Source boundary parameter of Monte Carlo inversion technology based on virtual source principle

Tian Zi-Ning; Ouyang Xiao-Ping; Chen Wei; Wang Xue-Mei; Deng Ning; Liu Wen-Biao; Tian Yan-Jie

doi:10.7498/aps.68.20191095

Abstract

In the in situ γ spectrometer based measurement of " hot particular”, " radioactive collection point” and " radioactive collection area”, only the position of the pollution source can be located roughly, but its boundary parameters such as the thickness of pollution source cannot be given. In this paper, the application of virtual technology to the scanning of γ spectrometer is studied. We convert γ spectrometer measurement objects into a four-layer theoretical model, which are attenuation thickness + radioactive hot area + attenuation thickness + disturb source. Then, the source item layer is virtualized into a point source by using virtual technology. So, the theoretical model is further simplified. Then the detection efficiency and peak/valley ratio parameter of source term are simulated by Monte Carlo method. Finally, the source term parameters are retrieved by using the least square method, and thus establishing the theoretical method and procedure of inversion calculation of source boundary parameters. In this paper, the theoretical and experimental results are shown to be consistent with each other. So, this method is verified to be correct and practicable. Currently, the method can accurately determine the depth distribution parameters of radioactive contamination area for uniformly distributed radio nuclides. In conclusion, the technical achievements can be used to accurately determine the boundary range of the radioactive hot zone, thus realizing the purpose of reducing the waste disposal capacity during the treatment. At the same time, the determination of the inert layer thickness parameters of the target nuclear warhead of Nuclear Test Ban Treaty has a significant reference value.

Keywords:

Authors and contacts

Northwest Institute of Nuclear Technology, Xi’an 710024, China

Corresponding author: Tian Zi-Ning, tzn1019@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11405134)

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References

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图 1 源边界参数反演理论模型

Figure 1. The inversion theory model of source boundary parameters.

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图 2 探测模式1

Figure 2. The detection mode 1.

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图 3 探测模式2

Figure 3. The detection mode 2.

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图 4 探测模式1的MCNP程序计算模型

Figure 4. Calculation model of MCNP procedure for detection mode 1.

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图 5 探测模式2的MCNP程序计算模型

Figure 5. Calculation model of MCNP procedure for detection mode 2.

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表 1 探测模式1实验能谱峰计数及处理结果

Table 1. Energy peak count of experimental spectrum and process results for detection mode 1.

测量对象	测量时长t/10⁵ s	N₂₄₁ (54—57 keV)	N₂₄₁ (59.54 keV)	N₂₃₉ (51.62, 129 keV)	A/10⁴ Bq
测量对象	测量时长t/10⁵ s	N₂₄₁ (54—57 keV)	N₂₄₁ (59.54 keV)	N₂₃₉ (51.62, 129 keV)	²⁴¹Am	²³⁹Pu
探测模式1	3.16	4325136	25339979	—	—	—
²³⁹Pu体源	2.00	—	75248200	239711, 52717	4.56	18.7

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表 2 探测模式2实验能谱峰计数及处理结果

Table 2. Energy peak count of experimental spectrum and process results for detection mode 2.

测量对象	测量时长 t/10⁵s	N₂₄₁ (26.4 keV)	N₂₄₁ (54—57 keV)	N₂₄₁ (59.54 keV)	A/× 10⁴ Bq
测量对象	测量时长 t/10⁵s	N₂₄₁ (26.4 keV)	N₂₄₁ (54—57 keV)	N₂₄₁ (59.54 keV)	26.4 keV	59.54 keV
探测模式2	4.00	240050	9531180	65964536	8.16	8.91
²⁴¹Am点源	0.565	4160024	—	65331456	7.74	8.38
²⁴¹Am体源	0.800	45346	—	2745773	0.423	0.532

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表 3 等效虚拟点源探测效率及峰谷比

Table 3. The detection efficiency and peak/valley of equivalent virtual point source.

h/cm	${\varepsilon _{241}}(h)$/10^–3	${\varepsilon _{239}}(h)$/10^–3	A₂₄₁/10⁴ Bq	A₂₃₉/10⁵ Bq	Q	${N}/{ { {N_{\rm v}} } }(h)$
–1.25	24.3	24.6	0.921	0.497	5.4	8.05
–1.60	17.9	19.5	1.24	0.629	5.0	6.99
–2.00	12.9	15.1	1.73	0.810	4.7	6.12
–2.40	9.45	11.9	2.36	1.03	4.4	5.44
–2.80	7.00	9.45	3.19	1.30	4.1	4.92
–3.20	5.24	7.60	4.26	1.61	3.8	4.51
–3.60	3.97	6.16	5.62	1.98	3.5	4.18
–3.80	3.47	5.56	6.45	2.20	3.4	4.04
–4.00	3.03	5.04	7.37	2.43	3.3	3.90

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表 4 不同组合下等效虚拟点的均方偏差计算数据

Table 4. The mean square deviation calculation data of equivalent virtual point at different combination.

w	h/cm	$\varepsilon (h)$/10^–3	${\varepsilon ^*}(h)$/10^–3	${N}/{ { {N_{\rm v}} } }(h)$	X₂/10^–3	X₃/10^–3	X₁	$\sigma (X)$
0.10	–1.25	24.3	24.6	8.05	—	—	—	—
0.90	–3.20	5.24	7.60	4.51	7.15	9.30	4.87	0.177
0.90	–3.60	3.97	6.16	4.18	6.00	8.01	4.56	0.308
0.90	–3.80	3.47	5.56	4.04	5.55	7.47	4.44	0.385
0.90	–4.00	3.03	5.04	3.90	5.16	6.99	4.31	0.458
0.10	–1.60	17.9	19.5	6.99	—	—	—	—
0.90	–3.20	5.24	7.60	4.51	6.51	8.79	4.76	0.217
0.90	–3.60	3.97	6.16	4.18	5.36	7.50	4.46	0.396
0.90	–3.80	3.47	5.56	4.04	4.91	6.96	4.33	0.479
0.90	–4.00	3.03	5.04	3.90	4.52	6.48	4.21	0.554
0.10	–2.00	12.9	15.1	6.12	—	—	—	—
0.90	–3.20	5.24	7.60	4.51	6.01	8.35	4.67	0.277
0.90	–3.60	3.97	6.16	4.18	4.86	7.06	4.37	0.474
0.90	–3.80	3.47	5.56	4.04	4.41	6.52	4.24	0.559
0.90	–4.00	3.03	5.04	3.90	4.02	6.04	4.12	0.635
0.10	–2.40	9.45	11.9	5.44	—	—	—	—
0.90	–3.20	5.24	7.60	4.51	5.66	8.03	4.61	0.327
0.90	–3.60	3.97	6.16	4.18	4.52	6.74	4.30	0.530
0.90	–3.80	3.47	5.56	4.04	4.06	6.20	4.18	0.616
0.90	–4.00	3.03	5.04	3.90	3.67	5.72	4.05	0.693

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表 5 不同组合下等效虚拟点的均方偏差计算数据

Table 5. The mean square deviation calculation data of equivalent virtual point at different combination.

h/cm	w	$\sigma (X)$	w	$\sigma (X)$	w	$\sigma (X)$	w	$\sigma (X)$	w	$\sigma (X)$
–1.25	0.10	—	0.20	—	0.30	—	0.40	—	0.50	—
–3.20	0.90	0.177	0.80	0.355	0.70	0.664	0.60	0.988	0.50	1.32
–3.60	0.90	0.308	0.80	0.223	0.70	0.508	0.60	0.848	0.50	1.20
–3.80	0.90	0.385	0.80	0.201	0.70	0.448	0.60	0.792	0.50	1.15
–4.00	0.90	0.458	0.80	0.210	0.70	0.399	0.60	0.744	0.50	1.11
–1.60	0.10	—	0.20	—	0.30	—	0.40	—	0.50	—
–3.20	0.90	0.217	0.80	0.195	0.70	0.360	0.60	0.568	0.50	0.784
–3.60	0.90	0.396	0.80	0.210	0.70	0.234	0.60	0.435	0.50	0.669
–3.80	0.90	0.479	0.80	0.262	0.70	0.203	0.60	0.384	0.50	0.622
–4.00	0.90	0.554	0.80	0.318	0.70	0.196	0.60	0.343	0.50	0.583
–2.00	0.10	—	0.20	—	0.30	—	0.40	—	0.50	—
–3.20	0.90	0.277	0.80	0.187	0.70	0.177	0.60	0.256	0.50	0.371
–3.60	0.90	0.474	0.80	0.328	0.70	0.210	0.60	0.181	0.50	0.272
–3.80	0.90	0.559	0.80	0.399	0.70	0.257	0.60	0.178	0.50	0.238
–4.00	0.90	0.635	0.80	0.465	0.70	0.307	0.60	0.193	0.50	0.215
–2.40	0.10	—	0.20	—	0.30	—	0.40	—	0.50	—
–3.20	0.90	0.327	0.80	0.264	0.70	0.209	0.60	0.173	0.50	0.167
–3.60	0.90	0.530	0.80	0.435	0.70	0.344	0.60	0.261	0.50	0.195
–3.80	0.90	0.616	0.80	0.510	0.70	0.407	0.60	0.309	0.50	0.225
–4.00	0.90	0.693	0.80	0.577	0.70	0.464	0.60	0.356	0.50	0.257

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h/cm	w	$\sigma (X)$	w	$\sigma (X)$	w	$\sigma (X)$	w	$\sigma (X)$
–1.25	0.60	—	0.70	—	0.80	—	0.9	—
–3.20	0.40	1.65	0.30	1.98	0.20	2.31	0.10	2.64
–3.60	0.40	1.55	0.30	1.90	0.20	2.26	0.10	2.61
–3.80	0.40	1.51	0.30	1.88	0.20	2.24	0.10	2.60
–4.00	0.40	1.48	0.30	1.85	0.20	2.22	0.10	2.60
–1.60	0.60	—	0.70	—	0.80	—	0.90	—
–3.20	0.40	1.00	0.30	1.23	0.20	1.45	0.10	1.67
–3.60	0.40	0.910	0.30	1.16	0.20	1.40	0.10	1.65
–3.80	0.40	0.872	0.30	1.13	0.20	1.38	0.10	1.64
–4.00	0.40	0.839	0.30	1.10	0.20	1.37	0.10	1.63
–2.00	0.60	—	0.70	—	0.80	—	0.90	—
–3.20	0.40	0.498	0.30	0.630	0.20	0.763	0.10	0.898
–3.60	0.40	0.410	0.30	0.561	0.20	0.716	0.10	0.875
–3.80	0.40	0.375	0.30	0.533	0.20	0.698	0.10	0.865
–4.00	0.40	0.347	0.30	0.509	0.20	0.681	0.10	0.857
–2.40	0.60	—	0.70	—	0.80	—	0.90	—
–3.20	0.40	0.194	0.30	0.244	0.20	0.305	0.10	0.372
–3.60	0.40	0.169	0.30	0.199	0.20	0.267	0.10	0.351
–3.80	0.40	0.174	0.30	0.186	0.20	0.252	0.10	0.342
–4.00	0.40	0.186	0.30	0.178	0.20	0.240	0.10	0.335

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表 6 体源参数的反演计算数据

Table 6. The inversion data of volume source parameters.

h_V/cm	体源厚度/cm	$\varepsilon ({h_{\rm{V}}})$ /10^–3	${\varepsilon ^*}({h_{\rm{V}}})$ /10^–2	${N}/{ { {N_{\rm v}} } }({h_{\rm{V} } })$	$\sigma (X)$
–2.80	0.80	4.54	0.689	4.69	0.444
–2.80	1.2	4.60	0.696	4.74	0.431
–2.80	1.6	4.70	0.705	4.81	0.414
–2.45	0.80	5.68	0.818	5.03	0.231
–2.45	1.2	5.76	0.826	5.07	0.217
–2.45	1.6	5.89	0.837	5.16	0.200
–2.45	2.0	6.05	0.851	5.26	0.181
–2.45	2.5	6.31	0.874	5.41	0.159
–2.45	3.0	6.65	0.903	5.63	0.163
–2.45	4.0	7.57	0.981	6.24	0.289
–2.45	4.9	8.78	1.08	7.12	0.539
–2.00	0.80	7.62	1.03	5.58	0.188
–2.00	1.2	7.75	1.04	5.64	0.212
–2.00	1.6	7.93	1.05	5.75	0.248
–2.00	2.0	8.17	1.07	5.88	0.295
–2.00	2.5	8.55	1.10	6.11	0.373
–2.00	3.0	9.03	1.14	6.41	0.474
–2.00	4.0	10.4	1.25	7.35	0.769
–1.50	0.80	10.7	1.33	6.43	0.744
–1.50	1.2	10.9	1.35	6.54	0.781
–1.50	1.6	11.2	1.37	6.68	0.834
–1.50	2.0	11.5	1.40	6.90	0.905
–1.50	3.0	12.9	1.50	7.79	1.18
–0.50	0.80	22.0	2.34	10.1	2.81

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表 7 等效虚拟点源探测效率、峰谷比及活度比

Table 7. The detection efficiency, peak/valley and acvitiy ratio of equivalent virtual point source.

h/cm	${\varepsilon _{26.4\;{\rm{keV}}}}(h)$/10^–3	${\varepsilon _{59.54\;{\rm{keV}}}}(h)$/10^–2	A_{26.4 keV}/10⁴ Bq	A_{59.54 keV}/10⁴ Bq	A_{59.54 keV}/A_{26.4 keV}	${N}/{ { {N_{\rm v}} } }(h)$
0.80	48.200	14.4	0.0519	0.318	6.10	17.0
0.40	13.500	8.79	0.1850	0.523	2.80	12.0
0	4.060	5.56	0.6150	0.826	1.30	9.3
–0.20	2.260	4.48	1.1100	1.030	0.90	8.4
–0.40	1.270	3.64	1.9700	1.260	0.60	7.7
–0.60	0.717	2.98	3.4900	1.540	0.40	7.1
–0.80	0.409	2.45	6.1200	1.880	0.30	6.6

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表 9 体源参数的反演计算数据

Table 9. The inversion data of volume source parameters.

h_V/cm	体源厚度/cm	${\varepsilon ^*}({h_{\rm{V}}})$/ 10^–2	$\varepsilon ({h_{\rm{V}}})$/ 10^–3	${N}/{ { {N_{\rm v}} } }({h_{\rm{V} } })$	$\sigma (X)$	h_V/cm	体源厚度/cm	${\varepsilon ^*}({h_{\rm{V}}})$/ 10^–2	$\varepsilon ({h_{\rm{V}}})$/ 10^–3	${N}/{ { {N_{\rm v}} } }({h_{\rm{V} } })$	$\sigma (X)$
0.75	1.00	3.54	10.4	11.90	1.5900	0.15	2.20	2.45	5.00	9.34	0.2310
0.75	0.60	3.47	8.06	11.40	1.0100	0.15	1.60	2.31	2.69	8.54	0.3470
0.75	0.30	3.44	7.23	11.20	0.8060	0.15	1.00	2.21	1.72	8.07	0.5920
0.25	2.00	2.59	5.49	9.61	0.3530	0.15	0.40	2.17	1.32	7.86	0.6920
0.25	1.90	2.56	4.91	9.44	0.2110	0	2.50	2.26	4.40	9.00	0.0900
0.25	1.80	2.54	4.42	9.29	0.0890	0	2.45	2.24	4.14	8.90	0.0470
0.25	1.70	2.51	4.00	9.14	0.0220	0	2.40	2.23	3.90	8.83	0.0640
0.25	1.60	2.49	3.63	9.03	0.1090	0	2.00	2.13	2.52	8.30	0.3950
0.25	1.50	2.47	3.32	8.92	0.1870	0	1.50	2.04	1.60	7.83	0.6260
0.25	1.30	2.43	2.81	8.72	0.3130	0	1.00	1.97	1.13	7.54	0.7470
0.25	0.80	2.37	2.04	8.38	0.5080	–0.25	1.10	1.65	0.602	6.86	0.8910
						–0.25	0.50	1.61	0.457	6.70	0.9300

DownLoad: CSV

表 8 不同组合下等效虚拟点的均方偏差计算数据

Table 8. The mean square deviation calculation data of equivalent virtual point at different combination.

h/cm	w	$\sigma (X)$	w	$\sigma (X)$	w	$\sigma (X)$	w	$\sigma (X)$	w	$\sigma (X)$
0.80	0.10	—	0.20	—	0.30	—	0.40	—	0.50	—
–0.40	0.90	2.414	0.80	1.783	0.70	2.807	0.60	3.832	0.50	4.86
–0.60	0.90	2.115	0.80	1.512	0.70	2.569	0.60	3.627	0.50	4.69
–0.80	0.90	1.951	0.80	1.362	0.70	2.433	0.60	3.510	0.50	4.59
0.40	0.10	—	0.20	—	0.30	—	0.40	—	0.50	—
–0.40	0.90	0.466	0.80	0.291	0.70	0.529	0.60	0.780	0.50	1.03
–0.60	0.90	0.177	0.80	0.119	0.70	0.286	0.60	0.567	0.50	0.857
–0.80	0.90	0.185	0.80	0.245	0.70	0.175	0.60	0.447	0.50	0.753
0	0.10	—	0.20	—	0.30	—	0.40	—	0.50	—
–0.40	0.90	0.190	0.80	0.160	0.70	0.168	0.60	0.235	0.50	0.327
–0.60	0.90	0.431	0.80	0.346	0.70	0.214	0.60	0.123	0.50	0.165
–0.80	0.90	0.620	0.80	0.512	0.70	0.350	0.60	0.197	0.50	0.112

DownLoad: CSV

h/cm	w	$\sigma (X)$	w	$\sigma (X)$	w	$\sigma (X)$	w	$\sigma (X)$
0.80	0.60	—	0.70	—	0.80	–	0.90	—
–0.40	0.40	5.88	0.30	6.91	0.20	7.93	0.10	8.96
–0.60	0.40	5.75	0.30	6.81	0.20	7.87	0.10	8.92
–0.80	0.40	5.67	0.30	6.75	0.20	7.83	0.10	8.90
0.40	0.60	–	0.70	—	0.80	–	0.90	—
–0.40	0.40	1.29	0.30	1.55	0.20	1.80	0.10	2.06
–0.60	0.40	1.15	0.30	1.44	0.20	1.73	0.10	2.03
–0.80	0.40	1.06	0.30	1.38	0.20	1.69	0.10	2.01
0	0.60	—	0.70	—	0.80	—	0.90	—
–0.40	0.40	0.427	0.30	0.532	0.20	0.639	0.10	0.747
–0.60	0.40	0.287	0.30	0.425	0.20	0.567	0.10	0.711
–0.80	0.40	0.207	0.30	0.361	0.20	0.523	0.10	0.689

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Vol. 68, Issue 23 - 2019-12-05

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