Experimental characterization of the neutron spectra generated by a high-energy clinical LINAC

Nuclear Instruments and Methods in Physics Research A 629 (2011) 329–336

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Experimental characterization of the neutron spectra generated by a high-energy clinical LINAC K. Amgarou n, V. Lacoste, A. Martin ˆ rete´ Nucle´aire (IRSN), Laboratoire de Me ´trologie et de Dosime´trie des Neutrons, F-13115 Saint Paul-Lez-Durance, France Institut de Radioprotection et de Su

a r t i c l e in f o

abstract

Article history: Received 24 September 2010 Received in revised form 4 November 2010 Accepted 11 November 2010 Available online 26 November 2010

The production of unwanted neutrons by electron linear accelerators (LINACs) has attracted a special attention since the early 50s. The renewed interest in this topic during the last years is due mainly to the increased use of such machines in radiotherapy. Specially, in most of developing countries where many old teletherapy irradiators, based on 60Co and 137Cs radioactive sources, are being replaced with new LINAC units. The main objective of this work is to report the results of an experimental characterization of the neutron spectra generated by a high-energy clinical LINAC. Measurements were carried out, considering four irradiation configurations, by means of our recently developed passive Bonner sphere spectrometer (BSS) using pure gold activation foils as central detectors. This system offers the possibility to measure neutrons over a wide energy range (from thermal up to a few MeV) at pulsed, intense and complex mixed n–g fields. A two-step unfolding method that combines the NUBAY and MAXED codes was applied to derive the final neutron spectra as well as their associated integral quantities (in terms of total neutron fluence and ambient dose equivalent rates) and fluence-averaged energies. & 2010 Elsevier B.V. All rights reserved.

Keywords: Medical LINAC Unwanted radiation Neutron spectrometry

1. Introduction The use of high-energy electron linear accelerators (LINACs) in radiotherapy still represents the most diffused medical technique to treat cancers [1]. The main benefit of these machines is their ability to irradiate the target tumour volume without a substantial compromise of the neighbouring healthy organs or tissues [2]. Additionally, their primary beams provide a good skin sparing, accurate penetration, uniform spatial dose distribution, less scattering, minor perturbation, sharp field edges and small penumbra [3]. However, the majority of the LINAC devices used in radiotherapy operates in electron or photon modes at rather high acceleration potentials (up to 25 MV). Accordingly, secondary neutrons may be generated via photo-nuclear (g,n) and electro-nuclear (e,n) reactions of incident photons and electrons, respectively, with any heavy nuclide (W, Pb, Ta, Fe, Cu, y) of the massive components and accessories located inside the gantry and along the primary beam line [4]. This unwanted radiation, with a high relative biological effectiveness (RBE) compared with that of electrons and photons [5], is transmitted into all directions and may undergo further interactions with the accelerator structure, the concrete walls, the patient itself and any other furniture present in the treatment room giving

n Corresponding author. Current address: Grup de Fı´sica de les Radiacions,  Facultat de Cie ncies, Universitat Autonoma de Barcelona, E-08193 Bellaterra, Spain. Tel.: + 34 93 581 1364; fax: + 34 93 581 2155. E-mail address: [email protected] (K. Amgarou).

0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.11.101

rise to a more complex spatial and energy distributions. The resulting neutron spectra have also a strong dependence on the accelerator design, operating energy and head components (target, flattering filter, jaws, collimators, bending magnet, y) as well as on the particular topology (dimension, wall dimension and composition, maze shape, door shielding, etc. ) of the treatment room. Consequently, this radiation is an issue of primary concern from the radioprotection point of view. In fact, as life expectancy of treated patients is steadily growing, the ICRP organization stressed, for the first time ever in its publication 103 [5], the requirement of determining the associated peripheral dose that they may receive during the planned medical treatments and that may suppose for them an eventual long-term secondary cancer. In a previous study [6], we have shown that our recently developed passive Bonner sphere spectrometer (BSS), based on gold-foil activation detectors [7], is a very simple and well adapted method to measure neutron spectra that are typically found around the most common medical LINACs. The principle of the BSS method, firstly introduced by Bramblett et al. in 1960 [8], consists of a set of multi-sphere polyethylene moderator assemblies of various sizes with a central detector mainly sensitive to thermal neutrons. It is the only neutron measuring system that is able to determine neutron spectra, independently on their direction of incidence, over a wide energy range (from thermal up to a few MeV). As the size of the sphere increases, the maximum response of the spheredetector combination shifts to higher neutron energies. Conversely, the BSS requires normally the use of logarithmic energy scales

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since, due to its limited energy resolution, it does not allow appreciating detailed (fine) structures as narrow peaks or spectrum oscillations and resonances. Therefore, only smooth distributions of possible neutron fluence peaks could be indicated by this system. The Laboratory of Neutron Metrology and Dosimetry (LMDN) of the Institute for Radiological Protection and Nuclear Safety (IRSN), moved by the possibility to open a future research collaboration with the University Hospital of Essen (Germany), has performed a measurement campaign to characterize, by means of the above passive BSS, the neutron spectra produced by a medical LINAC facility under four different irradiation configurations. In what follows, the results of this campaign are presented after being fully analysed and discussed in detail.

2. Materials and methods 2.1. Neutron spectra measurements The experimental set-up used in this work is described in [6]; therefore, only a brief explanation of those relevant aspects about the procedures used for data acquisition and unfolding is given in this section. The passive BSS consists of 10 polyethylene (0.95 g cm  3 density) spheres whose diameters were labelled in inch units (3, 3.5, 4, 4.5, 5, 6, 7, 8, 10 and 1200 ) for convenience. Gold (197Au) disc foils (15 mm diameter, 0.25 mm thick, 19.3 g cm  3 density and 99.99% purity) are placed horizontally in the centre of each sphere. All the above spheres have own aluminium (Al) supports with adapted heights to assure the same vertical position during the entire BSS irradiation run. The response matrix of the system was evaluated by means of the MCNPX 2.5.0 code [9] and experimentally validated with our standard calibration facilities [10]. 2.1.1. Data acquisition After neutron irradiation, the activated gold foils are measured using a portable 300  300 NaI(Tl) detector (model BicronTM) with an integrated photo-multiplier tube coupled to a compact (CanberraTM Unispec) module. It has a nominal energy resolution of  50 keV for the 137 Cs 662 keV g-ray photo-peak. The complete unit is placed vertically inside a 5 cm thick cylindrical lead (Pb) shield with 19.5 cm outer diameter. The Unispec module is controlled by the Genie-2000s spectroscopic software, which permits also the analysis of the recorded g-ray pulse-height distributions. The NaI(Tl) detection efficiency was evaluated using the MCNPX 2.5.0 code after being benchmarked with five (137Cs, 60Co, 22Na, 133Ba and 152Eu) certified standard sources [7]. 2.1.2. Unfolding procedures The unfolding of a given neutron spectrum, from the passive BSS measurement data and the knowledge of its response matrix, constitutes a clear example of an underdetermined problem in the sense that the number of measurements is much lower than that of the output neutron spectrum and infinite mathematical solutions could be taken. Complexity also arises from the fact that the BSS individual measurements cannot be considered as truly independent because the response functions of the spheres used are normally large smoothed curves, which overlap along extended neutron energy intervals. To obtain a physical acceptable result, it is crucial to restrict the space of solutions by including some kind of a priori information. This could be extracted, in most cases, from the laws governing the production of neutrons and their subsequent interactions with the surrounding materials. In the present work, we have used a two-step unfolding method that combines both the NUBAY [11] and MAXED [12] codes. These codes normally give quite satisfactory results when used separately but Reginatto and Zimbal [13] have demonstrated that their combination presents a high consistency.

2.1.2.1. NUBAY unfolding method. It performs a Bayesian approach analysis [14] of complex statistical problems using the Markov chain Monte Carlo technique and Gibbs sampling [15,16]. In this code, the measured neutron spectrum is assumed to be a linear superposition of three non-negative parametric functions: a thermal-Maxwellian distribution, an intermediate region fitted with a straight line in lethargy representation (i.e., as 1/E behaviour in terms of neutron fluence rate) and a high-energy (fast) fissionlike peak. Their mathematical formulations are given in [6]. Initial prior uniform distributions, with convenient lower and upper limits, must be chosen for the free parameters. Their posterior distributions are obtained by applying the rules of Bayes’ probability theory and taking into account the BSS measurement data and their associated overall uncertainties. Some parameters may be set to appropriate fixed values, instead of being free variables, when additional information is available, when the experimental data are not strong enough or when they do not play an important role in the final neutron spectrum. Once the NUBAY calculation is finished, the medians of the posterior distributions should be chosen as the output optimal values of the free parameters, in special for those with asymmetric sharp distributions, to derive the sought neutron spectrum. 2.1.2.2. MAXED unfolding method. It is based on the maximum entropy principle [17], which is considered one of the most powerful and robust technique for inverse reconstitutions of positive distributions in different types of mathematical inference problems. The approach followed in MAXED has the following aspects: (a) It lets the inclusion of an initial default spectrum (DS) with non-negative values at each of the chosen neutron energy bins in a well-defined and mathematically consistent way. The DS is usually obtained from Monte Carlo simulations of the given problem or from previous measurements usually performed in limited energy ranges with other neutron spectrometers. (b) It employs an annealing optimization algorithm [18], able to distinguish between different local optima by means of uphill and downhill moves, to correct the DS features that are not in agreement with the measurement data. (c) From a collection of admissible neutron spectra subject to constraints linked to the associated overall uncertainties of the BSS measurements, the MAXED solution is the one that maximizes the relative entropy of the system. (d) The output neutron fluence rate, at each of the energy bins used, is related to its initial value given by the DS, the BSS response matrix and a set of additional parameters (determined during the unfolding process from the measurement data and their associated uncertainties) allowing further calculations of the corresponding covariance matrix. Unlike NUBAY, MAXED provides a ‘‘free-form’’ solution (i.e., the output neutron spectrum does not have to fit any of basic parametric functions) but it may depend, to some extend, on the initial DS used. The two-step unfolding method consists on using the MAXED code in two different ways as follows: (a) To check whether the parameterization used in NUBAY was adequate by examining and modifying the features of the NUBAY output neutron spectrum that are not in agreement with the passive BSS measurements. (b) To carry out a sensitivity study based on the variations of some of the parameters obtained with NUBAY. This study serves to confirm the stability of the NUBAY solution and to corroborate the associated uncertainties on its output results.

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2.2. LINAC facility The Essen LINAC device is a Varians Clinac 2100C (Varian Medical Systems, Inc., Palo Alto, California). Inside the LINAC head, movable tungsten jaws offer the possibility of selecting different planar field areas of the incident beam at the isocentre (a reference position located along the beam axis at 100 cm distance from the target and around which the LINAC gantry can rotate completely). The additional use of the last inner multi-leaf collimator (MLC), below the movable jaws, offers the possibility of adjusting the above field areas to the irregular shapes of the tumours subjected to treatment. The layout of the Essen LINAC treatment room is shown in Fig. 1. 2.3. Irradiation conditions The neutron spectra measurements with the passive BSS were carried out for four different irradiation configurations.

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The irradiation conditions used in each configuration are given in Table 1. The MLC leaves were set in the irradiation configuration 2 to match the same beam field size as that defined by the movable jaws (i.e., 10 cm  10 cm at the isocentre). The selected beam field and the MLC setting were similar for both irradiation configurations 1 and 4. They also represent the conventional standard conditions commonly used for quality assurance (QA) protocols of high-energy clinical LINACs [19,20]. The photon and electron output doses were controlled and monitored with two inner (independent) ion chambers. As a frequent practice, each medical LINAC is usually calibrated using the above QA standard conditions and normalized in such way to deliver a maximum dose of 10  2 Gy per monitor unit (MU) of the ion chamber readings within a considered cubic water phantom placed in the isocentre. During all the BSS irradiations, the highest LINAC beam yield (600 MU min  1) was chosen and the time variation of photon and electron output doses were constantly below 0.1%.

Fig. 1. Plan views of the Essen LINAC treatment room. The locations of the measurement points are also indicated. Point A was chosen at the isocentre and point B at 1 m away along the patient plane in front of the gantry (i.e., at 1.414 m diagonal distance to the LINAC target). In this figure, the LINAC gantry is vertically illustrated at a 901 rotation angle.

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Table 1 LINAC irradiation conditions used in each configuration.

BSS position Operation mode Acceleration potential (MV) Jaws position MLCs’ position Irradiation time Gantry rotation angle (deg.) Beam yield (MU min  1) (a) (b) (c)

Irradiation configuration 1

Irradiation configuration 2

Irradiation configuration 3

Irradiation configuration 4

Isocentre Photon beam 18 10 cm  10 cm(a) Retracted(b) 5 min 0(c) 600

Isocentre Photon beam 18 10 cm  10 cm 10 cm  10 cm 5 min 0 600

Point B Photon beam 18 10 cm  10 cm Retracted 5 min 0 600

Isocentre Electron beam 20 10 cm  10 cm Retracted 5 min 0 600

Planar field area of the incident beam at isocentre. Out of field. LINAC primary beam directed towards the floor.

3. Results and data analysis Different initial prior uniform distributions were chosen for each of the parameters used by NUBAY to model the measured neutron spectra. A large number (106) of iterations was selected to ensure convergence. The posterior distributions were plotted, during the running processes, for the three neutron spectral components (thermal, at, intermediate, ai, and fast, af, magnitudes) and the mean energy, cf, of the fast peak. Additional distributions were also drawn for the integral quantities: total neutron fluence rate, Ftot, and ambient dose equivalent rate, H(10). At the end of each running process, the mean and median values of all these parameters were listed together with their standard deviations. Except for the thermal-Maxwellian peak and intermediate region magnitudes that showed asymmetric sharp distributions, the mean and median values of the other parameters were in good agreement with quasi-Gaussian posterior distributions. The final measured neutron spectra were then determined using the optimal (median) values of the NUBAY output parameters and the results obtained are shown in Fig. 2. Table 2 summarizes the total neutron fluences and the ambient dose equivalent rates of these spectra normalized to the LINAC monitor unit as well as the corresponding values of their fluence-averaged energies, Eav. As a convention, the overall relative uncertainties were evaluated as a square-root of the quadratic sum of the relative standard deviations given by NUBAY and the systematic one of the response functions (of about 4.5%). 3.1. MAXED checking As explained in Section 2.1.2, MAXED needs a priori information about the sought neutron spectrum in the form of an initial fluence rate value at each of the energy bins used. In general, any features in the DS that are contradicted by the passive BSS measured data will be modified by MAXED, while structures that are consistent with these measurements will be kept unchanged. In a first step, MAXED was used to determine the neutron fluence energy distribution. Two different default spectra were chosen as a priori information - A 1/E distribution, which is equivalent to a flat spectrum in lethargy representation. Although this DS is not the most favourable for MAXED and physically unacceptable, since it assumes a minimum of a priori information, it is a useful step that permits, in a first stage of exploratory, a qualitative evaluation of the measured neutron spectrum. - The solution spectrum derived from NUBAY. This choice is expected to provide MAXED with the maximum amount of a priori information available leading, therefore, to the determination of a reliable solution spectrum.

Fig. 2. Neutron fluence rate energy distributions measured with the IRSN passive BSS at the four irradiation configurations (see Table 1). For a good visualization the data of irradiation configuration 4 were multiplied by a factor of 10.

The MAXED solutions, for the four irradiation configurations after using flat and NUBAY default spectra, are shown in Fig. 3. The energy distribution of the fluence-to-ambient dose equivalent conversion factors, as defined by ICRP [21], was also drawn on the same figure to show the role played by the neutrons at each energy region. It has been found that:

 The shapes of the MAXED output neutron spectra using the



NUBAY solutions as default spectra were very consistent with the passive BSS measurements. Indeed, the deviations between the specific saturation activities of the spheres used and those calculated by folding the output neutron spectra with the response matrix were within the associated overall uncertainties of the BSS measurements. Consequently, there was an excellent agreement (on average within 1.0%) between the NUBAY output integral quantities and those obtained with MAXED using the NUBAY solutions as default spectra. The shapes of the intermediate and high-energy regions of the MAXED solutions using the flat DS approach those of the NUBAY output neutron spectra. This indicates that the resolution of our passive BSS is well-adapted for the MAXED code in these energy domains. However, when using a flat distribution for thermal neutrons (from 0.5 eV down to 10  3 eV), MAXED did not correctly estimate their fluence rates. This behaviour can be explained by the fact that the low weighted tails of the passive BSS response functions in this region [9] are inappropriate for the MAXED code

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Table 2 Normalized values to the LINAC monitor unit for the neutron fluence and ambient dose equivalent rates of the Essen LINAC as well as the fluence-averaged energies of the measured spectra with the IRSN passive BSS. Irradiation configuration 3

Irradiation configuration 4

2967 34 461.7 76.3 55.27 3.0

225 7 14 515.9 7 7.0 43.1 7 2.2

98 711 257.6 7 2.5 (1386 775)  10  2

(5987 64)  10  2 3597 14 (115.67 8.9)  10  2

Configuration 1

1.4 1.2

NUBAY solution MAXED solution (DS = NUBAY) Maxed solution (DS = 1/ E. flat in lethargy) fluence-to-ambient dose equivalent conversion factors

1.0

500 400 300

0.8 200

0.6 0.4

100

Fluence rate (104 cm-2 s-1)

Fluence rate (105 cm-2 s-1)

1.6

Configuration 2

0.2

12 10

300 6 200

4

100

2

0

Configuration 4

500 400

3

300

2

200

1

100

600

6

600

0 0 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 Neutron energy (MeV)

Fluence rate (103 cm-2 s-1)

4

400

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 Neutron energy (MeV)

h* (10) (pSv cm2)

Fluence rate (104 cm-2 s-1)

5

500

8

Configuration 3 NUBAY solution MAXED solution (DS = NUBAY) Maxed solution (DS = 1/ E. flat in lethargy) fluence-to-ambient dose equivalent conversion factors

NUBAY solution MAXED solution (DS = NUBAY) Maxed solution (DS = 1/ E. flat in lethargy) fluence-to-ambient dose equivalent conversion factors

0

0 0.0 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 Neutron energy (MeV) 6

600

14

600

h* (10) (pSv cm2)

1.8

h* (10) (pSv cm2)

Eav. (keV) H(10) (mSv MU  1)

Irradiation configuration 2

5 4

NUBAY solution MAXED solution (DS = NUBAY) Maxed solution (DS = 1/ E. flat in lethargy) fluence-to-ambient dose equivalent conversion factors

500 400

3

300

2

200

1

100

0

h* (10) (pSv cm2)

Ftot (103 cm  2 MU  1)

Irradiation configuration 1

0 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 Neutron energy (MeV)

Fig. 3. MAXED output neutron spectra using flat (in lethargy) and NUBAY solution as default spectra together with the energy distribution of the neutron fluence-to-ambient dose equivalent conversion factors.

to derive a thermal-Maxwellian peak from the initial flat DS. In this instance, the MAXED solution spectrum remains closer in shape to the initial flat DS than to the physically more realistic Maxwellianlike energy distribution. Even so, there is a global agreement (below 7% in the worst case) between the values of the ambient dose equivalent rates evaluated with MAXED using the flat DS and those resulting from NUBAY.

3.2. Sensitivity study In this step, MAXED was used to determine the sensitivity of the solution spectrum by inferring some modifications on the NUBAY DS. One of the main reasons for doing neutron spectrometry with the Bonner sphere system is to assess the ambient dose equivalent rate. As this operational quantity depends mainly on the fast neutrons, the parameters defining the high-energy region of the NUBAY solution spectrum (af and cf) were varied and the subsequent consequences were studied. Six different modified default

spectra, all originated from the NUBAY solution spectrum, were considered for each of the four irradiation configurations. For four of the six default spectra, the position of the high-energy peaks was successively set to 0.1, 0.5, 1.5 and 5 MeV. For the two other default spectra, the nominal magnitude of the high-energy peak of the NUBAY solution spectra were first divided and then multiplied by a factor of 2. The results of this sensitivity analysis are given in Fig. 4. For almost all these default spectra, MAXED have presented almost similar shapes at high-energy domain with peaks usually located around the same cf values obtained with NUBAY. This demonstrates that when reasonable a priori information was given to MAXED unfolding code, its output neutron spectra were rather unwavering and they were, in general, close to those given by NUBAY. The maximum spectral variations (with respect to NUBAY solutions) were observed only for the extreme cases of the modified default spectra with the high-energy peaks shifted to 0.1 or to 5 MeV. This sensitivity analysis also proved the robustness of the NUBAY output solutions for the four irradiation configurations. In addition, NUBAY gives a good estimation of the associated uncertainties to

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Configuration 2

Configuration 1

20 15

20 NUBAY cf = 0.1 MeV cf = 0.5 MeV cf = 1.5 MeV cf = 5.0 MeV af/2 2*af

10 5

Fluence rate (104 cm-2 s-1)

Fluence rate (104 cm-2 s-1)

25

16 12 8 4

0 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 Neutron energy (MeV)

0 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 Neutron energy (MeV) Configuration 3 6 5 4

Configuration 4 7

NUBAY cf = 0.1 MeV cf = 0.5 MeV cf = 1.5 MeV cf = 5.0 MeV af/2 2*af

3 2 1 0 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 Neutron energy (MeV)

Fluence rate (103 cm-2 s-1)

Fluence rate (104 cm-2 s-1)

7

NUBAY cf = 0.1 MeV cf = 0.5 MeV cf = 1.5 MeV cf = 5.0 MeV af/2 2*af

6 5 4

NUBAY cf = 0.1 MeV cf = 0.5 MeV cf = 1.5 MeV cf = 5.0 MeV af/2 2*af

3 2 1 0 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 Neutron energy (MeV)

Fig. 4. MAXED sensitivity analysis of the NUBAY output solutions (see more details in the text).

the integral quantities (i.e., total neutron fluence and ambient dose equivalent rates) since they were, in all cases, very consistent with the spread of the MAXED results using the above modified default spectra.

4. Discussion On the whole, the neutron spectra given in Fig. 2 are in accordance with those published recently by other authors for several medical LINAC facilities and under irradiation configurations that are similar or slightly different from the ones used in this work [22–27]. According to McCall et al. [28], the intermediate and thermal components of these spectra may be a consequence of the scattering effects of the originally high-energy photo-neutrons with the surrounding concrete walls, floor and ceiling as well as with any other furniture or instrument present in the treatment room. Although these two components have no significant weights when assessing the doses due to neutrons, their indirect consequences especially with respect to the induced radioactivity, on which they have a substantial contribution due to their radiative capture (n,g) reactions with almost all the metal elements, must not be ignored [29–32]. For the irradiation configurations 1 and 2, the derived spectra are quite hard with an important fast peak located at  0.9 MeV. This is in coherence with the giant dipole resonance (GDR) model that predicts a main high-energy neutron peak, due to nuclear evaporation process, in principle, very similar to that of fission [4]. The values of integral quantities obtained in the first irradiation configuration are somewhat lower (  5.1% for the total neutron fluence rate and  9% for the associated ambient dose equivalent rate) than those found previously with our passive BSS at an identical LINAC device but with a different room topology [33].

When compared with the values obtained with our passive BSS at the same irradiation configuration of a new generation LINAC device [6], they are relatively higher ( +6.5% for the total neutron fluence rate and + 3.6% for the associated ambient dose equivalent rate). Anyhow, all these divergences are within the associated experimental uncertainties. As a first approximation, we can assume that the fast component of the measured spectrum at the isocentre (point A) comes directly from an imaginary isotropic point source located within the LINAC target. Except the air between this imaginary source and point A, this distance is free from any other obstacle or shielding as illustrated in Fig. 1. With the above assumption, a neutron source strength, Q¼(222 726)  108 MU  1, could be estimated for the irradiation configuration 1 using the inverse square distance law of emission: Fisocentre ¼ ðQ =4prA2 Þ, rA being the distance from the fast source to the isocentre [28]. Unfortunately, there are scarce data available in the literature [23,34–36] about the LINAC neutron source strengths, which are necessary for a rapid assessment of the occupational dose at the maze entrance. Our estimation of the neutron source strength is about 1.82 and 2.31 times higher than those reported by McGinley [35] and Followill et al. [34], respectively, for old LINAC devices that are not equipped with the multileaf collimator (MLC). However, the manufacturer of the current LINAC models has introduced henceforth many changes in their corresponding head design to include the MLC accessory, which is of key importance in today’s radiotherapy. On the other hand, Howell et al. [23] have considered a similar LINAC device as in the present study but fully closed (with both jaws and MLC) and their measured Q-value was a factor of  0.78 smaller. This is probably a consequence of the LINAC head, which was completely enclosed, so that most of the generated photo-neutrons were blocked inside. At the same time, if we consider the inverse square distance law for the irradiation configuration 3, the ratio of the fast neutron

K. Amgarou et al. / Nuclear Instruments and Methods in Physics Research A 629 (2011) 329–336 B components, Fpoint =Fisocentre ¼ 0:3, obtained for the two points A fast fast and B (cf. Fig. 1) is very smaller than the expected value,
2 rA =rB ¼ 12. This means that a great amount of the photo-neutrons, emerging from the inner virtual source towards point B, may be filtered or absorbed by the structural lateral shielding of the LINAC head. Contrary to the case of point A (isocentre), where the generated photo-neutrons have a free path within the planar field of the primary photon beam to exit the LINAC head, they have to go through this lateral shielding, undergoing in this manner some attenuation phenomena mainly via successive inelastic scatterings before reaching point B. For this reason, the fast component of the measured neutron spectrum at point B is softened and shifted to lower energies, around 0.4 MeV as observed in Fig. 2. Another explanation of the disagreement from the above expected value could be also the inscatter phenomenon [37] that may reach its maximum contribution at the isocentre. This phenomenon represents those photo-neutrons, originally emitted away the considered direction, that are finally re-oriented back mainly after several elastic scattering with the LINAC lateral shielding. Nevertheless, the point source assumption is merely approximate and should be taken with a lot of care since the photo-neutron production takes place within several components located at different height levels inside the LINAC head. The use of the MLC in the irradiation configuration 2 has a minimal participation in the production of photo-neutrons but it may partially block their emission outside the LINAC head. This behaviour was corroborated by many authors [38–42] who have carried out several Monte Carlo simulations and they found that the most common main sources of neutrons within the LINAC head are the primary collimator followed by the movable jaws, target and flattering filter. The MLC, as being the lowest component below the movable jaws for this LINAC machine, participates in the neutron production only if its positioning leads to an eventual interception of the primary photon beam. Effectively, Howell et al. [43] have demonstrated that this production is even more enhanced when the primary photon beam is completely intercepted by any of the following configurations: jaws closed and MLC retracted or jaws opened and MLC closed. The low values obtained at the irradiation configuration 4 (up a factor 50 in terms of the total fluence rate) corroborate the fact that the LINAC electron beam, when operating at acceleration potential above 10 MV, does not generate enough neutrons as in the case of the photon mode. Nevertheless, the cross-sections of the electronuclear (e,n) reaction are normally two of orders of magnitude smaller (nearly a factor equivalent to the well-known fine structure constant, a ¼ e2 =_c ¼ 1=137) than the photo-nuclear (g,n) ones [4]. We believe that these electrons may also generate neutrons indirectly through the photo-nuclear (g,n) reaction of intermediate Bremsstrahlung photons. These represent a contamination radiation of the primary beam and could appear as consequence of the eventual scattered electrons that may be lost in several LINAC components and accessories such as the evacuated drift tubes, the bending magnet, the scattering foil and the steering/focusing coils. As observed in point B (see Fig. 2), the fast neutron component obtained in this last irradiation configuration is also shifted to lower energies. This puts into evidence that the neutrons generated within the LINAC gantry in direct electron mode, instead of having a free path, they were forced to travel across many obstacles within it before reaching the isocentre.

5. Conclusions The production of unwanted neutrons by a high-energy clinical LINAC was experimentally characterized by means of a passive

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Bonner sphere spectrometer and a two-step unfolding method that combines the NUBAY and MAXED codes. The measured neutron spectra at the isocentre were in accordance with the giant dipole resonance model that predicts a main peak, due to nuclear evaporation process, very similar to that of fission. When operating with direct electron beam, the neutron production was not enough (up to a factor 50 smaller in terms of the total fluence rate) compared to that taking place in a photon mode. The emitted neutrons within the planar field of the LINAC primary photon beam have a free path from any obstacle or shielding to exit the LINAC head. They may suffer also from the inscatter phenomenon that may reach its maximum contribution at the isocentre. However, the generated neutrons outside the primary beam have to go through the gantry structures, hence that they are able to undergo some attenuation phenomena mainly via successive inelastic scatterings. The estimated neutron source strength, although being very approximate, is very comparable to the value reported by other authors for similar LINAC devices. The multi-leaf collimator (MLC), which is the lowest component below the movable jaws for the considered LINAC machine, participates in the neutron production only if its positioning leads to an eventual interception of the primary photon or electron beam. The measured intermediate and thermal components obtained for the four irradiation configurations, despite their insignificant weights when assessing the doses due to neutrons, may be of great importance in the evaluation of the induced radioactivity inside the treatment room.

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