Radiation shielding analysis of a special linear accelerator for electron beam and X-ray

Abstract

The King AbdulAziz City for Science & Technology in the Kingdom of Saudi Arabia plans to build a 10 MeV, 15 kW linear accelerator (LINAC) for electron beam and X-ray. The accelerator will be supplied by EB Tech, Republic of Korea, and the design and construction of the accelerator building will be conducted in the cooperation with EB Tech. This report presents the shielding analysis of the accelerator building using the Monte Carlo N-Particle Transport Code (MCNP). In order to improve the accuracy in estimating deep radiation penetration and to reduce computation time, various variance reduction techniques, including the weight window (WW) method, the deterministic transport (DXTRAN) spheres were considered. Radiation levels were estimated at selected locations in the shielding facility running MCNP6 for particle histories up to 1.0×10⁺⁸. The final results indicated that the calculated doses at all selected detector locations met the dose requirement of 50 mSv/yr, which is the United State Nuclear Regulatory Commission (U.S. NRC) requirement.

Keywords

Monte Carlo transport MCNP electron linear accelerator radiation shielding occupational dose limit variance reduction

1 Introduction

The King AbdulAziz City for Science & Technology (KACST) in the Kingdom of Saudi Arabia has a plan to build a 10 MeV, 15 kW LINAC for electron beam and X-ray, which is to be supplied by EB Tech in Republic of Korea. The purpose of building the accelerator is to conduct researches on the irradiation of agricultural products and industrial materials, and the environmental applications. The design and construction of the accelerator building will be carried out jointly between EB Tech and KACST.

The electron accelerator is required to be properly shielded to protect the workers and public at the facility [1]. Recommendations for the design and installation of radiation shielding for X-ray and gamma-ray can be found in NCRP No. 49(1976) and for accelerators with energies over 10 MeV in NCRP No. 151 (2005) [2, 3].

This report discusses the shielding analysis for the accelerator facility at KACST using the MCNP Monte Carlo radiation transport code [4, 5]. The MCNP transport code provides extensive continuous nuclear cross section libraries and is capable of describing complex 3D geometries. For this reason, the MCNP code has been widely used in the design of medical and industrial particle accelerators shielding, X-ray diagnosis, and medical radiography [6 –10].

MCNP6 is a combination of MCNP5 and MCNPX and contains many improvements in the handling of the physics and geometry. In this paper, the dosage calculations and shielding analysis were performed using MCNP5 and MCNP6 to assure the agreement between the two codes. In addition, the use of variance reduction (VR) techniques, including the weight window (WW) and DXTRAN spheres, was investigated in order to reduce uncertainties of point detector doses. The variance reduction techniques, especially the DXTRAN sphere are shown to be an effective way to reduce detector uncertainties.

2 Method

The MCNP5 and MCNP6 Monte Carlo particle transport codes [4, 5] were used in this shielding analysis. Specifically, the MCNPX 2.70, MCNP5 1.60 and MCNP 6.1 codes were installed on a workstation with 2 CPUs, each 16 CPU cores. The codes ran under the Windows 8.1 operating system.

The deep radiation penetration as in the shield building introduces large statistical errors using the Monte Carlo transport method and use of some types of variance reduction schemes is highly desirable. In this analysis, the methods of weight window (WW) and DXTRAN spheres in MCNP [11 –13], were used to improve the accuracy of point detector and reduce the computation time.

The WW method was used to generate a cell or mesh-based importance function in space. The importance function controls the particle weights and splitting or uses the Russian roulette approach for the deep penetration of radiation. The WW method can be used effectively to generate the importance function automatically in modeling the shielding facility.

The DXTRAN sphere is a deterministic transport method which can be used to improve particle sampling near a tally. The DXTRAN sphere consists of inner and outer spheres. After a collision, a particle is placed on the outermost DXTRAN sphere by the next event estimator and continues to travel inside the sphere. The DXTRAN spheres can be used to improve the accuracy of detector tallies which indicated extremely low photon fluxes and large statistical errors. A maximum of five DXTRAN spheres are allowed in each problem.

The F5 point detector tally in MCNP was used to determine photon flux at the detector position. The computed F5 tallies were first normalized to the source strength equivalent to the accelerator current, and then converted to the dose equivalent (μSv) values using the photon flux-to-dose rate conversion by MCNP [14–15].

3 Model

The linear electron accelerator is of the standing wave accelerating type with a working frequency of 2856 MHz. The system consists of the following components: electron source, accelerating structure, beam scanning system, solid state modulator, klystron and RF wave guide line. The source of the microwave pulses is a klystron, which generates microwave pulses with a pulse power of approximately 5 MW. The injected electrons from the electron source are accelerated along the accelerating column, pass through thin titanium foil, and then collide with the tantalum target to generate X-rays. The tantalum target can be removed so that the facility operates in the electron beam mode.

A shielding barrier surrounds the electron accelerator at the center of the building. A conveyer is installed to transport materials to be irradiated into the building. Figures 1 and 2 illustrate the first-floor layout of the irradiation facility and 3D view of MCNP model. The shielding barrier is made of concrete; the primary barrier has a thickness of 300 cm, and the secondary barrier has a thickness of 50 cm to 70 cm. A conveyor enters the building entrance, passes under the accelerator and returns back to the entrance.

Fig.1

First-floor layout of the irradiation facility.

Fig.2

3D View of MCNP model.

The main parameters of the linear electron accelerator, target and barrier are as follows;

Electron energy: 10 MeV.

Maximum beam power: 15 kW.

Average electron beam current: 1.5 mA.

Maximum pulse amplitude of the electron beam current: 0.25 A.

Electron beam pulse duration: 15μsec.

Target material: Tantalum (width: 110 cm, depth: 10 cm, thickness: 0.9 cm).

Barrier material: concrete, density: 2.3 g/cm3, Primary barrier: 300 cm, Secondary barriers: 50–70 cm.

The geometry of electron beam accelerator and shielding barriers were modeled for the MCNP calculation. Figure 2 shows the 3D view of the MCNP model. Figures 3 and 4 show 2D views of the geometry model on the planes at z = 50 cm and y = 950 cm. MCNP input limits the number of detectors to 20. The locations of 20 detectors were selected based on (1) expected high radiation outside the building, (2) working area, and (3) a reference location inside the building(detector #20). Table 1 lists the coordinates of locations of these 20 point detectors. Figure 5 shows the locations of point detectors and dose tallies. The detector tally #195 is a reference detector and is located inside thebuilding.

Fig.3

2D View of MCNP model (Z = 50).

Fig.4

2D View of MCNP model (Y = 950).

Table 1

Locations of point detectors

Tally No.	x	y	Z
5	150	810	100
15	250	810	100
25	340	680	100
35	770	–10	100
45	1860	400	100
55	1860	680	100
65	1535	1720	100
75	770	1720	100
85	–10	1490	100
95	770	1220	380
105	1180	1220	380
115	1320	680	380
125	1320	200	380
135	770	1221	545
145	1001	1221	545
155	1110	681	610
165	770	270	660
175	560	1220	730
185	770	680	910
195	175	1440	100

Fig.5

Locations of the point detectors and flux tallies.

4 Results

Monte Carlo calculations were performed using the MCNP5 and MCNP6 codes to determine photon fluxes and doses at the point detectors located around the accelerator building and their results are discussed. MCNP6 is a combination of MCNP5 and MCNPX and contains many improvements in the handling of the physics and geometry. MCNP6 does not exactly reproduce the particle tracks of MCNP5 because of the model improvements and changes of several default options. Different variance reduction techniques were employed in order to optimize the accuracies and computation time in the calculations.

The X-ray doses of point detectors computed by using MCNP5 and MCNP6 are compared in Table 2. It is shown that the results of MCNP5 generally agree with those of MCNP6 within relative errors. The average error of MCNP6 is 0.3122, which is slightly higher than 0.2439 for MCNP5. The tally results are considered to be reliable when the relative error is less than 0.5 (50%).

Table 2
X-ray doses by MCNP5 vs. MCNP6

Detector MCNP5 MCNP6

Mean Relative Mean Relative

Value Error Value Error

5 3.4474E-02 0.1162 3.8294E-02 0.2102

15 4.4833E-02 0.1136 5.0577E-02 0.2312

25 1.6340E-01 0.2919 1.3981E-01 0.2013

35 3.1435E-02 0.0803 2.9794E-02 0.0875

45 2.4563E-03 0.1707 3.0715E-03 0.2473

55 1.0055E-02 0.0601 9.6631E-03 0.0596

65 9.6595E-04 0.8425 8.2426E-05 0.2755

75 7.9212E-04 0.2111 6.5297E-04 0.1656

85 1.1454E-06 0.2101 1.4307E-06 0.4509

95 1.3907E-04 0.2869 1.5008E-04 0.4524

105 2.1598E-01 0.4747 9.1604E-02 0.2474

115 2.0810E-01 0.1117 3.1780E-01 0.4046

125 1.9334E-02 0.7533 1.2509E-03 0.1586

135 7.8732E-06 0.0923 1.9787E-05 0.4084

145 5.4735E+00 0.2384 7.9979E+00 0.3713

155 6.3381E-03 0.2263 4.6701E-02 0.8884

165 4.7163E-04 0.1806 3.1633E-03 0.8370

175 9.0869E-07 0.1594 8.3555E-07 0.1685

185 3.5147E-01 0.1094 3.8633E-01 0.2643

195 9.7162E+00 0.1492 8.6252E+00 0.1147

Avg. Error 0.2439 0.3122

Detector	MCNP5	MCNP6
5	3.4474E-02	0.1162	3.8294E-02	0.2102
15	4.4833E-02	0.1136	5.0577E-02	0.2312
25	1.6340E-01	0.2919	1.3981E-01	0.2013
35	3.1435E-02	0.0803	2.9794E-02	0.0875
45	2.4563E-03	0.1707	3.0715E-03	0.2473
55	1.0055E-02	0.0601	9.6631E-03	0.0596
65	9.6595E-04	0.8425	8.2426E-05	0.2755
75	7.9212E-04	0.2111	6.5297E-04	0.1656
85	1.1454E-06	0.2101	1.4307E-06	0.4509
95	1.3907E-04	0.2869	1.5008E-04	0.4524
105	2.1598E-01	0.4747	9.1604E-02	0.2474
115	2.0810E-01	0.1117	3.1780E-01	0.4046
125	1.9334E-02	0.7533	1.2509E-03	0.1586
135	7.8732E-06	0.0923	1.9787E-05	0.4084
145	5.4735E+00	0.2384	7.9979E+00	0.3713
155	6.3381E-03	0.2263	4.6701E-02	0.8884
165	4.7163E-04	0.1806	3.1633E-03	0.8370
175	9.0869E-07	0.1594	8.3555E-07	0.1685
185	3.5147E-01	0.1094	3.8633E-01	0.2643
195	9.7162E+00	0.1492	8.6252E+00	0.1147
Avg. Error		0.2439		0.3122

Histories = 1×10⁺⁷, Units =μSv/hr.

Table 3 compares results of MCNP6 calculations using combinations of weight window (WW) and DXTRAN spheres techniques. A 3D weight window was generated over the geometry model. Two DXTRAN spheres, DXT1 and DXT2 were selected at L1(x = 1535, y = 1340, z = 100) and L2(x = 350, y = 1490, z = 100), respectively. DXT1 and DXT2 spheres block the passage of the conveyor tunnel at the two locations. Table 3 indicates that the weight window (WW) technique generally reduced the detector errors compared to the calculations without any variance reduction. Relative errors for detectors #155 and #165 were significantly reduced from 0.8884 to 0.3675 and from 0.8370 to 0.1683, respectively. The average error is also reduced from 0.3122 to 0.2652. Also Table 3 indicates that WW+DXT1 reduced the average error from 0.3122 to 0.2722, and that WW+DXT1+DXT2 further reduced the average error to 0.2636 when compared to the case using WW only.

Table 3

X-ray doses by MCNP6 and combinations of WW, DXT1, and DXT2

Detector	MCNP6		WW		WW+DXT1		WW+DXT1+DXT2
	Mean	Relative	Mean	Relative	Mean	Relative	Mean	Relative
	Value	Error	Value	Error	Value	Error	Value	Error
5	3.8294E-02	0.2102	2.7201E-02	0.0738	2.8549E-02	0.0766	3.3546E-02	0.1048
15	5.0577E-02	0.2312	3.6921E-02	0.0835	3.5501E-02	0.0672	4.8038E-02	0.1799
25	1.3981E-01	0.2013	1.0875E-01	0.0952	1.0570E-01	0.0778	1.1347E-01	0.0769
35	2.9794E-02	0.0875	2.5508E-02	0.0721	2.4858E-02	0.0691	2.3054E-02	0.0629
45	3.0715E-03	0.2473	2.1399E-03	0.2958	2.8207E-03	0.2591	2.3280E-03	0.2151
55	9.6631E-03	0.0596	8.3040E-03	0.0757	9.8978E-03	0.1623	8.1695E-03	0.1277
65	8.2426E-05	0.2755	5.7564E-05	0.4171	6.8404E-05	0.5029	1.4730E-04	0.4013
75	6.5297E-04	0.1656	3.6423E-04	0.0642	4.4941E-04	0.0619	4.0559E-04	0.0738
85	1.4307E-06	0.4509	1.0178E-06	0.3596	7.4410E-07	0.2270	9.0060E-07	0.4484
95	1.5008E-04	0.4524	1.0055E-04	0.3256	8.6935E-05	0.2074	6.1213E-05	0.1374
105	9.1604E-02	0.2474	1.1596E-01	0.6877	1.1749E-01	0.4258	4.2139E-02	0.3196
115	3.1780E-01	0.4046	1.4732E-01	0.1152	1.5394E-01	0.1830	2.9204E-01	0.3832
125	1.2509E-03	0.1586	1.3821E-03	0.2288	1.4782E-03	0.1458	1.0861E-03	0.1203
135	1.9787E-05	0.4084	6.7747E-06	0.1129	1.1792E-05	0.3283	7.1569E-06	0.1232
145	7.9979E+00	0.3713	8.9361E-01	0.6347	1.7846E+00	0.6122	1.2911E+00	0.6557
155	4.6701E-02	0.8884	5.5017E-03	0.3675	2.9154E-02	0.7713	7.6004E-03	0.6397
165	3.1633E-03	0.8370	3.0654E-04	0.1683	1.0852E-03	0.7117	4.1156E-04	0.3070
175	8.3555E-07	0.1685	1.1144E-06	0.3995	5.8537E-07	0.1724	9.5303E-07	0.2015
185	3.8633E-01	0.2643	2.7880E-01	0.1169	2.6242E-01	0.1720	4.9995E-01	0.4157
195	8.6252E+00	0.1147	1.7444E+00	0.6103	2.5338E+00	0.2114	2.2772E+00	0.2778
Avg. Error		0.3122		0.2652		0.2722		0.2635
Max. Error		0.8884		0.6877		0.7713		0.6557

WW = weight window, DXTn = DXTRAN at Ln. Histories = 1×10⁺⁷, Units =μSv/hr.

Table 4 shows the results of the MCNP6 calculations when DXTRAN sphere were placed around the detectors, #155 and #165, which have large relative errors. The DXTRAN spheres (DTX3) changed the relative error from 0.8884 to 0.1801 for #155 and from 0.8370 to 0.1093 for #165. In addition, the use of a DXTRAN sphere on each of the detectors reduced the average error of both detectors from 0.3122 to 0.2691. Table 4 indicates that placing a DXTRAN sphere around the detector is an effective means to improve the accuracy of a point detector.

Table 4

X-ray doses by MCNP6 and WW+DXT3

Detector	MCNP6		WW+DTX3
	Mean	Relative	Mean	Relative
	Value	Error	Value	Error
5	3.8294E-02	0.2102	4.3145E-02	0.2579
15	5.0577E-02	0.2312	4.6217E-02	0.2437
25	1.3981E-01	0.2013	1.2458E-01	0.1396
35	2.9794E-02	0.0875	4.7274E-02	0.5202
45	3.0715E-03	0.2473	2.3330E-03	0.4598
55	9.6631E-03	0.0596	8.3546E-03	0.0836
65	8.2426E-05	0.2755	6.0941E-05	0.5529
75	6.5297E-04	0.1656	4.3042E-04	0.0679
85	1.4307E-06	0.4509	3.9394E-07	0.1271
95	1.5008E-04	0.4524	1.0646E-04	0.3440
105	9.1604E-02	0.2474	5.2856E-02	0.4332
115	3.1780E-01	0.4046	1.2559E-01	0.1256
125	1.2509E-03	0.1586	1.0893E-03	0.1098
135	1.9787E-05	0.4084	7.1202E-06	0.1315
145	7.9979E+00	0.3713	5.9692E-01	0.6217
155	4.6701E-02	0.8884	3.6294E-03	0.1801
165	3.1633E-03	0.8370	3.3309E-04	0.1093
175	8.3555E-07	0.1685	5.4243E-07	0.1476
185	3.8633E-01	0.2643	3.4122E-01	0.1640
195	8.6252E+00	0.1147	1.4626E+00	0.5626
Avg. Error		0.3122		0.2691
Max. Error		0.8884		0.6217

WW = weight window, DXT3 = DXTRAN at detectors #155 and #165. Histories = 1×10⁺⁷, Units =μSv/hr.

Table 5 summarizes results of final dose calculations using MCNP6. The problem was run as an electron, photon and neutron transport problem to account for all reactions including the (γ,n) reaction. The weight window and DXTRAN spheres on selected point detectors were used. The computation was continued until electrons reached a total of 1×10⁺⁸ histories. The average error of point detectors is found to be 15.55% and the maximum relative error is about 32.79%.

Table 5

Final dose for the accelerator facility includes (γ,n) reaction, unit = mSv/yr

Detector	MCNP6+WW
	Mean value	Relative Error
5	6.8240E-02	0.0494
15	8.6658E-02	0.0549
25	2.2624E-01	0.0581
35^a	6.9478E-02	0.0826
45	6.2218E-03	0.2051
55^a	2.0286E-02	0.0750
65^a	7.3328E-04	0.3003
76	9.0634E-04	0.0353
85	1.3967E-06	0.1938
95	2.2366E-04	0.3150
105	4.2372E-01	0.3279
115	3.9686E-01	0.1878
125^a	2.8006E-03	0.0986
135	1.8812E-05	0.0860
145	4.5202E+00	0.2990
155	1.8469E-02	0.2651
165	8.1032E-04	0.1038
175	1.2886E-06	0.0688
185	5.5516E-01	0.0444
195^a	8.2238E+00	0.2591
Avg. Error		0.1555
Max.Error		0.3279

Histories = 1×10⁺⁸, WW = Weight Window. ^a = WW+DXTRAN sphere.

According to 10CFR20.1201 [16], the occupational dose limit for adults is 50 mSv/yr for the work load of 2000 hr/yr and the occupancy factor of 1. Table 5 indicates that calculated doses at all point detectors is less than the dose limit of 50 mSv/yr and met the NRC occupational dose limit. The point detector tally #195 is a reference detector and its dose is higher than other detectors tallies since it is located inside the building.

5 Conclusions

The King AbdulAziz City for Science & Technology (KACST) in the Kingdom of Saudi Arabia has a plan to build a 10 MeV, 15 kW LINAC for electron beam and X-ray. This paper discusses the shielding analysis for the accelerator facility at KACST using the MCNP Monte Carlo radiation transport code. A total of 20 detectors were selected at high radiation locations and area accessed by working personnel.

In order to improve the accuracy of dose calculation, variation reduction techniques such as weight-window (WW) and DXTRAN, were employed. The use of weight-window and DXTRAN spheres reduced the average and maximum errors of detector tallies, and is shown to be an effective way to improve dose statistics. The final calculation was carried out for photon, electron and neutron particles to account for all reactions including (γ,n) using MCNP6. The calculated doses at all detector locations are found to be less than the NRC occupational dose limit of 50 mSv/yr.

When the 10 MeV LINAC accelerator at The King Abdul Aziz City for Science & Technology (KACST) is in operation, measurements of dose at locations surrounding building are being planned for comparisons with the results of MCNP dose calculations.

References

Shultis

J.K.

and Faw

R.E.

, Radiation Shielding, Prentice Hall, New Jersey, 1996.

National Council on Radiation Protection and Measurements, NCRP No. 49, Structural Shielding Design and Evaluation for Medical Use of X Rays and Gamma Rays of Energies Up to 10MeV, 1976.

National Council on Radiation Protection and Measurements, NCRP No. 151, Structural Shielding Design and Evaluation for Megavoltage X-and Gamma-Ray Radiotherapy Facilities, December 31, 2005.

Pelowitz

D.B.

Ed. MCNP User’s Manual, Version 2.7.0, LA-CP-11-00438.

Pelowitz

D.B.

, Ed., MCNP User’s Manual, Version 2.6.0, LA-CP-07-1473.

Rodenas

, Leon

and Verdu

, Application of the monte carlo method to shielding analysis in medical linear accelerators, J Nucl Sci Tech (Suppl 1) 37 (2000), 441–445.

Darby

K.H.

et al., Accelerator Facility Shielding Design, Univ. of Tennessee Honors Thesis Projects, http://trace.tennessee.edu/uk_chanonoproj/1830

Kang

W.G.

et al., Shielding design of a mobile electron accelerator using monte carlo technique, J of Radiation Industry V3 (2009), 79–85.

Pontoriero

, Amato

, Iati

, De Renzis

and Pergolizzi

, Evaluation of the dose perturbation around gold and steel fiducial markers in a medical linac through Geant4 Monte Carlo simulation, J Xray Sci Technol 23 (2015), 135–140.

10.

Kulkami

, Dendere

, Nicolls

and Douglas

T.S.

, Monte-Carlo simulation of a slot-scanning digital mammography system for tomosynthesis, J Xray Sci Technol 24 (2016), 191–206.

11.

Booth

T.E.

, A Sample Problem for Variance Reduction in MCNP, LA-10363-MS..

12.

Olsher

R.H.

, A practical look at monte carlo variance reduction methods in radiation shielding, Nuclear Engineering and Technology 38(3) (2006).

13.

Hendricks

J.S.

and Culbertson

C.N.

, An Assessment of MCNP Weight Windows, LA-UR-0055, Los Alamos National Laboratory.

14.

ANS-6.11 Working Group, M.E. Battat, chairman, American National Standard Neutron and Gamma-Ray Factors, ANSI/ANS-6.1.1-1977, N666, American Nuclear Society, LaGrange Park, Illinois, 1977.

15.

Protection ICRP Committee 3 Task Group, P. Grande andM.C. O’Riordan, chairman, Data for Against Ionizing Radiation from External Sources: Supplement to ICRP Publication 15, ICRP-21, International Commission on Radiological Protection, Pergamon Press, April 1971.

16.

US Code of Federal Regulations, Occupational Dose Limit for Adults, 10CFR20.1201.