

ORIGINAL ARTICLE 

Year : 2017  Volume
: 40
 Issue : 2  Page : 8489 


Estimation of induced air activity in 30 MeV proton accelerator: Comparative study of Monte Carlo simulations and analytical calculations
Biju Keshavkumar, S Anand, Kapil Deo Singh, Tapas Bandyopadhyay
Health Physics Division, Health Safety and Environment Group, Bhabha Atomic Research Centre, Mumbai, Maharashtra, India
Date of Submission  01Mar2017 
Date of Decision  04Apr2017 
Date of Acceptance  30Apr2017 
Date of Web Publication  13Jul2017 
Correspondence Address: Biju Keshavkumar Health Physics Division, Health Safety and Environment Group, Bhabha Atomic Research Centre, Mumbai  400 085, Maharashtra India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/rpe.RPE_10_17
The induced radioactivity concentrations of ^{41}Ar, ^{13}N, and ^{15}O in air in 30 MeV proton accelerator vaults has been estimated using Fluka Monte Carlo simulations and National Council on Radiation Protection (NCRP) 144 based analytical methods. The results obtained by these methods are compared and discussed. It is found that analytical calculations using NCRP 144 guidelines underestimate the ^{41}Ar concentrations about three times while ^{15}O concentrations are overestimated about ten times when compared to Monte Carlo estimates. However, the ^{13}N concentrations estimated by both the methods are found to be in good agreement. It is seen that the analytical calculations ignore the significantly large contribution of ^{41}Ar formation by the neutrons above thermal energy. The overestimation of ^{15}O is caused by the large crosssection value assigned in the analytical calculations. Keywords: ^{41}Ar, Fluka, induced air activity, Monte Carlo
How to cite this article: Keshavkumar B, Anand S, Singh KD, Bandyopadhyay T. Estimation of induced air activity in 30 MeV proton accelerator: Comparative study of Monte Carlo simulations and analytical calculations. Radiat Prot Environ 2017;40:849 
How to cite this URL: Keshavkumar B, Anand S, Singh KD, Bandyopadhyay T. Estimation of induced air activity in 30 MeV proton accelerator: Comparative study of Monte Carlo simulations and analytical calculations. Radiat Prot Environ [serial online] 2017 [cited 2020 Feb 27];40:849. Available from: http://www.rpe.org.in/text.asp?2017/40/2/84/210572 
Introduction   
Medium energy proton accelerators have been widely in use for medical isotope production, material science studies, nuclear physics research, etc. The secondary radiations, neutrons, and gammas produced by the interaction of the primary proton beam in the target rooms need to be shielded adequately to protect the personnel working around and the public. Another important radiation safety aspect needs to be addressed is the induced activity generated in air and the accelerator components. The knowledge of the radioactivity concentration in air is a prerequisite to decide the ventilation requirements and the waiting period for the personal entry into the accelerator vaults after the beam is shut off. Furthermore, these estimates are essential to assess individual and population dose from the gaseous discharges from the facility. A recent review of the various radiation safety issues relevant to proton medical accelerator has been made by Mukherjee.^{[1]}
The estimation of the induced radioactive concentrations can be made using analytical methods based on semiempirical formulations as well as detailed Monte Carlo simulation methods. The analytical calculations are quick and approximate and considered as conservative estimates, fairly acceptable in most of the radiation protection calculations. However, these calculations are not very suitable for some cases involving complex source distributions and shield geometries. Monte Carlo methods are more accurate and amenable to solve complex problems in a realistic manner, but timeconsuming. It is always worthwhile to know how close these assessments are. There are various analytical methodologies suggested in the literature to estimate the activation of air inside the proton accelerator vault and the environmental impact.^{[2],[3],[4]} The studies of Birattari et al.^{[5],[6]} discusses in detail the analytically based estimations of neutron activation of air in cyclotron facilities and population dose calculations. Many Monte Carlo simulation based studies have also been reported in the literature on the air activity estimation inside the high energy accelerator vaults. The ^{41}Ar concentration in 0.1–1 GeV proton accelerators vaults are studied using Monte Carlo simulation and the results are compared with the analytical estimation.^{[7]} Nonthermal contribution to the ^{41}Ar production has also been discussed in the abovementioned paper. A study by Gutermuth et al.^{[8]} reported the Monte Carlo estimation of induced air activation in a high energy ion accelerator and compared with the analytical calculations. The above studies ^{[7],[8]} reports a factor of 2–3 difference in the values of ^{41}Ar concentrations estimated by analytical and Monte Carlo methods. Another study ^{[9]} calculates the ^{41}Ar production in a 16.5 MeV positron emission tomography medical cyclotron vault by the Monte Carlo simulations for 1 h beam irradiation and compares with the measurement. Induced activity in air and cooling water is estimated by Nakane et al.^{[10]} by multiplying the Monte Carlo simulated spectra of protons and neutrons in the proton accelerator tunnels of 600 MeV, 3 GeV, and 50 GeV energy with the corresponding activation crosssection data.
The present study is on the estimation of induced radioactivity concentration in typical 30 MeV proton accelerator vaults. This paper attempts a comparison of computed resident air activity by Monte Carlo simulations and analytical method suggested in National Council on Radiation Protection (NCRP) 144 report.^{[2]} The shortlived radioactive isotopes produced in air, namely,^{41}Ar,^{13}N, and ^{15}O having environmental concern are being studied in detail, by varying the enclosure volumes and targets. The production of induced radioactivity of ^{11}C and ^{3}H in air is negligible for 30 MeV proton energy and not considered in the present study.
Materials and Methods   
Major fraction of the ^{41}Ar is produced by the absorption of thermal neutrons by ^{40}Ar, slowed down through multiple collisions of fast neutrons with the containment shield walls and floor. Significant crosssections exist even above the thermal region also.^{13}N and ^{15}O are produced by the fast neutron reactions and the (n, 2n) crosssection starts at about 11.3 and 17 MeV, respectively. The nuclear reactions responsible for production and the other important parameters of these isotopes are given in [Table 1]. The (n, 2n) production crosssections as a function of neutron energy are presented in [Figure 1].^{[11]} The calculations are made using Fluka ^{[12],[13]} Monte Carlo simulations as well as using the analytical guidelines suggested by NCRP 144 report. Monte Carlo method is the most accurate method of estimations as it is capable of modeling geometry, interactions, spatial, and energy distribution of neutron fluence and respective crosssections for the production in an exact manner. In the analytical calculations, the ^{41}Ar concentration is assumed as exclusive thermal neutron absorption process, and the thermal neutron flux is proportional to the inner surface area of the vault.^{13}N and ^{15}O concentrations are calculated using the path length of the neutron beam in air, high energy neutron fluence above the production threshold and the average crosssection of the reaction over that energy range. As the induced radioactivity depends on the neutron flux, volume of the vault, ventilation rate, etc., a study is made for the concentrations in two different vault dimensions, having volumes 64 m ^{3}and 1000 m ^{3}. Tantalum (Ta) and copper (Cu) are considered for the total loss of accelerated projectiles as most of the beam dumps are made of these materials. A typical ventilation rate of ten air changes per hour is assumed in the calculations.  Figure 1: Energy dependant production crosssections of ^{41}Ar, ^{13}N and ^{15}O
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Monte Carlo simulations
A validated Monte Carlo code Fluka2011.2C.3 is used for the simulations to estimate the induced air activity concentration inside the vault. Fluka is capable of making predictions about residual nuclei produced in hadronic and electromagnetic showers and time evolution of the radionuclide inventory calculations online. The isotope production and decay as a function of irradiation time and cooling time are calculated analytically using the Bateman equations.
To estimate the neutron yield and energy distribution from the protons bombarded in the target material (Ta and Cu), a pencil beam of protons falling on the thick stopping cylindrical target in vacuum is modeled [Figure 2]. The thickness and radius of the target are kept as the range of protons in that material. The values of range of 30 MeV protons are obtained using SRIM code.^{[14]} The energy and angleintegrated neutron yield are obtained by scoring the neutron fluence crossing a spherical surface around the target using USRBDX card.  Figure 2: Schematic diagram of irradiation geometry in the concrete vault
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The induced air activity is estimated, by simulating a pencil beam of protons falling on a thick target in a irradiation cuboid vault of dimensions 4 m × 4 m × 4 m (64 m ^{3}) and 10 m × 10 m × 10 m (1000 m ^{3}) filled with dry air. A beam tube is also modeled through which proton beam moves so that the activation of air by proton is avoided. The target is assumed at the center of the vault. The induced activity in the air is simulated using RESNUCLEI card for 10 h of proton irradiation. The buildup of the ^{41}Ar,^{13}N, and ^{15}O activity inside the nonventilated vault at various time intervals during irradiation and decay for 4 h after the beam is stopped is obtained using the combination of cards IRRPROFI, RADDECAY, DCYTIMES, and DCYSCORE.
The relative error of the ^{15}O results obtained by Monte Carlo simulations with protons as the primary particle is higher than acceptable even after simulating 100 million histories. So as to reduce the error, the simulations were carried out in two steps. First, the neutron emission spectra are generated from the 30 MeV protons stopped in the respective target. Subsequently, the simulations were made for an isotropic neutron source assumed at the center of vault having a neutron energy distribution of the high energy part (above 17 MeV energy) of the spectrum. The results were properly weighted so that the estimates are unbiased.
Analytical calculations of saturated activity in nonventilated vault
The saturation activity concentration in the nonventilated accelerator vaults is calculated using the methodology suggested in NCRP 144 report. The methodology and formulae are explained the following sections.
^{41}Ar concentrations
The saturated activity concentration of ^{41}Ar in the nonventilated vault, A_{s} in Bq/cm ^{3}is calculated using the formula:
Where N_{A} is the Avogadro number, A is the atomic weight of element, f is the weight fraction composition of argon in air, ρ is the density of air and σth is the thermal neutron capture crosssection of ^{40}Ar (660 mbarns). The thermal neutron fluence, φ_{th}, can be obtained by formula:^{[15]}
Where Y is the total yield of neutrons, S is the surface area of the enclosure in cm ^{2}. Upon substitution in Equation 1
where F is a factor, 1.9E7. Here, the values of neutron yield, Y used for analytical calculations is obtained by the present Fluka simulations.
^{15}O and ^{13}N concentrations
The yield of ^{13}N and ^{15}O activity per unit neutron path length, S_{j} (Bq/m) in the air is estimated using the following formula:
Where φ_{HE} is the high energy neutron yield above the reaction threshold, N_{A} is the Avogadro's number, A_{i} is the mass number of the target atom, is the weight fraction of the target atoms in air, ρ is the density of air and σ_{i}is the crosssection. Considering the crosssection as 40 mb for ^{15}O production and 10 mb for ^{13}N production through (n, 2n) reactions, the factors (S_{j}) are 4.2E+7 and 3.9E+7, respectively for a high energy neutron yield, φ_{HE}, of 10^{12}n/s. The value of φ_{HE} used for calculation here is the high energy neutron yield above the (n, 2n) reaction threshold obtained from the present Fluka simulations.
The saturation activity, A_{s} (Bq/cm ^{3}) is given by:
where L is the path length (m) and V is the volume of the vault (cm ^{3}). L is calculated as the radius of the vault while assuming the volume of the vault (64 m ^{3}and 1000 m ^{3}) as a sphere.
Saturated activity in ventilated vault
The saturated activity in the nonventilated vault [Equation 5] is further corrected for the ventilation rates. The saturated induced radioactivity concentration (Bq/cm ^{3}) in the vault with ventilation is given by:
where A_{s} (Bq/cm ^{3}) is the saturated activity in the nonventilated vault and λ_{d} and λ_{V} are the constants for removal by radioactive decay [Table 1] and ventilation (10 air changes per hour), respectively.
Results and Discussion   
Neutron energy spectrum and yield
Two target materials are studied here, to know the influence of the difference in yield and neutron energy distribution on the activation results. The energy and angleintegrated neutron yield from Cu and Ta target for 30 MeV protons obtained by Fluka simulations are presented in [Table 2]. Fifty million histories are simulated, and the percentage relative error of the results is presented in the parenthesis. The neutron yield reported in the International Atomic Energy Agency report ^{[16]} for Ta and Cu target is also presented in the table for comparison purpose. The estimated yields by this simulation study agree with the literature value. The total yield of neutrons from Ta target is about 65% higher than that of Cu. Furthermore, the high energy neutron yields above the threshold energy for (n, 2n) nuclear reactions in the respective target materials are also presented in [Table 2]. The neutron yield above 11.3 MeV (^{13}N production threshold) is found almost same for Cu and Ta target, whereas the neutron yield corresponding to the ^{15}O production is about 26% more from Ta than Cu. The Monte Carlo simulated neutron yields have been used for induced activity in analytical calculations. [Figure 3] presents the normalized neutron fluence spectra emitted from the Cu and Ta targets. It is seen that the spectrum is different for Ta and Cu target.  Table 2: The neutron yields from the 30 MeV protons absorbed in Ta and Cu targets obtained by the Fluka simulations
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 Figure 3: Energy distribution of neutron yield from Cu and Ta thick target
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Induced resident air activity
The neutroninduced activity buildup of ^{41}Ar,^{15}O, and ^{13}N as a function of time is obtained for 10 h of proton beam irradiation and 4 h of cooling in both the accelerator vaults using Fluka. [Figure 4] presents the neutroninduced activity buildup of ^{41}Ar,^{15}O, and ^{13}N as a function of time with Cu target in nonventilated 64 m ^{3}vault. A 100 million histories are simulated and the relative error of the results is within 5%. [Table 3] presents saturated resident air activity concentrations inside the vaults per 1 μA proton beam loss in the target having a ventilation of 10 air changes per hour from the Fluka simulations and the analytical method based calculations.  Figure 4: The buildup and decay of the air activity in the nonventilated vault of volume 64 m^{3}for Cu target as 10 h of 30 MeV, 1 μA of proton beam irradiation and further 4 h of cooling obtained by Fluka simulations
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 Table 3: The resident saturated ^{41}Ar, ^{13}N and ^{15}O activity concentrations (Bq/cm^{3}/μA) calculated using Monte Carlo simulations and analytical method after correcting for a ventilation removal of ten air changes per hour
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^{41}Ar concentrations
From [Table 3], it is observed that the analytical values of ^{41}Ar concentration are showing a large underestimation as compared to the Monte Carlo results. Analytical results are merely about 34%–37% of the Monte Carlo results. This variation is consistently same for the different room volumes and target material. Since the empirical formula used for analytical calculations assumes the activation is caused only by thermal, the increase in the Monte Carlo simulation values is by the contribution of nonthermal part of the neutron spectrum. The thermal neutron contribution is also analyzed by folding the neutron spectra inside the vault with the appropriate capture crosssections. It is found that thermal neutron contribution by the above said method is found about 35%–40%, which is analogous to the study ^{[7]} reported earlier for 0.1–1 GeV protons. However, this study also supports the proposal of changing the value of factor F [Equation 3] to 5.7E7 rather than 1.9E7 in analytical calculations.
^{13}N concentrations
It is found that the analytical method overestimates the saturated ^{13}N air activities by 24%–46% when compared to Monte Carlo results. The difference in the values may be attributed due to the difference in the approach used by these methods. For example, the reaction yield is analytically calculated using a crosssection of 10 mb, which is the maximum crosssection at around 20 MeV energy (ENDF/B VII.1, 2012) while Monte Carlo simulations use the energy dependent crosssections and corresponding fluence distributions in the estimations. The kind of order of overestimation observed in ^{13}N concentrations is reasonably acceptable in the radiation protection calculations.
^{15}O concentrations
From the ^{15}O concentrations presented in [Table 3], it can be observed that there is a huge overestimation in analytical calculations around a factor of 7–12. This difference could be due to the use of higher crosssection value, 40 mb that is prescribed by NCRP 144 report. It is noticed that the average crosssection value for the reaction is only 5.2 mb for the neutron energy range of 17–30 MeV as per ENDF/B VII data. Hence, the analytical calculations with the value of crosssection as 5.2 mb make a reasonable estimate comparable to Monte Carlo results.
Conclusions   
The induced activity of ^{41}Ar,^{13}N, and ^{15}O in 30 MeV proton accelerator vaults is estimated using Fluka Monte Carlo simulations and analytical solutions based on semiempirical formulae, and the results are compared. It is observed that analytical calculations underestimate the ^{41}Ar concentrations by a factor of ~3 compared to realistic Monte Carlo simulations. The underestimation of the analytical formula is caused by the nonaccounting of the activation process by the epithermal neutrons (energy >0.025 eV). However, in the case of ^{13}N production, the analytical based estimates are reasonably agreeing with the Monte Carlo estimate, and in the case of ^{15}O, the values are largely overestimated by the analytical formula, a factor of about ten times due to the large difference in the crosssection data. Based on this study, it is recommended that the analytical expression [Equation 3] may be modified by introducing a correction factor for the accurate estimates of ^{41}Ar and ^{15}O induced activities, and the results are needed to be experimentally validated in the future.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4]
[Table 1], [Table 2], [Table 3]
