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Investigation of neutron source model based on EAST plasma shape
Fusion Engineering and Design 153 (2020) 111487
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Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Investigation of neutron source model based on EAST plasma shape a,b
a
a,b
a
T
a,
Liangsheng Huang , Liqun Hu , Mengjie Zhou , Luying Niu , Guoqiang Zhong *, Zijun Zhanga, Kai Lia,b, Bing Honga, Min Xiaoa, Ruixue Zhanga,b a b
Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, 230031, China University of Science and Technology of China, Hefei, 230026, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Plasma neutron source EAST Magnetic surface configuration Neutron flux monitor
Plasma neutron source is an important input for neutronics analysis of tokamak devices, and also a bridge connecting plasma physics and fusion engineering design. In order to describe the spatial distribution of plasma neutron source more accurately in tokamak device, a plasma neutron source model based on EAST plasma shape (NSM-PS) is established. The model will help to improve the reliability of neutron transport. A neutron source generator (NSG) is developed to solve the polar distribution of the neutron emissivity based on NSM-PS, and a source card file is generated which can be used directly by Monte Carlo program. The difference between the neutron source model described by the magnetic surface approximation equation and NSM-PS are analyzed in terms of neutron emissivity, neutron spectrum and neutron wall loading. Finally, the full integration of the neutron emissivity calculated by NSG in the polar direction is compared with the neutron rate measured by the neutron flux monitor, which indirectly verifies the reliability of NSM-PS.
1. Introduction EAST is a fully superconducting tokamak experimental device designed and built by China. It was first used for plasma discharge in 2006. In 2014, the auxiliary heating system of EAST was completed upgrade, and its performance was greatly improved, making the total source power nearly 30 MW [1], in which high power NBI heating deuterium plasma produced a large amount of 2.45 MeV neutrons and a few 14 MeV neutrons. In the recent experiment of EAST, the neutron yield reached 3.9 × 1014 counts/shot [2], which made the research on a series of problems such as activation of structural materials, environmental dose and safety of workers more and more important. Therefore, neutronics analysis and dose distribution calculations are necessary for EAST device, while plasma neutron source is the basis of neutron transport calculation. The EAST device has two divertors that can be operated with limiter, upper single null, lower single null and double null magnetic field configuration [1,3]. The divertor configuration can improve the confinement of plasma, making it easier to enter the high-constraint mode. At present, many neutron source models for neutronics analysis of fusion reactors have a magnetic surface configuration described by a magnetic surface approximation equation (MSAE) [4–7], but they are not exactly consistent with the actual plasma configuration. In order to adapt the characteristics of EAST plasma configuration and more
⁎
accurately describe the spatial distribution of the neutron source, a neutron source model is proposed in this paper. The model spatial distribution is characterized with the magnetic flux distribution calculated by Grid-Shafranov equation which is solved by equilibrium inversion algorithm EFIT. The subsequent contents are as follows: Section 2 describes the process and method of establishing a plasma neutron source model based on EAST plasma shape (NSM-PS). Section 3 introduces the calculation process of the neutron source generator. Section 4 analyzes the differences of neutron emissivity, neutron spectrum and neutron wall loading between the two neutron source models, and uses a neutron flux monitor on EAST to verify the reliability of NSM-PS. Section 5 is the conclusions. 2. Deuterium plasma neutron source model 2.1. Fusion reaction and neutron produce Deuterium plasma discharge on the EAST device has a variety of fusion reactions, including D-D reaction and D-T reaction:
D + D → T + p (3.022MeV ) Q = 4.033MeV
(1)
D + D → 3He + n (2.449MeV ) Q = 3.269MeV
(2)
Corresponding author. E-mail address: [email protected] (G. Zhong).
https://doi.org/10.1016/j.fusengdes.2020.111487 Received 18 November 2019; Received in revised form 11 January 2020; Accepted 12 January 2020 0920-3796/ © 2020 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 153 (2020) 111487
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Table 1 Reactivity fitting Coefficients of three fusion reactions. Coefficient
D(d,p)T
D(d,n)3He
T(d,n)4He
BG(keV0.5) mrc2(keV) C1 C2 C3 C4 C5 C6 C7 (Δ σν )max
31.397 937814 5.657 × 10−12 3.413 × 10−3 1.992 × 10−3 0 1.051 × 10−5 0 0 0.35%
31.397 937814 5.434 × 10−12 5.858 × 10−3 7.682 × 10−3 0 −2.964 × 10-6 0 0 0.3%
34.383 1124656 1.173 × 10−9 1.514 × 10−2 7.519 × 10−2 4.606 × 10−3 1.350 × 10−2 −1.068 × 10-4 1.366 × 10−5 0.25%
(Δ σν )max (%) represents the maximum deviation of fitting from the input data.
be described by MS. In the cylindrical coordinate system (R, Z , φ) , the MSAE can be described as [4,6,7]:
Fig. 1. Branching ratio between D(D,p)T and D(D,n)3He, E is relative energy of deuteron in centroid coordinates, and BR is branching ratio. 4
2 ⎧ R = R 0 + Aρ cos (α + δi sinα ) + R esh [1 − ρ ] ⎨ Z = kAρsinα + Z 0 ⎩
(3)
D + T → He + n (14.029MeV ) Q = 17.59MeV
where, R 0 is the major radius of surface centroid, A is the minor radius, ρ is the normalized radius, R esh is the Shafranov radial displacement, k is the elongation factor, Z0 is the plasma axial shift, and α is the poloidal angle. If 0 < α ≤ π , δi is the upper triangularity factor δu . If π < α ≤ 2π , δi is the lower triangularity factor δl . Comparing the shapes of the MS described by the MSAE with the actual, we find that there are differences between the two MS shapes, especially the divertor shaped discharge. There is a large deviation on the side of X-point (the polar magnetic field is zero), which may have a great influence on the polar distribution of the neutron emissivity. As shown in Fig. 2, the plasma parameters in the MSAE are derived from the calculation results of the equilibrium inversion EFIT.
The branching ratio of the two D-D reactions is shown in Fig. 1 [8]. For the EAST tokamak device, E is in the shaded region, and the branching ratio is approximately 1:1. Due to the accumulation of tritium and the high reaction cross section of D-T, there will be 14 MeV neutrons, but the proportion of neutrons is only within the range of 0.1–2% [4,9]. In order to simplify the plasma neutron source model, this paper only considers 2.45 MeV neutrons. 2.2. D-D thermonuclear fusion neutron emissivity Thermonuclear fusion reaction will occur when the plasma temperature and density reach certain conditions. Let the density of the reaction nucleus be Ni and Nj respectively, the corresponding normalized velocity distribution functions are fi (vi ) and f j (vj ) , the relative velocity is g = vi − vj , the reaction cross section is σ (g ) , and the neutron emissivity per unit volume is dS / dV :
dS = Ni Nj σ (g ) g , dV
(7)
(4) 3
where, σ (g ) g = ∬ fi (vi ) f j (vj ) gσ (g ) dvi dvj , in cm /s, and g is related to ion temperature Ti . When the ion temperature Ti ∈ (0.2, 100]keV , σ (g ) g has the following numerical expression [8,10]:
〈σν〉 (Ti ) ⎧ ⎪ ⎪ θ= Ti / ⎧1 − ⎨ ⎨ 1 ⎩ ⎪ ⎪ ⎩
= C1∙θ ξ /(mr c 2Ti3 ) ∙e−3ξ Ti ∙ [C 2 + Ti ∙ (C 4 + Ti ∙C 6)] ⎫, + Ti ∙ [C 3 + Ti ∙ (C 5 + Ti ∙C 7)] ⎬ ⎭ ξ= (BG2 /(4θ))1/3
(5)
The coefficients in the formula are shown in Table 1. For D-D reaction, the probability of D(D,n)3He is 0.5, and dS / dV can be written as:
dSDD = 0.5⋅ND2 σg (Ti ) , dV
(6)
2.3. The polar distribution of neutron emissivity In the equilibrium state of plasma, according to the ideal MHD → → equation, there is formula J × B = ∇p. Dot the left and right sides of → → the formula with B and J , the results are both zero, indicating that the current and the magnetic field are on a torus, and the pressure p is perpendicular to the torus, so p = const on the torus, called magnetic surface (MS). The plasma density and temperature are approximately constant on MS, so the neutron emissivity on the polar distribution can
Fig. 2. The comparison between the last closed magnetic surface described by the MSAE (dotted red line) and the plasma boundary calculated by EFIT (solid blue line); (a) is the configuration of the limiter; (b),(c) and (d) are the configuration of the upper single null, lower single null and double null divertor respectively (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). 2
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Assuming that the polar profile is described by a rectangular grid Gi, j (i,j = 1,2,…,n), Pi, j is the probability of generating fusion neutrons per n n unit time, with ∑i= 1 ∑ j= 1 Pi,j = 1; assuming the ion temperature Ti, j on
In order to solve the problem that the MSAE cannot completely describe the actual configuration of MS, the polar magnetic flux (ψ ) distribution calculated by the equilibrium inversion algorithm EFIT is used to describe the polar distribution of neutron emissivity. Information about the equilibrium inversion algorithm EFIT on the EAST device are shown in Refs. [11] and [12]. The conversion between polar magnetic flux and normalized radius is: ρ =
ψ − ψ0 ψsep − ψ0
the grid, the energy Ei, j ∼ N (b, σi2, j ) of the emitted neutrons, with σi2, j = 1227.4 × Ti, j . Therefore, the total neutron spectrum distribution E still obeys the Gaussian distribution, which has:
, where n
subscript 0 and sep represent the magnetic flux value at the magnetic axis and boundary respectively.
E∼N
2.4. Ion temperature and density distributions of plasma
1−ρ ⎨ ⎪ Ti (ρ) = Ti, sep + (Ti, ped − Ti, sep ) 1 − ρ ped ⎩
(8)
(9)
where, the subscripts ped indicates the value of the corresponding variable at the pedestal; αn is the ion density index, αT and βT are the ion temperature indexes. Since there is no pedestal phenomenon in the low confinement mode during the plasma operation, then [4,6,7]:
(10)
2.5. Neutron spectrum and angular distribution There are two ways to describe the energy spectrum of neutron source in the calculation of neutron transport: Standard Gaussian fusion spectrum (SG) and Muir velocity Gaussian fusion spectrum (MG). SG and MG have little difference in actual neutronics analysis [7,13]. Therefore, this paper assumes that the energy spectrum of the neutron emitted by the plasma obeys SG, then:
p (E ) = c⋅exp ⎡− ⎢ ⎣
(E − b)2 ⎤ , ⎥ a2 ⎦
(11)
where b is the average energy in keV and a is the energy width in keV. The full width at half maximum (FWHM) of the neutron spectrum [14] is:
ΔEn (fwhm) ≈
4Mn M ln2 α ⋅ QTi , Mn + Mα Mn
⎞
i=1 j=1
⎠
(13)
The main function of Neutron Source Generator (NSG) is to calculate the neutron emissivity distribution in the polar direction based on NSM-PS. After normalizing the neutron emissivity distribution, the three-dimensional discrete source file will be automatically generated and can be directly used in Monte Carlo codes, such as the SEDF card of MCNP [16] code. The calculation process of NSG is shown in Fig. 3. The off-line EFIT calculated data is stored in MDSplus on EAST, and the magnetic flux distribution can be obtained by accessing MDSplus with MATLAB language. An introduction to MDSplus is given in reference [17]. Ion density is calculated by electron density distribution, effective charge numbers and H/D ratio. After the treatment of lithium powder on the vacuum vessel wall, the main impurity during the discharge is lithium, (3-Zeff) 1 then nD≈ 2 1+n / n n e . Assuming that Zeff profile is flat, this value is H D the line averaged ion effective charge Z¯eff , and the relative uncertainty is 18% [18]. NSG is represented by red and blue dotted boxes in Fig. 3. In the process of calculating the neutron emissivity distribution, the plasma region is divided into a rectangular grid of 129 × 129, with the R direction being 1.1∼2.8 m and Z direction being −1.3∼1.3 m. Neutron spectrum of plasma is calculated by Monte Carlo method. According to the distribution data on the profile, random sampling is carried out by using the probability of neutron emissivity and the statistics of neutron energy corresponding to ion temperature at the emission position. Then, combined with the real physical process, the energy of all the emitted neutrons are counted to obtain the neutron spectrum, which is consistent with the analytical calculation results in Section 2.5. Combined with angular distribution, neutron emissivity profile and energy spectrum, a neutron source is obtained and processed into text document, which is compiled into source file for the EAST device's neutronic analysis. The green arrow part uses neutron flux monitor and neutron wall loading to verify the plasma neutron source.
,
2 αn ⎧ ni (ρ) = ni0 [1 − ρ ] 2 ]αT ⎨ T ( ρ ) = T [1 − ρ i0 ⎩ i
n
3. Neutron source generator
Otherwise, ρped ≤ ρ ≤ 1
⎧ ni (ρ) = ni, sep + (ni, ped − ni, sep ) 1 − ρ ⎪ 1 − ρped
n
∑ ∑ Pi,j⋅σi2,j⎟
The ion temperature distribution can be obtained by measuring the width of energy spectrum, which will provide an effective means for ion temperature diagnosis. The angular distribution of neutron source in plasma is assumed to be isotropic [4,15].
The temperature and density distributions of ions are closely related to the confinement modes of plasma. According to the characteristics of the high confinement mode (H-mode), there is a very high pressure gradient near the plasma boundary, which forms a temperature and density pedestal in the plasma region. When the plasma is in H-mode, Ti and ni can be expressed as [6,7]: If 0 ≤ ρ ≤ ρped , then 2 αn ⎧ ni (ρ) = ni, ped + (ni0 − ni, ped )[1 − (ρ / ρped ) ] ⎨ Ti (ρ) = Ti, ped + (Ti0 − Ti, ped )[1 − (ρ / ρped ) βT ]αT ⎩
n
⎛ P ⋅b , ⎜∑ ∑ i, j ⎝ i=1 j=1
4. Model analysis (12)
According to the characteristics of NSM-PS, the model is only applicable to calculate the distribution of fusion neutrons generated by thermonuclear reactions. Therefore, the plasma parameters used in the model analysis are specific - with low hybrid wave’s auxiliary heating, but no neutral beam injection. This paper selects the EAST deuterium plasma discharge classic shot #77160. The basic parameters of the shot are: plasma current Ip = 450kA , electron line density ne = 3 × 1019m−3 , lower hybrid waves heating power PLHW = 2.6MW , electron cyclotron resonance heating power PECRH = 0.7MW , and the MS is the configuration of the upper single null divertor.
Here the subscript n and α represent the neutron and the reaction product 3He or 4He, respectively. For D-D reaction, b= 2449keV , a = 49.546 Ti . For D-T reaction, b = 14029keV , a = 106.299 Ti . The FWHM is proportional to Ti . Since the temperature distribution in the polar profile of the plasma is not uniform, the neutron spectrum is not single, but overlapped by the energy spectrum at different positions. The larger the ion temperature is, the wider the energy spectrum will be. Therefore, this paper makes the following theoretical explanations to the energy spectrum in the polar profile. 3
Fusion Engineering and Design 153 (2020) 111487
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Fig. 3. NSG calculation flow chart.
MSAE, there is a neutron emissivity distribution outside the plasma boundary, which is inconsistent with the actual discharge situation. However, due to the low neutron emissivity at the boundary, the influence on neutronic analysis is basically negligible. The main reason is that the magnetic surface of NSM-MSAE is described by Eq. (7), when ρ = 0 , R and Z represent the coordinates of the magnetic axis, and as ρ increases, the magnetic surface is always symmetric with respect to Z = Z0 , with no deviation in the Z direction. This result can provide a reference for MSAE improvement by adding an offset in z-axis direction. The distribution of Smsae − Sps indicates that the neutron emissivity calculated by NSM-MSAE is lower near the magnetic axis than that calculated by NSM-PS, but higher on the upper and lower sides of the magnetic axis. Fig. 5 shows the neutron spectrum calculated by NSG using the Monte Carlo method. The average energy of neutrons produced by NSM-PS and NSM-MSAE is 2449 keV, and the FWHM obtained by Gaussian function fitting are 76.03 keV and 76.15 keV, respectively. The FWHM of NSM-MSAE is 0.16% larger than that of NSM-PS. The FWHM calculated analytically by formula (13) are 76.39 keV and
4.1. Neutron emissivity and neutron spectrum In order to compare the difference between the neutron emissivity generated by NSM-MSAE (NSM-MSAE represents the neutron source model described by MSAE on the magnetic surface) and NSM-PS, a corresponding calculation module was added in NSG, where the least square method was used to solve the Eq. (7), and the Monte Carlo method mentioned in other references was also used [6,7]. The plasma parameters of the shot #77160 at 3.82 s were used as the input of NSG, and the polar distribution of neutron emissivity of the two models were calculated respectively, as shown in Fig. 4. In Fig. 4, the red curve and the black curve represent plasma boundary and limiter, respectively. When ρ = 0 , the positions of neutrons produced by NSM-PS and NSM-MSAE are on the magnetic axis (green cross). From the boundary to the core, the neutron emissivity 2 increases in the form of Gaussian function e−(ρ / con) .The outer side of the neutron emissivity distribution of NSM-PS is in good agreement with the plasma boundary, and all of them are within the boundary. In NSM-
Fig. 4. Full integral normalized neutron emissivity polar distribution map. Left side is the distribution of the neutron emissivity logarithmically processed value log (Sps ) calculated by NSM-PS. In the middle graph, the distribution of log (Smsae ) is from NSM-MSAE. Right side is the distribution of Smsae − Sps . 4
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Fig. 7. NWL distribution of four neutron source models.
Fig. 5. Neutron spectrum produced by NSM-PS and NSM-MSAE models.
76.53 keV respectively, and the difference between the results of Monte Carlo numerical method and that of the analytical formula is less than 0.5%. In summary, the neutron spectrum produced by the two models have little difference.
4.2. Neutron wall loading The neutron wall loading (NWL) is the fusion neutron power loaded per unit area on the first wall of the vacuum vessel [19]. These neutrons are directly generated by the plasma and do not interact with any material. Therefore, the change of NWL can directly reflect the information of the neutron source of the plasma and can also verify the correctness of the SDEF file generated by the NSG procedure. In order to better understand the information of NWL reflecting neutron sources, two point source models (P1 and P2) are set up besides NSM-PS and NSM-MSAE. As shown in Fig. 6-(a), the blue solid and red solid are the positions of P1 and P2 point sources, respectively. In this paper, we use the idea of neutronics parametric modeling. Firstly, the plasma geometric boundary is divided into 36 modules in an equiangular manner. Then each module is described by a torus, and finally all the torus surfaces are integrated to form a plasma source geometry, as shown in Fig. 6-(b). According to the current EAST discharge situation, the number of neutrons generated per unit time is set as 1.0 × 1014. Combined with plasma source geometry and SDEF file generated by NSG for neutron transport calculation, the NWL of each module in the first wall is obtained, and the specific results are shown in Fig. 7. Fig. 8
Fig. 8. NWL’s difference distribution between different neutron source models. P2 − P1 represents[(N2 − N1)/ N1] × 100% .
shows the distribution of NWL differences among different neutron source models. P1 is located on the symmetry axis of the Z axis of the plasma boundary. Let this point be the coordinate origin, and the NWL is symmetrically distributed. The deviation between the point source position (magnetic axis) of P1 and the origin of the coordinate is known (the radial deviation is 4.62 cm, and the Z deviation is 1.93 cm). The NWL of module 27 is lower than that of module 10, indicating that the magnetic axis is offset from the origin in the positive direction of Z. The difference of NWL between P1 and P2 on module 10 is small, about 0.88%, indicating that the deviation in Z direction is small. Compared with P1, the NWL of P2 is smaller on module 18 and 19, and larger on module 1, 2, 35 and 36. Moreover, the difference of NWL in these modules is relatively large, up to 12.37%, indicating that the magnetic axis has deviation from the origin along the R direction, and the deviation is large. According to the NWL analysis of P1 and P2, the deviation of the center position of the plasma neutron source in Z direction can be studied from two modules 10 and 27, and the deviation of R direction can be studied from several modules 1, 2, 17, 18, 19, 20, 35 and 36. In Fig. 8, the variation of NWL difference distribution between the three neutron source models (NSM-PS, NSM-MSAE and P2) and P1 are similar respectively, but the variation degree are different, indicating that the deviation trend of the center position of the neutron source is the same
Fig. 6. (a) Module division diagram; (b) Corresponding to the 45 ° CAD model generated by (a). 5
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can describe the neutron source distribution more accurately and consistent with the actual discharge situation. The neutron emissivity calculated by NSM-MSAE is lower near the magnetic axis than that calculated by NSM-PS, but higher on the upper and lower sides of the magnetic axis. The average energy of neutrons produced by NSM-PS and NSM-MSAE is 2449 keV, and the FWHM obtained by Gaussian function fitting are 76.03 keV and 76.15 keV respectively. The FWHM of NSM-MSAE is 0.16% larger than that of NSMPS. The maximum difference in NWL between NSM-PS and NSM-MSAE is 4.0.5%. This result can provide a reference for MSAE improvement by adding an offset in z-axis direction. In addition, the full integration of neutron emissivity by NSG in the polar direction was compared with the neutron rate measured by NFM: the change trend of neutron rate calculated by NSG is synchronized with that of NFM. The average neutron rate calculated by NSG is 9.762 × 109n/s, which is 4.67% lower than the average neutron rate measured by NFM. The analysis shows that the difference between the calculated result of NSG and the measured result of NFM is within a reasonable range, and the result is credible, which can indirectly verify the accuracy of NSM-PS.
Fig. 9. The neutron rate calculated by NSG is compared with the experimental data measured by the NFM. 3He represents the NFM data, and NSG represents the calculation result of NSM-PS.
CRediT authorship contribution statement
and offset is different. It can be seen from the NWL difference distribution of MSAE-PS that the distribution is basically symmetric, indicating that the center position of the neutron source in the two models has little difference in Z direction; the middle is greater than zero and the two sides are less than zero, and the maximum difference is 4.0.5%. Therefore, the radial value relationship of the center positions of the neutron sources of NSM-PS, NSM-MSAE and P2 is: Rps > Rmsae > Rp2 .
Liangsheng Huang: Conceptualization, Methodology, Software, Writing - original draft, Investigation, Visualization. Liqun Hu: Writing - review & editing, Supervision, Project administration. Mengjie Zhou: Writing - original draft, Writing - review & editing. Luying Niu: Resources, Investigation. Guoqiang Zhong: Validation, Writing - review & editing, Funding acquisition. Zijun Zhang: Writing - original draft. Kai Li: Resources. Bing Hong: Visualization. Min Xiao: Resources. Ruixue Zhang: Resources.
4.3. Neutron rate
Declaration of Competing Interest
By using the neutron diagnosis systems on EAST, the full integration in the polar direction of the neutron emissivity calculated by NSG is compared with the neutron rate measured by the neutron flux monitor (NFM) to indirectly verify the accuracy of NSM-PS. The evolution of low-yield neutron fluence over time is mainly monitored by a highly sensitive 3He proportional counter tube detector with a maximum time resolution of 1 ms [20]. The full integration of the neutron emissivity at 3.82 s, 4.06 s, 4.54 s, 5.02 s, 5.50 s and 5.98 s of the shot #77160 was calculated using NSG, as shown in Fig. 9. 3He-1 ms is the NFM data with a time resolution of 1 ms, while 3He-10 ms is the data processed after smoothing and reducing the time resolution of the original data to 10 ms. The change in neutron rate calculated by NSG is synchronized with NFM, and there is a fluctuation that first decreases and then increases. The average neutron rate calculated by NSG is 9.762 × 109n/s, which is 4.67% lower than the average neutron rate measured by NFM. The possible reasons for the results are as follows: there is a certain error in fitting the density index and temperature index; in addition, a small number of photoneutrons are not considered. The error bar value is the result of considering the relative uncertainty of thez¯eff , which indicates that the distribution of effective charge has a great influence on the neutron rate. To sum up, the difference between the calculated result of NSG and the measured result of NFM is within a reasonable range, and the result is credible, which indirectly verifies the accuracy of NSM-PS.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors would like to thank members of EAST experimental team and Professor Bo Lyu (ASIPP, China) for their support and help in this research. This work was supported by the National Natural Science Foundation of China (No. 11605241). Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.fusengdes.2020. 111487. References [1] B.N. Wan, G.S. Xu, Advances in experimental research towards high confinement and steady state operation on the Experimental Advanced Supercon-ducting Tokamak (in Chinese), Sci. Sin-Phys. Mech. Astron 49 (2019) 045205, , https://doi. org/10.1360/SSPMA2018-00233. [2] Kai Li, Hu Liqun, et al., Calibration of the gamma-ray measurement procedure in the EAST neutron activation system, Fusion Eng. Des. 148 (2019) 1112–1178, https://doi.org/10.1016/j.fusengdes.2019.111278. [3] ASIPP official website: http://english.ipp.cas.cn/. [4] Y. Chen, Y. Wu, Effect of fusion neutron source numerical models on neutron wall loading in a D-D tokamak device, Plasma Sci. Technol. 15 (2003) 2, https://doi.org/ 10.1088/1009-0630/5/2/011. [5] E. Polunovskiy, SEDF card for the ITER standard neutron source inductive operation scenario with 500MW of fusion power, IDM ITER D 2KS8CN v1.4, (2010). [6] C. Fausser, A.L. Puma, F. Gabriel, R. Villari, Tokamak D-T neutron source models for different plasma physics confinement modes, Fusion Eng. Des. 87 (2012) 787–792, https://doi.org/10.1016/j.fusengdes.2012.02.025.
5. Conclusions In this paper, a deuterium plasma neutron source model is established based on EAST plasma shape, and the calculation of neutron spectrum is explained theoretically. Write the NSG to solve the neutron emissivity and generate the source file for neutronic calculations. The differences between NSM-MSAE and NSM-PS in neutron emissivity, neutron spectrum and NWL are analyzed. The results show that NSM-PS 6
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7
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Investigation of neutron source model based on EAST plasma shape a,b
a
a,b
a
T
a,
Liangsheng Huang , Liqun Hu , Mengjie Zhou , Luying Niu , Guoqiang Zhong *, Zijun Zhanga, Kai Lia,b, Bing Honga, Min Xiaoa, Ruixue Zhanga,b a b
Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, 230031, China University of Science and Technology of China, Hefei, 230026, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Plasma neutron source EAST Magnetic surface configuration Neutron flux monitor
Plasma neutron source is an important input for neutronics analysis of tokamak devices, and also a bridge connecting plasma physics and fusion engineering design. In order to describe the spatial distribution of plasma neutron source more accurately in tokamak device, a plasma neutron source model based on EAST plasma shape (NSM-PS) is established. The model will help to improve the reliability of neutron transport. A neutron source generator (NSG) is developed to solve the polar distribution of the neutron emissivity based on NSM-PS, and a source card file is generated which can be used directly by Monte Carlo program. The difference between the neutron source model described by the magnetic surface approximation equation and NSM-PS are analyzed in terms of neutron emissivity, neutron spectrum and neutron wall loading. Finally, the full integration of the neutron emissivity calculated by NSG in the polar direction is compared with the neutron rate measured by the neutron flux monitor, which indirectly verifies the reliability of NSM-PS.
1. Introduction EAST is a fully superconducting tokamak experimental device designed and built by China. It was first used for plasma discharge in 2006. In 2014, the auxiliary heating system of EAST was completed upgrade, and its performance was greatly improved, making the total source power nearly 30 MW [1], in which high power NBI heating deuterium plasma produced a large amount of 2.45 MeV neutrons and a few 14 MeV neutrons. In the recent experiment of EAST, the neutron yield reached 3.9 × 1014 counts/shot [2], which made the research on a series of problems such as activation of structural materials, environmental dose and safety of workers more and more important. Therefore, neutronics analysis and dose distribution calculations are necessary for EAST device, while plasma neutron source is the basis of neutron transport calculation. The EAST device has two divertors that can be operated with limiter, upper single null, lower single null and double null magnetic field configuration [1,3]. The divertor configuration can improve the confinement of plasma, making it easier to enter the high-constraint mode. At present, many neutron source models for neutronics analysis of fusion reactors have a magnetic surface configuration described by a magnetic surface approximation equation (MSAE) [4–7], but they are not exactly consistent with the actual plasma configuration. In order to adapt the characteristics of EAST plasma configuration and more
⁎
accurately describe the spatial distribution of the neutron source, a neutron source model is proposed in this paper. The model spatial distribution is characterized with the magnetic flux distribution calculated by Grid-Shafranov equation which is solved by equilibrium inversion algorithm EFIT. The subsequent contents are as follows: Section 2 describes the process and method of establishing a plasma neutron source model based on EAST plasma shape (NSM-PS). Section 3 introduces the calculation process of the neutron source generator. Section 4 analyzes the differences of neutron emissivity, neutron spectrum and neutron wall loading between the two neutron source models, and uses a neutron flux monitor on EAST to verify the reliability of NSM-PS. Section 5 is the conclusions. 2. Deuterium plasma neutron source model 2.1. Fusion reaction and neutron produce Deuterium plasma discharge on the EAST device has a variety of fusion reactions, including D-D reaction and D-T reaction:
D + D → T + p (3.022MeV ) Q = 4.033MeV
(1)
D + D → 3He + n (2.449MeV ) Q = 3.269MeV
(2)
Corresponding author. E-mail address: [email protected] (G. Zhong).
https://doi.org/10.1016/j.fusengdes.2020.111487 Received 18 November 2019; Received in revised form 11 January 2020; Accepted 12 January 2020 0920-3796/ © 2020 Elsevier B.V. All rights reserved.
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Table 1 Reactivity fitting Coefficients of three fusion reactions. Coefficient
D(d,p)T
D(d,n)3He
T(d,n)4He
BG(keV0.5) mrc2(keV) C1 C2 C3 C4 C5 C6 C7 (Δ σν )max
31.397 937814 5.657 × 10−12 3.413 × 10−3 1.992 × 10−3 0 1.051 × 10−5 0 0 0.35%
31.397 937814 5.434 × 10−12 5.858 × 10−3 7.682 × 10−3 0 −2.964 × 10-6 0 0 0.3%
34.383 1124656 1.173 × 10−9 1.514 × 10−2 7.519 × 10−2 4.606 × 10−3 1.350 × 10−2 −1.068 × 10-4 1.366 × 10−5 0.25%
(Δ σν )max (%) represents the maximum deviation of fitting from the input data.
be described by MS. In the cylindrical coordinate system (R, Z , φ) , the MSAE can be described as [4,6,7]:
Fig. 1. Branching ratio between D(D,p)T and D(D,n)3He, E is relative energy of deuteron in centroid coordinates, and BR is branching ratio. 4
2 ⎧ R = R 0 + Aρ cos (α + δi sinα ) + R esh [1 − ρ ] ⎨ Z = kAρsinα + Z 0 ⎩
(3)
D + T → He + n (14.029MeV ) Q = 17.59MeV
where, R 0 is the major radius of surface centroid, A is the minor radius, ρ is the normalized radius, R esh is the Shafranov radial displacement, k is the elongation factor, Z0 is the plasma axial shift, and α is the poloidal angle. If 0 < α ≤ π , δi is the upper triangularity factor δu . If π < α ≤ 2π , δi is the lower triangularity factor δl . Comparing the shapes of the MS described by the MSAE with the actual, we find that there are differences between the two MS shapes, especially the divertor shaped discharge. There is a large deviation on the side of X-point (the polar magnetic field is zero), which may have a great influence on the polar distribution of the neutron emissivity. As shown in Fig. 2, the plasma parameters in the MSAE are derived from the calculation results of the equilibrium inversion EFIT.
The branching ratio of the two D-D reactions is shown in Fig. 1 [8]. For the EAST tokamak device, E is in the shaded region, and the branching ratio is approximately 1:1. Due to the accumulation of tritium and the high reaction cross section of D-T, there will be 14 MeV neutrons, but the proportion of neutrons is only within the range of 0.1–2% [4,9]. In order to simplify the plasma neutron source model, this paper only considers 2.45 MeV neutrons. 2.2. D-D thermonuclear fusion neutron emissivity Thermonuclear fusion reaction will occur when the plasma temperature and density reach certain conditions. Let the density of the reaction nucleus be Ni and Nj respectively, the corresponding normalized velocity distribution functions are fi (vi ) and f j (vj ) , the relative velocity is g = vi − vj , the reaction cross section is σ (g ) , and the neutron emissivity per unit volume is dS / dV :
dS = Ni Nj σ (g ) g , dV
(7)
(4) 3
where, σ (g ) g = ∬ fi (vi ) f j (vj ) gσ (g ) dvi dvj , in cm /s, and g is related to ion temperature Ti . When the ion temperature Ti ∈ (0.2, 100]keV , σ (g ) g has the following numerical expression [8,10]:
〈σν〉 (Ti ) ⎧ ⎪ ⎪ θ= Ti / ⎧1 − ⎨ ⎨ 1 ⎩ ⎪ ⎪ ⎩
= C1∙θ ξ /(mr c 2Ti3 ) ∙e−3ξ Ti ∙ [C 2 + Ti ∙ (C 4 + Ti ∙C 6)] ⎫, + Ti ∙ [C 3 + Ti ∙ (C 5 + Ti ∙C 7)] ⎬ ⎭ ξ= (BG2 /(4θ))1/3
(5)
The coefficients in the formula are shown in Table 1. For D-D reaction, the probability of D(D,n)3He is 0.5, and dS / dV can be written as:
dSDD = 0.5⋅ND2 σg (Ti ) , dV
(6)
2.3. The polar distribution of neutron emissivity In the equilibrium state of plasma, according to the ideal MHD → → equation, there is formula J × B = ∇p. Dot the left and right sides of → → the formula with B and J , the results are both zero, indicating that the current and the magnetic field are on a torus, and the pressure p is perpendicular to the torus, so p = const on the torus, called magnetic surface (MS). The plasma density and temperature are approximately constant on MS, so the neutron emissivity on the polar distribution can
Fig. 2. The comparison between the last closed magnetic surface described by the MSAE (dotted red line) and the plasma boundary calculated by EFIT (solid blue line); (a) is the configuration of the limiter; (b),(c) and (d) are the configuration of the upper single null, lower single null and double null divertor respectively (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). 2
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Assuming that the polar profile is described by a rectangular grid Gi, j (i,j = 1,2,…,n), Pi, j is the probability of generating fusion neutrons per n n unit time, with ∑i= 1 ∑ j= 1 Pi,j = 1; assuming the ion temperature Ti, j on
In order to solve the problem that the MSAE cannot completely describe the actual configuration of MS, the polar magnetic flux (ψ ) distribution calculated by the equilibrium inversion algorithm EFIT is used to describe the polar distribution of neutron emissivity. Information about the equilibrium inversion algorithm EFIT on the EAST device are shown in Refs. [11] and [12]. The conversion between polar magnetic flux and normalized radius is: ρ =
ψ − ψ0 ψsep − ψ0
the grid, the energy Ei, j ∼ N (b, σi2, j ) of the emitted neutrons, with σi2, j = 1227.4 × Ti, j . Therefore, the total neutron spectrum distribution E still obeys the Gaussian distribution, which has:
, where n
subscript 0 and sep represent the magnetic flux value at the magnetic axis and boundary respectively.
E∼N
2.4. Ion temperature and density distributions of plasma
1−ρ ⎨ ⎪ Ti (ρ) = Ti, sep + (Ti, ped − Ti, sep ) 1 − ρ ped ⎩
(8)
(9)
where, the subscripts ped indicates the value of the corresponding variable at the pedestal; αn is the ion density index, αT and βT are the ion temperature indexes. Since there is no pedestal phenomenon in the low confinement mode during the plasma operation, then [4,6,7]:
(10)
2.5. Neutron spectrum and angular distribution There are two ways to describe the energy spectrum of neutron source in the calculation of neutron transport: Standard Gaussian fusion spectrum (SG) and Muir velocity Gaussian fusion spectrum (MG). SG and MG have little difference in actual neutronics analysis [7,13]. Therefore, this paper assumes that the energy spectrum of the neutron emitted by the plasma obeys SG, then:
p (E ) = c⋅exp ⎡− ⎢ ⎣
(E − b)2 ⎤ , ⎥ a2 ⎦
(11)
where b is the average energy in keV and a is the energy width in keV. The full width at half maximum (FWHM) of the neutron spectrum [14] is:
ΔEn (fwhm) ≈
4Mn M ln2 α ⋅ QTi , Mn + Mα Mn
⎞
i=1 j=1
⎠
(13)
The main function of Neutron Source Generator (NSG) is to calculate the neutron emissivity distribution in the polar direction based on NSM-PS. After normalizing the neutron emissivity distribution, the three-dimensional discrete source file will be automatically generated and can be directly used in Monte Carlo codes, such as the SEDF card of MCNP [16] code. The calculation process of NSG is shown in Fig. 3. The off-line EFIT calculated data is stored in MDSplus on EAST, and the magnetic flux distribution can be obtained by accessing MDSplus with MATLAB language. An introduction to MDSplus is given in reference [17]. Ion density is calculated by electron density distribution, effective charge numbers and H/D ratio. After the treatment of lithium powder on the vacuum vessel wall, the main impurity during the discharge is lithium, (3-Zeff) 1 then nD≈ 2 1+n / n n e . Assuming that Zeff profile is flat, this value is H D the line averaged ion effective charge Z¯eff , and the relative uncertainty is 18% [18]. NSG is represented by red and blue dotted boxes in Fig. 3. In the process of calculating the neutron emissivity distribution, the plasma region is divided into a rectangular grid of 129 × 129, with the R direction being 1.1∼2.8 m and Z direction being −1.3∼1.3 m. Neutron spectrum of plasma is calculated by Monte Carlo method. According to the distribution data on the profile, random sampling is carried out by using the probability of neutron emissivity and the statistics of neutron energy corresponding to ion temperature at the emission position. Then, combined with the real physical process, the energy of all the emitted neutrons are counted to obtain the neutron spectrum, which is consistent with the analytical calculation results in Section 2.5. Combined with angular distribution, neutron emissivity profile and energy spectrum, a neutron source is obtained and processed into text document, which is compiled into source file for the EAST device's neutronic analysis. The green arrow part uses neutron flux monitor and neutron wall loading to verify the plasma neutron source.
,
2 αn ⎧ ni (ρ) = ni0 [1 − ρ ] 2 ]αT ⎨ T ( ρ ) = T [1 − ρ i0 ⎩ i
n
3. Neutron source generator
Otherwise, ρped ≤ ρ ≤ 1
⎧ ni (ρ) = ni, sep + (ni, ped − ni, sep ) 1 − ρ ⎪ 1 − ρped
n
∑ ∑ Pi,j⋅σi2,j⎟
The ion temperature distribution can be obtained by measuring the width of energy spectrum, which will provide an effective means for ion temperature diagnosis. The angular distribution of neutron source in plasma is assumed to be isotropic [4,15].
The temperature and density distributions of ions are closely related to the confinement modes of plasma. According to the characteristics of the high confinement mode (H-mode), there is a very high pressure gradient near the plasma boundary, which forms a temperature and density pedestal in the plasma region. When the plasma is in H-mode, Ti and ni can be expressed as [6,7]: If 0 ≤ ρ ≤ ρped , then 2 αn ⎧ ni (ρ) = ni, ped + (ni0 − ni, ped )[1 − (ρ / ρped ) ] ⎨ Ti (ρ) = Ti, ped + (Ti0 − Ti, ped )[1 − (ρ / ρped ) βT ]αT ⎩
n
⎛ P ⋅b , ⎜∑ ∑ i, j ⎝ i=1 j=1
4. Model analysis (12)
According to the characteristics of NSM-PS, the model is only applicable to calculate the distribution of fusion neutrons generated by thermonuclear reactions. Therefore, the plasma parameters used in the model analysis are specific - with low hybrid wave’s auxiliary heating, but no neutral beam injection. This paper selects the EAST deuterium plasma discharge classic shot #77160. The basic parameters of the shot are: plasma current Ip = 450kA , electron line density ne = 3 × 1019m−3 , lower hybrid waves heating power PLHW = 2.6MW , electron cyclotron resonance heating power PECRH = 0.7MW , and the MS is the configuration of the upper single null divertor.
Here the subscript n and α represent the neutron and the reaction product 3He or 4He, respectively. For D-D reaction, b= 2449keV , a = 49.546 Ti . For D-T reaction, b = 14029keV , a = 106.299 Ti . The FWHM is proportional to Ti . Since the temperature distribution in the polar profile of the plasma is not uniform, the neutron spectrum is not single, but overlapped by the energy spectrum at different positions. The larger the ion temperature is, the wider the energy spectrum will be. Therefore, this paper makes the following theoretical explanations to the energy spectrum in the polar profile. 3
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Fig. 3. NSG calculation flow chart.
MSAE, there is a neutron emissivity distribution outside the plasma boundary, which is inconsistent with the actual discharge situation. However, due to the low neutron emissivity at the boundary, the influence on neutronic analysis is basically negligible. The main reason is that the magnetic surface of NSM-MSAE is described by Eq. (7), when ρ = 0 , R and Z represent the coordinates of the magnetic axis, and as ρ increases, the magnetic surface is always symmetric with respect to Z = Z0 , with no deviation in the Z direction. This result can provide a reference for MSAE improvement by adding an offset in z-axis direction. The distribution of Smsae − Sps indicates that the neutron emissivity calculated by NSM-MSAE is lower near the magnetic axis than that calculated by NSM-PS, but higher on the upper and lower sides of the magnetic axis. Fig. 5 shows the neutron spectrum calculated by NSG using the Monte Carlo method. The average energy of neutrons produced by NSM-PS and NSM-MSAE is 2449 keV, and the FWHM obtained by Gaussian function fitting are 76.03 keV and 76.15 keV, respectively. The FWHM of NSM-MSAE is 0.16% larger than that of NSM-PS. The FWHM calculated analytically by formula (13) are 76.39 keV and
4.1. Neutron emissivity and neutron spectrum In order to compare the difference between the neutron emissivity generated by NSM-MSAE (NSM-MSAE represents the neutron source model described by MSAE on the magnetic surface) and NSM-PS, a corresponding calculation module was added in NSG, where the least square method was used to solve the Eq. (7), and the Monte Carlo method mentioned in other references was also used [6,7]. The plasma parameters of the shot #77160 at 3.82 s were used as the input of NSG, and the polar distribution of neutron emissivity of the two models were calculated respectively, as shown in Fig. 4. In Fig. 4, the red curve and the black curve represent plasma boundary and limiter, respectively. When ρ = 0 , the positions of neutrons produced by NSM-PS and NSM-MSAE are on the magnetic axis (green cross). From the boundary to the core, the neutron emissivity 2 increases in the form of Gaussian function e−(ρ / con) .The outer side of the neutron emissivity distribution of NSM-PS is in good agreement with the plasma boundary, and all of them are within the boundary. In NSM-
Fig. 4. Full integral normalized neutron emissivity polar distribution map. Left side is the distribution of the neutron emissivity logarithmically processed value log (Sps ) calculated by NSM-PS. In the middle graph, the distribution of log (Smsae ) is from NSM-MSAE. Right side is the distribution of Smsae − Sps . 4
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Fig. 7. NWL distribution of four neutron source models.
Fig. 5. Neutron spectrum produced by NSM-PS and NSM-MSAE models.
76.53 keV respectively, and the difference between the results of Monte Carlo numerical method and that of the analytical formula is less than 0.5%. In summary, the neutron spectrum produced by the two models have little difference.
4.2. Neutron wall loading The neutron wall loading (NWL) is the fusion neutron power loaded per unit area on the first wall of the vacuum vessel [19]. These neutrons are directly generated by the plasma and do not interact with any material. Therefore, the change of NWL can directly reflect the information of the neutron source of the plasma and can also verify the correctness of the SDEF file generated by the NSG procedure. In order to better understand the information of NWL reflecting neutron sources, two point source models (P1 and P2) are set up besides NSM-PS and NSM-MSAE. As shown in Fig. 6-(a), the blue solid and red solid are the positions of P1 and P2 point sources, respectively. In this paper, we use the idea of neutronics parametric modeling. Firstly, the plasma geometric boundary is divided into 36 modules in an equiangular manner. Then each module is described by a torus, and finally all the torus surfaces are integrated to form a plasma source geometry, as shown in Fig. 6-(b). According to the current EAST discharge situation, the number of neutrons generated per unit time is set as 1.0 × 1014. Combined with plasma source geometry and SDEF file generated by NSG for neutron transport calculation, the NWL of each module in the first wall is obtained, and the specific results are shown in Fig. 7. Fig. 8
Fig. 8. NWL’s difference distribution between different neutron source models. P2 − P1 represents[(N2 − N1)/ N1] × 100% .
shows the distribution of NWL differences among different neutron source models. P1 is located on the symmetry axis of the Z axis of the plasma boundary. Let this point be the coordinate origin, and the NWL is symmetrically distributed. The deviation between the point source position (magnetic axis) of P1 and the origin of the coordinate is known (the radial deviation is 4.62 cm, and the Z deviation is 1.93 cm). The NWL of module 27 is lower than that of module 10, indicating that the magnetic axis is offset from the origin in the positive direction of Z. The difference of NWL between P1 and P2 on module 10 is small, about 0.88%, indicating that the deviation in Z direction is small. Compared with P1, the NWL of P2 is smaller on module 18 and 19, and larger on module 1, 2, 35 and 36. Moreover, the difference of NWL in these modules is relatively large, up to 12.37%, indicating that the magnetic axis has deviation from the origin along the R direction, and the deviation is large. According to the NWL analysis of P1 and P2, the deviation of the center position of the plasma neutron source in Z direction can be studied from two modules 10 and 27, and the deviation of R direction can be studied from several modules 1, 2, 17, 18, 19, 20, 35 and 36. In Fig. 8, the variation of NWL difference distribution between the three neutron source models (NSM-PS, NSM-MSAE and P2) and P1 are similar respectively, but the variation degree are different, indicating that the deviation trend of the center position of the neutron source is the same
Fig. 6. (a) Module division diagram; (b) Corresponding to the 45 ° CAD model generated by (a). 5
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can describe the neutron source distribution more accurately and consistent with the actual discharge situation. The neutron emissivity calculated by NSM-MSAE is lower near the magnetic axis than that calculated by NSM-PS, but higher on the upper and lower sides of the magnetic axis. The average energy of neutrons produced by NSM-PS and NSM-MSAE is 2449 keV, and the FWHM obtained by Gaussian function fitting are 76.03 keV and 76.15 keV respectively. The FWHM of NSM-MSAE is 0.16% larger than that of NSMPS. The maximum difference in NWL between NSM-PS and NSM-MSAE is 4.0.5%. This result can provide a reference for MSAE improvement by adding an offset in z-axis direction. In addition, the full integration of neutron emissivity by NSG in the polar direction was compared with the neutron rate measured by NFM: the change trend of neutron rate calculated by NSG is synchronized with that of NFM. The average neutron rate calculated by NSG is 9.762 × 109n/s, which is 4.67% lower than the average neutron rate measured by NFM. The analysis shows that the difference between the calculated result of NSG and the measured result of NFM is within a reasonable range, and the result is credible, which can indirectly verify the accuracy of NSM-PS.
Fig. 9. The neutron rate calculated by NSG is compared with the experimental data measured by the NFM. 3He represents the NFM data, and NSG represents the calculation result of NSM-PS.
CRediT authorship contribution statement
and offset is different. It can be seen from the NWL difference distribution of MSAE-PS that the distribution is basically symmetric, indicating that the center position of the neutron source in the two models has little difference in Z direction; the middle is greater than zero and the two sides are less than zero, and the maximum difference is 4.0.5%. Therefore, the radial value relationship of the center positions of the neutron sources of NSM-PS, NSM-MSAE and P2 is: Rps > Rmsae > Rp2 .
Liangsheng Huang: Conceptualization, Methodology, Software, Writing - original draft, Investigation, Visualization. Liqun Hu: Writing - review & editing, Supervision, Project administration. Mengjie Zhou: Writing - original draft, Writing - review & editing. Luying Niu: Resources, Investigation. Guoqiang Zhong: Validation, Writing - review & editing, Funding acquisition. Zijun Zhang: Writing - original draft. Kai Li: Resources. Bing Hong: Visualization. Min Xiao: Resources. Ruixue Zhang: Resources.
4.3. Neutron rate
Declaration of Competing Interest
By using the neutron diagnosis systems on EAST, the full integration in the polar direction of the neutron emissivity calculated by NSG is compared with the neutron rate measured by the neutron flux monitor (NFM) to indirectly verify the accuracy of NSM-PS. The evolution of low-yield neutron fluence over time is mainly monitored by a highly sensitive 3He proportional counter tube detector with a maximum time resolution of 1 ms [20]. The full integration of the neutron emissivity at 3.82 s, 4.06 s, 4.54 s, 5.02 s, 5.50 s and 5.98 s of the shot #77160 was calculated using NSG, as shown in Fig. 9. 3He-1 ms is the NFM data with a time resolution of 1 ms, while 3He-10 ms is the data processed after smoothing and reducing the time resolution of the original data to 10 ms. The change in neutron rate calculated by NSG is synchronized with NFM, and there is a fluctuation that first decreases and then increases. The average neutron rate calculated by NSG is 9.762 × 109n/s, which is 4.67% lower than the average neutron rate measured by NFM. The possible reasons for the results are as follows: there is a certain error in fitting the density index and temperature index; in addition, a small number of photoneutrons are not considered. The error bar value is the result of considering the relative uncertainty of thez¯eff , which indicates that the distribution of effective charge has a great influence on the neutron rate. To sum up, the difference between the calculated result of NSG and the measured result of NFM is within a reasonable range, and the result is credible, which indirectly verifies the accuracy of NSM-PS.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors would like to thank members of EAST experimental team and Professor Bo Lyu (ASIPP, China) for their support and help in this research. This work was supported by the National Natural Science Foundation of China (No. 11605241). Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.fusengdes.2020. 111487. References [1] B.N. Wan, G.S. Xu, Advances in experimental research towards high confinement and steady state operation on the Experimental Advanced Supercon-ducting Tokamak (in Chinese), Sci. Sin-Phys. Mech. Astron 49 (2019) 045205, , https://doi. org/10.1360/SSPMA2018-00233. [2] Kai Li, Hu Liqun, et al., Calibration of the gamma-ray measurement procedure in the EAST neutron activation system, Fusion Eng. Des. 148 (2019) 1112–1178, https://doi.org/10.1016/j.fusengdes.2019.111278. [3] ASIPP official website: http://english.ipp.cas.cn/. [4] Y. Chen, Y. Wu, Effect of fusion neutron source numerical models on neutron wall loading in a D-D tokamak device, Plasma Sci. Technol. 15 (2003) 2, https://doi.org/ 10.1088/1009-0630/5/2/011. [5] E. Polunovskiy, SEDF card for the ITER standard neutron source inductive operation scenario with 500MW of fusion power, IDM ITER D 2KS8CN v1.4, (2010). [6] C. Fausser, A.L. Puma, F. Gabriel, R. Villari, Tokamak D-T neutron source models for different plasma physics confinement modes, Fusion Eng. Des. 87 (2012) 787–792, https://doi.org/10.1016/j.fusengdes.2012.02.025.
5. Conclusions In this paper, a deuterium plasma neutron source model is established based on EAST plasma shape, and the calculation of neutron spectrum is explained theoretically. Write the NSG to solve the neutron emissivity and generate the source file for neutronic calculations. The differences between NSM-MSAE and NSM-PS in neutron emissivity, neutron spectrum and NWL are analyzed. The results show that NSM-PS 6
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