to picobarns, yielding light on quadrupole moments in the tin chain neutron-deficient nuclei near the N=Z line and and investigate novel decay modes such as isotopes of very heavy elements. They will be super-allowed α-decay in 112Ba-108Xe-104Te and separated from the intense background in the cluster radioactivity in 114,112Ba. The S3 recoil spectrometer [6]. The spectrometer measurement of masses will give access to consists of two stages, the first one of which is binding energies and the role of the Wigner a momentum achromat that lets the reaction term. Among the heavy elements, we shall products pass through while the primary beam focus on the actinides. This includes the is suppressed with a factor of 103. development of the N=126 shell closure in 210- Subsequently the ions of interest are selected in 213Ac and 213-215Th, the appearance of octupole a mass separator with a resolution of 300. The deformation in 225-228U, and the possible combination of the momentum achromat and emergence of a superheavy spherical shell gap the mass separator results in a final rejection as seen through K-isomers in 249-252Fm and 252- power of 1013. An angular acceptance of ±50 254No. mrad, a magnetic rigidity acceptance of ±7 % The mean-square charge radii, magnetic and a charge-state acceptance of ±10 % are dipole and electric quadrupole moments can be aimed at. This means two charge states on extracted from the hyperfine interaction either side of the centrally chosen charge state

32 S. FRANCHOO will be transmitted. A high-resolution mode diameter. The 254No isotopes arrive with a that separates the charge states as well as a mean energy of 37 MeV. In this mass region converging mode with a better transport the ion rate amounts to 1 particle per second efficiency at the price of a wider beam spot are only but the beam would be almost 100% pure. proposed. To illustrate with an example, for the For the 116Sn(40Ar,4n)152Er reaction at 167 208Pb(48Ca,2n)254No reaction at 217 MeV a MeV, on the other hand, the expected rate transmission efficiency of 56% is estimated for reaches 8.6 104 particles per second yet with a 5 charge states within a circular area of 50 mm purity of 1% only.

Fig. 1. Drawing of the Reglis gas cell. The S3 beam arrives from the left and the gas enters from below (orange). The stopped particles (red) are evacuated on the top right side

C. Principle of the detector quadrupoles (RFQ), in which their emittance is greatly reduced before being fed into various To take the best advantage of the experimental set-ups. At the same time, we capabilities of the accelerator and the shall be able to instantaneously perform laser spectrometer, a detection set-up with high spectroscopy in the gas jet by scanning the efficiency is in order. The ions should be made resonance wavelength across the hyperfine available for several measurement set-ups so structure. This is possible because the low they should be transferable as a beam at low density in the uniform jet keeps pressure emittance. Moreover and in spite of the 1013 broadening small such that sufficient resolution rejection power of S3, some secondary beams can be achieved. will still be significantly contaminated by their A±1 neighbours and additional selectivity is D. Intrajet laser spectroscopy desirable. The thickness of the entrance window is We therefore aim to stop the reaction of the utmost importance as some of the products in a buffer gas at high pressure [7]. secondary beams carry energies below as little They will be neutralised through collisions as 1 MeV per nucleon. For critical cases we with the gas atoms, extracted from the gas cell can afford not more than a couple of in a well-defined cold and supersonic jet and micrometers of material. On the other hand the resonantly re-ionised by laser light. They will window should span a diameter of 50 mm and then be sent through a series of radiofrequency remain rigid enough to withstand the pressure

33 LOW-ENERGY EXPERIMENTS AT THE S3 SPECTROMETER difference with the high vacuum inside S3. We latter providing higher power levels. From a choose a titanium foil that is supported by a proof-of-principle experiment that was honeycomb grid, both fused together by performed on 214-215At an overall efficiency of friction stir welding. 10% and a selectivity of 3000 appears within reach [9]. The FWHM resolution of the For the buffer gas a compromise is hyperfine spectrum came down to 400 MHz sought between the stopping power in the gas during this measurement, but at S3 we intend cell and the load on the pumping system. We to achieve 100 MHz, which will be essentially use argon at 200 to 500 mbar purified to the due to the gas temperature, the jet divergence part-per-billion level. Special care is taken for and the laser linewidth. This number can be the mechanical design of the cell so we obtain compared to the natural linewidth of the atomic a gas flow that is as laminar as possible, transition of 4 MHz but remains amply avoiding turbulences that would trap the sufficient to probe the hyperfine structures, the particles. The flow transports the radioactive splittings of which typically amount to 300 particles to the exit hole with an evacuation MHz in the actinides. time of several hundreds of milliseconds, setting a limit for the shortest lifetimes we can E. Beam manipulation and mass efficiently measure. The exit hole takes the spectrometry shape of a Laval nozzle. The thermodynamic The ions that emerge from the properties of the jet are defined by the supersonic jet will be captured in a S-RFQ. background pressure in the experimental The name derives from its geometrical shape, chamber as well as the contour of the nozzle, the purpose of which is to move the ions the machining of which demands a dedicated vertically out of the axis along which the effort with a precision of 5 µm. Several nozzles broadband laser is sent in. A quadrupole mass were tested, the latest design producing a filter (QMF) with a resolving power of 100 homogeneous supersonic jet of Mach 8 at a further cleans the beam. It is followed by a temperature of 18 K over a distance of 25 mm. RFQ-buncher, which is filled with 10-2 to 10-3 For development purposes the jet was mbar of helium and cools and prepares the visualised with Planar Laser-Induced beam for injection into a drift tube. The tube Fluorescence and modelled with the Comsol lifts the ions to 3 kV and transfers them to the and Ansys flow codes [8]. Pilgrim multireflection time-of-flight mass Laser ionisation happens in two or more spectrometer (MR-tof-MS) [10]. The latter steps. The last step may not be resonant and basically comprises a linear trap with an simply allow one of the atomic electrons to electrostatic mirror on either end, between reach the continuum. One of the resonant steps which the particles travel back and forth until is used for probing the hyperfine structure and they are spatially separated from isobaric requires a narrow bandwidth. It irradiates the contaminants because of their mass gas jet perpendicularly and is expanded into a differences. A resolution of 105 can be laser sheet to cover as large a section of the jet achieved for an input emittance of 10 as possible. It is planned to implement a π.mm.mrad, corresponding to a flight path of system of both solid-state as well as dye lasers some hundreds of meters in 10 ms. For a half- at high repetition rate, the former being life of 100 ms, Pilgrim is expected to attain a relatively free of safety constraints and the sensitivity of one particle per ten seconds.

34 S. FRANCHOO

While the transmission through S3 can the next two years. Stable beams will be be evaluated at 50% on average, the produced by heating a metallic filament that is thermalisation, neutralisation and transport of mounted inside the gas cell. In order to the particles in the gas cell are estimated at mimimise adverse effects on the gas flow, the more than 25%. The rate of laser ionisation heat excess is removed by water cooling. One depends on the availability of a suitable of the first elements to extract will be erbium, scheme and can be taken at 50%, the capture which is the chemical homologue of fermium. efficiency in the RFQ sequence at 80%. The Since laser-ionisation schemes are poorly overall efficiency of our set-up before injection known for the actinides we are interested in at into Pilgrim would then reach at least 5%. S3, they will be developed from better studied Reglis and Pilgrim are presently transitions in the lanthanides. According to the installed at the LPC laboratory nearby Ganil in current timeline, S3 should become available Caen, where they can be commissioned over for experiments in 2023.

Fig. 2. The Reglis and Pilgrim set-ups as they are presently installed at the LPC laboratory in Caen for commissioning

F. Decay spectroscopy electronics with automatic gain switching. The ions that emerge from Pilgrim will Particular attention will be paid to combining a be implanted in a thin carbon foil that is high efficiency and resolution with a low surrounded by a small but segmented silicon energy threshold. Two germanium detectors array. Simple ion counting as well as decay can be integrated in a compact geometry for spectroscopy through electron and α-radiation registering coincident γ-rays. The addition of a will be handled by a new generation of tape station for β-decay studies, which is

35 LOW-ENERGY EXPERIMENTS AT THE S3 SPECTROMETER helpful for those physics cases at N=Z, is also Institut national de physique nucléaire et de foreseen. physique des particules for continuous support.

III. CONCLUSIONS REFERENCES

The new S3 spectrometer at Ganil shall [1]. P. Gysbers et al., Discrepancy between unlock new N=Z nuclei and very heavy experimental and theoretical β-decay rates isotopes for experimental research. Because of resolved from first principles. Nature Physics, the extraordinary low cross sections to produce in print, 2019. these nuclei, a dedicated detector set-up that is [2]. F. Nowacki et al., Shape Coexistence in 78Ni sensitive to count rates of a few particles per as the Portal to the Fifth Island of Inversion. second has been constructed and is now being Physical Review Letters 117, 272501 (2016). commissioned. The Reglis gas cell provides the [3]. T. Togashi et al., Quantum Phase Transition in base for laser spectroscopy in a supersonic jet, the Shape of Zr isotopes. Physical Review probing the hyperfine structure to yield charge Letters 117, 172502, 2016. radii and electromagnetic moments. The [4]. M. Mahzoon et al., Forging the Link between Pilgrim trap is properly suited for mass Nuclear Reactions and Nuclear Structure. measurements, recording the time of flight as Physical Review Letters 112, 162503 (2014). the ion path is reflected between two electrostatic mirrors. In order to overcome the [5]. Ghribi et al., Status of the Spiral-2 linac cryogenic system. Cryogenics 85, 44, 2017. slow evacuation time of the gas cell, which constitutes the main limitation of our [6]. F. Déchery et al., The Super Separator experiment when accessing the shortest lived Spectrometer S3 and the associated detection isotopes, the development of a smaller gas systems. Nuclear Instruments and Methods B 376, 125, 2016. volume that incorporates electrical radiofrequency fields is being considered. [7]. R. Ferrer et al., In-gas laser ionization and spectroscopy experiments at the ACKNOWLEDGMENTS Superconducting Separator Spectrometer: Conceptual studies and preliminary design. The Reglis and Pilgrim experiments Nuclear Instruments and Methods in Physics have been conceived and built and are since Research B 317, 570, 2013. operated by a collaboration of the Ganil, IPN- [8]. Zadvornaya et al., Characterisation of Orsay, Irfu-Saclay, and LPC-Caen laboratories Supersonic Gas Jets for High-Resolution and the universities of Jyväskylä, Leuven, and Laser-Ionisation Spectroscopy of Heavy Mainz. We are grateful to the many Elements. Physical Review X 8, 041008, 2018. administrators, technicians, engineers, and [9]. R. Ferrer et al., Towards high-resolution laser physicists who have made the project possible. ionization spectroscopy of the heaviest We thank the Programme blanc of the Agence elements in supersonic gas jet expansion. national de recherche for its essential part in Nature Communications 8, 14520, 2017. the funding of Reglis and the Brix network [10]. P. Chauveau et al., Pilgrim, a Multi-Reflection within the Interuniversity Attraction Poles of Time-of-Flight Mass Spectrometer for Spiral2- the Belgian Science Policy Office for its S3 at Ganil. Nuclear Instruments and Methods contribution to Pilgrim. We are indebted to the in Physics Research B 376, 211, 2016.

36 Nuclear Science and Technology, Vol.9, No. 2 (2019), pp. 37-44 Dosimetric characteristics of 6 MV photons from TrueBeam STx medical linear accelerator: simulation and experimental data

N. D. Ton1, B. D. Linh1,*, Q.T. Pham2 1 Institute for Nuclear Science and Technology, 179 Hoang Quoc Viet, Cau Giay, Ha Noi 2 Department of Radiation Oncology and , 108 Military Central Hospital, Ha Noi *Corresponding author, Email: [email protected] (Received 17 October 2019, accepted 14 November 2019)

Abstract: A TrueBeam STx is one of the most technologically advanced linear accelerators for radiotherapy and radiosurgery. The Monte Carlo simulation widely used in many applications in various fields such as , astrophysics, particle physics, and medicine. The Geant4/GATE Monte Carlo toolkit is developed for the simulation in imaging diagnostics, , radiotherapy, and radiation biology to more accurately predict beam radiation dosimetry. In this work, we present the simulation results of the dosimetric characteristics of a 6 MV photon beam of TrueBeam STx medical LINAC using Monte Carlo Geant4/GATE. The percentage depth dose (PDD), central axis depth dose (Profile) have been simulated and compared with those measured in a water phantom for field sizes 10×10 cm2 via the gamma-index method. These results will permit to check calculation data given by the treatment planning system. Keywords: Geant4/GATE, Radiotherapy, TrueBeam STx, Phase Space file, PDD, Profile.

I. INTRODUCTION anatomical sites, where the electron transport approximations from analytic or semi-analytic The characteristics of the photon beam dose calculation algorithms are not accurate as Percentage Depth Dose and Profile in a enough. The long computation time becomes medical linear accelerator (Linac) are essential a reason to hinder MC simulation from for building the beam model and guarantee the widespread use in the routine clinical practice dose distribution for input into Treatment [2-4]. However, due to industrial secrets, this Planning System (TPS) [1]. TrueBeam STx is information is sometimes unavailable to the one of the latest generation Linac of Varian It general medical physics community. has different characteristics with the previous TrueBeam STx Linac of Varian Medical Linac such as two modes of photon Flattening Systems is an example. Instead, Phase Space Filter (FF) and Flattening Filter Free (FFF). files (PhS) for each of the beam have been TrueBeam STx can be used for many forms of made available to the Varian TrueBeam STx advanced treatment techniques including users [5]. Although the accuracy of these PhS image-guided radiotherapy (IGRT), intensity- among different TrueBeam STx installations modulated radiotherapy (IMRT) and RapidArc was proven [6-8], it is advisable to validate radiotherapy technology. them by comparing the dose distributions Monte Carlo (MC) method is a produce in the MC simulation with popular method to estimate accurate dose experimental measurements performed on a distributions for clinical beams in TrueBeam STx Linac. Besides, the radiotherapy. Especially, the method is verification of the geometry in this machine is important for planning heterogeneous also required.

©2019 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute DOSIMETRIC CHARACTERISTICS OF 6 MV PHOTONS FROM TRUEBEAM STX …

Geant4/GATE MC code is one of the imaging and Cone Beam computed most popular MC open-source applied tomography (CBCT) capability. One of the key nowadays in medical physics, especially the features is the availability of two modes of radiotherapy field [9, 10]. Much scientific photon beams: FF (Flattening Filter) and FFF research has been carried out to accurately (Flattening Filter Free). FFF beams delivered simulate complex geometry in order to find an with ―conventional‖ medical linear accelerators overall reasonable agreement between have the conical flattening filter removed and calculated and experimental doses for Linac replaced by a thin copper foil (about 1mm [11-14]. In Vietnam, this study is the first one thick). This foil is the same for all energies. to assess the capabilities of Geant4/GATE in Truebeam STx having 6, 8, 10, 15 MV the prediction of characteristics of the standard FF and 6 MV, 10 MV with the new TrueBeam STx Linac 6 MV photon beam. FFF beam for photon beams. FFF beams offer a maximum high dose rate of 1400 MU/min for The aim of this work is to evaluate the 6 MV FFF and 2400 MU/min for 10 MV FFF, accuracy of Geant4/GATE in simulating respectively [15-17]. characteristics of 6 MV photons from TrueBeam STx Linac. In order to establish this B. The Phase Space files goal, PDD and Profile were investigated by The TrueBeam STx Phase Space files Geant4/GATE with Varian PhS and were for 6 MV FF with the International Atomic measured by a Blue Phantom system (The Blue Energy Agency (IAEA) format [18] have been Phantom 2, CC013 ionization chamber, made by Varian using the Geant4 MC toolkit RAZOR chamber, and electronic equipment). [19]. These files were verified as radiation Simulations and experimental results were sources to allow users to perform accurate compared in specifications of dose difference simulations, which were recorded immediately relative to the maximum dose of the upstream of the movable at a distance of 73.3 measurement, we explain the details of this in cm from the isocenter. Therefore, users are section III. The gamma index was also required to code into their MC application only performed using a 2%/2mm standard of dose- the geometrical details of the components of difference (DD) and distance-to-agreement the treatment head below the PhS surface, (DTA). including the jaws and MLC. Each PhS file of 9 II. MATERIALS AND METHODS 6 MV FF beam contains 10 original histories and 5×107 particles. The initial source is an A. The Varian TrueBeam STx electron beam. The energy spectrum of this TrueBeam STx with High Definition source is non-Gaussian with a peak at 6.13 120-MLC (Multi-Leaf Collimator) has at MeV and a tail extending up to 6.35 MeV. In central 32 leaf pairs of 2.5 mm and 28 leaf order to speed up the accelerator head pairs of 5 mm leaf thickness to achieve high simulation, PhS file stored three types of precise target conformation and minimize the particles including photon, electron, positron. penumbra effect, which can be used for The details of the header of each file are Stereotactic Radiosurgery (SRS), Stereotactic reported [5]. The simulation has been used not (SRT) and Stereotactic only photon but also electron and positron in Body Radiation Therapy (SBRT). The PhS. This allows considering electron and TrueBeam STx is also equipped with kV/MV positron contaminations from the photon beam.

38 N. D. TON, B. D. LINH, Q.T. PHAM

C. Experimental measurements maximum dose (1.5 cm) scans were made for FF 6 MV with 10×10 cm2 field size. To avoid The Blue Phantom 2 in a large any ripple effect in the measurement, a PDD 48×48×48 cm3 water phantom a three scan was started from the bottom of the tank dimensions (3D) scanning system was used moving toward the surface of the water. Data [20]. Fig. 1 was shown actually a photo of Blue processing and analysis were performed using Phantom 2 under TrueBeam STx head in the IBA’s OmniPro Accept with application experiment. The scan in water was acquired at setting for a geometric mean smoothing the same source-to-surface distance (SSD) = function with a value of 3 mm. Appropriate 100 cm. Beam scanning and collecting data stopping power ratio factors were used for were performed in accordance with electron ionization values to PDD values professional guidelines, such as AAPM Task conversion. Measured PDD curve was Group [21, 22]. The ionization chamber CC13 compared to Golden Beam Data (GBD) and and RAZOR chamber [20] were used for beam the reproducibility of the measurement data. data collection and dosimetric measurement GBD was provided by Varian, which often use following reference [22] recommendation. for commissioning measurements. A CC13 is a cylindrical ionization chamber with comparison of the PDD with the Gamma Index a sensitive volume of about 0.13 cm3 and an criteria of 2%/2 mm yielded a gamma pass rate inner diameter of the outer electrode about 6.0 of 97%. Therefore, the accuracy of this mm. The effective point offset in the measurement can be considered to be within measurement of this chamber is 1.8 mm for 6, 2%/2 mm. 8 MV and 2 mm for 10, 15 MV photon beams. The RAZOR is a compact chamber for D. Geant4/GATE measurements of small fields and of ranges For many years, the Geant4-based with high dose gradients. The RAZOR has GATE MC code has been developed as an sensitive volume and the radius cavity are 0.01 open-source MC program for nuclear medicine cm3 and 1.0 mm, respectively. simulation, with a focus on PET and SPECT imaging [23]. This toolkit allows creating a simulation on the basis of simple macro- command instead of handling tedious C++ syntaxes of Geant4 code. It helps a quicker learning phase for new users and makes a small size of the GATE work folder easy to share within the community. Details about the GATE capabilities and validation are presented elsewhere [23-25]. A new GATE v8.2 was used for this simulation [26]. 6 Varian PhS files of smaller Fig.1. Photograph of Blue Phantom (IBA, size (2 GBs) were imported into GATE and Germany) scanning water phantom below used for the downstream of the jaws as a TrueBeam STx head in the experimental setup. source in the Linac. These individual files were Measurements include PDD along the then concatenated to one large PhS file. After central axis and crossline profile at the depth of exiting the PhS plane, the particle passes

39 DOSIMETRIC CHARACTERISTICS OF 6 MV PHOTONS FROM TRUEBEAM STX … through the second collimator as the Y and X final assessment of the dose distribution jaws and MLC. Data for the material and quality. For the regions of significant geometry of the Linac components were disagreement, the Gamma Index value is obtained from the TrueBeam STx Monte Carlo greater than unity that will be apparent relative. package [19]. The gamma pass rate was defined as a Geant4 Electromagnetic physics package quotient of the passing points and all points. 3 (G4EmStandardPhysics_option3) was used For the global Gamma Index passing criteria of for precise dose calculations and particle- 2%/2 mm, a good agreement, a high matter interactions or radiation transport in the agreement, and a reasonable agreement simulation. G4EmStandardPhysics_option3 between the measured and simulated dose designed for any applications required higher distribution were observed with over 99%, accuracy of electrons, hadrons, and ion 95% and 90% of the points of PDD and cross- tracking without a magnetic field. The package plane profile, respectively. has been presented in Poon and Arce at al. for radiotherapy application [27, 28] and III. RESULTS AND DISCUSSION recommended in Varian documents [19]. The 6 PhS files stored 3×108 photon, range cuts for gamma, electron, and positron electron, and positron particles, which have are fixed to 0.1 mm in a water phantom, 1 mm been simulated. Approximately 6×109 particle in the world volume, and 10 mm in TrueBeam histories from 6 PhS files were performed such material volume, respectively. that the statistical uncertainty in the dose for A virtual water phantom with 30×30×30 the voxels inside the radiation field was less cm3 volume was installed at an SSD equal to than 0.2% at the depth of maximum water 100 cm as the measurement. It is used for the phantom. The simulation results take into MC estimation of the absorbed dose account the electron and positron distribution. Voxel size was set to 3×3×3 mm2 contamination in the photon beam. for a field size of 10×10 cm2. A. PDD curve E. Gamma Index method In this paper, the quantity PDD defined Data analysis was based on comparisons as the quotient, expressed as a percentage, of between GATE simulations and measurements the absorbed dose at a predefined depth (dx) to using the Gamma Index method [29], which the absorbed maximum dose at a fixed became a ―gold standard‖ method for the reference depth of d0 = 1.5 cm, along the comparison in dose distribution [13]. This central axis of the beam. Fig. 2 shows the method was conducted with a percentage dose comparison between measured and GATE difference (ΔD) criteria and distance to estimated PDD with SSD = 100 cm for a agreement (DTA) of of 1%/1mm and 10×10 cm2 field for FF 6 MV photon beam and 2%/2mm. If the Gamma Index value is greater the Gamma Index distribution. The maximum than unity, it indicates a position where the dose was detected at 1.5 cm of depth in both agreement between the measured and measurement and simulation. The statistical simulated dose maps do not meet the uncertainty of bins scoring PDD was between predefined criteria. Passing criteria were met if 0.02% to 0.04% and all bins scoring more than the gamma index was no larger than 1. An 50% of the maximum absorbed dose was important feature of this method is that the 0.02% to 0.2%. The distribution of Gamma

40 N. D. TON, B. D. LINH, Q.T. PHAM

Index is shown in Fig. 2, there is only one dose of the measurement as equation 1. This point was larger than 1. The evaluation using discrepancy is never greater than 2%.mm, the Gamma Index with 2%/2 mm criteria for 2%.

PDD obtained was greater than 98%. There is a | | (1) good agreement between the computed and measured PDD. Where, D1 and D2 are the value of

Fig. 3 shows the percentage dose simulated and measured, respectively, D0 is the difference of the PDD relative to the maximum maximum dose of the measurement.

Fig.2: Comparison of measured (black line) and GATE simulation estimated (red circle) PDD of TrueBeam STx FF 6 MV photon beam with SSD =100 cm for 10×10 cm2 field. The distribution of gamma index points of PDD (blue plus).

Fig. 3: Percentage dose difference between the simulated and measured PDD relative to the maximum dose of the measurement.

41 DOSIMETRIC CHARACTERISTICS OF 6 MV PHOTONS FROM TRUEBEAM STX …

Fig. 4: Comparison of measured (black line) and GATE simulation estimated (red circle) cross-plane profile at 1.5 cm for TrueBeam STx FF 6 MV photon beam for 10×10 cm2 field. The distribution of gamma index points of the cross-plane profile (blue plus).

Fig. 5: Percentage dose difference between the simulated and measured cross-plane profile at 1.5 cm of depth relative to the maximum dose of the measurement.

B. Cross-plane Profile criteria of 1%/1 mm. Although the gamma indices in the penumbra region (at ±5 cm) are The comparison of profile at 1.5 cm in bigger than those in the inside field, there is the water tank between the simulation and still a reasonable agreement between measure is shown in Fig. 4. The statistical computed and measured the cross-plane uncertainty of the simulation is in the range of profile at 1.5 cm depth. 0.02% to 0.2%. For the Gamma Index criteria of 2%/2 mm, the distribution is presented in For cross-plane profiles inside the field Fig. 4 and the average pass rates for the cross- region, the percentage dose difference is less plane profile was ≥ 94%. This agreement than 1.5%. The result of the percentage dose notably worsens with the more stringent difference is shown in Fig. 5. The differences

42 N. D. TON, B. D. LINH, Q.T. PHAM in the penumbra region (at ±5 cm) are bigger for clinical radiotherapy treatment planning,‖ than those in the inside field. These Med. Phys. 25, 1773–1829, 1998. differences probably represent the number of [2]. N. Reynaert et al., ―Monte Carlo treatment simulated particles in which less number of planning for photon and electron beams,‖ simulated particles will be found in the Radiation Physics and Chemistry 76, 643–686, penumbra and result in a big statistical 2007.

fluctuations in MC simulation and a big [3]. E. Spezi and G. Lewis, ―An overview of difference relative [30, 31]. Monte Carlo treatment planning for radiotherapy,‖ Radiation Protection Dosimetry IV. CONCLUSIONS 131, 123–129, 2008.

The aim of this work is to validate the [4]. O. Chibani and C.-M. Ma, ―On the potential application Geant4/GATE software discrepancies between Monte Carlo dose for the Varian TrueBeam STx. In this study, calculations and measurements for the 18 MV the characteristics of 6 MV photons of Varian photon beam,‖ Med. Phys. 34, 1206– 1216, 2007. TrueBeam STx include PDD and crossline profile, which was simulated based on [5]. M. Constantin et al., ―Modeling the TrueBeam Geant4/GATE using Varian PhS file, and linac using a CAD to Geant4 geometry Varian manufacturer’s information. A PDD implementation: Dose and IAEA-compliant curve and beam profile for 10×10 cm2 field Phase Space calculations,‖ Medical Physics size in a water phantom using Geant4/GATE 38, 4018–4024, 2011. simulation show a good agreement with [6]. C. Glide-Hurst et al., ―Commissioning of the measured dose data for FF 6 MV photon beam Varian TrueBeam linear accelerator: A multi- produced by the Linac. The percentage dose institutional study,‖ Medical Physics 40, difference and Gamma Index method were 031719, 2013. used for comparison. The agreement between [7]. G. P. Beyer, ―Commissioning measurements simulations and experimental data proved that for photon beam data on three TrueBeam Geant4/GATE can be used for accurate Monte linear accelerators, and comparison with Carlo dose estimation. Trilogy and Clinac 2100 linear accelerators,‖ J. Appl. Clin. Med. Phys. 14, 273–288, 2013. ACKNOWLEDGMENT [8]. Rodrigues et al., ―A Monte Carlo simulation The authors would like to thank framework for electron beam dose calculations VINATOM for the support under the grant using Varian Phase Space files for TrueBeam Linacs‖, Medical Physics 42, 2389-2403, number CS/19/04-02, MSc. Nguyen Ngoc 2015. Quynh at INST for his kind help in the run of Geant4/GATE and all medical physicist at [9]. S. Agostinelli et al., ―Geant4—a simulation Department of Radiation Oncology and toolkit‖, Nucl. Instr. and Meth. in Phys. Res. A Radiosurgery, 108 Military Central Hospital. 506, 250, 2003.

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44 Nuclear Science and Technology, Vol.9, No. 2 (2019), pp. 45-51

Conceptual designing of a slow positron beam system using Simion simulation program

Cao Thanh Long, Huynh Dong Phuong, Nguyen Trung Hieu, Tran Quoc Dung Center for Nuclear Techniques, 217 Nguyen Trai Street, District 1, Hochiminh City Email: [email protected], [email protected], [email protected], [email protected] (Received 30 October 2019, accepted 19 November 2019)

Abstract: The slow positron beam system is an important device in the study of positron physics and techniques, especially in materials research. This paper presents obtained results in studying and applying a charged particles trajectory simulation program – Simion for building feasible design models for the system. The built models with different designs based on reference designs of some typical systems include a straight-shaped model, a 500 bent-shaped model and a 900 bent-shaped model. Some positron beam trajectory calculation tests have been performed for comparison between the models. From the tests, the 500 bent-shaped model has been proposed as a conceptual design for building a real slow positron beam system in the future in Vietnam. Keywords: Slow positron beam system, simulation program, Simion, conceptual design.

I. INTRODUCTION positrons with low energy of several eV. The positron beam is then pre-accelerated by a pre- Positron annihilation techniques play an accelerator and guided to an energy filter to important role in the study of micro-defect of separate the slow monoenergetic positrons out materials, nanostructures, porous materials, of the original beam. The separated slow surface analysis, etc. [1]. However, the study monoenergetic beam is then guided through an of surface structure, layers or interface regions accelerator to be accelerated to necessary high cannot be performed with traditional isotope energy depending on research purposes, positron sources because the energy of the directed to the sample chamber and interacts positrons emitted from the sources varies in a with the investigated sample. wide range (positrons from the isotope source with high energy go very deeply into the Center for Nuclear Techniques (CNT) sample, which reduces the chance of positron has been using positron annihilation techniques interaction as well as the formation of including positron annihilation lifetime and positronium on the material surface) [2]. Slow Doppler broadening spectroscopy for studying positron beam systems have been developed to some metal material properties, carbon solve that problem. They are applied widely in nanotubes, and zeolite. However, the main materials science, physics of solid state, positron sources used for these studies are 22Na condensed matter and surface [2]. In general, with continuous energy spectrum that limits the the slow positron beam systems in the world study of surface properties of materials. have different designs but follow a general Therefore, the need to build a slow positron operating principle. A fraction of high energy beam system at CNT in the future to perform positrons emitted from a radioactive source are such studies is essential. To ensure the slowed down (moderated) to become slow construction feasibility of the system, necessary

©2019 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute CONCEPTUAL DESIGNING OF A SLOW POSITRON BEAM SYSTEM USING … work in this early stage which needs to be done particles in these fields when introducing the is to study and use an appropriate charged electrode configuration with voltage and initial particles trajectory simulation program to conditions of the particles [8]. Simion is conceptually design the system. We have used intended to provide direct and highly interactive Simion as the main tool for the purpose of methods for simulating a wide variety of general conceptual designing. Among typical simulation ion optics problems such as modeling ion source programs, Simion has been widely used to and detector optics, ion traps, quadrupoles, etc. model ion optics problems including calculating Electrostatic and magnetic fields can be and simulating electrostatic fields, magnetic modeled as boundary value problem solutions fields and trajectories of charged particles flying of a partial differential equation called the through these fields. The program is highly Laplace equation (or the Poisson equation). The interactive and has been used effectively in specific method used within Simion to solve this many research projects on designing and equation is an over-relaxation technique, which building slow positron beams at the Institute of is a finite difference method to obtain a best Radiation Physics, Helmholtz-Centre Dresden- estimate of potentials for each point within the Rossendorf (Germany), Lawrence Livermore fields. After the electrostatic and magnetic fields National Laboratory (USA), University of Bath have been obtained, a standard fourth-order (UK) and in other countries such as Romania, Runge-Kutta method is used for numerical Israel, China [3-6]. Besides that, some initial integration of the charged particle trajectory in simulation tests for the reference design of the three dimensions based on the particle definition SPONSOR system from the Institute of parameters provided by users. In particular, Radiation Physics, Helmholtz-Centre Dresden- Simion provides functions of extensive support Rossendorf were performed successfully at in the definition of geometry, data logging, and CNT in 2017. The good agreement between our visualization. One of the most useful features of simulated results and experimental data from the Simion is the capability of using user programs SPONSOR system demonstrated that Simon can inside the program. This feature allows users to be used well for conceptual designing of a slow directly utilize a variety of programming positron beam system [7]. languages including Lua, C++, C, PRG, etc. to flexibly and efficiently extend simulation This paper presents results of applying capabilities of the program. Simion program to build some design models for the system based on design principles of B. Methods some built systems in the world and propose a According to several reference system feasible conceptual design of the system that designs, we have successfully built some can be used to prepare for the stage of detailed simulation models that can be possible designs engineering design and construction of the for the system by using Simion. Due to system in the future. application limitations of the program, the II. CONTENTS design models are only used to simulate the operating principle of slow positron beam A. Overview of Simion program systems rather than specify detailed Simion is a software package used engineering designs. Three main individual primarily to model electrostatic and magnetic simulation models of the slow positron beam fields and calculate trajectories of charged system have been built including:

46 CAO THANH LONG et al.

- The straight-shaped model using the - The 900 bent-shaped model based on ExB filter (figure 1). the design of a slow positron beam system - The 500 bent-shaped model based on the from Martin Luther University Halle- design of the SPONSOR system [9, 10] (figure 2). Wittenberg, Germany [11] (figure 3).

Fig. 1. The straight-shaped model using ExB filter.

Fig. 2. The 500 bent-shaped model.

Fig. 3. The 900 bent-shaped model. Some positron trajectory calculation tests selected model has been proposed as a feasible have been performed for each model in order to conceptual design for the future system. Tables investigate the influence of design parameters of of design parameters for the proposed conceptual each model on the quality of positron beam design include geometry parameters, electric obtained on targets, thereby determining which parameters and design parameters of coils model was the most reasonable design. The creating magnetic fields.

47 CONCEPTUAL DESIGNING OF A SLOW POSITRON BEAM SYSTEM USING …

C. Results and Discussions uniform distribution source with a radius of 2 mm for each model. The initial kinetic energy Case 1: Simulation of the trajectory of a of the beam was 3 eV. The voltages that were monoenergetic positron beam applied to the pre-accelerator and the Simion has been used to calculate the accelerator of each model were 27 V and 30 trajectories for 1000 monoenergetic positrons kV, respectively. The simulation results are in a beam emitted isotropically from a circular shown below in table I, figure 4 and figure 5. Table I. The simulation results for trajectory of a monoenergetic positron beam Straight-shaped 500 bent-shaped 900 bent-shaped

model model model Total number of positrons from 1000 1000 1000 source Total number of positrons 789 807 795 coming to target The ratio of positron number coming to target to total positron 78.9% 80.7% 79.5% number Beam radius on target 2.75 mm 2.39 mm 2.79 mm

Fig. 4. Spatial distribution of positron beam on the target of the straight-shaped model (left), the 500 bent- shaped model (middle) and the 900 bent-shaped model (right)

(FWHM = 5.50 eV) (FWHM = 1.34 eV) (FWHM = 5.71 eV) Fig. 5. Energy distribution of positron beam on the target of the straight-shaped model (left), the 500 bent- shaped model (middle) and the 900 bent-shaped model (right)

48 CAO THANH LONG et al.

From the simulation results, it has been model was more mono-energetic than those of found that the quality of positron beam the others. obtained on the targets is influenced by the model designs. The models with the different Case 2: Simulation of the trajectory of a designs do not have completely identical monoenergetic positron beam in case that a uniform magnetic fields along their axes, solenoid deviated from its original position resulting in different qualities of obtained Another trajectory calculation test has positron beam on the targets. been done for each model with the same The results of the beam radius of monoenergetic positron beam in case that the positron beam on the targets show that solenoid surrounding the accelerator of each obtained positron beam in case of using the 500 model deviated from its original position. bent-shaped model has better convergence compared to the others. Furthermore, full width Distributions of positron beam on the target of at half maximum (FWHM) of the energy each model have been investigated for distribution of positron beam on the target for comparison. We have simulated two situations the 500 bent-shaped model was smaller than that the solenoid deviations were 1 cm and 2 those of the others. It has shown that the cm. The simulation results are shown below in obtained positron beam of the 500 bent-shaped figure 6, figure 7 and figure 8.

Fig.6. Spatial distribution of positron beam on the target of the straight-shaped model in case of solenoid deviation of 0 cm (left), 1 cm (middle) and 2 cm (right).

Fig.7. Spatial distribution of positron beam on the target of the 500 bent-shaped model in case of solenoid deviation of 0 cm (left), 1 cm (middle) and 2 cm (right).

49 CONCEPTUAL DESIGNING OF A SLOW POSITRON BEAM SYSTEM USING …

Fig. 8. Spatial distribution of positron beam on the target of the 900 bent-shaped model in case of solenoid deviation of 0 cm (left), 1 cm (middle) and 2 cm (right). The comparison results have shown that modeling and simulation of the trajectory of the solenoid deviation influenced the quality of positron beam flying through electrostatic the positron beam that comes to the targets. For fields and magnetic fields of a slow positron the straight-shaped model, there were a few beam system. Research of searching for other positrons obtained on the target in case of simulation programs to combine with Simion solenoid deviation of 1 cm. In the case of a should be done to further optimize the solenoid deviation of 2 cm, we have even got conceptual design. no positrons coming to the target. For the 900 bent-shaped model, the obtained positron REFERENCES beam has deviated much more from the target [1]. P. K. Pujari, K. Sudarshan and D. Dutta (Ed.), 0 center compared with that of the 50 bent- "11th International Workshop on Positron and shaped model. The beam has even distorted its Positronium Chemistry (PPC-11)", Journal of shape when increasing the solenoid deviation Physics: Conference Series, Volume 618, to 2 cm. Therefore, we have concluded that Conference 1, 2015. 0 the 50 bent-shaped model in this simulation [2]. P. G. Coleman (Ed.), “Positron Beams and case would be the optimal model compared their applications”, World Scientific, with the others. Singapore, 2000. [3]. F. A. Selim, A.W. Hunt, J.A. Golovchenko, R. III. CONCLUSIONS H. Howell, R. Haakenaasen, K.G. Lynn, “Improved source and transport of We have come up with the selection of monoenergetic MeV positrons”, Nuclear the 500 bent-shaped model as a conceptual Instruments and Methods in Physics Research design for our slow positron beam system B 171 (2000), 182-188, 2000. based on simulation test results and consideration of the design feasibility of the [4]. S. May-Tal Beck, D. Cohen, E. Cohen, A. Kelleher, O. Hen, J. Dumas, E. Piasetzky, N. simulation models. The proposed model can be Pilip, G. Ron, I. Sabo-Napadensky, R Weiss- a good basis for detailed engineering design Babai, “Design of the Slow POsitron faciliTy and construction of the system in the future. (SPOT) in Israel”, 13th International The study results have also demonstrated that Workshop on Slow Positron Beam Techniques Simion program is a very suitable tool for and Applications, 2014.

50 CAO THANH LONG et al.

[5]. C. K. Cheung, P. S. Naik, C. D. Beling, S. Fung, [9]. Wolfgang Anwanda, Gerhard Brauer, Maik H. M. Weng, “Performance of a slow positron Butterling, Hans-Rainer Kissener, Andreas beam using a hybrid lens design”, Department Wagner, “Design and Construction of a Slow of Physics, University of Hong Kong, Pokfulam Positron Beam for Solid and Surface Road, Hong Kong, PR China, 2006. Investigations”, Defect and Diffusion Forum [6]. Xu Hong-Xia, Liu Jian-Dang, Gao Chuan-Bo, Vol. 331, 2012. Weng Hui-Min, Ye Bang-Jiao, “SIMION [10]. Wolfgang Anwanda, Gerhard Brauer, simulation of a slow pulsed positron beam”, Hans-Rainer Kissener, “Magnetically Department of Modern Physics, University of guided slow positron beam for defect Science and Technology of China, Hefei 230026, China, 2012. studies”, Positron Group of TU Dresden at Research Centre Rossendorf, Dresden, [7]. Cao Thanh Long, Nguyen Trung Hieu, Tran Germany, 1994. Quoc Dung, Huynh Dong Phuong, “Some initial results of simulating a positron beam [11]. R. Krause-Rehberg, “Simple design for a system by using SIMION”, Nuclear Science continuous magnetically guided positron and Technology, Vol.7, No. 3, 17-24, 2017. beam – and – News from the EPOS project”, [8]. David J. Manura, David A. Dahl, “SIMION Institute of Physics, Martin Luther Version 8.0/8.1 User Manual”, Document Revision University Halle-Wittenberg, Germany, 5, Scientific Instrument Services Inc., 2011. 2010.

51 INSTRUCTIONS FOR AUTHORS

GENERAL INFORMATION MANUSCRIPT PREPARATION Nuclear Science and Technology (NST), an Manuscripts must be written in English with international journal of the Vietnam Atomic adequate margins and indented paragraph. All Energy Society (VAES) and Vietnam Atomic manuscript must use SI (metric) units in text, Energy Institute (VINATOM), quarterly publishes figures, and tables. Manuscripts should in general articles related to theory and application of nuclear be organized in the following order: title, names of science and technology. All papers and technical authors and their complete affiliation including zip notes will be refereed. code, abstract (not exceeding 200 words), It is understood that the paper has been neither keywords (up to 7), introduction, main body of a published nor currently submitted for publication paper, acknowledgments, references, appendices, elsewhere. The copyright of all published papers table & figure captions, tables and figures. and notes will be transferred in VAES. Unnecessary sections may be omitted.

DETAILED FIELDS Headings: Use I, II,… for major headings and A, B, … for secondary headings. NST coves all fields of nuclear science and technology for peaceful utilization of nuclear Mathematical formulas: All mathematical energy and radiation. Authors should choose one formulas should be clearly written, with special of the following fields at the time they submit consideration to distinctive legibility of sub-and their manuscript: 1) Nuclear Physics, 2) Nuclear superscripts. Equation (at least the principal ones) Data, 3) Reactor Physics, 4) Thermal Hydraulics, should be numbered consecutively using Arabic 5) Nuclear Safety, 6) Nuclear I&C, 7) Nuclear numerals in parentheses in the right hand margin. Fuel and Materials, 8) Tables and Figures: Tables should be numbered Management, 9) Radiation Protection, 10) with Roman numerals. Figures should be Radiation Technology, 11) Nuclear Techniques in numbered consecutively with Arabic numerals in Food and Agriculture, 12) Nuclear Medicine and order of their first appearance and have a complete Radiotherapy, 13) Nuclear Techniques in descriptive title. They should be typed on separate Industries, 14) Environment Radioactivity, 15) sheets. Tables should no repeat data which are Isotope Hydrology, 16) Nuclear Analytical available elsewhere in the paper. Figures should Methods, 17) Health Physics, 18) Fusion and be original ink drawing or computer drawn figures Laser Technology. in the original and of high quality, ready for direct MANUSCRIPT SUBMISSION reproduction. Figures should be referred to in the text as, for example, Fig. 1., or Fig. 2. . Manuscript for publication should be submitted to the Editorial Office in triplicate by postal mail. Reference: References should be listed at the end For electronical submission use of the text and presented as follows: [email protected]. [1] C. Y. Fu et al., Nuclear Data for Science and Technology, S. M. Qaim (Ed.), p. 587 (1991). Submission Address [2] C. Kalbach, Z. Phys, A283, 401 (1977). Department of Planning, R&D Management Vietnam Atomic Energy Institute, 59 Ly Thuong [3] S. Shibata, M. Imamura, T. Miyachi and M. Kiet Street, Hanoi, Vietnam Mutou, “Photonuclear spallation reactions in E-mail: [email protected]. Cu”, Phys. Rev. C 35, 254 (1987).

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