• Acta Physica Sinica
  • Vol. 69, Issue 11, 112801-1 (2020)
Li Deng1、2, Rui Li2、*, Xin Wang2, and Yuan-Guang Fu2
Author Affiliations
  • 1Institute of Applied Physics and Computational Mathematics (IAPCM), Beijing 100094, China
  • 2CAEP Software Centre for High Performance Numerical Simulation (CAEP-SCNS), Beijing 100088, China
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    DOI: 10.7498/aps.69.20200279 Cite this Article
    Li Deng, Rui Li, Xin Wang, Yuan-Guang Fu. Monte Carlo simulation technology based on characteristic γ-ray spectrum analysis[J]. Acta Physica Sinica, 2020, 69(11): 112801-1 Copy Citation Text show less

    Abstract

    Monte Carlo method is an ideal way to simulate criticality, shielding and nuclear detection. JMCT is a multipurpose 3D Mont Carlo (MC) neutron-photon-electron and coupled neutron /photon /electron transport code which is developed by IAPCM. The program is developed based on the combinatorial geometry parallel infrastructure JCOGIN and has the most functions of general Monte Carlo particle transport code, including the various variance reduction techniques. In addition, some new algorithms, such as Doppler broadening on-the-fly (OTF), uniform tally density (UTD), consistent adjoint driven importance sampling (CADIS), fast criticality search of boron concentration (FCSBC), the domain decomposition (DD), the two-level parallel computation of MPI and OpenMP, etc. have been developed, where the number of geometry zones, materials, tallies, depletion zones, memories and period of random number are big enough to simulate various extremely complicated problems. Also the JMCT is hybrid the discrete ordinate SN program JSNT to generate source biasing factors and weight window parameters for deep-penetration shielding problems. The input is based on the CAD modeling, and the result is a visualized output. The JMCT can provide technology support for radiation shielding design, reactor physics and criticality safe analysis. Especially, the JMCT is coupled depletion and thermal-hydraulic code for simulating the reactor feedback effect, including depletion, thermal feedback. In recent years, new function of γ-ray spectrum analysis has been developed.In this paper, the working principles of timing measure are introduced. The advanced calibration count is developed for distinguishing between inelastic γ-ray and capture γ-ray based on time bin tally. On the other hand, when neutron collides with nuclide, the secondary photon is labeled into the primary line photon and primary continuous photon, where energy of primary line photon does not change with the incident neutron energy, such as carbon spectral-line at 4.43 MeV and oxygen spectral-line at 6.13 MeV. The element components of detected object can be determined by the primary line photon. On the other hand, expect value estimator (EVE) is used to produce the secondary photons. The advantage of EVE does not leak any event even with a small probability which is important for detecting the hide exploder. However the shortage of the EVE results in producing a great number of photons with small weight. If all of these small weight photons are simulated one by one, a great amount of computation time and memory will be consumed. For avoiding this case, a new algorithm is design by coupling EVE and DE (direct estimator). The all of secondary photons from EVE only make the direct tally take a little computing time, then end the photon history and return to the DE production photon model (one photon production at most). Final, the total tally is a summation of EVE direct tally and DE scattering tally. The use of new algorithm to realize the analysis of γ-ray spectrum will increase only a little computing time. The numerical tests are done by using own Monte Carlo code JMCT. The correctness and validity of the algorithm are shown preliminarily.
    $N(E,t) = \int_0^t {S(t'){N_\delta }(E,t - t'){\rm{d}}t'} ,$(1)

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    $\int_{{t_a}}^{{t_b}} N(E,t){\rm{d}}t \!=\! \int_{{t_a}}^{{t_b}} {{\rm{d}}t} \int_0^t S(t'){N_\delta }(E,t \!-\! t'){\rm{d}}t'.$(2)

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    $S(t \pm nt) = S(t),~~ n = 1,2, \cdots ,$(3)

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    $S(t) =\begin{cases} {{S_0}{f_\delta }(t),}&{\;0 \leqslant t < \tau ,}\\ {0,}&{\;\tau \leqslant t < T,} \end{cases}$(4)

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    $\begin{split} N(E,t) =\; & {S_0}\left[ \sum\limits_{n = 1}^\infty \int_{ - nT}^{ - nT + \tau } {f_\delta }(t'){N_\delta }(E,t - t'){\rm{d}}t' \right.\\ & \left.+ \int_0^{\min (t,\tau )} {{f_\delta }(t'){N_\delta }(E,t - t'){\rm{d}}t'} \right]\\ =\;& {S_0}\left[\sum\limits_{n = 1}^\infty \int_0^\tau {f_\delta }(t'){N_\delta }(E,t - t' + nT){\rm{d}}t' \right.\\ & \left.+ \int_0^{\min (t,\tau )} {{f_\delta }(t'){N_\delta }(E,t - t'){\rm{d}}t'} \right],\\ & \qquad t \in [0,T].\\[-10pt] \end{split}$(5)

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    ${N_{\rm{I}}} = \int_0^\tau {N(E,t){\rm{d}}t} .$(6)

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    ${N_{{\rm{II}}}} = \int_\tau ^{2\tau } {N(E,t){\rm{d}}t} .$(7)

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    ${N_\delta }(E,t) = \sum\limits_{i = 1}^4 {N_i^\delta (E){f_i}(t)} ,$(8)

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    $\begin{split} &{N_{\rm{I}}}(E) - {N_{{\rm{II}}}}(E)\\ \approx \; & {S_0}\left\{N_1^\delta (E) + N_2^\delta (E)\left[\int_0^\tau \left( {1 - \frac{{2t}}{\tau }} \right){f_2}(t){\rm{d}}t \right.\right.\\ & \left.\left.- \int_\tau ^{2\tau } {\left( {2 - \frac{t}{\tau }} \right){f_2}(t){\rm{d}}t}\right] - \frac{\tau }{2}N_3^\delta (E){f_3}(\tau ) \right\}. \end{split}$(9)

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    $\begin{split}{J_\gamma }({E_0},t) =\; & \int_0^t \int\nolimits_{{r} \in S} \int\nolimits_{{\varOmega } \cdot {n} < 0}\int_0^{{E_0}}{n}\\ & \times {\varOmega }\phi ({r},E,{\varOmega },t){\rm{d}}t{\rm{d}}{r}{\rm{d}}{\varOmega }{\rm{d}}E ,\end{split}$(10)

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    $\begin{split} R({E_0},h) ={}& \eta ({E_0})\int_0^{{E_0}} D({E_0},E)G(E,h){\rm{d}}E, \\ & 0 \leqslant h < {E_0}, \end{split} $(11)

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    $N(h,t) = \int_0^{{E_{\max }}} {R({E_0},h){J_\gamma }({E_0},t){\rm{d}}{E_0}} .$ (12)

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    ${E_\gamma }(i,j) =\begin{cases} {E_G^{(i)},}&{{\rm{LP}} \ne 2,{\text{原级线光子}},}\\ {E_G^{(i)} + \dfrac{{{A_i}}}{{{A_i} + 1}}{E_{\rm{n}}},}& {\rm{LP}} = 2,{E_n} > {E_{{\rm{line}}}},\\ {}&{\text{原级连续光子}}, \end{cases}$(13)

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    $\sum\limits_{k = 1}^{j - 1} {{p_{i,k}}} \leqslant \xi < \sum\limits_{k = 1}^j {{p_{i,k}}} $(14)

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    ${w_{i,j}} = {p_{i,j}}{w_\gamma },~j = 1, \cdots ,J.$(15)

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    ${\text{光子总计数}} = {\rm{EVE{\text{光子直穿计数}} + DE{\text{光子散射计数}}}}{\rm{.}}$ (16)

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    Li Deng, Rui Li, Xin Wang, Yuan-Guang Fu. Monte Carlo simulation technology based on characteristic γ-ray spectrum analysis[J]. Acta Physica Sinica, 2020, 69(11): 112801-1
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