There are several proton therapy facilities in operation or planned in Taiwan, and these facilities are anticipated to not only treat cancer but also provide beam services to the industry or academia. The simplified approach based on the Monte Carlo-based data sets (source terms and attenuation lengths) with the point-source line-of-sight approximation is friendly in the design stage of the proton therapy facilities because it is intuitive and easy to use. The purpose of this study is to expand the Monte Carlo-based data sets to allow the simplified approach to cover the application of proton beams more widely.

In this work, the MCNP6 Monte Carlo code was used in three simulations to achieve the purpose, including the neutron yield calculation, Monte Carlo-based data sets generation, and dose assessment in simple cases to demonstrate the effectiveness of the generated data sets.

The consistent comparison of the simplified approach and Monte Carlo simulation results show the effectiveness and advantage of applying the data set to a quick shielding design and conservative dose assessment for proton therapy facilities.

This study has expanded the existing Monte Carlo-based data set to allow the simplified approach method to be used for dose assessment or shielding design for beam services in proton therapy facilities. It should be noted that the default model of the MCNP6 is no longer the Bertini model but the CEM (cascade-exciton model), therefore, the results of the simplified approach will be more conservative when it was used to do the double confirmation of the final shielding design.

Not only the galactic cosmic rays but also the solar cosmic rays, protons account for a large part of the composition of these cosmic rays. It is an effective method to test and verify the radiation damage of electronic components in space with high-energy proton beams. According to the statistics of Particle Therapy Co-Operative Group (PTCOG) as of December 2020 [

Taiwan is a small island, which is highly populated. Most of these proton therapy facilities are located in areas with high population density, radiation shielding design and dose assessment have become important issues. In the initial design stage of the proton therapy facilities, multiple changes to the shielding design are predictable. Therefore, the simplified approach based on the point-source line-of-sight approximation is friendly because it is intuitive and easy to use. In principle, by selecting shielding parameters according to the problem, the shielding thickness of any wall or the transmission dose rate at any location outside the shield can be quickly estimated. In the final design stage of the facility, Agosteo [

During the proton beam services, the excess proton beam will be directed to the beam dump. In the radiation shielding design, it is considered an important beam loss point. The simplified approach is one of the options [

Based on the experience in establishing shielding parameters [

In this study, the literature whose beam energy and target material are close to proton therapy was selected as the target of neutron yield calculation. Not only the experimental results of Meier et al. [

This study uses the MCNP6 Monte Carlo code based on the pointwise cross-section library as a tool to calculate the depth dose distribution or dose attenuation curve of a series of beam/target/shield combinations. The data is fitted by using

In ^{2}); _{0} and _{0} and ^{2}/proton and g/cm^{2}, respectively.

^{3}, respectively. Depending on the proton energy, the thicknesses of the tissue targets are 9, 18, 29, 42, and 56 cm; the thicknesses of the graphite targets are 6, 11, 19, 25, and 34 cm; the thicknesses of the iron and copper targets are 1.5, 3, 5, 7, and 9.5 cm. In the geometry and material configurations, a hollow spherical shell with an inner radius of 9,000 cm and a thickness of 600 cm is adopted. The shell material is PMMA with a density of 0.94 g/cm^{3}. Not only the primary beam (proton) but also the secondary particles (protons, neutrons, photons, and electrons) produced by the primary beam with the target and shell are tracked in a simplified shielding model, as shown in

^{3} and a three-leg labyrinth design, the thickness of the labyrinth wall is 150 cm, and the shielding thickness is assumed to be 200 cm of concrete. Thirty-six detectors are installed outside the laboratory for evaluating the dose rate, and two detectors are installed in the direction of the proton beam direction (red) and the labyrinth entrance (blue) for observing the neutron spectra.

In this study, MCNP6 was used to simulate the radiation transport calculation of the aforementioned laboratory, and the results will be used as the reference for comparison of the simplified approach. In the transport calculation, the radiation source is a 250 MeV proton beam, which directly bombards the beam dump located in the center of the laboratory. The composition of the beam dump includes graphite, iron, and PMMA. The parameter setting of the transport calculation is consistent with those in the shielding parameter generation. The results include dose rates outside the laboratory and neutron spectra at proton beam direction outside the room (red) and labyrinth entrance (blue).

According to the principle of shielding parameter production, (H_{1}, _{1}) and (H_{2}, _{2}) are the shielding parameters obtained from the curve fitting of the depth dose in the shallow and deep regions [_{1}, _{1}) to evaluate the shallow dose of PMMA and concrete with a shielding thickness of less than 150 cm or iron and lead with a shielding thickness of less than 75 cm, otherwise, (H_{2}, _{2}) was recommended to use to evaluate the deep dose. Based on the shielding design in

_{n}_{n}

^{−8} to 10^{−18} μSv/proton, which from the proton beam loss point at the beam dump in the center of the laboratory to the outdoor covers about 10 orders of magnitude attenuation. Outside the laboratory, the position with the highest dose is approximately 10^{−11} μSv/proton in the beam direction, and the position with the lowest dose is approximately 10^{−18} μSv/proton in the upper right corner of the laboratory.

Regarding the time spent on dose assessment around the facility, the simplified approach takes 2 hours to complete, while the direct Monte Carlo simulation takes 8 hours (equivalent to 1 working day) for modeling and debugging, and 120 hours for transport calculation, which can be solved through parallel calculation. If the transport calculation time is not taken into account, the Monte Carlo simulation is four times that of the simplified method.

Radiation shielding is an important issue for those proton therapy facilities located in densely populated areas. Monte Carlo simulation is the most accurate method, but it is not practical in the preliminary design of the facility. The simplified approach based on the point-source light-of-sight approximation would be a good choice at this stage. The principle of using the simplified approach is to select the appropriate target material, shielding material, and proton beam energy. This study has expanded the existing Monte Carlo-based data set to allow the simplified approach to be used for dose assessment or radiation shielding design for beam services in proton therapy facilities. The data sets related to the beam dump are added. The energy range of the proton beam contained in the database is from 100 to 300 MeV, the target material covers tissue, graphite, iron, and copper, and the shielding material covers PMMA, concrete, iron, and lead. This study proves that the Monte Carlo-based data sets are reliable through the following steps. The first step is to validate the physical model used to generate the data sets by neutron yield. The second step is that the data sets are used to evaluate dose rates and compare them with the accurate Monte Carlo method. Besides, it should be noted that the default model of the MCNP6 is no longer the Bertini model but the CEM model, therefore, the results of the simplified approach will be more conservative when it was used to do the double confirmation of the final shielding design.

This research was funded by the Radiation Protection Association R.O.C.

No potential conflict of interest relevant to this article was reported.

Conceptualization: Lai BL, Sheu RJ. Funding acquisition: Chang SL. Investigation and methodology: Lai BL, Sheu RJ. Writing of the original draft: Lai BL. Writing of the review and editing: Lai BL, Chang SL. All the authors have proofread the final version.

Comparison of experimental measurements and Monte Carlo calculations, including beams bombarding high-density (A) and low-density target materials (B). MCNP6, Monte Carlo N-Particle transport code; CEM, cascade-exciton model.

The secondary radiation generated by the proton beam bombarding the target transports in the simplified shielding model. The shaded area is the geometric shadow and the small black square is the target’s shadow.

Plan view of a hypothetical proton beam irradiation laboratory (from [

Dose attenuation curve of 250 MeV proton beam bombarding a graphite target with polymethyl methacrylate (PMMA) shielding.

The angular distribution of the source term (H_{1}, H_{2}) and the attenuation length (_{1}, _{2}) of the 250 MeV proton beam bombarding the targets at the shallow and deep shielding regions.

The dose rate distribution of laboratory (A), the neutron spectra outside the beam direction wall, and labyrinth entrance (B).

Comparing the calculation results of the simplified approach and Monte Carlo simulation for dose around the laboratory. MCNP6, Monte Carlo N-Particle transport code; CEM, cascade-exciton model.