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Neutron energy spectra inside a PET cyclotron vault room
Nuclear Instruments and Methods in Physics Research A 463 (2001) 375–386
Neutron energy spectra inside a PET cyclotron vault room H!ector Ren!e Vega-Carrillo* Centro Regional de Estudios Nucleares, Universidad Autonoma de Zacatecas, Apdo Postal 336, 98000 Zacatecas, Zac. Mexico Received 20 July 2000; received in revised form 3 November 2000; accepted 5 November 2000
Abstract Neutron energy spectra were measured at three locations inside the vault room of a PET cyclotron. Measured neutron fields were produced during 17.2 MeV protons and 8.6 MeV deuterons colliding with Faraday cup, and 8.6 MeV deuterons colliding with 14N. Measurements were performed using a Bonner sphere spectrometer whose active 6 LiI(Eu) scintillator was replaced by two pairs of thermoluminscent dosimeters. Modified neutron spectrometer was calibrated using bare 252Cf and D2O moderated 252Cf neutron sources. Thermoluminiscent dosimeters were calibrated using g-rays from 137Cs and 60Co sources. From this calibration, a single factor was derived that allow us to obtain the thermal neutron net signal used to unfold neutron spectra. MCNP 4A code was used to calculate neutron spectra at those sites were measurements were taken. For MCNP calculations a source term for protons colliding with graphite was calculated using a semiempirical model. Due the lack of source term for neutrons produced during 8.6 MeV deuterons nuclear reactions, with carbon and 14N, several models were tried. From experimental and calculated results a systematic behavior of neutron spectra was observed regardless the primary neutron source. This behavior was a peak indicating the presence of evaporation neutrons due to the large amount of iron in cyclotron. # 2001 Elsevier Science B.V. All rights reserved. PACS: 28.20.Gd; 29.20.Hm; 29.30.Hs Keywords: PET; Cyclotron; Neutron; MCNP; Bonner spheres
1. Introduction Positron Emission Tomography, PET, widely used for diagnostic purposes, is a non-invasive medical imaging technique used to determine location and concentration of physiologically active compounds in human body [1].
*Fax: +1-52-492-2-70-43. E-mail address: [email protected] (H.R. VegaCarrillo). URL: http://cantera.reduaz.mx/rvega.
In PET, 15O, 13N, 11C and 18F are used, these have short half-lives and are produced at hospitals, mostly using charged-particle accelerator facilities. PET isotope production is carried out using nuclear reactions that produces undesirable neutrons. Table 1 shows PET isotopes nuclear reactions features. An accelerated beam of charged particles produce radiation as a consequence of interactions between charged particle beam and surrounding media it collides, thus bremsstrahlung and characteristic X-rays, prompt g-rays, neutrons and delayed radiation (b and g) are produced. The lack
0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 2 3 4 - 0
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Table 1 Positron-emitting isotopes used in PET studies Nuclear reaction
Q-value (MeV)
Positron emitter
Half life (minutes)
11
2.764 2.922 5.217 0.280 3.536 +5.073 2.437 +2.792
11
20.385 20.385 9.965 9.965 2.037 2.037 109.77 109.77
B(p,n)11C N(p,a)11C 16 O(p,a)13N 12 C(d,n)13N 15 N(p,n)15O 14 N(d,n)15O 18 O(p,n)18F 20 Ne(d,a)18F 14
of electric charge and the ways they interact with matter, makes neutron field characterization a difficult problem. A single location to describe neutron production is difficult to establish because neutron-producing reactions can occur at many points inside the accelerator, such as target, beam stopper and beam deflector. According to NCRP 51 [2], shielding design requires an estimate of radiation emission rate from the accelerator. To make this estimation, parameteres like: species and energy of accelerated particle, target material, particle-beam current, angular distribution and energy spectrum of produced radiation, should be known. Nuclear reactions have been studied extensively for a broad range of targets and particles. In general, it has been established that [3,4], even at high proton energies, resulting neutron spectrum from thick targets may be described as consisting of three main components: Cascade neutrons, evaporation neutrons and epithermal and thermal neutrons arising from slowing down of evaporation and cascade neutrons. In this investigation neutron energy spectra were measured at three locations inside the vault room of a PET cyclotron. Neutron spectra were measured during 17.2 MeV protons and 8.6 MeV deuterons colliding with Faraday cup, and 8.6 MeV deuterons colliding with 14N. Measurements were performed using a Bonner sphere spectrometer, BSS, whose active 6LiI(Eu) scintillator was replaced by two pairs of thermoluminscent dosimeters (two TLD600 and two TLD700). Modified BSS was calibrated using bare and D2O moderated 252Cf neutron source. Thermoluminis-
C C 13 N 13 N 15 O 15 O 18 F 18 F 11
cent dosimeters, TLDs, were calibrated using g-rays from 137Cs and 60Co sources. From this calibration, a single factor was derived that allow us to obtain the thermal neutron net signal. MCNP 4A code was used to calculate neutron spectra at those sites were measurements were taken. For MCNP calculations a source term for protons colliding with graphite was calculated using a semiempirical model derived by Alsmiller et al. Due to the lack of a source term for neutrons produced during 8.6 MeV deuterons nuclear reactions, with carbon and 14N, several models were used. From experimental and calculated results a systematic behavior of neutron spectra was observed regardless the primary neutron source. This was a peak in the energy interval 0.3 to 4 MeV, with a maximum at approximately 1 MeV indicating the presence of evaporation neutrons produced during nuclear reactions that are modified by the large amount of iron in the cyclotron.
2. Materials and methods 2.1. Facility description PET cyclotron is located at the Research Imaging Center at the University of Texas Health Science Center in San Antonio, TX. PET cyclotron is Scanditronix MC 17F capable of accelerating protons or deuterons to 17.2 MeV and 8.6 MeV, respectively. Maximum charged particle current is 65 mA, with an extraction efficiency of
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approximately 80% for protons and 60% for deuterons [5]. Magnets, radiofrequency source, cooling system, target, beam probe, Faraday cup (beam stopper), and an ion source complete the cyclotron. Monitoring charged particle beam in the cyclotron, beam stability, particle selection, and target handling are all determined from the control room. Radioisotopes produced are automatically transported to hot cell at radiochemical laboratory. Cyclotron is housed in a 518 518 366-cm3 vault shielded by reinforced concrete, Fig. 1 shows cyclotron facility. Vault walls are 152 cm thick, ceiling is 122 cm thick, access to vault is via a motor-driven concrete door 122 cm thick. Cyclotron is located at the first floor of the Research Imaging Center building. Three of the cyclotron’s vault walls are adjacent to equipment room, radiochemistry laboratory, and restrooms. The fourth wall is adjacent to outside loading dock area. A vault room plant view is shown in Fig. 2. 2.2. Bonner spectrometer modification and calibration There is not single spectrometer with ideal response to neutrons from thermal to fast energies. BSS is often used to obtain neutron spectra over a
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Fig. 1. PET cyclotron schematic diagram.
wide range of neutron energies (thermal to 400 MeV), but it has a poor energy resolution, and an unfolding code is required [6]. Pulse pileup and large dead times in intensive or pulsed neutron fields is another BSS drawback. To overcome this last a passive thermal neutron detector can be used instead of active 6LiI(Eu) BSS detector. In this work was decided to use TLDs as thermal neutron detector in the BSS. The use of paired TLDs in mixed radiation fields has been widely used, however few works have
Fig. 2. Partial plant view of first floor at the University of Texas Health Science Center, where PET cyclotron vault room is located.
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reported using pairs of TLDs in multispheres [7–10]. BSS was modified in the following manner: A high-density polyethylene plug with the same geometry and dimensions as the aluminum holder for scintillator, light pipes, photomultiplier tube and base was built. At plug upper section, four small holes were done to hold 4 TLDs, 2 TLD600 and 2 TLD700. Bare, 200 , 300 , 500 , 800 , 1000 and 12 inch-diameter polyethylene spheres were used. Two pairs of TLD-600 and TLD-700 in each sphere were used to measure thermal neutrons. TLD-600 contains 95.6% 6Li, while the TLD-700 contains 99.9% 7Li. Both have approximately same density and atomic numbers, and the same response to g rays. For thermal neutrons, TLD600 response is larger than TLD-700. TLDs are 0.3175 0.3175 0.0889-cm3-ribbon type from Harshaw (Solon, OH). When exposing TLD-600 and TLD-700 in a mixed neutron g radiation field, measured response is the result of g-ray and neutron responses, g n Rnþg 600 ¼ R600 þ R600
ð1Þ
g n Rnþg 700 ¼ R700 þ R700
ð2Þ
is the total TLD 600 measured here, Rnþg 600 response, Rn600 is neutron contribution, and Rg600 is g-ray contribution to TLD-600 response. Rnþg 700 is the total response of TLD 700, Rn700 andRg700 are the respective contributions to TLD 700 response of neutrons and g-rays. When pairs of TLD 600 and TLD 700 dosimeters are used to measure thermal neutrons, a common practice is to assume that both have the same response to photons [7,11–15]. Because Rn700 is practically null, the simple difference between responses of both dosimeters is used as an indicator of net neutron response. During this study, photon responses of both dosimeters were measured with 60Co and 137Cs g sources. TLD 600 to TLD 700 g response ratio was used as a correction factor, k, to equalize the g-ray response of both TLDs. Net neutron signal was calculated using, nþg Rn ¼ Rnþg 600 k R700 :
ð3Þ
Bare 252Cf and D2O moderated 252Cf neutron sources were used to calibrate BSS with TLDs and BSS with 6LiI scintillator. During calibration, measurements with bare thermal detectors, 6LiI and TLDs, were carried out to check if statistical differences in count rates show up due polyethylene plug that hold TLDs. BSS with 6LiI and BSS with TLDs were used to measure neutron energy spectra of bare 252Cf and D2O moderated 252Cf neutron sources, this measurements were used to find the relationship between BSS with TLDs and BSS with 6LiI experimental responses. 2.3. MCNP calculations 2.3.1. Cyclotron and vault room modeling General Monte Carlo Neutron Photon Transport, MCNP, code version 4A [16] was utilized to calculate neutron transport inside vault room. Faraday cup was modeled as 2.3-cm-diameter carbon sphere. Because information about the deflector material was unavailable it was also modelled as a 2.3 cm diameter carbon sphere. Inside this spheres neutron source was located. Vault room concrete density was assumed be 2.3 g/cm3, iron was used to model cyclotron’s magnets, meanwhile wires and cyclotron ‘‘dees’’ were modelled as copper made. Air inside vault room was included in the model. For simplicity vault room door was modelled as thick as vault walls. Neutron flux spectra were tallied at those locations where measurements with BSS with TLDs were carried out. For source terms used in MCNP calculations two different situations were considered: neutrons produced by protons interacting with carbon and those produced when deuterons interact with carbon and 14N. 2.3.2. Neutrons emitted during (p, C) reaction At proton energies below 10 MeV, dominant interaction is by the compound nucleus formation, which is left in excited state with a number of allowed decay channels. Compound nucleus tends to reach ground state by particle emission described by an evaporation process. Energy
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distribution of emitted neutrons can be estimated by,
slabs as
nðEÞ dE / E expðE=TÞ
nðE; yÞ ¼
ð4Þ
here, T is nuclear temperature, usually between 1 and 10 MeV. However, at higher energy development of intranuclear cascade become important. In this case, several neutrons can be emitted in succession, while nuclear temperature falls from an initial value to zero. Intranuclear cascade develops through interaction of individual nucleons inside the nucleus. Using intranuclear-cascade-evaporation model, Bertini [17,18] generated a large amount of data of non-elastic cross-sections and the energy and angular distributions of emitted neutrons and protons. These data are for neutrons and protons, in the energy range 25–400 MeV, colliding with a variety of targets. To make these data more accessible, Alsmiller et al. [19] developed analytical models and tables of their coefficients, using leastsquare method to fit Bertini’s data. Nevertheless Alsmiller’s expressions are valid for 25–400 MeV protons it was assumed that coefficients and semiempirical equations gave reasonable results for 17 MeV protons. Therefore coefficients for neutron emission and non-elastic crosssection models at 17 MeV protons were assumed to be the same as those at 25 MeV, calculations were carried out as Nakamura et al. [20] To apply Alsmiller expressions, Faraday cup model was subdivided into n thin slabs, each of a thickness Dx. As protons penetrates Faraday cup, was assumed protons loses energy according to continuous slowing-down model without changing direction. Average kinetic energy ðEk Þ in the kth slab was calculated using, Dx dE Ek ¼ Ek1 ; k ¼ 1; 2; . . . ; n ð5Þ 2 dx k1 where Ek1 is protons average kinetic energy in the k 1 carbon slab, and ðdE=dxÞk1 is the stopping power of Ek1 MeV protons in carbon. Proton stopping power was calculated using the computer code TRIM 92 [21]. Energy spectra of neutrons emitted within each slab were calculated and summed over all thin
n X k¼1
1 Fk ðE; yÞ þ Gk ðE; yÞ 4p
Ak sðEk ÞNDx1027
ð6Þ
where sðEk Þ is the non-elastic cross-section expressed in millibarns and was calculated using [22] ( ) n X 1 Ek i exp sðEk Þ ¼ ai ð7Þ 400 400 i¼0 here, Fk ðE; yÞ stands for the cascade neutronemission spectrum, " i # n X 1 E Fk ðE; yÞ ¼ exp bi ðyÞ ð8Þ Ek E k i¼0 and Gk ðEÞ represents the evaporation neutronemission spectrum, " j # n X 1 E Gk ¼ exp cj : ð9Þ 25 25 j¼0 Ak ¼ Ak1 exp½sðEk1 ÞNDx , N is target’s atomic density, and ai , bi and ci are coefficients calculated by Alsmiller et al. 2.3.3. Neutrons emitted during (d, C) reaction No neutron source term was available for deuterons as impinging particles, thus several different spectra were tried. A conservative approach is to assume that source term is monoenergetic. For exoenergetic nuclear reactions source term energy must be equal to maximum energy achievable in the reaction. In case of endoenergetic nuclear reactions source term energy must be equal to the kinetic energy of the incident charged particle. Following this conservative criteria two monoenergetic neutron sources were used. Evaporation and Maxwellian sources terms were also used. Source terms used to calculate neutron spectra produced during deuteron interactions were, 1. Isotropic, monoenergetic neutron sources: 8.27 and 13.92 MeV. 2. Isotropic, Maxwellian source given by QðEÞ ¼ CE 1=2 expðE=TÞ; where C is a normalization factor, and T¼ 5 MeV.
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3. Isotropic evaporation source given by QðEÞ ¼ CE expðE=TÞ; where C is a normalization factor, and T¼ 5 MeV. During calculations source terms were located at Faraday cup and deflector locations. From the sixneutron tally types available in MCNP we used tally type 5, which gives the neutron flux at a point detector. To assure a statistical relative error less than 5% in each spectra’s energy bin, considered reliable for point detectors, 106 histories were used for each run. No variance reduction techniques were used. 2.4. Bonner sphere measurements Neutron field inside the cyclotron vault has three components: neutrons produced by charged particle interactions with cyclotron’s internal components (primary source), those produced inside the cyclotron due to interaction of the primary source neutrons with components of the cyclotron (secondary source), and neutrons that after leaking out the cyclotron, collide with bunker walls and are returned back to the room. Characterization and measurement of these components individually cannot be done because precise localization of points where charged particles interact within the structure of the cyclotron is unknown. Also vault dimensions do not allow use of experimental techniques to measure the neutron room return spectrum. Nuclear reactions at target area, with 14N or Faraday cup, and at deflector site are sources of fast neutrons. These collide with cyclotron components, losing energy and leaking out from cyclotron, then interact with walls and air in the room. Some of these neutron are returned back to the room, others continue interacting with the concrete components loosing energy until they are absorbed or leak out from the vault. Due to vault wall thickness leaking neutron field is expected to be highly thermal. A fundamental assumption in this work was that neutrons are only produced in cyclotron at two sites, the target and deflector. BSS with TLDs was used during measurements, for Faraday cup, target and deflector sites, BSS was located approximately 100 cm from the
Fig. 3. Sites where BSS was located during measurements. Position 1 is at 100 cm from Faraday cup. Position 10 is at 100 cm from target, site 2 is at 100 cm from deflector. Third site is indicated by position 3.
assumed reaction point along the line of the charged particle beam trajectory. The third measurement site was selected away target and deflector locations. Fig. 3 shows sites where BSS was located. Site 1 was used during protons and deuterons reactions on Faraday cup, site 1’ was used during deuteron reactions with the 14N target. For deuteron beam, BSS was located close to deflector, labeled as site 2 in Fig. 3. Site 3 was used to measure neutrons produced during interactions of deuterons with Faraday cup. For 17.2 MeV protons impinging on carbon Faraday cup (p, C), neutrons are produced if nuclear reaction is with 13C. This isotope is approximately 1% of the natural carbon; then neutron production is weak. For this reaction, measurements were carried out only at site 1. For 8.6 MeV deuterons interacting with Faraday cup (d, C), measurements were taken on sites 1–3, meanwhile intections with 14N target, (d, 14N), were taken on sites 1 and 2. TLDs annealing was carried out 24 h before measurements. Annealing cycle consisted of heating TLDs for 60 min at 4008C in a porcelain container, then letting them cool down to room temperature by moving the TLDs from the porcelain container to a stainless steel planchet. After cooling, TLDs were stored in a plastic container inside a cadmium box to reduce unwanted neutron exposure. In this
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process each individual TLD was tracked. After annealing, TLDs were handled away from ultraviolet lights to avoid introducing TLDs response bias [23]. In each measurement 5 TLD600 and 4 TLD700 were used as controls to remove the background radiation contribution during TLD handling. After reading TLDs, an average value of the TLD-600 and TLD-700 for each sphere, and controls, was calculated. Net neutron signal per irradiation time per microampere for each detector was calculated. This net neutron signal was used during unfolding process. BSS have m spheres, the relationship between detector counts Cj , detector response function Rj ðEÞ and neutron spectrum FðEÞ is described by Fredholm first kind integral equation, Z E max dERj ðEÞFðEÞ for j ¼ 1; 2; . . . ; m Cj ¼ E min
ð10Þ
Although several methods exist to get formal solution of this equation [24–26], none of these are applicable when response function Rj ðEÞ is not known analytically, which is the case for BSS. In general, Rj ðEÞ is experimentally determined or calculated, and usually approximated by a response matrix having discrete values. Thus, one is left with the problem of solving m linear equations in N unknowns, process named unfolding, where m is the number of spheres used, and N is the number of energy points, or intervals, needed to define the spectrum. Integral equation becomes, Cj ¼
N X
Rij Fi
for j ¼ 1; 2; . . . ; m
ð11Þ
i¼1
where Cj are the counts from jth detector, Rij is the jth detector response to neutrons in the ith energy interval, meanwhile Fi is neutron fluence in the ith energy interval. Since number of detectors is less that number of points used to describe the spectrum, (m5N), no unique solution of Eq. (11) exists. Then approximate unfolding procedures must be applied to solve it. Recently, several procedures have been proposed to unfold neutron spectra from BSS [27–29]. BUNKIUT unfolding code was used to obtain neutron energy spectrum from the BSS measurements. The BUNKIUT input is the sphere
381
diameters with the thermal neutron detector readouts and their experimental uncertainities, in the output the code shows an error that indicates the agreement of BUNKIUT’s solution with the experimental data given in the input.
3. Results and discussion The comparision between the differential neutron energy distributions of 252Cf and D2O moderated 252Cf neutron sources measured with Bonner spheres with 6LiI(Eu) and TLDs pairs were in good agreement [30]. From measurements with bare TLD pairs and 6 LiI thermal detectors using bare and D2O moderated 252Cf neutron sources no difference was observed in detectors output, therefore polyethylene plug, buit to hold TLDs, do not produce any neutron scattering effect different that 6LiI scintillator lucite light pipes. From measurements to determine TLD600 and TLD700 response to 137Cs and 60Co g-rays a factor k ¼ 0:80 0:06 was measured. This factor allows us to use Eq. (3) to obtain net neutron signal from TLD600 and TLD700 readings. Measured neutron spectra produced during (d, C) reaction at sites 1–3 are shown in Fig. 4, their uncertainities are 1.8, 8.6 and 2.1%, respectively. Here spectrum at site 1 shows a peak from 0.2 to 7 MeV with maximum at approximately 2 MeV, thermal and epithermal neutrons are very small. As measurement site moved to site 2, peak is shifted to energy range 0.1–3.7 MeV with maximum at approximately 0.45 MeV, here a relatively larger thermal and epithermal neutrons show up in comparision with site 1. At site 3 thermal neutrons have largest peak, meanwhile hard peak shifts from 0.05 to 1.9 MeV with maximum at approximately 0.2 MeV. This result is consistent with neutron moderation physics, harder spectra were observed near to sites where neutrons are produced, site 1 and 2, meanwhile neutrons reaching site 3 are strongly thermalized due to neutron collisions with vault room environment. Fig. 5 shows neutron spectra measured at site 10 and 2 during (d, 14N) reaction, their uncertainities are 4.3 and 3.1%, respectively. In both sites there
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Fig. 4. Neutron spectra produced during deuterons interacting with Faraday cup at three locations inside PET vault room. Uncertainities are 1.8% for spectrum at site 1, 8.6% for spectrum at site 2 and 2.1% for spectrum at site 3.
Fig. 5. Neutron spectra produced during deuterons interacting with 14N target. Measurements were carried out at site 10 and site 2 inside PET vault room. Uncertainities are 4.3% for spectrum at site 10 and 3.1% for spectrum at site 2.
Fig. 6. Neutron spectrum measured at site 1 inside PET vault room, when produced when protons collide with Faraday cup. Uncertainity is 6.4%.
is a neutron peak from 0.2 to 7 MeV with maximum at approximately 1 MeV. These spectra are consistent with the fact that larger amount of neutrons are produced at target site, and those measured at site 2 are the contribution of neutrons produced at site 10 that are transported to site 2 plus those produced when deuterons collide with deflector. Comparing neutron spectra from deuterons colliding with Faraday cup at site 1, and deuterons colliding with 14N at site 10 , shows larger amount of thermal neutrons. The probable explanation is that 14N target is closer to vault room wall than Faraday cup, then BSS detects those wall returned thermal and epithermal neutrons. Neutron spectra, measured at site 1, produced during (p, C) nuclear reaction is show in Fig. 6, it has an uncertainity of 6.4%. This spectra presents a peak between 0.1 and 3.6 MeV, with maximum at approximately 0.45 MeV, these neutrons requires less collisions to thermalize, this could be the explanation to the presence of a large amount of thermal neutrons, that is not observed at the same site for reactions with deuterons. To compare MCNP calculated spectra, with spectra
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Fig. 7. Normalized, calculated and experimental, neutron spectra at sites 1 and 10 for deuterons on Faraday cup and 14 N. Calculated is at site 1, using Maxwellian source term located at Faraday cup and deflector. Calculated spectrum error is 52.5%.
measured with BSS with TLDs, spectra were normalized. For deuterons the best results were obtained when Maxwellian ðT¼ 5 MeVÞ source term was used. In Fig. 7 experimental and calculated normalized neutron spectra are shown. Calculated spectrum was tallied at site 1 using Maxwellian ðT¼ 5 MeVÞ source term. Each energy bin has an error less than 1.6%, only the bin with the largest energy has an error of 2.5%. Experimental spectra are from neutrons produced during deuterons colliding with 14N target, measured at site 10 , and deuterons impinging on Faraday cup and measured at site 1. In this figure MCNP spectrum do not resembles any experimental spectra. MCNP spectra is softer than experimental ones, peak is broader, however thermal contribution is close to thermal neutrons measured at site 10 during (d,14N) nuclear reaction. Calculated normalized spectra tallied at site 2, using Maxwellian ðT¼ 5 MeVÞ located at Faraday
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Fig. 8. Normalized, calculated and experimental, neutron spectra at site 2 for deuterons on Faraday cup and 14N. Calculated is at site 2, using Maxwellian source term located at Faraday cup. Calculated spectrum error is 55%.
cup and deflector is shown in Fig. 8. In this figure experimental spectra measured at site 2, for neutrons produced for deuterons colliding with 14 N and Faraday cup. Here, MCNP calculation is close to both experimental spectra, although MCNP spectrum is sligthy softer and peak is broader. Each energy bin, but the last one, has an error less than 2%, the last energy bin has an error of 4.8%. During calculations at site 3 all neutron source terms we used gives approximately the same results. In the energy range 1–20 MeV, differences were observed only when monoenergetic sources (8.27 and 13.92 MeV) were used as source term. Measured neutron spectra at site 3, produced by deuterons impinging on Faraday cup is shown in Fig. 9 with calculated neutron spectra, tallied at site 3, using Maxwellian ðT¼ 5 MeVÞ source term located at Faraday cup and deflector. This spectrum has an error less than 3% in all the energy bins except the last one that has an error of
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Fig. 9. Normalized, calculated and experimental, neutron spectra at site 3, produced when deuterons collide with Faraday cup. Calculated was using Maxwellian source term located at Faraday cup. Calculated spectrum error is 55%.
Fig. 10. Normalized, calculated and experimental, neutron spectra at site 1 for protons on Faraday cup. Calculated spectrum was using Alsmiller source term located at Faraday cup. Calculated spectrum error is 1.4%.
4. Conclusions 4.3%. MCNP and measured spectra are practically the same, meaning that calculated spectrum is the same regardless the source term used during calculations, except with monoenergetic source, where a peak at the upper energy section is expected. Normalized neutron spectra, measured and calculated, at site 1 produced by protons interacting with Faraday cup is shown in Fig. 10. Calculated spectrum was tallied at site 1 and using the source term derived through Alsmiller’s formalism, this has an error less than 1.4% in each energy bin. Meanwhile experimental spectrum has an uncertainity of 6.4%. Both spectra have the same peak features at the energy upper level section, but amplitude, the same difference is observed in the thermal neutron section. Nevertheless differences, one may conclude that source term calculated through Alsmiller formalism gives acceptable results facing the fact of lack of better source term.
PET cyclotron is used to produce radioisotopes to perform a non-invasive imaging technique with medical purpose. PET isotopes have short halflives and they are produced in situ at health centers. During isotopes productions undesirable neutron field is produced making neutrons the main shielding problem to deal with. Neutron shielding and health physics program design, require to know neutron energy spectrum as detailed as possible, neutron spectrum measurement is not trivial task. To measure neutron spectra inside a PET vault room BSS was modified changing original active thermal neutron detector by a passive thermal neutron detector using paired TLD technique. A factor that equalizes TLD600 and TLD700 g-ray responses was obtained for photons produced by 137Cs and 60Co sources. Polyethylene plug used to hold TLDs at the center of Bonner spheres do not produce any neutron scattering effect different from the original 6LiI plug array. BSS with TLDs was calibrated using a
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bare 252Cf and a D2O moderated 252Cf neutron sources, from this procedure a calibration factor was obtained that correlates BSS with 6LiI with BSS with TLDs results. Nuclear reactions with 17.2 MeV protons and 8.6 MeV deuterons colliding with Faraday cup, electrostatic deflector and 14N were used. Produced neutron fields were measured at three sites with BSS with TLDs. Spectra were unfolded using BUNKIUT code and UTA4 response matrix. Monte Carlo calculations were carried out, using MCNP code, to determine neutron spectra produced for both charged particles beam. The lack of a source term for protons, a source term was derived using Alsmiller formalism, and for deuterons several source terms were used. Obtained results allow us to conclude: BSS with TLDs can be used to measure neutron energy spectra at locations were neutron field is strong, highly contaminated with g-rays or is pulsed. With proper calibration factor unfolding can be done using response matrix for scintillators. Source term for (d, C) reaction calculated with Alsmiller formalism gives acceptable results during calculations. None of source terms used in the aim to calculate neutron spectra produced by (d, 14N), at site 10 or produced by (d, C) at site 1 reproduce experimental spectra. However this source term can be used to calculate neutron spectra measured for both pervious nuclear reactions at site 2. From calculations at site 3, using Maxwellian ðT¼ 5 MeVÞ or Evaporation ða¼ 5 MeVÞ source term, resulting (d, C) neutron spectra reproduce well the measured spectrum regardless source term. This is also valid, from thermal to approximately 7 MeV, when monoenergetic neutron source term were used (8.6 and 13.97 MeV). Measurements and MCNP calculated spectra indicate a systematic behavior: intense peak in the energy interval 0.3–4 MeV, with a maximum at approximately 1 MeV indicating the presence of evaporation neutrons produced during nuclear reactions, regardless nuclear reaction, this is consistent with other facilities measurements [10, 31–36]. Neutrons above 2 MeV are scattered below 1 MeV by inelastic scattering with the massive amount of iron in cyclotron magnets. Inelastic scattering threshold of major isotope in iron, 56Fe,
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is around 850 keV. Neutrons below 2 MeV are elasticaly scatterd with a smaller energy loss per collision, thus Cyclotron iron is the dominant effect in determining the energy upper section features of neutron field inside vault room.
Acknowledgements This work was partially supported by CONACyT (Mexico). Help, support and assistance from faculty and staff of Nuclear Engineering Teaching Laboratory of The University of Texas at Austin, and The University of Texas Health Science Center at San Antonio is highly appreciated.
References [1] H.G. Jacobson, Instrumentation in positron emission tomography, JAMA 259 (10) (1988) 1531. [2] NCRP-51: Radiation Protection Design Guidelines for 0.1–100 MeV Particle Accelerator Facilities, National Council on Radiation Protection and Measurements, Report No. 51, 1977, pp. 25–27. [3] H.W. Patterson, R.H. Thomas, in: Accelerator Health Physics, Academic Press, New York, 1973, p. 446. [4] S. Pearlstein, Systematics of neutron emission spectra from high-energy proton bombardment, Nucl. Sci. Eng. 95 (1987) 116. [5] N.E. Hertel, Neutron Shielding Analysis of the University of Texas Health Science Center Research Imaging Center PET Cyclotron, UT-NETL-NH-T9201, 1992. [6] E. Garcia, H.R. Vega-Carrillo, D. Miramontes, L. McBride, Noniterative unfolding algorithm for neutron spectrum measurements with Bonner spheres, IEEE Trans. Nucl. Sci. NS-46 (1) (1999) 28. [7] G.R. Holeman, The measurement of accelerator produced stray neutron spectra, Am. J. Pub. Health 60 (9) (1970) 1824. [8] G.R. Holeman, K.W. Price, L.F. Friedman, R. Nath, Neutron spectral measurements in an intense photon field associated with a high-energy X-ray radiotherapy machine, Med. Phys. 4 (8) (1977) 508. [9] J.E. Sweezy, N.E. Hertel, K.G. Veinot, R.A. Karam, Performance of multisphere spectrometry systems, Radiat. Prot. Dosim. 78 (4) (1998) 263. [10] K.G. Veinot, N.E. Hertel, K.W. Brooks, J.E. Sweezy, Multisphere neutron spectra measurements near a high energy medical accelerator, Health Phys. 75 (3) (1998) 285.
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[11] S.I. Tanaka, Y. Furuta, Usage of a thermoluminescence dosimeter as a thermal neutron detector with high sensitivity, Nucl. Instr. and Meth. 133 (1976) 495. [12] B.R. Archer, S.C. Bushong, Multivariate analysis of TLD orientation effects, Med. Phys. 7 (4) (1980) 352. [13] J.D. Cossairt, A.J. Elwyn, W.S. Freeman, W.C. Salsbury, P.M. Yurista, Measurements of neutrons in enclosures and outside of shielding at the Tevatron, 22nd Midyear Topical Meeting on Instrumentation, South Texas Chapter of the Health Physics Society, San Antonio TX, USA, December 4–8, 1988, pp. 190–199. [14] H. Dinter, K. Tesch, Fluence spectra and dose equivalents of neutrons behind shielding of high energy proton accelerators, Eighth International Conference on Radiation Shielding Proccedings, Arlington, TX, USA, April 24– 28, 1994, pp. 280–287. [15] B.R. Archer, S.C. Bushong, Multivariate analysis of TLD orientation effects, Med. Phys. 7 (4) (1980) 352. [16] J.F. Briestmeister (Ed.), MCNP-A General Monte Carlo N-Particle Transport Code, Los Alamos National Laboratory, Report LA-12625-M, 1993. [17] H.W. Bertini, Low energy intranuclear cascade calculations, Phys. Rev. 131 (4) (1963) 1801. [18] H.W. Bertini, Low energy intranuclear cascade calculations, Phys. Rev. 138 (1965) AB2. [19] R.G. Alsmiller, M. Leimdorfer, J. Barish, Analytical representation of nonelastic cross sections and particleemission spectra from nucleon-nucleus collisions in the energy range 25–400 MeV, Oak Ridge National Laboratory, ORNL 4046, 1967, pp. 1–121. [20] T. Nakamura, M. Yoshida, K. Shin, Spectral measurements of neutrons and photons from thick targets of C, Fe, Cu and Pb by 50 MeV protons, Nucl. Instr. and Meth. 151 (1978) 493. [21] J.F. Ziegler, TRIM, The transport of ions in matter, Version 92.xx, IBM-Research, 1992. [22] T. Nakamura, M. Fujii, K. Shin, Neutron production from thick targets of Carbon, Iron, Copper and Lead by 30- and 52 MeV protons, Nucl. Sci. Eng. 83 (1983) 444. [23] B.-S. Barak, Ultraviolet sensitivity and photo-transferred thermoluminiscense of the Harshaw and Panasonic used TLDs-a comparision, Appl. Radiat. Isot. 40 (8) (1989) 687.
[24] G.M. Wing, A Primer on Integral Equations of the First Kind, Soc. Ind. Appl. Math. (1991). [25] E.A. Belogorlov, V.P. Zhigunov, Interpretation of the solution to the inverse problem for the positive function and the reconstruction of neutron spectra, Nucl. Instr. and Meth. A 235 (1985) 146. [26] H.J.J. Riele, Aprogram for solving first kind Fredholm integral equations by means of regularization, Comp. Phys. Commun. 36 (1985) 423. [27] J.H. Haney, T.E. Barnhart, C.S. Zaidins, Extraction of neutron spectral information from Bonner-sphere data, Nucl. Instr. and Meth. A 431 (1999) 551. [28] B. Mukherjee, BONDI-97: A novel neutron energy spectrum unfolding tool using genetic algorithm, Nucl. Instr. and Meth. A 432 (1999) 305. [29] M. Reginatto, P. Goldhagen, MAXED, a computer code for maximum entropy deconvolution of multisphere neutron spectrometer data, Health Phys. 77 (5) (1999) 579. [30] H.R. Vega-Carrillo, N.E. Hertel, A.J. Teachout, B.W. Wehring, Paired thermoluminiscent dosimeter technique in Bonner sphere spectrometry, Trans. Am. Nucl. Soc. 73 (1995) 356. [31] C. Birattari, A. Salomone, Neutron spectrum measurements at a 40-MeV proton cyclotron, Health Phys. 49 (5) (1985) 919. [32] T. Ishikawa, M. Kumazaki, T. Nakamura, Measurement and calculation of neutron leakage through labyrinth from 35 MeV proton accelerator room, J. Nucl. Sci. Technol. 29 (2) (1992) 978. [33] H. Dinter, K. Tesch, D. Dworak, Studies on the neutron field behind the shielding of proton acceleratros. Part II: Iron shielding, Nucl. Instr. and Meth. A 368 (1996) 273. [34] V. Vylet, J.C. Liu, S.H. Rokni, L.-X. Thai, Measurements of neutron spectra at the stanford linear accelerator center, Radiat. Prot. Dosim. 70 (1–4) (1997) 425. [35] J.C. Liu, S. Rokni, V. Vylet, R. Arora, E. Semones, A. Justus, Neutron detection time distributions of multisphere LiI detectors and AB rem meter at a 20 MeV electron LINAC, Radiat. Prot. Dosim. 71 (4) (1997) 251. [36] L.E. Moritz, T. Suzuki, M. Noguchi, Y. Oki, T. Miura, S. Miura, H. Tawara, S. Ban, H. Hirayama, K. Kondo, Characteristics of the neutron field in the KEK counter hall, Health Phys. 58 (4) (1990) 487.
Neutron energy spectra inside a PET cyclotron vault room H!ector Ren!e Vega-Carrillo* Centro Regional de Estudios Nucleares, Universidad Autonoma de Zacatecas, Apdo Postal 336, 98000 Zacatecas, Zac. Mexico Received 20 July 2000; received in revised form 3 November 2000; accepted 5 November 2000
Abstract Neutron energy spectra were measured at three locations inside the vault room of a PET cyclotron. Measured neutron fields were produced during 17.2 MeV protons and 8.6 MeV deuterons colliding with Faraday cup, and 8.6 MeV deuterons colliding with 14N. Measurements were performed using a Bonner sphere spectrometer whose active 6 LiI(Eu) scintillator was replaced by two pairs of thermoluminscent dosimeters. Modified neutron spectrometer was calibrated using bare 252Cf and D2O moderated 252Cf neutron sources. Thermoluminiscent dosimeters were calibrated using g-rays from 137Cs and 60Co sources. From this calibration, a single factor was derived that allow us to obtain the thermal neutron net signal used to unfold neutron spectra. MCNP 4A code was used to calculate neutron spectra at those sites were measurements were taken. For MCNP calculations a source term for protons colliding with graphite was calculated using a semiempirical model. Due the lack of source term for neutrons produced during 8.6 MeV deuterons nuclear reactions, with carbon and 14N, several models were tried. From experimental and calculated results a systematic behavior of neutron spectra was observed regardless the primary neutron source. This behavior was a peak indicating the presence of evaporation neutrons due to the large amount of iron in cyclotron. # 2001 Elsevier Science B.V. All rights reserved. PACS: 28.20.Gd; 29.20.Hm; 29.30.Hs Keywords: PET; Cyclotron; Neutron; MCNP; Bonner spheres
1. Introduction Positron Emission Tomography, PET, widely used for diagnostic purposes, is a non-invasive medical imaging technique used to determine location and concentration of physiologically active compounds in human body [1].
*Fax: +1-52-492-2-70-43. E-mail address: [email protected] (H.R. VegaCarrillo). URL: http://cantera.reduaz.mx/rvega.
In PET, 15O, 13N, 11C and 18F are used, these have short half-lives and are produced at hospitals, mostly using charged-particle accelerator facilities. PET isotope production is carried out using nuclear reactions that produces undesirable neutrons. Table 1 shows PET isotopes nuclear reactions features. An accelerated beam of charged particles produce radiation as a consequence of interactions between charged particle beam and surrounding media it collides, thus bremsstrahlung and characteristic X-rays, prompt g-rays, neutrons and delayed radiation (b and g) are produced. The lack
0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 2 3 4 - 0
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Table 1 Positron-emitting isotopes used in PET studies Nuclear reaction
Q-value (MeV)
Positron emitter
Half life (minutes)
11
2.764 2.922 5.217 0.280 3.536 +5.073 2.437 +2.792
11
20.385 20.385 9.965 9.965 2.037 2.037 109.77 109.77
B(p,n)11C N(p,a)11C 16 O(p,a)13N 12 C(d,n)13N 15 N(p,n)15O 14 N(d,n)15O 18 O(p,n)18F 20 Ne(d,a)18F 14
of electric charge and the ways they interact with matter, makes neutron field characterization a difficult problem. A single location to describe neutron production is difficult to establish because neutron-producing reactions can occur at many points inside the accelerator, such as target, beam stopper and beam deflector. According to NCRP 51 [2], shielding design requires an estimate of radiation emission rate from the accelerator. To make this estimation, parameteres like: species and energy of accelerated particle, target material, particle-beam current, angular distribution and energy spectrum of produced radiation, should be known. Nuclear reactions have been studied extensively for a broad range of targets and particles. In general, it has been established that [3,4], even at high proton energies, resulting neutron spectrum from thick targets may be described as consisting of three main components: Cascade neutrons, evaporation neutrons and epithermal and thermal neutrons arising from slowing down of evaporation and cascade neutrons. In this investigation neutron energy spectra were measured at three locations inside the vault room of a PET cyclotron. Neutron spectra were measured during 17.2 MeV protons and 8.6 MeV deuterons colliding with Faraday cup, and 8.6 MeV deuterons colliding with 14N. Measurements were performed using a Bonner sphere spectrometer, BSS, whose active 6LiI(Eu) scintillator was replaced by two pairs of thermoluminscent dosimeters (two TLD600 and two TLD700). Modified BSS was calibrated using bare and D2O moderated 252Cf neutron source. Thermoluminis-
C C 13 N 13 N 15 O 15 O 18 F 18 F 11
cent dosimeters, TLDs, were calibrated using g-rays from 137Cs and 60Co sources. From this calibration, a single factor was derived that allow us to obtain the thermal neutron net signal. MCNP 4A code was used to calculate neutron spectra at those sites were measurements were taken. For MCNP calculations a source term for protons colliding with graphite was calculated using a semiempirical model derived by Alsmiller et al. Due to the lack of a source term for neutrons produced during 8.6 MeV deuterons nuclear reactions, with carbon and 14N, several models were used. From experimental and calculated results a systematic behavior of neutron spectra was observed regardless the primary neutron source. This was a peak in the energy interval 0.3 to 4 MeV, with a maximum at approximately 1 MeV indicating the presence of evaporation neutrons produced during nuclear reactions that are modified by the large amount of iron in the cyclotron.
2. Materials and methods 2.1. Facility description PET cyclotron is located at the Research Imaging Center at the University of Texas Health Science Center in San Antonio, TX. PET cyclotron is Scanditronix MC 17F capable of accelerating protons or deuterons to 17.2 MeV and 8.6 MeV, respectively. Maximum charged particle current is 65 mA, with an extraction efficiency of
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approximately 80% for protons and 60% for deuterons [5]. Magnets, radiofrequency source, cooling system, target, beam probe, Faraday cup (beam stopper), and an ion source complete the cyclotron. Monitoring charged particle beam in the cyclotron, beam stability, particle selection, and target handling are all determined from the control room. Radioisotopes produced are automatically transported to hot cell at radiochemical laboratory. Cyclotron is housed in a 518 518 366-cm3 vault shielded by reinforced concrete, Fig. 1 shows cyclotron facility. Vault walls are 152 cm thick, ceiling is 122 cm thick, access to vault is via a motor-driven concrete door 122 cm thick. Cyclotron is located at the first floor of the Research Imaging Center building. Three of the cyclotron’s vault walls are adjacent to equipment room, radiochemistry laboratory, and restrooms. The fourth wall is adjacent to outside loading dock area. A vault room plant view is shown in Fig. 2. 2.2. Bonner spectrometer modification and calibration There is not single spectrometer with ideal response to neutrons from thermal to fast energies. BSS is often used to obtain neutron spectra over a
377
Fig. 1. PET cyclotron schematic diagram.
wide range of neutron energies (thermal to 400 MeV), but it has a poor energy resolution, and an unfolding code is required [6]. Pulse pileup and large dead times in intensive or pulsed neutron fields is another BSS drawback. To overcome this last a passive thermal neutron detector can be used instead of active 6LiI(Eu) BSS detector. In this work was decided to use TLDs as thermal neutron detector in the BSS. The use of paired TLDs in mixed radiation fields has been widely used, however few works have
Fig. 2. Partial plant view of first floor at the University of Texas Health Science Center, where PET cyclotron vault room is located.
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reported using pairs of TLDs in multispheres [7–10]. BSS was modified in the following manner: A high-density polyethylene plug with the same geometry and dimensions as the aluminum holder for scintillator, light pipes, photomultiplier tube and base was built. At plug upper section, four small holes were done to hold 4 TLDs, 2 TLD600 and 2 TLD700. Bare, 200 , 300 , 500 , 800 , 1000 and 12 inch-diameter polyethylene spheres were used. Two pairs of TLD-600 and TLD-700 in each sphere were used to measure thermal neutrons. TLD-600 contains 95.6% 6Li, while the TLD-700 contains 99.9% 7Li. Both have approximately same density and atomic numbers, and the same response to g rays. For thermal neutrons, TLD600 response is larger than TLD-700. TLDs are 0.3175 0.3175 0.0889-cm3-ribbon type from Harshaw (Solon, OH). When exposing TLD-600 and TLD-700 in a mixed neutron g radiation field, measured response is the result of g-ray and neutron responses, g n Rnþg 600 ¼ R600 þ R600
ð1Þ
g n Rnþg 700 ¼ R700 þ R700
ð2Þ
is the total TLD 600 measured here, Rnþg 600 response, Rn600 is neutron contribution, and Rg600 is g-ray contribution to TLD-600 response. Rnþg 700 is the total response of TLD 700, Rn700 andRg700 are the respective contributions to TLD 700 response of neutrons and g-rays. When pairs of TLD 600 and TLD 700 dosimeters are used to measure thermal neutrons, a common practice is to assume that both have the same response to photons [7,11–15]. Because Rn700 is practically null, the simple difference between responses of both dosimeters is used as an indicator of net neutron response. During this study, photon responses of both dosimeters were measured with 60Co and 137Cs g sources. TLD 600 to TLD 700 g response ratio was used as a correction factor, k, to equalize the g-ray response of both TLDs. Net neutron signal was calculated using, nþg Rn ¼ Rnþg 600 k R700 :
ð3Þ
Bare 252Cf and D2O moderated 252Cf neutron sources were used to calibrate BSS with TLDs and BSS with 6LiI scintillator. During calibration, measurements with bare thermal detectors, 6LiI and TLDs, were carried out to check if statistical differences in count rates show up due polyethylene plug that hold TLDs. BSS with 6LiI and BSS with TLDs were used to measure neutron energy spectra of bare 252Cf and D2O moderated 252Cf neutron sources, this measurements were used to find the relationship between BSS with TLDs and BSS with 6LiI experimental responses. 2.3. MCNP calculations 2.3.1. Cyclotron and vault room modeling General Monte Carlo Neutron Photon Transport, MCNP, code version 4A [16] was utilized to calculate neutron transport inside vault room. Faraday cup was modeled as 2.3-cm-diameter carbon sphere. Because information about the deflector material was unavailable it was also modelled as a 2.3 cm diameter carbon sphere. Inside this spheres neutron source was located. Vault room concrete density was assumed be 2.3 g/cm3, iron was used to model cyclotron’s magnets, meanwhile wires and cyclotron ‘‘dees’’ were modelled as copper made. Air inside vault room was included in the model. For simplicity vault room door was modelled as thick as vault walls. Neutron flux spectra were tallied at those locations where measurements with BSS with TLDs were carried out. For source terms used in MCNP calculations two different situations were considered: neutrons produced by protons interacting with carbon and those produced when deuterons interact with carbon and 14N. 2.3.2. Neutrons emitted during (p, C) reaction At proton energies below 10 MeV, dominant interaction is by the compound nucleus formation, which is left in excited state with a number of allowed decay channels. Compound nucleus tends to reach ground state by particle emission described by an evaporation process. Energy
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distribution of emitted neutrons can be estimated by,
slabs as
nðEÞ dE / E expðE=TÞ
nðE; yÞ ¼
ð4Þ
here, T is nuclear temperature, usually between 1 and 10 MeV. However, at higher energy development of intranuclear cascade become important. In this case, several neutrons can be emitted in succession, while nuclear temperature falls from an initial value to zero. Intranuclear cascade develops through interaction of individual nucleons inside the nucleus. Using intranuclear-cascade-evaporation model, Bertini [17,18] generated a large amount of data of non-elastic cross-sections and the energy and angular distributions of emitted neutrons and protons. These data are for neutrons and protons, in the energy range 25–400 MeV, colliding with a variety of targets. To make these data more accessible, Alsmiller et al. [19] developed analytical models and tables of their coefficients, using leastsquare method to fit Bertini’s data. Nevertheless Alsmiller’s expressions are valid for 25–400 MeV protons it was assumed that coefficients and semiempirical equations gave reasonable results for 17 MeV protons. Therefore coefficients for neutron emission and non-elastic crosssection models at 17 MeV protons were assumed to be the same as those at 25 MeV, calculations were carried out as Nakamura et al. [20] To apply Alsmiller expressions, Faraday cup model was subdivided into n thin slabs, each of a thickness Dx. As protons penetrates Faraday cup, was assumed protons loses energy according to continuous slowing-down model without changing direction. Average kinetic energy ðEk Þ in the kth slab was calculated using, Dx dE Ek ¼ Ek1 ; k ¼ 1; 2; . . . ; n ð5Þ 2 dx k1 where Ek1 is protons average kinetic energy in the k 1 carbon slab, and ðdE=dxÞk1 is the stopping power of Ek1 MeV protons in carbon. Proton stopping power was calculated using the computer code TRIM 92 [21]. Energy spectra of neutrons emitted within each slab were calculated and summed over all thin
n X k¼1
1 Fk ðE; yÞ þ Gk ðE; yÞ 4p
Ak sðEk ÞNDx1027
ð6Þ
where sðEk Þ is the non-elastic cross-section expressed in millibarns and was calculated using [22] ( ) n X 1 Ek i exp sðEk Þ ¼ ai ð7Þ 400 400 i¼0 here, Fk ðE; yÞ stands for the cascade neutronemission spectrum, " i # n X 1 E Fk ðE; yÞ ¼ exp bi ðyÞ ð8Þ Ek E k i¼0 and Gk ðEÞ represents the evaporation neutronemission spectrum, " j # n X 1 E Gk ¼ exp cj : ð9Þ 25 25 j¼0 Ak ¼ Ak1 exp½sðEk1 ÞNDx , N is target’s atomic density, and ai , bi and ci are coefficients calculated by Alsmiller et al. 2.3.3. Neutrons emitted during (d, C) reaction No neutron source term was available for deuterons as impinging particles, thus several different spectra were tried. A conservative approach is to assume that source term is monoenergetic. For exoenergetic nuclear reactions source term energy must be equal to maximum energy achievable in the reaction. In case of endoenergetic nuclear reactions source term energy must be equal to the kinetic energy of the incident charged particle. Following this conservative criteria two monoenergetic neutron sources were used. Evaporation and Maxwellian sources terms were also used. Source terms used to calculate neutron spectra produced during deuteron interactions were, 1. Isotropic, monoenergetic neutron sources: 8.27 and 13.92 MeV. 2. Isotropic, Maxwellian source given by QðEÞ ¼ CE 1=2 expðE=TÞ; where C is a normalization factor, and T¼ 5 MeV.
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3. Isotropic evaporation source given by QðEÞ ¼ CE expðE=TÞ; where C is a normalization factor, and T¼ 5 MeV. During calculations source terms were located at Faraday cup and deflector locations. From the sixneutron tally types available in MCNP we used tally type 5, which gives the neutron flux at a point detector. To assure a statistical relative error less than 5% in each spectra’s energy bin, considered reliable for point detectors, 106 histories were used for each run. No variance reduction techniques were used. 2.4. Bonner sphere measurements Neutron field inside the cyclotron vault has three components: neutrons produced by charged particle interactions with cyclotron’s internal components (primary source), those produced inside the cyclotron due to interaction of the primary source neutrons with components of the cyclotron (secondary source), and neutrons that after leaking out the cyclotron, collide with bunker walls and are returned back to the room. Characterization and measurement of these components individually cannot be done because precise localization of points where charged particles interact within the structure of the cyclotron is unknown. Also vault dimensions do not allow use of experimental techniques to measure the neutron room return spectrum. Nuclear reactions at target area, with 14N or Faraday cup, and at deflector site are sources of fast neutrons. These collide with cyclotron components, losing energy and leaking out from cyclotron, then interact with walls and air in the room. Some of these neutron are returned back to the room, others continue interacting with the concrete components loosing energy until they are absorbed or leak out from the vault. Due to vault wall thickness leaking neutron field is expected to be highly thermal. A fundamental assumption in this work was that neutrons are only produced in cyclotron at two sites, the target and deflector. BSS with TLDs was used during measurements, for Faraday cup, target and deflector sites, BSS was located approximately 100 cm from the
Fig. 3. Sites where BSS was located during measurements. Position 1 is at 100 cm from Faraday cup. Position 10 is at 100 cm from target, site 2 is at 100 cm from deflector. Third site is indicated by position 3.
assumed reaction point along the line of the charged particle beam trajectory. The third measurement site was selected away target and deflector locations. Fig. 3 shows sites where BSS was located. Site 1 was used during protons and deuterons reactions on Faraday cup, site 1’ was used during deuteron reactions with the 14N target. For deuteron beam, BSS was located close to deflector, labeled as site 2 in Fig. 3. Site 3 was used to measure neutrons produced during interactions of deuterons with Faraday cup. For 17.2 MeV protons impinging on carbon Faraday cup (p, C), neutrons are produced if nuclear reaction is with 13C. This isotope is approximately 1% of the natural carbon; then neutron production is weak. For this reaction, measurements were carried out only at site 1. For 8.6 MeV deuterons interacting with Faraday cup (d, C), measurements were taken on sites 1–3, meanwhile intections with 14N target, (d, 14N), were taken on sites 1 and 2. TLDs annealing was carried out 24 h before measurements. Annealing cycle consisted of heating TLDs for 60 min at 4008C in a porcelain container, then letting them cool down to room temperature by moving the TLDs from the porcelain container to a stainless steel planchet. After cooling, TLDs were stored in a plastic container inside a cadmium box to reduce unwanted neutron exposure. In this
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process each individual TLD was tracked. After annealing, TLDs were handled away from ultraviolet lights to avoid introducing TLDs response bias [23]. In each measurement 5 TLD600 and 4 TLD700 were used as controls to remove the background radiation contribution during TLD handling. After reading TLDs, an average value of the TLD-600 and TLD-700 for each sphere, and controls, was calculated. Net neutron signal per irradiation time per microampere for each detector was calculated. This net neutron signal was used during unfolding process. BSS have m spheres, the relationship between detector counts Cj , detector response function Rj ðEÞ and neutron spectrum FðEÞ is described by Fredholm first kind integral equation, Z E max dERj ðEÞFðEÞ for j ¼ 1; 2; . . . ; m Cj ¼ E min
ð10Þ
Although several methods exist to get formal solution of this equation [24–26], none of these are applicable when response function Rj ðEÞ is not known analytically, which is the case for BSS. In general, Rj ðEÞ is experimentally determined or calculated, and usually approximated by a response matrix having discrete values. Thus, one is left with the problem of solving m linear equations in N unknowns, process named unfolding, where m is the number of spheres used, and N is the number of energy points, or intervals, needed to define the spectrum. Integral equation becomes, Cj ¼
N X
Rij Fi
for j ¼ 1; 2; . . . ; m
ð11Þ
i¼1
where Cj are the counts from jth detector, Rij is the jth detector response to neutrons in the ith energy interval, meanwhile Fi is neutron fluence in the ith energy interval. Since number of detectors is less that number of points used to describe the spectrum, (m5N), no unique solution of Eq. (11) exists. Then approximate unfolding procedures must be applied to solve it. Recently, several procedures have been proposed to unfold neutron spectra from BSS [27–29]. BUNKIUT unfolding code was used to obtain neutron energy spectrum from the BSS measurements. The BUNKIUT input is the sphere
381
diameters with the thermal neutron detector readouts and their experimental uncertainities, in the output the code shows an error that indicates the agreement of BUNKIUT’s solution with the experimental data given in the input.
3. Results and discussion The comparision between the differential neutron energy distributions of 252Cf and D2O moderated 252Cf neutron sources measured with Bonner spheres with 6LiI(Eu) and TLDs pairs were in good agreement [30]. From measurements with bare TLD pairs and 6 LiI thermal detectors using bare and D2O moderated 252Cf neutron sources no difference was observed in detectors output, therefore polyethylene plug, buit to hold TLDs, do not produce any neutron scattering effect different that 6LiI scintillator lucite light pipes. From measurements to determine TLD600 and TLD700 response to 137Cs and 60Co g-rays a factor k ¼ 0:80 0:06 was measured. This factor allows us to use Eq. (3) to obtain net neutron signal from TLD600 and TLD700 readings. Measured neutron spectra produced during (d, C) reaction at sites 1–3 are shown in Fig. 4, their uncertainities are 1.8, 8.6 and 2.1%, respectively. Here spectrum at site 1 shows a peak from 0.2 to 7 MeV with maximum at approximately 2 MeV, thermal and epithermal neutrons are very small. As measurement site moved to site 2, peak is shifted to energy range 0.1–3.7 MeV with maximum at approximately 0.45 MeV, here a relatively larger thermal and epithermal neutrons show up in comparision with site 1. At site 3 thermal neutrons have largest peak, meanwhile hard peak shifts from 0.05 to 1.9 MeV with maximum at approximately 0.2 MeV. This result is consistent with neutron moderation physics, harder spectra were observed near to sites where neutrons are produced, site 1 and 2, meanwhile neutrons reaching site 3 are strongly thermalized due to neutron collisions with vault room environment. Fig. 5 shows neutron spectra measured at site 10 and 2 during (d, 14N) reaction, their uncertainities are 4.3 and 3.1%, respectively. In both sites there
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Fig. 4. Neutron spectra produced during deuterons interacting with Faraday cup at three locations inside PET vault room. Uncertainities are 1.8% for spectrum at site 1, 8.6% for spectrum at site 2 and 2.1% for spectrum at site 3.
Fig. 5. Neutron spectra produced during deuterons interacting with 14N target. Measurements were carried out at site 10 and site 2 inside PET vault room. Uncertainities are 4.3% for spectrum at site 10 and 3.1% for spectrum at site 2.
Fig. 6. Neutron spectrum measured at site 1 inside PET vault room, when produced when protons collide with Faraday cup. Uncertainity is 6.4%.
is a neutron peak from 0.2 to 7 MeV with maximum at approximately 1 MeV. These spectra are consistent with the fact that larger amount of neutrons are produced at target site, and those measured at site 2 are the contribution of neutrons produced at site 10 that are transported to site 2 plus those produced when deuterons collide with deflector. Comparing neutron spectra from deuterons colliding with Faraday cup at site 1, and deuterons colliding with 14N at site 10 , shows larger amount of thermal neutrons. The probable explanation is that 14N target is closer to vault room wall than Faraday cup, then BSS detects those wall returned thermal and epithermal neutrons. Neutron spectra, measured at site 1, produced during (p, C) nuclear reaction is show in Fig. 6, it has an uncertainity of 6.4%. This spectra presents a peak between 0.1 and 3.6 MeV, with maximum at approximately 0.45 MeV, these neutrons requires less collisions to thermalize, this could be the explanation to the presence of a large amount of thermal neutrons, that is not observed at the same site for reactions with deuterons. To compare MCNP calculated spectra, with spectra
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Fig. 7. Normalized, calculated and experimental, neutron spectra at sites 1 and 10 for deuterons on Faraday cup and 14 N. Calculated is at site 1, using Maxwellian source term located at Faraday cup and deflector. Calculated spectrum error is 52.5%.
measured with BSS with TLDs, spectra were normalized. For deuterons the best results were obtained when Maxwellian ðT¼ 5 MeVÞ source term was used. In Fig. 7 experimental and calculated normalized neutron spectra are shown. Calculated spectrum was tallied at site 1 using Maxwellian ðT¼ 5 MeVÞ source term. Each energy bin has an error less than 1.6%, only the bin with the largest energy has an error of 2.5%. Experimental spectra are from neutrons produced during deuterons colliding with 14N target, measured at site 10 , and deuterons impinging on Faraday cup and measured at site 1. In this figure MCNP spectrum do not resembles any experimental spectra. MCNP spectra is softer than experimental ones, peak is broader, however thermal contribution is close to thermal neutrons measured at site 10 during (d,14N) nuclear reaction. Calculated normalized spectra tallied at site 2, using Maxwellian ðT¼ 5 MeVÞ located at Faraday
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Fig. 8. Normalized, calculated and experimental, neutron spectra at site 2 for deuterons on Faraday cup and 14N. Calculated is at site 2, using Maxwellian source term located at Faraday cup. Calculated spectrum error is 55%.
cup and deflector is shown in Fig. 8. In this figure experimental spectra measured at site 2, for neutrons produced for deuterons colliding with 14 N and Faraday cup. Here, MCNP calculation is close to both experimental spectra, although MCNP spectrum is sligthy softer and peak is broader. Each energy bin, but the last one, has an error less than 2%, the last energy bin has an error of 4.8%. During calculations at site 3 all neutron source terms we used gives approximately the same results. In the energy range 1–20 MeV, differences were observed only when monoenergetic sources (8.27 and 13.92 MeV) were used as source term. Measured neutron spectra at site 3, produced by deuterons impinging on Faraday cup is shown in Fig. 9 with calculated neutron spectra, tallied at site 3, using Maxwellian ðT¼ 5 MeVÞ source term located at Faraday cup and deflector. This spectrum has an error less than 3% in all the energy bins except the last one that has an error of
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Fig. 9. Normalized, calculated and experimental, neutron spectra at site 3, produced when deuterons collide with Faraday cup. Calculated was using Maxwellian source term located at Faraday cup. Calculated spectrum error is 55%.
Fig. 10. Normalized, calculated and experimental, neutron spectra at site 1 for protons on Faraday cup. Calculated spectrum was using Alsmiller source term located at Faraday cup. Calculated spectrum error is 1.4%.
4. Conclusions 4.3%. MCNP and measured spectra are practically the same, meaning that calculated spectrum is the same regardless the source term used during calculations, except with monoenergetic source, where a peak at the upper energy section is expected. Normalized neutron spectra, measured and calculated, at site 1 produced by protons interacting with Faraday cup is shown in Fig. 10. Calculated spectrum was tallied at site 1 and using the source term derived through Alsmiller’s formalism, this has an error less than 1.4% in each energy bin. Meanwhile experimental spectrum has an uncertainity of 6.4%. Both spectra have the same peak features at the energy upper level section, but amplitude, the same difference is observed in the thermal neutron section. Nevertheless differences, one may conclude that source term calculated through Alsmiller formalism gives acceptable results facing the fact of lack of better source term.
PET cyclotron is used to produce radioisotopes to perform a non-invasive imaging technique with medical purpose. PET isotopes have short halflives and they are produced in situ at health centers. During isotopes productions undesirable neutron field is produced making neutrons the main shielding problem to deal with. Neutron shielding and health physics program design, require to know neutron energy spectrum as detailed as possible, neutron spectrum measurement is not trivial task. To measure neutron spectra inside a PET vault room BSS was modified changing original active thermal neutron detector by a passive thermal neutron detector using paired TLD technique. A factor that equalizes TLD600 and TLD700 g-ray responses was obtained for photons produced by 137Cs and 60Co sources. Polyethylene plug used to hold TLDs at the center of Bonner spheres do not produce any neutron scattering effect different from the original 6LiI plug array. BSS with TLDs was calibrated using a
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bare 252Cf and a D2O moderated 252Cf neutron sources, from this procedure a calibration factor was obtained that correlates BSS with 6LiI with BSS with TLDs results. Nuclear reactions with 17.2 MeV protons and 8.6 MeV deuterons colliding with Faraday cup, electrostatic deflector and 14N were used. Produced neutron fields were measured at three sites with BSS with TLDs. Spectra were unfolded using BUNKIUT code and UTA4 response matrix. Monte Carlo calculations were carried out, using MCNP code, to determine neutron spectra produced for both charged particles beam. The lack of a source term for protons, a source term was derived using Alsmiller formalism, and for deuterons several source terms were used. Obtained results allow us to conclude: BSS with TLDs can be used to measure neutron energy spectra at locations were neutron field is strong, highly contaminated with g-rays or is pulsed. With proper calibration factor unfolding can be done using response matrix for scintillators. Source term for (d, C) reaction calculated with Alsmiller formalism gives acceptable results during calculations. None of source terms used in the aim to calculate neutron spectra produced by (d, 14N), at site 10 or produced by (d, C) at site 1 reproduce experimental spectra. However this source term can be used to calculate neutron spectra measured for both pervious nuclear reactions at site 2. From calculations at site 3, using Maxwellian ðT¼ 5 MeVÞ or Evaporation ða¼ 5 MeVÞ source term, resulting (d, C) neutron spectra reproduce well the measured spectrum regardless source term. This is also valid, from thermal to approximately 7 MeV, when monoenergetic neutron source term were used (8.6 and 13.97 MeV). Measurements and MCNP calculated spectra indicate a systematic behavior: intense peak in the energy interval 0.3–4 MeV, with a maximum at approximately 1 MeV indicating the presence of evaporation neutrons produced during nuclear reactions, regardless nuclear reaction, this is consistent with other facilities measurements [10, 31–36]. Neutrons above 2 MeV are scattered below 1 MeV by inelastic scattering with the massive amount of iron in cyclotron magnets. Inelastic scattering threshold of major isotope in iron, 56Fe,
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is around 850 keV. Neutrons below 2 MeV are elasticaly scatterd with a smaller energy loss per collision, thus Cyclotron iron is the dominant effect in determining the energy upper section features of neutron field inside vault room.
Acknowledgements This work was partially supported by CONACyT (Mexico). Help, support and assistance from faculty and staff of Nuclear Engineering Teaching Laboratory of The University of Texas at Austin, and The University of Texas Health Science Center at San Antonio is highly appreciated.
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