Radiation dose distribution of liquid fueled Thorium Molten Salt Reactor

Radiation dose distribution of liquid fueled Thorium Molten Salt Reactor 1 2 first-author https://orcid.org/0000-0003-4767-366X 2 corresp Corresponding author, xiaxiaobin@sinap.ac.cn Corresponding author, xiaxiaobin@sinap.ac.cn xiaxiaobin@sinap.ac.cn 2 https://orcid.org/0000-0001-7671-8316 2 3 https://orcid.org/0000-0002-5876-464X 2 2 University of Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China Siemens Shanghai Medical Equipment Ltd., Shanghai 201318, China Siemens Shanghai Medical Equipment Ltd., Shanghai 201318, China A liquid fueled thorium molten salt reactor (TMSR-LF), one of the Generation IV reactors, was designed by the Shanghai Institute of Applied Physics, Chinese Academy of Sciences. This study uses the Monte Carlo N-Particle Transport code to calculate the neutron and gamma dose rate distributions around the reactor. Multiple types of tallies and variance reduction techniques were employed to reduce calculation time and obtain convergent calculation results. Based on the calculation and analysis results, the TMSR-LF radiation shield with a 60 cm serpentine concrete layer and a 120 cm ordinary concrete layer is able to meet radiation requirements. The gamma dose rate outside the reactor biological shield was 16.1 mSv∙h -1 ; this is higher than the neutron dose rate of 3.71×10 -2 mSv∙h -1 . The maximum thermal neutron flux density outside the reactor biological shield was 1.89×10 3 cm -2 ∙s -1 , which was below the 1×10 5 cm -2 ∙s -1 limit. This means that the radiation effect caused by neutron activation can be disregarded. Liquid fueled Molten salt reactor Neutron and gamma Dose rate 1. INTRODUCTION 1 The Generation IV International Forum categorized molten salt reactor (MSR) as a Generation IV reactor due to its numerous advantages like good neutron economy, inherent safety, online reprocessing, reduced production of radioactive waste, and nuclear non-proliferation [ 1 1 - 3 3 1-3 ]. In 2011, the Chinese Academy of Sciences launched a thorium MSR project and established a research center at the Shanghai Institute of Applied Physics. This project focused on the development of a Liquid Fueled Thorium Molten Salt Reactor (TMSR-LF). The TMSR-LF1 is the first prototype with a thermal power design of 2 MW, using LiF-BeF 2 -ZrF 4 -UF 4 as its fuel and primary coolant. Fuel dissolved in molten salt coolant is a representative characteristic compared to traditional reactors [ 4 4 , 5 5 ]. As a fission reactor, the TMSR-LF1 is a strong source of neutrons and gamma radiation during operation and even following shutdown. The radiation dose of TMSR-LF1 is mainly sourced from the neutron and gamma rays produced by the fission of fuels in the reactor core and by the decay of fission products [ 6 6 ]. Therefore, radiation dose distribution around the reactor is important, for shielding design and radiation protection. To protect people and equipment from radiation damage, the selection of a suitable shielding material and optimization of the shielding structure is necessary in shielding design. The TMSR-LF1 biological shield is composed of a serpentine concrete shield and an ordinary concrete shield. A 60 cm serpentine concrete layer was used inside ordinary concrete to reduce the neutron and photon energy flux densities to protect the ordinary concrete structure. The reactor neutron and gamma dose rate distributions inside and outside the reactor shield have been calculated using the MCNP5 code. Within the biological shielding layer of the reactor, the neutron dose rate is higher than the gamma dose rate. As neutrons generate many secondary gamma rays when they are moderated and absorbed in the concrete shield, the gamma dose rate outside the reactor concrete shielding layer was higher than the neutron dose rate. To limit the radiation effects of thermal neutron activation products in the areas where personnel need entry following the shutdown of the reactor, the thermal neutron flux density should be less than 1×10 5 cm -2 ∙s -1 during normal operating conditions. Based on the results, the thermal neutron flux density outside the concrete shield layers of TMSR-LF1 meets this requirement. 2. CALCULATION METHODS AND MODELS 1 The widely used methods for shielding calculation of reactors are the discrete ordinate (SN) method and the Monte Carlo (MC) method [ 7 7 ][ 8 8 ]. The shielding calculation of the TMSR-LF1 uses the Monte Carlo N-Particle Transport (MCNP) code. This is based on the MC method, which may be used to theoretically duplicate a statistical process (such as the interaction of nuclear particles with materials). This code is particularly useful for complex problems that cannot be modeled by computer codes that use deterministic methods. MCNP5 was developed at the Los Alamos National Laboratory, and is applicable to neutrons, photons, electrons, and coupled neutron/photon/electron transportation. For its ability to deal with complex three dimensional (3D) geometry, a rich set of integrated variance reduction techniques and the support for parallel computing have been widely used in shielding design [ 9 9 ]. There are some differences in the TMSR-LF1 compared to solid fuel reactors [ 10 10 ]. For example, the coolant temperature exceeds 600 °C, the power density is high in the reactor core, and molten salt is used as coolant; these features have introduced significant challenges to shielding design. TMSR-LF1 uses serpentine concrete as the heat shield as it possesses excellent heat resistance and has no strict requirements regarding the irradiation environment [ 11 11 , 12 12 ]. The entire reactor cabin is divided into upper and lower regions by a 30 cm steel plate. The reactor core is located in the lower part of the reactor cabin, and the control rod drive motor, main pump drive motor, and measurement equipment are located in the upper region of the reactor cabin. The side shielding system in the lower region of the TMSR-LF1 consists of a 60 cm serpentine concrete shield layer and a 120 cm ordinary concrete shield layer. The bottom shielding system of the lower region consists of a 40 cm serpentine concrete shield layer and a 120 cm ordinary concrete shield layer. The side shielding system of the upper region of the TMSR-LF1 consists of a 120 cm ordinary concrete shield layer, and the top shielding system of the upper region consists of a 180 cm ordinary concrete shield layer. Table 1 Table 1 details the additional design parameters. 1 1 Parameter 1 1 Specification 1 1 Thermal power 1 1 2 MW 1 1 Fuel and coolant 1 1 LiF-BeF 2 -ZrF 4 -UF 4 (65.30-28.71-4.79-1.20 mol%) 1 1 Fuel 235 U enrichment 1 1 19.75% 1 1 7 Li abundance 1 1 99.95 atom % 1 1 Coolant inlet temperature 1 1 630 °C 1 1 Coolant outlet temperature 1 1 650 °C 1 1 Reactor fuel region diameter/height 1 1 234 cm/180 cm 1 1 Serpentine concrete inner diameter/thickness 1 1 640 cm/60 cm 1 1 Serpentine concrete density 1 1 2.26 g/cm 3 1 1 Serpentine concrete chemical composition 1 1 SiO 2 -MgO-CaO-Al 2 O 3 -Fe 2 O 3 -H 2 O (33.47-28.58-14.20-5.3-4.9-13.55 wt.%) 1 1 Ordinary concrete inner diameter/thickness 1 1 760 cm/120 cm 1 1 Ordinary concrete density 1 1 2.30 g/cm 3 The TMSR-LF1 reactor has a relatively compact core composed of a fuel region and graphite reflector. The reactor, including the 3 cm thickness reactor vessel, has a diameter of 237 cm and is 320 cm in height. The active region containing the graphite reflector is 230 cm in diameter and 180 cm in height. The fuel region, a hexagonal prism, is located in the center of the active region; this region contains 244 fuel channels that are 4 cm in diameter, where the center distance between adjacent channels is 10 cm. Above the fuel region is a 12 cm compressed steel plate made of Hastelloy-N and a 62.6 cm high covering gas region. Below the fuel region, is a support steel plate made of Hastelloy-N with an 8 cm thickness, a fuel chamber that is 10 cm in height, and an ellipsoidal graphite reflective layer that had a maximum thickness of approximately 40 cm. The reactor vessel is made of Hastelloy-N, and is 3 cm in thickness [ 13 13 ]. The primary loop heat exchanger was placed in the reactor to reduce the radiation effect of the primary loop radioactivity. a 3D simulation model was constructed, based on the design parameters of TMSR-LF1, as shown in Fig. 1 Fig. 1 . Then, the MCNP5 code was used to conduct coupled neutron/gamma transport. 2.1 Neutron emission rate of reactor 2 The MCNP5 code provides the statistical average dose probability distribution per neutron by tracking neutrons and neutron-induced gamma rays. The final calculated dose rate is the statistical average multiplied by the neutron emission rate of the reactor. The neutron emission rate of the reactor is largely dependent on the thermal power of the reactor. As the thermal power of TMSR-LF1 is 2 MW, the number of neutrons released per second may be calculated using two methods. The first method uses theory calculation with Formula (1) [ 14 14 , 15 15 ], while the second method calculates the average energy deposition of one neutron in the reactor core cell using the MCNP5 code [ 16 16 ]. Then, the number of neutrons released per second of the reactor core based on reactor power may be derived by Formula (2)[ 17 17 ]: <math display="block" id="M1"><mrow><mi>N</mi><mo>=</mo><mfrac><mi>P</mi><mi>E</mi></mfrac><mo>×</mo><mi>n</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mtext> MW</mtext></mrow><mrow><mn>190</mn><mtext> MeV</mtext></mrow></mfrac><mo>×</mo><mn>2.42</mn><mo>≈</mo><mn>1.60</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>17</mn></mrow></msup><mtext> neutrons/s</mtext></mrow></math> <math display="block" id="M2"><mrow><mi>N</mi><mo>=</mo><mfrac><mi>P</mi><mtext>ε</mtext></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mtext> MW</mtext></mrow><mrow><mn>80.13</mn><mtext> MeV</mtext></mrow></mfrac><mo>≈</mo><mn>1.56</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>17</mn></mrow></msup><mtext> neutrons/s</mtext></mrow></math> where N is the number of neutrons released per second in the reactor core; E is the energy released by one 235 U fission (~190 MeV excluding the energy of the neutrino); n is the number of neutrons produced by one 235 U fission (i.e., 2.42 [ 14 14 ]); and <math id="M3"><mtext>ε</mtext></math> is the average energy deposition of one neutron in the reactor core calculated by MCNP5 code using the detector of energy deposition tally F6:NP (i.e., 80.13 MeV). These two methods produce very similar results, demonstrating that both methods are applicable. On a conservative basis, the number of neutrons released per second of 2 MW TMSR-LF1 was adopted as 1.60×10 17 neutrons/s. When the reactor is in a shutdown scenario, the radionuclides in the reactor core continue to produce radiation effects during the decay process. At the end of life for the TMSR-LF1, the number of gamma released per second by the reactor core fission products and activation products was approximately 7.02×10 17 s -1 at the zero moment of reactor shutdown. The gamma emission rate was reduced to 2.35×10 16 s -1 following 12 d of reactor shutdown attenuation. These data were calculated using the ORIGEN-S code. This code is the depletion and decay module in the SCALE code system and has been widely used in nuclear reactor and processing plant design studies, spent fuel transportation and storage studies, burnup credit evaluations, decay heat and radiation safety analyses, and environmental assessments [ 18 18 ]. The TMSR-LF1 fuel salt contains a large amount of 9 Be; the neutrons are produced by the (α, n) between alpha particles with 9 Be, and are produced by the (γ, n) between gamma rays with 9 Be [ 19 19 - 21 21 19-21 ]. The number of neutrons released per second by (α, n) and (γ, n) is approximately 3.15×10 15 neutrons/s at the zero moment of the shutdown scenario, and the neutron emission rate was reduced to 2.46×10 12 s -1 following 12 d of reactor shutdown attenuation [ 22 22 ]. The radiation impact of neutrons and gamma for the reactor shutdown scenario is much smaller than the radiation impact during reactor operation. The fuel salt is discharged into the fuel salt tank located underground following 12 d of cooling decay [ 23 23 ]. Therefore, the radiation dose impact for the TMSR-LF1 reactor shutdown scenario may be ignored compared to the radiation impact during reactor operation. 2.2 Spectra of neutron and gamma 2 The neutron and gamma energy spectra are the premise of analyzing the radiation dose distribution of neutrons and gamma rays. The neutron and gamma energy spectra may be used to predict the dose distribution in advance, and provide guidance to select suitable shielding materials. The energy spectrum of neutrons produced by 235 U fission in the reactor core follows the Maxwell–Boltzmann distribution after being sufficiently moderated by graphite [ 24 24 , 25 25 ]. The peak of the neutron energy spectrum of the reactor core is related to the moderator and the reactor core temperature. The neutron energy after completely slowing down may be derived using Formula (3): <math display="block" id="M4"><mrow><msub><mi>E</mi><mrow><mi>k</mi><mi>T</mi></mrow></msub><mo>=</mo><mi>k</mi><mo>×</mo><mi>T</mi><mo>=</mo><mn>8.62</mn><mo>×</mo><mfrac><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup><mtext>eV</mtext></mrow><mtext>K</mtext></mfrac><mo>×</mo><mn>903</mn><mtext> K</mtext><mo>≈</mo><mn>7.78</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mtext> eV</mtext></mrow></math> where E kT is the neutron energy after being sufficiently moderated; k is the Boltzmann constant (i.e., 8.62×10 -5 eV/K); and T is the temperature of the graphite moderator in the reactor core (903 K). The theoretical calculation of the TMSR-LF1 core neutron energy should be 7.78×10 -2 eV after being sufficiently moderated. TMSR-LF1 is a thermal neutron reactor, as such, the spectra of neutron and gamma shown in Figure 2 Figure 2 was calculated with the MCNP5 code using the ring detector tally F5. The maximum neutron flux density was approximately 2.2×10 13 cm -2 ∙s -1 in the reactor core fuel region and approximately 2.6×10 11 cm -2 ∙s -1 outside the reactor vessel. The maximum gamma flux density was approximately 8.4×10 12 cm -2 ∙s -1 in the reactor core fuel region, and approximately 1.9×10 11 cm -2 ∙s -1 outside the reactor vessel. The neutron spectrum with energy ranging from 10 -9 to 10 MeV was divided into 100 energy groups using geometric progression. The gamma spectrum with energy ranging from 0 to 5 MeV was divided into 50 energy groups using arithmetic progression. The computational variances of each neutron and gamma energy groups were less than 5% when the number of neutron histories was 2×10 8 . The peak of the neutron spectrum of 235 U fission was approximately 2 MeV, and the peak of the neutron spectrum in the reactor core fuel area was approximately 10 -7 MeV following graphite moderation. This was slightly larger than the theoretical results of formula (3) (i.e., 7.78×10 -8 MeV). The percentage of neutrons in this energy segment had lowered and the percentage of neutrons in the high-energy segments had increased outside the reactor vessel. The peak of gamma spectrum in the reactor core fuel area was approximately 0.25 MeV, and the gamma spectrum had become "harder" outside of the reactor vessel as the gamma with low energy rapidly reduces relative to the high-energy gamma when it travels through the graphite reflector and reactor vessel. 2.3 Variance reduction techniques 2 The surface detector tally F2 and the ring detector tally F5 have been used to calculate the dose rate outside the biological shield. It is necessary for the shielding calculation of TMSR-LF1 to solve the deep penetration problem as a result of the thick concrete shield. Two calculation techniques were used together to reduce calculation variance and obtain convergent calculation results. The first was the Surface Source Write Card (SSW) used to generate a surface radioactive source. The second technique was the Weight Window Generation Card (WWG) used to estimate the importance of the space-energy regions of phase space. The calculation process may be divided into four steps: i. Creation of an elaborate TMSR-LF1 core model, and use of the nuclear criticality (KCODE) card, where SSW produces a KCODE nuclear criticality surface source file for use in subsequent MCNP calculations; ii. Replacement of the KCODE nuclear criticality source card with the general source card, use of a fission turnoff card to turn off fission in the reactor core, and use of the Surface Source Read Card to read the nuclear criticality surface source file to continue the calculation; iii. Use of the WWG to estimate the importance of the space-energy regions of the phase space and produce a weight window file; iv. Use of the importance function written on the weight window cards (WWE:N, WWE:P); we replaced the neutron and photon importance (IMP:N,IMP:P) in the calculation model card and continued the calculation. 3. RESULTS AND DISCUSSION 1 The radial flux density distribution of neutrons and gamma around the reactor was calculated by the MCNP5 code using the Mesh-Based Weight Window Generator (MESH) and the track-length detector tally F4; the latter is referred to as the Superimposed Mesh Tally (FMESH). The radial dose rate distribution of neutrons and gamma around the reactor was converted from the flux density distribution by using flux-to-dose conversion factors recommended in the International Symposium on the System of Radiological Protection (ICRP) Publication 74 [ 26 26 , 27 27 ]. By graphically displaying the calculation results of FMESH, the dose rate distribution of neutrons and gamma may be reflected more intuitively. The dose rate distribution of neutrons and gamma around the reactor are shown in Figure 3(a) and 3(b) Figure 3(a) and 3(b) , respectively. The neutron dose rate in the reactor core was higher than 1×10 9 mSv/h, while the gamma dose rate was lower than 1×10 8 mSv/h. Figure 3 Figure 3 shows that the neutron dose rate was higher than the gamma dose rate in the reactor core and around the reactor vessel, while the gamma dose rate is higher than the neutron dose rate outside the concrete shield. The minimum neutron dose rate in the lower region of the reactor cabin exceeded 1×10 6 mSv/h, while the minimum gamma dose rate exceeded 1×10 5 mSv/h. The maximum neutron dose rate in the upper region of the reactor cabin was lower than 1×10 6 mSv/h, while the maximum gamma dose rate was lower than 1×10 4 mSv/h. The 30 cm shielding steel plate between the upper and lower regions of the reactor cabin is able to effectively reduce the radiation dose rate of the upper region, particularly for the gamma dose rate. If the number of simulated particles was below 5×10 8 , the number of particles counted in the outer concrete was limited, and the variance of the calculated data for the outermost layer of ordinary concrete exceeded 5% using the detector tally F4. As such, irregular jagged colors appeared in the outer boundary area of the ordinary concrete in Fig. 3 Fig. 3 . The radiation dose distribution outside the concrete shielding layer, particularly at the top of the reactor, was not well represented using FMESH4. The SSW Card and WWG Card were used to reduce variance. This was during the calculation of radiation dose rates with varied concrete shield thicknesses using the surface detector tally F2 and ring detector tally F5. The calculation process is described in detail below using the example of the radiation dose rate distribution in serpentine concrete and ordinary concrete on the side of the reactor cabin. The tally segment card FS2 was used to intercept the concrete layer on the side of the reactor into upper, middle, and lower regions with the upper and bottom of the reactor fuel as the boundary during the calculation of tally F2 ( Fig. 4 Fig. 4 ). Section 2 provides the details of the calculation process and steps. When the number of simulated particles was 5E+8, the variances of all calculated data were less than 5% based on the combined used of SSW and WWG. The serpentine concrete on the side of the reactor was divided into four layers, and the ordinary concrete was divided into eight layers, each with a thickness of 15 cm. Tally F2 calculated the average dose rate of the surface, while the calculation using tally F5 selected the same height position to the center of the reactor fuel area. The radiation dose rate distribution in serpentine concrete and ordinary concrete was given by calculating the neutron and gamma dose rates corresponding to different concrete thicknesses ( Fig. 4 Fig. 4 ). The equations for the gamma dose rate as a function of serpentine thickness, calculated using tally F2 in the upper, middle, and lower regions on the side of the reactor were Formulas (4), (5), and (6), respectively. The equation for gamma dose rate as a function of serpentine thickness calculated using tally F5 was Formula (7): <math display="block" id="M5"><mrow><msub><mi>D</mi><mrow><mtext>upper</mtext></mrow></msub><mo>=</mo><mn>6.64</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mn>5</mn></msup><mi>exp</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.065</mn><mi>x</mi></mrow><mo>)</mo></mrow><mtext> mSv/h</mtext></mrow></math> <math display="block" id="M6"><mrow><msub><mi>D</mi><mrow><mtext>middle</mtext></mrow></msub><mo>=</mo><mn>1.17</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mn>6</mn></msup><mtext> exp</mtext><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.063</mn><mi>x</mi></mrow><mo>)</mo></mrow><mtext> mSv/h</mtext></mrow></math> <math display="block" id="M7"><mrow><msub><mi>D</mi><mrow><mtext>lower</mtext></mrow></msub><mo>=</mo><mn>7.05</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mn>5</mn></msup><mtext> exp</mtext><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.062</mn><mi>x</mi></mrow><mo>)</mo></mrow><mtext> mSv/h</mtext></mrow></math> <math display="block" id="M8"><mrow><msub><mi>D</mi><mrow><mtext>F</mtext><mn>5</mn></mrow></msub><mo>=</mo><mn>1.21</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mn>6</mn></msup><mtext> exp</mtext><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.063</mn><mi>x</mi></mrow><mo>)</mo></mrow><mtext> mSv/h</mtext></mrow></math> where <math id="M9"><mi>x</mi></math> is the thickness of serpentine concrete (cm); <math id="M10"><mrow><msub><mi>D</mi><mrow><mtext>upper</mtext></mrow></msub></mrow></math> is the gamma dose rate of the upper region on the side of the reactor, where the correlation factor ( R 2 ) of Formula (4) was 0.9993; <math id="M11"><mrow><msub><mi>D</mi><mrow><mtext>middle</mtext></mrow></msub></mrow></math> is the gamma dose rate of the middle region on the side of the reactor, where the R 2 of Formula (5) was 0.9977; <math id="M12"><mrow><msub><mi>D</mi><mrow><mtext>lower</mtext></mrow></msub></mrow></math> is the gamma dose rate of the lower region on the side of the reactor, where the R 2 of Formula (6) was 0.9977; and <math id="M13"><mrow><msub><mi>D</mi><mrow><mtext>F</mtext><mn>5</mn></mrow></msub></mrow></math> is the gamma dose rate of the same height position to the center of the reactor fuel area on the side of the reactor, where the R 2 of Formula (7) was 0.9998. The gamma dose rate on the side of the reactor showed a good exponential relationship with the thickness of the serpentine concrete with an R 2 > 0.99 [ 28 28 ]. Based on formula (4~7), the 10 th -value layer thickness of the gamma dose rate on the side of the serpentine concrete was 35–38 cm. The dose rate in the middle region facing the reactor fuel was higher than the dose rate in the upper and lower regions. The results using the F2 and F5 tallies were relatively close. The calculated data using F5 was slightly larger than F2 as the radiation dose levels in the center of the reactor active area were higher than those in the upper and lower regions. Increasing the number of F5 detectors reduced the statistical efficiency of the MCNP code, whereby the variance of the F5 calculation result was greater than the F2 result [ 29 29 ]. Therefore, the calculation data of the middle region using tally F2 was selected as the result for neutron and gamma radiation dose distribution. Formula (8) shows that the neutron dose rates vary with the serpentine concrete shield thickness as fitted with the surface detector tally F2 results. <math display="block" id="M14"><mrow><msub><mi>D</mi><mrow><mtext>neutron</mtext></mrow></msub><mo>=</mo><mn>6.56</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mn>6</mn></msup><mtext> exp</mtext><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.112</mn><mi>x</mi></mrow><mo>)</mo></mrow><mtext> mSv/h</mtext></mrow></math> In this formula, <math id="M15"><mrow><msub><mi>D</mi><mrow><mtext>neutron</mtext></mrow></msub></mrow></math> is the neutron dose rate of the middle region on the side of the reactor; <math id="M16"><mi>x</mi></math> is the thickness of serpentine concrete, where the R 2 of Formula (8) was 0.9997. The neutron dose rate in serpentine concrete was higher than the gamma dose rate. However, the neutron dose rate decline with increased serpentine concrete thickness was more rapid than the gamma dose rate. The gamma and neutron dose rates varied with ordinary concrete shield thickness on the side of the reactor fitted with the surface detector; the tally F2 results are shown in Formulas (9) and (10). In these formulas, <math id="M17"><mi>x</mi></math> is the thickness of serpentine concrete (e.g., 60 cm); <math id="M18"><mi>y</mi></math> is the thickness of the ordinary concrete (0–120 cm); <math id="M19"><mrow><msub><mi>D</mi><mrow><mtext>gamma</mtext></mrow></msub></mrow></math> is the gamma dose rate of the middle region on the side of the reactor, where the R 2 of Formula (9) was 0.9998; <math id="M20"><mrow><msub><mi>D</mi><mrow><mtext>neutron</mtext></mrow></msub></mrow></math> is the neutron dose rate of the middle region on the side of the reactor, where the R 2 of Formula (10) was 0.9996. There was a good fit between the exponential formula of gamma and neutron dose rates with ordinary concrete thickness. The neutron dose rate in ordinary concrete was lower than the gamma dose rate, and the neutron dose rate decline with ordinary concrete was more than the decline of the gamma dose rate. <math display="block" id="M21"><mtable columnalign="left"><mtr><mtd><msub><mi>D</mi><mrow><mtext>gamma</mtext></mrow></msub><mo>=</mo><mn>1.17</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mi>exp</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.063</mn><mi>x</mi></mrow><mo>)</mo></mrow><mo>×</mo><mi>exp</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.061</mn><mi>y</mi></mrow><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mn>2.67</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup><mi>exp</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.061</mn><mi>y</mi></mrow><mo>)</mo></mrow><mo> </mo><mtext> mSv/h</mtext></mtd></mtr></mtable></math> <math display="block" id="M22"><mtable columnalign="left"><mtr><mtd><msub><mi>D</mi><mrow><mtext>neutron</mtext></mrow></msub><mo>=</mo><mn>6.56</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mi>exp</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.112</mn><mi>x</mi></mrow><mo>)</mo></mrow><mo>×</mo><mi>exp</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.094</mn><mi>y</mi></mrow><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mtext>           </mtext><mo>=</mo><mn>7.91</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mi>exp</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.094</mn><mi>y</mi></mrow><mo>)</mo></mrow><mtext> mSv/h</mtext></mtd></mtr></mtable></math> 3.1 Distribution of Neutron Flux Density 2 Reactor neutrons activate the surrounding materials; therefore, the neutron flux density distribution is one major focus of radiation protection. Based on TMSR-LF1 radiation safety requirements, the thermal neutron flux density outside the concrete shielding layer should be less than 1×10 5 cm -2 ∙s -1 to reduce the radiation effect caused by neutron activation [ 30 30 , 31 31 ]. Gamma rays are also generated by (n, γ) reactions during the neutron absorption process. The calculation of neutron flux density distribution is necessary to analyze changes in the radiation dose rate distributions of neutrons and gamma rays. Combined with the peak distribution of neutron spectrum in the fuel region of the reactor core, the energy range of the neutron spectrum was divided into four energy segments: thermal neutron ( E ≤ 0.414 eV), intermediate neutron (0.414 eV ≤ E ≤ 0.1 MeV), fast neutron (0.1 MeV ≤ E ≤ 1MeV), and super-fast neutrons (1 MeV ≤ E ≤ 20 MeV) [ 32 32 , 33 33 ]. Thermal neutrons descend at a slower pace than the other three segments in the graphite reflector; this is helpful in terms of forming a more uniform power distribution in the reactor core. The fast and super-fast neutrons (0.1 MeV ≤ E ≤ 20 MeV) have increased as the thermal and intermediate neutrons ( E ≤ 0.1 MeV) are reduced quickly outside the graphite reflector ( Fig. 5a Fig. 5a ). The reason for this is the presence of a 0.5 cm thick fuel salt layer, which has large thermal neutron absorption cross-sections and releases high-energy neutrons after 235 U fission between the graphite reflector and reactor vessel. The thermal neutron flux density is higher than the fluxes of other neutrons, and therefore, thermal neutrons are the dominant component of neutrons outside the reactor vessel. When neutrons pass through the concrete shielding layer, thermal neutrons are absorbed by the concrete shielding layer, and neutrons of the other three energy segments also slow down into the thermal neutrons by the concrete shielding layer. The thermal neutron flux density outside the concrete shielding layer was still higher than the neutron flux density of the other three energy segments ( Fig. 5 Fig. 5 ). As the primary factor of neutron activation, the thermal neutron flux density outside the reactor shield remained the focus of attention in calculating the neutron flux density distribution. The thermal neutron flux density distributions in serpentine concrete and ordinary concrete were determined by calculating the thermal neutron flux density corresponding to differing concrete thicknesses using tally F2. The fitted equations of the thermal neutron flux density on the side and top of the reactor with concrete thickness are expressed in Formulas (11) and (12), respectively. The extrapolated thermal neutron flux density outside the ordinary concrete shield using Formula (11) was 1.89×10 3 cm -2 ∙s -1 , and the extrapolated thermal neutron flux density above the ordinary concrete shielding layer with a 180 cm thickness using Formula (12) was 11 cm -2 ∙s -1 . The latter value is below the thermal neutron flux density limit of 1×10 5 cm -2 ∙s -1 for neutron activation. From Formula (11), the 10 th -value layer thicknesses of the thermal neutron flux density on the side of the reactor for serpentine concrete was approximately 20.9 cm, while this value on the side of the reactor for ordinary concrete was approximately 25.6 cm. As the hydrogen content per unit volume of serpentine concrete was higher than that of ordinary concrete, serpentine concrete outperformed the ordinary concrete in terms of thermal neutron shielding. The 10 th -value layer thicknesses of the thermal neutron flux density above the top of the reactor for ordinary concrete was approximately 23.5 cm, which may be derived from Formula (12): <math display="block" id="M23"><mrow><msub><mo>∅</mo><mrow><mtext>side</mtext></mrow></msub><mo>=</mo><mn>6.81</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>10</mn></mrow></msup><mi>exp</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.11</mn><mi>x</mi></mrow><mo>)</mo></mrow><mo>×</mo><mi>exp</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.09</mn><mi>y</mi></mrow><mo>)</mo></mrow><mo>=</mo><mn>1.89</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mn>3</mn></msup><msup><mrow><mtext> cm</mtext></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>⋅</mo><msup><mtext>s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>,</mo></mrow></math> <math display="block" id="M24"><mrow><msub><mo>∅</mo><mrow><mtext>top</mtext></mrow></msub><mo>=</mo><mn>4.75</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mn>8</mn></msup><mtext> exp</mtext><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.098</mn><mi>h</mi></mrow><mo>)</mo></mrow><mo>=</mo><mn>11</mn><msup><mrow><mtext> cm</mtext></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>⋅</mo><msup><mtext>s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>,</mo></mrow></math> where <math id="M25"><mi>x</mi></math> is the thickness of the serpentine concrete on the side of the reactor (60 cm); <math id="M26"><mi>y</mi></math> is the thickness of ordinary concrete on the side of the reactor (120 cm); <math id="M27"><mrow><msub><mo>∅</mo><mrow><mtext>side</mtext></mrow></msub></mrow></math> is the thermal neutron flux density outside the reactor shield. The R 2 of Formula (11) was 0.998 <math id="M28"><mrow><mo>;</mo><mo> </mo><mi>h</mi></mrow></math> is the thickness of ordinary concrete at the top of the reactor (180 cm); <math id="M29"><mrow><msub><mo>∅</mo><mrow><mtext>top</mtext></mrow></msub></mrow></math> is the thermal neutron flux density above the shield on the top of the reactor, and the R 2 of Formula (12) was 0.994. 3.2 Distribution of Radiation Dose 2 The average energy of the gamma rays and that of the neutrons was 0.9 and 2 MeV, respectively [ 14 14 , 34 34 , 35 35 ]. The neutrons were moderated by graphite into thermal neutrons in the reactor core, whereby most of their energy was deposited in the reactor core. The density of the graphite reflection layer was 1.86 g/cm 3 , and its shielding performance for gamma rays was low. Gamma rays were generated by (n, γ) reactions when the neutron was moderated in the graphite reflective layer, such that the gamma dose rate increases in the graphite reflective layer. The gamma dose rate increased quickly in the 0.5 cm thick fuel salt layer as many thermal neutrons were absorbed by 235 U and many gamma rays were released by fission reactions. The reactor vessel made of Hastelloy-N material that was 3 cm thick demonstrated good shielding performance for neutrons and gamma ( Fig. 6a Fig. 6a ). The 30 cm shielding steel plate located between the upper and lower reactor regions was able to reduce the neutron and gamma dose rate of the upper region of the reactor cabin, particularly by decreasing the gamma dose rate. This effectively protects the equipment located in the upper region of the reactor cabin from excessive radiation ( Fig. 6b Fig. 6b ). The neutron dose rate was higher than the gamma dose rate inside the concrete shielding, although the neutron dose rate diminishes relatively rapidly and is lower than gamma dose rate outside the concrete shielding. The irradiation effects of gamma rays are the focus of radiation safety. The gamma dose rate was 16.1 mSv∙h -1 outside the side concrete shield, and the gamma dose rate was 1.19×10 -2 mSv∙h -1 above the top concrete shield. The neutron dose rate was much lower than the gamma dose rate outside the concrete shielding layer. From Formula (10), it was possible to extrapolate the dose rate of neutrons on the outer surface of the concrete shield facing the reactor fuel; this rate was 9.99×10 -2 mSv∙h -1 . From Formula (13), it was possible to extrapolate the dose rate of neutrons of the top concrete shield facing the reactor fuel; it was 6.55×10 -4 mSv∙h -1 . <math display="block" id="M30"><mrow><msub><mi>D</mi><mrow><mtext>top</mtext></mrow></msub><mo>=</mo><mn>3</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mn>4</mn></msup><mtext> exp</mtext><mrow><mo>(</mo><mrow><mo>−</mo><mn>0.098</mn><mi>h</mi></mrow><mo>)</mo></mrow><mo>=</mo><mn>6.55</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mtext> mSv</mtext><mo>⋅</mo><msup><mtext>h</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> where <math id="M31"><mi>h</mi></math> is the thickness of ordinary concrete at the top of the reactor (180 cm); and <math id="M32"><mrow><msub><mi>D</mi><mrow><mtext>top</mtext></mrow></msub></mrow></math> is the dose rate of neutrons of the ordinary concrete shield at top of the reactor, where the R 2 of the equation was 0.994. The dose rate outside the ordinary concrete shielding layer on the side of the reactor was higher than the radiation dose rate above the ordinary concrete on the top of the reactor. This was mainly because the 30 cm shielding steel plate was set on top of the reactor, and the distance between the reactor fuel zone and the top concrete shielding layer was greater than the distance between the reactor fuel zone and the side concrete shielding layer. Rooms around the side of the reactor were underground, and there was almost no need for people to enter during operation of the reactor. The reactor building hall was located above the concrete shielding layer on top of the reactor, and some areas of the reactor building hall required personnel to enter only for a short period of time during the operation of the reactor. The personnel entry operation requirements and radiation divisions during reactor operation were preconditions for shielding design. 4. CONCLUSION 1 This study used the MCNP5 code to calculate the neutron and gamma dose rate distributions around the TMSR-LF reactor, and the axial and radial radiation dose rate distributions of the reactor have been given respectively. The side shielding system comprised of a 60 cm thick thermal shield made of serpentine concrete and a 120 cm thick primary shield made of ordinary concrete. The top shielding system comprised of a 30 cm steel platform and a 180 cm thick primary shield made of ordinary concrete. The neutron flux density followed exponential regressions in the serpentine concrete and ordinary concrete. The serpentine concrete outperformed the ordinary concrete in terms of its thermal neutron shielding performance because of the higher hydrogen content per unit volume. The thermal neutron flux density outside the shielding layer and above the ordinary concrete on top of the reactor was 1.89×10 3 and 11 cm -2 ∙s -1 , respectively. The maximum thermal neutron flux density in the personnel accessible areas was below the 1×10 5 cm -2 ∙s -1 limit, thus proving the effectivity of the shielding system in reducing the radiation effect caused by neutron activation. The radiation dose rate in the upper region of the reactor cabin was significantly lower than that in the lower region of the reactor cabin. The 30 cm shielding steel plate was able to effectively reduce the radiation dose level around the equipment in the upper region of the reactor cabin, thus protecting them from excessive radiation. The neutron dose rate was higher than the gamma dose rate in the concrete shielding layer of the reactor. The gamma dose rate and neutron dose rate followed exponential regressions in the serpentine concrete and ordinary concrete, whereby the neutron dose rate decreased more rapidly than the gamma dose rate in the concrete shielding layer. The gamma dose rate outside the ordinary concrete shielding layer was 16.1 mSv∙h -1 , and the neutron dose rate was 3.71×10 -2 mSv∙h -1 . The gamma dose rate above the ordinary concrete shield on the reactor top was 1.19×10 -2 mSv∙h -1 , and the neutron dose rate was 6.55×10 -4 mSv∙h -1 . The gamma dose rate outside the concrete shielding layer was much higher than the neutron dose rate, and the radiation dose rate of neutrons and gamma outside the concrete shielding layer was higher than the radiation dose rate on the concrete shielding layer at the top of the reactor. The variances of all results using tally F2 and tally F5 was less than 5% when the number of simulated particles was 5×10 8 . The application of the SSW and the WWG cards with tally F2 and tally F5 was able to effectively reduce calculation time and obtain convergent calculation results. References M.H. Jiang , H.J. Xu and Z.M. Dai . Advanced fission energy program-TMSR nuclear energy system . 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All authors read and approved the final manuscript. 10.1007/s41365-021-00857-3 This work was supported by the Chinese Academy of Sciences TMSR Strategic Pioneer Science and Technology Project (No. XDA02010000). 2020-09-29 2020-11-25 2020-11-27 2021-02-25 2021-02-01 2021-03-12 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2021 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-021-00857-3 http://dx.doi.org/10.1007/s41365-021-00857-3 . 2021 Nuclear Science and Techniques 02 32