Thermal neutron flux in an electron synchrotron room

Nuclear Instruments and Methods 189 (1981) 377-386 North-Holland Publishing Company

377

THERMAL NEUTRON FLUX IN AN ELECTRON SYNCHROTRON ROOM Toshiso KOSAKO and Takashi NAKAMURA Institute for Nuclear Study, The University of Tokyo, Midori-cho 3-2-1, Tanashi, Tokyo, Japan Received 10 April 1981

To estimate the generation of neutrons in electron accelerators is important for radiation shielding and protection. The generation of photoneutrons and the slowing down and the thermalization process caused by high energy electrons have been analyzed by the combination of an electromagnetic cascade shower calculation and a two-dimensional SN neutron transport calculation. The comparisonbetween experiment and calculation was fairly good within a factor 2. This thermal neutron flux is applied to the estimation of radioactive 41Ar generation in the electron synchrotron room.

1. Introduction It is of fundamental interest and importance for radiation protection to estimate accurately the generation of gamma rays and neutrons from a high energy accelerator. There has hitherto been much discussion [ 1 - 3 ] on such neutron problems. For example, Coleman and Alsmiller Jr. calculated [ 1] the generation of neutrons and their shielding for protons from 540 MeV to 2 GeV, and Swanson calculated [2] photoneutrons emitted from various targets bombarded by electrons below 100 MeV. Wadman III measured [3] the neutron attenuation after stopping 80 MeV alpha particles by a tantalum target. But these works were almost always restricted to a simplified geometry such as a thick target or a beam dump, or to the attenuation of neutrons in a slab shield. In this study, we measured thermal neutrons in the actual complicated geometry around a large scale accelerator, the 1.3 GeV electron synchrotron of the Institute for Nuclear Study, the University of Tokyo, and evaluated the experimental results by the combination of the following process: the electron beam loss, the photon generation, the photoneutron generation and the neutron slowing down and thermalization. We tried to describe the beam loss mechanismas accurately as we could, since it is usually the greatest cause of error for accurate estimation of absolute radiation doses around an actual large scale accelerator. There has been little work done which deals with the complete process from the beam loss mechanism to the thermal neutron production thoroughly. Our work is very unique and directly useful for radiation shielding and 0029-554X/81/0000---0000/$02.50 © 1981 North-Holland

protection around the accelerator. As an example, the production of 41Ar by (n, 7) reaction could be estimated from the thermal neutron flux as shown in the appendix.

2. Mechanism of thermal neutron production

First, the electrons are accelerated up to 15 MeV by a linac and injected into the synchrotron ring of about 12 m diameter, as shown in fig. 1. After this injection, electrons are accelerated to a chosen energy between 500 MeV and 1.3 GeV and some of the electrons are converted to high energy photons for an elementary particle experiment by colliding with a platinum internal target. The residual beams (more than 99%) are decelerated in the ring and enter the iron yoke magnet as shown in fig. 2. These electrons in iron cause the electromagnetic cascade shower and the photons emitted from the shower then produce the secondary neutrons by photoneutron reactions. The photoneutron reaction cross section of iron given by Costa et al. [4] and Jones et al. [5] is shown in fig. 3, and the shape is characterized by a giant resonance peak of 60 mb at about 17 MeV with a tail to the higher energy region. Considering the weighting by superposition with the photon spectrum mentioned later, the contribution of the giant resonance region for neutron production amounts to 98.5% of the total. The neutrons generated in the iron are thermalized by multiple scattering with the concrete surrounding the accelerator room.

T. Kosako, T. Nakamura / Thermal neutron flux

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3. Measurement of thermal neutron flux The thermal neutron flux was measured by gold activation foils set on the iron yoke magnet of octants 1 to 8, at the rear of the injection linac and at the center of the electron synchrotron room. The setting positions of gold foils are shown as black dots with identification numbers in fig. 1. These positions are all 150 cm above the floor. The gold foils used in this experiment have disk shapes of 0.1 m m thickness and 1 cm diameter and 150 mg weight. The physical properties [6] of gold foils are listed in table 1. The

Table 1 Physical properties of gold foil a). Abundance Reaction Cross-section

~-ray energy Branching ratio Half-life a) Ref. 6. b) Ref. 7. c) Ref. 8.

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87.61% 6.18 d

T. Kosako,T. Nakamura/ Thermalneutronflux gold foils were irradiated during synchrotron operation for 2 0 8 2 0 s (about 5.8 h) with an electron energy of 725 MeV and electron density o f 1.52 X 1012 e-/s (on the beam monitor at the straight section 6, S - 6 : 1 0 0 mA). The induced radioactivities were measured by setting a gold foil on the Ge(Li) detector surface. The absolute peak efficiency of the Ge(Li) detector was experimentally obtained by setting the gamma standard sources of STCo, 6°Co, 2~Na and S4Mn on the detector surface. The measured efficiency is shown in fig. 4. A typical measured result is shown in fig. 5. The 412 keV photopeak o f 198Au by (n, 7) reaction is observed, but the 356 keV gamma ray from 196Au by (7, n) reaction is not. The thermal neutron flux was obtained by the cadmium-ratio method between the bare gold foil activity and a 1 mm thick cadmium-

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Cd = cadmium ratio at the position of octant 8, defined by Cd -- Bare/Cd-cover, 1.537, tl = irradiation time of gold foil, 20 820 s, t2 -- start time of measurement, about 1000 s, At -- counting time, about 30 s. Thermal neutron fluxes obtained by eq. (1) are shown in table 2. The spatial distribution of the thermal neutron flux is almost uniform along the iron yoke magnet excluding octant 6. On octant 6, the thermal neutron flux is higher than the rest, since the electron beam is dispersed into the iron yoke magnet by a scraper. The thermal neutron flux at the center of the synchrotron room is low since the thickness of Table 2 Thermal neutron flux in the electron synchrotron room measured by 197Au activation foil a).

Position

Thermal neutron flux (n/cm2/s)

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x 104 x 103 × 103 x 103 × 104 x 104 x 103 × 103 x 10 a X 103

a) ES operation condition: electrons 725 MeV, 1.52 X 1012 e-Is, 176 W.

concrete of the central roof area of 1.8 m radius is 25 cm, which allows more neutron leakage compared with the other part of 75 cm roof thickness. The thermal neutron flux at the rear of the linac is also low because of the large distance from the source part generating neutrons and the large vacancy around the linac.

4. E v a l u a t i o n o f experimental results The experimental results of thermal neutron fluxes produced on the electron synchrotron operation were evaluated by a theoretical treatment from electron beam loss until thermal neutron production. 4.1. Energy loss process o f the electron beam The energy loss process of the electron beam is of fundamental importance in this analysis. The electron beam pulse was accelerated by the electron linear accelerator under the condition of pulse width, APw, of 1.5 X 10 -6 s, peak current, Ip, of 200 X 10 -3 A, repetition frequency, H1, of 21 Hz, and electron energy, El, of 15 × 106 eV. The electron intensity, D1, was derived from Ip • APw 101a D~ = 1.602 X 10 -19 H~ = 3.93 × (e-/s),

(2)

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(3)

These electron beams were injected into the electron synchrotron and accelerated up to an energy, E2, of 725 X 106 eV with a repetition frequency, //2, of 8.63 X 106 Hz. The beam currents, Iav, were 100 mA during the synchrotron operation at the beam monitor fixed at straight section 6 (S-6 position). The electron intensity in the ring doughnut of the synchrotron was _ Iav

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(5)

A part of this electron beam was converted to photons for a high energy physics experiment with the internal platinum target of 0.01 radiation length at S-4 position. Thereafter the electron beam lost its

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energy by the scraper of the S-6 position and was dispersed into the iron yoke magnet as shown in fig. 6. The slippage of the electron trajectory is calculated from the momentum compaction factor [9], a, as follows:

AR = a(Ap/p) R ,

(6)

where R = radius of trajectory, 400 cm, ~ = slippage of trajectory, p = momentum, ~p = variation of momentum, a = momentum compaction factor, 0.35 when R = 400 cm. Since the momentum loss, ~p/p, is about 0.01 at the internal target and 0.20 at the scraper, the slippage of trajectory, z~d~, at these points is about 1.4 cm and 28 cm, respectively. The total slippage is 29.4 cm and the electron beam begins to oscillate around this position and the amplitude of this oscillation U s is then 28 cm. Considering the distance from the inner surface of the doughnut to the iron yoke surface, do, is 15 cm and the bump of the scraper, d b, is 2 mm, the distance from the scraper to the electron injection point into the yoke magnet along the main ring, d, is obtained by approximating the cosine trajectory of the electron, as follows (zXRs - dg - db) = z2~ s • cos[(d/do)" 90°1 .

(7)

rest of the beam also lose their energy with a small angle incidence to the iron yoke, as do those of the major beam.

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Finally the majority of electrons were dispersed into the 18 cm thick iron yoke with an angle of 7.68 ° according to the trajectory shown in fig. 6. The remainder of the electron beam also loses its energy at the beam incidence and beam extraction positions shown in fig. 1. As these losses are considered to be spilled ones, we may assume that the electrons of the

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T. Kosako, T. Nakamura / Thermal neutron flux

382

according to the process mentioned above. To estimate accurately the number of photons produced, a Monte Carlo calculation of the electromagnetic cascade shower was performed using the EGS code [10]. In this code, the following reactions are considered: bremsstrahlung, electron-positron pair production, positron annihilation, Compton scattering, photoelectric effect, multiple scattering, Bhabha scattering, and Moeller scattering. The calculation was performed under the condition that a 725 MeV electron comes into an 18 cm thick iron slab at a 7.68 ° incident angle. The cut-off energies of photon and electron are 100 keV and 1.0 MeV, respectively. 2678 electrons were injected in this analog Monte Carlo calculation to obtain transmitted and backscattered photon spectra, and 500 electrons, to obtain photon spectrum inside the iron. From this calculation, the energy deposition was found to be 7.90% on the incident beam side due to backscattering, 92.1% inside the iron, and 0.02% in the forward direction due to penetration. These photon energy spectra calculated with the EGS code are shown in fig. 7, and they are considerably softer than the bremsstrahlung spectrum from a thin target due to multiple scattering and backscattering in iron.

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4.3. Neutron generation and slowing down Neutrons are generated by the Fe(7, Tn) reaction caused by photons from the electromagnetic cascade shower when electrons enter the iron yoke magnet on the last stage of acceleration. The total neutron yield of one incident electron of energy Eo entering iron is given by the following equation, Eo

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where o(k) = microscopic Fe(7, Tn) cross section shown in fig. 3, N = atomic number of iron per unit volume, dL(k)/dk = differential track length of photons in iron, k = photon energy. The differential track length of photons was calculated in the case of 500 electrons incident with energy Eo = 725 MeV and at incident angle of 7.68 ° on iron, 18 cm thick, by using the EGS code. The calculated values of dL/dk is shown in fig. 8 and the values of o and dL/dk are tabulated in table 3. From the product of o and dL/dk in table 3, the

giant resonance region from 11 MeV to 25 MeV has an overwhelming contribution to the neutron generation. From eq. (9), we got Yn(Eo)=0.0814 neutrons/electron for Eo = 725 MeV and an incident angle of 7.68 °, then the total neutron yield becomes 1.24× 1011 n/s for a total electron incidence of 1.52 X 1012 e-/s. This neutron flux is comparable to the level in the core of a research reactor. This neutron yield of 1.24 X 1011 n/s becomes 7.02 × 10 ix n/s • kW by dividing by 176 W from eq. (5) and this value is 92.4% of 7.6 X 1011 n/s • kW which was obtained from the calculation for normal incidence of 500 or 1000 MeV electrons on a semi-infinite iron target by Swanson [2]. These two values are close despite the different incident geometries; one (ours) has an incident angle of 7.68 ° and the other (Swanson's) is for normal incidence on semi-infinite iron. The energy spectrum of emitted neutrons has three components consisting of the giant resonance reaction of photons around 18 MeV, the quasi-deuteron effect of higher energy photons and the n production reaction of photons above 140 MeV, but the last

T. Kosako, T. Nakamura / Thermal neutron flux Table 3 Calculated differential track length of photons in an 18 cm thick iron slab on a 725 MeV electron incidence with 7.680 .

F.

Energy (MeV)

Cross section of Fe(3,, n) (mb)

Diff. track length (cm/MeV/e-)

=~ 10-2

11- 12 12- 13 13- 14 14- 15 15- 16 16- 17 17- 18 18- 19 19- 20 20- 21 21- 22 22- 23 23- 24 24- 25 25- 50 50-100 100-150 150-200 200-250 250-300 300-350 350-400 400-450 450-500 500-550 550-600 600-650 650-700 700-725

3.7 8.1 14.3 20.5 41.7 56.7 61.4 57.7 54.6 45.7 34.4 26.7 18.7 16.4 16.0 15.0 18.0 24.0 29.0 34.0 40.0 34.0 29.0 20.0 10.0 5.0 -

4.4876 4.1390 3.2962 3.2686 2.5382 2.6154 1.8469 1.8844 1.6687 1.5893 1.5234 1.1748 1.3104 0.8936 0.5848 0.1624 0.04866 0.02205 0.01358 0.01168 0.006407 0.005470 0.003415 0.002290 0.001728 0.001764 0.0006459 0.0008871 0.0002169

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[121). and the parameter t~ of iron (z = 26) was determined to be 2.6 using the recommended value [13]. The whole shape of the neutron energy spectrum was synthesized by connecting eqs. (10) and (11) at about 10 MeV. This is shown in fig. 9. These generated neutrons are slowed down to be thermalized in the synchrotron room. This neutron thermalization process was calculated by the two-dimensional discrete ordinate transport code, DOT 3.5 [14]. The calculational geometry was simplified by assuming that the iron yoke magnet and the surrounding concrete shield were both cylinders of the actual dimensions. The neutron source was normalized to one and its synthesized spectrum is given in fig. 9. The cross-sectional view of this geometrical model is shown in fig. 10. The chemical composition and atomic density of concrete and iron for this calculation are tabulated in table 4. The cross-section data used in this calculation are from DLC-58/HELLO [15], composed of 47 groups from 60 MeV to thermal energy. The Legen-

( 1O)

where $(En) = n e u t r o n flux, En = neutron energy (in MeV), T = nuclear temperature (in MeV). As the measured nuclear temperature of heavy material such as lead shows [11] a weak dependence on the incident electron energy, we obtained the nuclear temperature T of iron to be 2.08 MeV by semi-log plotting [energy on the linear scale and $(En)/En on the log scale] of experimental data [12] of 55 and 85 MeV electron incident on iron. The n e u t r o n spectrum due to the quasi-deuteron effect is empirically expressed [13] as follows,

q~(En) ~ En c~ ,

1o0

10-4

component contributes only a small fraction in our case. The spectrum due to the giant resonance reaction is given by the Maxwellian distribution based upon the evaporation model as follows,

~(ErO = (En/T 2) e x p ( - E n / T ) ,

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T. Kosako, 7'. Nakamura / Thermal neutron flux

384

in the synchrotron room aro obtained by the following formula,

Table 4 Atomic density of concrete and iron for the neutron transport calculation by DOT 3.5 code

~ ( E t h ) = Ye" r n " xI/th , Density (atoms/cm 3 )

Concrete component H O Si Ca Fe

5.95 4.48 2.00 1.52 7.38

Iron Fe

7.70 X 1022

where Ye = incident electron number, 1.52 X 1012 e - / s , Yn = generated neutrons in the iron yoke, 0.0814 n/e-, qqh=thermalization fraction in the electron synchrotron room, 1.71 X 10 -7 (nth/cm2)/n. From eq. (12), qb(Eth ) becomes 2.11 X 104 n t h / cm2/s. As the average of thermal neutron fluxes measured at octant 1 to octant 8 (see table 2) by the gold activation foil was qb(Eth ) = (1.06 -+ 0.53) X 104 (nth/cm2/s), the former calculated value agrees rather well within a factor 2 with the experimental value. The discrepancy may be accounted for by the following reasons. The simplified geometrical model of the electron synchrotron room may be insufficient for the accurate calculation of neutron transport, since the area where an approximation of cylindrical geometry was difficult, such as a space surrounding an injection linac and the beam extraction part of experimental channel, were neglected in this model. Neglecting these increases the neutron leakage from the electron synchrotron room. Since the volume of these areas is 22.9% of the total volume of the room, the calculated thermalization factor must be a smaller

X 1021 X 1022 X 1022 X 1021 × 1020

dre coefficient of angular expansion for the scattering cross-section was set to P3- The angular quadrature of the SN calculation was set to Sas. The calculated neutron spectrum on the yoke magnet in the synchrotron room is shown in fig. 11 with the input source spectrum. The calculated neutron spectrum has a moderated lIE spectrum below about 100 keV and above it the vestige of the source neutron spectrum still remains. The calculated fraction of thermalized neutrons from source neutrons is 1.71 X 10 -7 tO one source neutron. The thermal neutron fluxes, ¢(Eth ),

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108

T. Kosako, T. Nakamura / Thermal neutron flux value. On the other hand, the complicated structural materials in the synchrotron room such as in the supports and the power supplies were also neglected, and they occupy 14.0% volume of the total. These materials play the role of neutron scatterers and increase the thermalization factor. The fact that the calculated value overestimates the experimental one means that the former effect is greater than the latter. 5. Conclusion The thermal neutron flux in the electron synchrotron room was measured with a gold activation foil for the synchrotron operation at 725 MeV electron energy and 1.52× 10~2e-/s beam intensity. The measured result was evaluated by the calculation, starting from electron energy loss in the iron yoke magnet, dealing with the electron-photon cascade shower in iron and the production of photoneutrons and their thermalization in the synchrotron room surrounded with a concrete shield. The calculated result could reproduce the experimental result within a factor 2. Appendix

Application to the estimation of 4~Ar production The thermal neutron flux in the synchrotron room obtained in the text was used to estimate the generation of 4aAr, which is one of the airborne radioactive materials of concern [ 1 6 - 1 8 ] . 41Ar was produced from the neutron capture reaction of 4°Ar which is included by 1.286 o/w * in air. The neutron capture cross-section in the thermal neutron region is (630-+ 20) mb by Stehn et al. [7] and the effective capture cross-section in the epithermal region is 56.7% of the thermal capture cross-section in the neutron field with a Cd-ratio of 2.78 in the thermal neutron reactor by French [19]. In the case of our electron synchrotron room, the Cd-ratio was 1.54 and is rather close to the above Cd-ratio, then the contribution of the epithermal neutron capture reaction was considered to be the same percentage as above. The number of 4~Ar, NA, generated in the synchrotron room is obtained by the following equation, N A = Y e " Yn " I / ~ EAr" (1 + f ) " xrd'~h" Vi I ,

* Weight percent.

(13)

385

where E Ar = macroscopic thermal neutron capture cross-section of 4°Ar, 1.470 × 10 -7 cm -1, f = the fraction of epithermal neutron capture-cross section to the thermal neutron capture cross-section of 4°At, 0.567, 'I'~h = calculated thermalization fraction per one source neutron generated in the ith region of the synchrotron room, V/ = the volume of the ith region of the synchrotron room, i = the cylindrical region number of the synchrotron room used in the calculation, 29 regions, Ye = electron number in the synchrotron ring, 1.52 X 1012 e-/s, Yn = number of neutrons generated in the iron yoke magnet by one electron, 0.0814 n/e-. The saturated activity, A, of 41Ar was obtained by A = NA,

(14)

and A is 9.44 × l0 s dps, that is 25.5/aCi. Considering the actual volume of the electron synchrotron room including linac and experimental beam channel to be 4.292 × 108 cm 3, the concentration of 41Ar radioactivity per unit volume becomes A' = 5.94 X l0 -8/ICi/cm 3 .

(15)

The authors gratefully acknowledge the collaboration of the following persons of the Institute for Nuclear Study (INS) of the University of Tokyo in the experiment of electron synchrotron (ES): Dr. Y. Murata, Dr. S. Honma, Dr. K. Yoshida, Dr. S. Kato, Mr. K. Kohno, Mr. T. Ohkubo and the machine members of ES. The calculation in this paper was done with the FACOM M-180 II AD computer in INS.

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T. Kosako, 7". Nakamura / Thermal neutron flux

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