Tesch, K

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Particle Accelerators1982 Vol. 12 pp.169-1750031-2460/82/1203-0169$06.50/0© Gordon and Breach, Science Publishers, Inc.Printed in the United States of AmericaTHE ATTENUATION OF THE NEUTRON DOSE EQUIVALENT IN ALABYRINTH THROUGH AN ACCELERATOR SHIELDK. TESCHDeutsches Elektronen-Synchrotron DESY Notkestr. 85, 2000 Hamburg 52, Fed. Rep. Germany(Received February 9,1982; in final form June 16,1982)The attenuation of neutron dose equivalent in concrete labyrinths with rectangular bends was studied by means ofneutron sources and rem counters. The number of bends, the length of each section, and the width of the labyrinthcould be varied. The results of these measurements were compared with the dose equivalent attenuation found ina labyrinth at the DESY 7-GeV electron synchrotron, with published data from a proton accelerator and from anuclear reactor. An empirical formula describing the neutron dose equivalent is presented.1. INTRODUCTIONTen years ago Gollon and Awschalom publishedneutron attenuation calculations for penetrationsin hadron shields. They introduced their articleas follows: "Among the various problems in-volved in the design of accelerator radiationshielding, the problem of personnel and vehiclepenetrations has received the least attention inthe shielding literature." 1 This statement is stillvalid; the situation has not changed in the mean-time. The reason for it is at least threefold: (i) Atoperating accelerators there is generally neitherspace nor time available for systematic experi-mental radiation studies; (ii) The diffusion ofneu-trons is a complicated process that can only betreated theoretically using approximations andby means of the most advanced computationaltechniques. These approximate theoretical re-sults must be checked experimentally; (iii) Atsome large accelerator centers, rather crude es-timates are available, sometimes published in in-ternal papers, and these are thought to be ade-quate in view of the great uncertainty inherentin the estimate of the beam loss (source term)near the labyrinth. Nevertheless, in designingaccess ways for new accelerator installationswhere space for mazes is very limited, we havefound it desirable to have simple and experimen-tally verified expressions describing the neutrondose equivalent attenuation in such labyrinths.Simple formulae of this kind are not availableat present. Much experimental and theoreticalwork has been done in this field for nuclear re-actors, but the geometries are limited to ducts of169small diameter; broad access ways are not com-mon at reactor stations. Experimental studies ofneutron attenuation in labyrinths at acceleratorsare described in Refs. 2-5. All measurements aredone by means of threshold detectors. Only Ste-venson and Squier combined the results ofthreshold detectors to determine the attenuationof the neutron dose equivalent, which is relevantfor protection considerations. Alsmiller and So-lomit06 calculated the neutron production nearthe mouth of a labyrinth and the fluxes of thermaland low-energy neutrons at some points alongthe maze. In other calculations (Refs. ·7, 1, and8), the unphysical assumption of a constant neu-tron energy is made.Detailed Monte Carlo calculations have beenmade by Vogt9 for the very large access ways ofthe CERN SPS. Some of these calculations andexperiments were combined to give an approxi-mate "universal" attenuation curve suitable forproton accelerators. 1o For the short rudimentalmazes common at small medical accelerators,McCall et al. 11 put together three "cookbook"approaches; they give similar results for the ge-ometry for which they are tailored, but fail whenapplied to the labyrinths considered in this paper.In order to collect more information, we firststudied the attenuation of the neutron dose equiv-alent in concrete labyrinths by means of isotopicneutron sources. The similarity between thespectrum of accelerator-produced medium-en-ergy neutrons and the spectrum of the well-known AmBe source or a fission spectrum hadalready been used to study attenuation parame-ters. 12 The number of bends of the labyrinth and170 K. TESCHFIGURE 1 Dose equivalent attenuation in a straight accessway. Two source positions S 1 and S 2 are indicated.2. MEASUREMENTS WITH NEUTRONSOURCES2.1 Dose Equivalent Attenuation in the FirstSectionThe dose equivalent distribution in the firstsection of a labyrinth (i.e., in a straight accessway) was measured up to a length of 13 m andfor both widths mentioned above. Examples areshown in Fig. 1,' source position S1, and the leftpart of Fig. 4, where the dose equivalent is givenas a function of the distance from the source,normalized at rl = 1 m (the mouth of the laby-rinth).· Small deviations from the llr2-law areseen. With increasing distance, this scatteringcontribution first increases and then decreases.Such a decrease in addition to the l/r2-depen-dence has also been observed in Refs. 2 and 5;it has been explained by absorption in air, thoughthe resulting cross section turned out to be un-usually large. This behavior is more clearlyshown in Fig. 2 where the ratio of scattering con-Two cross sections were used, A = 2.2 x 1 m2and A = 2.2 x 2 m2 • The neutron source waspositioned at S as shown in the figures. The di-mensions of the source housing were chosen tosimulate a section of an accelerator tunnel. Weused a 2-mCi Cf252 spontaneous-fission sourceand a l-Ci Am:l41 -Be source. Because no differ-ence in the attentuation of neutrons emitted bythese sources was detectable, we used bothsources simultaneously in order to increase theintensity.The neutron dose equivalent was measuredwith moderated neutron counters. We used cy-lindrical counters after Andersson and Braun andspherical counters after Leake. For the most re-cent measurements of the dose response func-tions of these instruments, see Refs. 13 and 14.The instruments show an oversensitivity in thelower keV-region. Because the neutron spectrumis degraded in energy during the diffusion proc-ess, the instrumental oversensitivity leads to asystematic error in the measured attenuation fac-tor, which is therefore an upper limit and a con-servative estimate for shielding calculations. Theabsolute efficiencies of the detectors were deter-mined by calibrated neutron sources in an essen-tially scattering-free geometry. After carefulelimination of all electrical noise, the lowest de-tectable neutron dose was limited by the doseequivalent rate of cosmic neutrons, which wasfound to be roughly 1.8 mremla inside the lab-yrinth and 3.5 mremla outside.14 r, (m)1412121010t-----I2m.~..................................5 2~ Heavy concrete'\ ~ Ordinary concrete&;2"'" 511/r2 . "'-1 ".HThe measurements with isotopic neutron sourceswere performed in labyrinths constructed of con-crete .blocks. A few examples are shown in theinserts of Figs. 1, 4, and 5. At critical pointswhere neutrons could disturb the measurementsby penetrating the concrete blocks, we usedheavy concrete (p = 3.7 g cm- 3) instead of or-dinary concrete. All mazes had' a roof of 80 cmordinary concrete; the height inside was 2.2 m.the length and the cross section of each bendcould be varied systematically. Then we com-pared the resulting attenuation curves with theattenuation in an existing labyrinth at the DESYelectron synchrotron and with published dataobtained at a proton' accelerator and at a nuclearreactor.NEUTRON ATTENUATION IN A LABYRINTH 171H scatteredH directwhere h is the height of both the source and thedetector and r the distance between them. Forr ~ h,FIGURE 2 The ratio of scattered neutron dose equivalentto dose equivalent due to direct neutrons as a function ofdistance (from the source) inside the first section of a maze.width 1mA=2.2 m2CHtotal = -42 (1 + 0.37). (2)'ITrWe checked these relations with our sources anddetectors above a thick concrete floor. A com-parison is shown in Fig. 3. The agreement is notgood and may partly be due to the oversensitivityof the detector to multiply scattered neutrons,but both calculation and measurement give a con-stant contribution of scattered neutrons for largerdistances (r ;:::: 4m).The reason for the dose equivalent distributionshown in Fig. 2 is the neutrons multiply scatteredinside the source housing ("the accelerator room")and then streaming down the access way. Thiscontribution can be simulated with the source in,for example, position S2, Fig. 1, which gives amuch stronger attenuation along the labyrinth.The deviations from the 1/r2-law depend mainlyon the source building; they were found to bemuch smaller than those illustrated in Figs. 1 and4 if, e.g., the concrete wall opposite to the mouthof the labyrinth is removed.14 r, (m)1210width 2 mA= 4.4 m2x xequ. 1measurementheight 0,5 m//~-v.-::.::.-- =------------ - - - - - - - --/ I" -;' hei ht 1mIyH scatteredH directtribution to direct radiation (both unnormalized)is given for two maze cross sections.The varying contribution of scattered neutronscannot be explained by the presence of the lab-yrinth walls, because (i) the contribution is largerfor a larger width of the labyrinth (which wasalready observed in Ref. 1 and (ii) the ratio ofneutrons scattered from a surface to direct neu-trons becomes constant for larger distances fromthe source.The last-mentioned behavior has been studiedrecently by Jenkins. 15 For a neutron source anda detector placed at some heights above a con-crete'floor, he calculated the contribution of neu-trons scattered from the floor. 'His expression forthe total dose equivalent (due to direct and scat-tered neutrons) can be rewritten asFIGURE 3 The ratio of scattered neutron dose equivalentto dose equivalent due to direct neutrons as a function ofdistance (from the source) above, a concrete floor.CHtotal = -421fT(h 2 1) 1/21.5 - + -r2 41 +-------(h 2 1) 3/2 ,1+8 -+-r2 4(1)10 12 14 r(m)172 K. TESCHo 1 2r2 [m)FIGURE 5 The attenuation of the neutron dose equivalentin a labyrinth with 3 sections. The width is 1 m.Hcan be described by exponentials. The first part(at low r2 values) is independent of the cross-sectional area, A, of the labyrinth; the seconddepends on A. The explanation is simple. Thefirst exponential describes the "disappearance"of the source and of the scattering material nearthe source behind the corner, while the secondand much smaller portion describes the atten-uation of neutrons scattered near the mouth ofthe second section into this section. The latterpart should be proportional to the cross sectionsof the first leg and of the second leg. If both areequal, a dependence on A n is expected, wheren takes a value between 1.0 and 2.0. A fit givesr-- GI4\1~ 2·r, \\."-"-"\\\2.2. Dose Equivalent Attenuation in theSecond and Third SectionExamples of measured dose equivalent distri-butions in the second and third section of a lab-yrinth are given in Figs. 4 and 5. If the dose inthe second leg is normalized to unity at r2 = 0,the attenuation curve is found to be independentof the length of the first section and independentof the position of the source in the source hous-ing.The curve is made up of 2 parts, both of whichFor typical labyrinths in actual use, the doseequivalent due to scattered neutrons roughlyequals that of direct neutrons (see Fig. 2). Thusit is convenient to approximate the dose equiv-alent by increasing the direct contribution by afactor of two.H4FIGURE 4 The attenuation of the neutron dose equivalentin a labyrinth with 2 sections. The width is 2 m.NEUTRON ATTENUATION IN A LABYRINTH 173+ O.022A 1.3 exp ( - 2~~5)]/ [1 + O.022A 1.3 ]'2 in m; A in m2 (3)The scattered contribution from the walls of thesecond section is very small. The second expo-nential continues for several meters out of thelabyrinth. When we removed the second half ofthese walls no change in the dose equivalent read-ings was observed.A "neutron trap''"; (see T in Fig. 5) had no sig-nificant influence on the dose distribution in thesecond leg and is an unnecessary complicationof the labyrinth.For the dose equivalent distribution in the thirdsection we found exactly the same curve if thedose is normalized to unity at'3 = o.3. MEASUREMENTS ATACCELERATORS, DISCUSSIONThe secondary radiation to be considered in de-signing labyrinths at high-energy accelerators isproduced at large angles, typically at 90°. Underthese conditions, medium-energy neutrons, suchas giant-resonance neutrons or evaporation neu-trons, are the most important component. Nolarge difference is expected between the atten-uation of the dose equivalent of these particlesand the neutrons investigated in the previous sec-tion. We checked this hypothesis in an existingthree-legged labyrinth through the shielding ofthe DESY 7-GeV electron synchrontron. Theheight of the labyrinth was 2.2 m, the width was1.4 m. The detectors in the first section wereshielded with 5 em of lead. First we checked thedose equivalent attenuation with the isotopicneutron sources and found agreement with ourprevious results. Then we measured the atten-uation with the accelerator running in many dif-ferent modes (electron or positron acceleration,one bunch or multibunch mode, etc.), the re-sulting attenuation curves were nearly identical.As expected, for the first section of the labyrinthwe obtained good agreement between the twoneutron fields. The dose equivalent due to neu-trons scattered into the second section is roughlya factor of 2 higher for accelerator-produced neu-trons than for isotopic-source neutrons becauseof spectral differences. This factor of two persistsin the short third section, Le., the effect of thesecond bend is the same for both spectra.From these measurements and the results andsimple phenomenological considerations of Sec-tion 2, we derive the following recipe for esti-mating the dose equivalent in a labyrinth. Firstthe strength of the neutron source due to theestimated beam loss is calculated as an equiva-lent point source. With additional information ofthe spectrum, this gives the dose equivalent Hat a certain distance. If a line source is a moreappropriate model, an equivalent point sourcemay be considered by assuming the length of theline source is twice the width of the labyrinth.Then the dose equivalent in the labyrinth is givenby(4)!z(r2) = 2[exp ( - O~~5)+ O.022A 1.3 exp ( - 2~~5)]/ [1 + O.022A 1.3 ]!J(r3) = [exp ( - O~~5)+ O.022A 1.3 exp ( - 2~~5)]/ [1 + O.022A1.3],where a is the distance from the source to themouth of the first section, the 'j are the coordi-nates as defined in Figs. 4 and 5, '2 and '3 aregiven in m, A is the cross-sectional area of themaze in m2 • The 'j of the last section can beextended to values outside the last section.In Fig. 6 the values from Eq. 3 are comparedwith results from a proton accelerator. 5 The func-tion f2('2) describes well the attenuation of thedose equivalent measured inside the second legof a labyrinth at a 7-GeV proton beam if nor-malized to unity at the beginning of the section.This function is also in agreement with an ap-proximate curve which is in practical use at theCERN laboratory. 10 Also shown in Fig. 6 is theattenuation of the neutron fluence as measuredby Stevenson and Squier by means of thresholddetectors. The greater attenuation of the high-energy neutrons, especially for neutrons at athreshold of 20 MeV, supports the assumptionthat our equation can be applied to acceleratorsof much higher energies.Recently a Monte-Carlo calculation has been174 K.TESCH:\ dose equi valent'\ attenuation: Stevenson, Squier (ref. 5) H\ equ.1, A=5.3 m2\\ (this work)\\ fluence attenuation (ref. 5):\,En = 6······· 25 MeV10-1 \ 10-1\ -'- En > 20 MeV\\\ 10- 1\\'\'\\\ '\~:\\ ~~10-2 \ 10-2'"\ '\'\'\\ '\'\\ '\ '\ 10- 2'\'\\\10-3 \ 10- 3\"\"Maerker, Muckenthaler (ref. 16)equ.3 A:O,83m2 (this work)10- 110 12FIGURE 6 Comparison between the measurements of Ste-venson and Squier (Ref. 5) and our results.performed by Y. Sizong17 to study the attenua-tion of dose equivalent in the second section ofthe labyrinth of the above mentioned proton ac-celerator. For a primary neutron energy of 1.5MeV, the results from the Monte-Carlo codeMORSE are in agreement both with the ex-perimental curve and with the results of Eq. (3)(Fig. 6).In Fig. 7, a comparison is made with the fastneutron dose equivalent attenuation measured ata nuclear reactor. 16 The duct had a cross sectionA of only 0.91 x 0.91 m2 • The results are directlycomparable with our measurements since we alsoused a neutron source with a fission spectrum.The approximate agreement indicates that the A-dependence seems to be reasonable though it wasdetermined by only two A-values.Therefore Eq. (4) is applicable at electron- andproton accelerators and for fast neutrons at nu-clear reactors. The errors may be not much largerFIGURE 7 Comparison between the measurements at anuclear reactor (Ref. 16) and our results.than those introduced by the imperfect responsecurve of the moderated neutron detectors (rem-meters) used in this e~periment and elsewherefor routine health physics purposes.REFERENCES1. P. J. Gollon and M. Awschalom, IEEE Trans. Nuci. Sci.NS-18, 741 (1971).2. W. S. Gilbert et aI., Lawrence Radiation LaboratoryReport UCRL-17941, 1968.3. W. Schimmerling and M. Awschalom, IEEE Trans. Nuel.Sci. NS 16, 604 (1969).4. V. E. Borodin, L. P. Obryashikowa, and M. N. Chi-mankov, Serpukkov Inst. High Energy Physics, Orz 71-84, 1971.5. G. R. Stevenson and D. M. Squier, Health Physics 24,87 (1973).6. R. G. Alsmiller and E. Solomito, Nucl. Instrum. Methods73, 280 (1969).NEUTRON ATTENUATION IN A LABYRINTH 1757. M. M. d'Hombres et aI., Saclay Nuclear Research Cen-ter, CEA-R-3491, 1968.8. C. S. Perret, Int. Conf. Protection against Acceleratorand Space Radiation, CERN, 1971, p. 714.9. H. G. Vogt, CERN 75-14, 1975.10. G; R. Stevenson, CERN 76-04, 1976.11. R. C. McCall et aI., Stanford Linear Accelerator Center,SLAC-Pub-2440, 1979.12. K. Tesch, Part. Accelerators 9, 201 (1979).13. K. G. Harrison, Nucl. Instrum. Methods 166, 197 (1979).14. W. G. Alberts et aI., Phys. Techn. Bundesanstalt, Braun-schweig, PTB-ND-17, 1979.15. T. M. Jenkins, Health Physics 39, 41 (1980).16. A. E. Profio, Radiation Shielding and Dosimetrie (J.Wiley & Sons, New York, 1979) p. 469.17. Y. Sizong, Part. Accel. 12, No.2 (to be published).

The Attenuation Of The Neutron Dose Equivalent In A Labyrinth through An accelerator Shielding

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