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TRANSPORT STUDY OF NEUTRON AND PHOTON ATTENUATION THROUGH LITHIUM HYDRIDE AND TUNGSTEN SPHERICAL MEDIA

, ." .

by John A. Peoples und Daniel Fieno

Lewis Reseurch Center CZeveZund, Ohio

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N A T I O N A L AERONAUTICS A N D SPACE A D M I N I S T R A T I O N WASHINGTON, D. C. J A N U A R Y 1969

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NASA TECHNICAL NOTE NASA TN 0-4989 -- -- -~-

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AFWL (WL/L-2) In ~ KIRTLAND AFB, N MEX ~ ~

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TRANSPORT STUDY OF NEUTRON AND PHOTON ATTENUATION THROUGH LITHIUM HYDRIDE AND TUNGSTEN SPHERICAL MEDIA

by John A. Peoples and Daniel Fieno

Lewis Research Center

Cleveland, Ohio

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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • JANUARY 1969

TECH LIERARY KAFB, NM

I llllllllll1 lllll lllll lllll nllll~llllll1lll DL3158b

NASA T N D-4989

TRANSPORTSTUDYOFNEUTRONANDPHOTONATTENUATION

THROUGH LITHIUM HYDRIDE AND TUNGSTEN

SPHERICAL MEDIA

By John A. Peoples and Daniel F i eno

Lewis R e s e a r c h C e n t e r Cleveland, Ohio

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION .~

For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTl price $3.00

TECH LIBRARY KAFB. NM

1 111111 11111 11111 11111 IIDIIIII 1111 1111 1111 0131586

NASA TN D-4989

TRANSPORT STUDY OF NEUTRON AND PHOTON ATTENUATION

THROUGH LITHIUM HYDRIDE AND TUNGSTEN

SPHERICAL MEDIA

By John A. Peoples and Daniel Fieno

Lewis Research Center Cleveland, Ohio

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTI price $3.00

ABSTRACT

The Sn transport theory and a point kernel method were used to study the attenuation of (1) point fission neutrons in LiH and Li'H, (2) point 8.00-MeV photons in tungsten, and (3) neutrons and secondary photons from a fas t reactor through a laminated W-Li'H shield. The results show that the two methods calculate in agreement neutron and photon doses through these media provided (1) at least a P3S16 transport calculation is used, and (2) for neutron attenuation, the point kernel method uses a distributed neutron re- moval cross section for Li and Li6 of 0.1000 cm2/g and 0.1156 cm2/g. ton source strength and distributions in the tungsten shells of the laminated tungsten- Li6H shield were also determined using a P3SI6 transport calculation.

Secondary pho-

ii

ABSTRACT

The Sn transport theory and a point kernel method were used to study the attenuation of (1) point fission neutrons in LiH and Li6H, (2) point S.OO-MeV photons in tungsten, and (3) neutrons and secondary photons from a fast reactor through a laminated W-Li6H shield. The results show that the two methods calculate in agreement neutron and photon doses through these media provided (1) at least a P 3S16 transport calculation is used, and (2) for neutron attenuation, the point kernel method uses a distributed neutron re­moval cross section for Li and Li6 of 0.1000 cm2/g and 0.1156 cm2/g. Secondary pho­ton source strength and distributions in the tungsten shells of the laminated tungsten­Li6H shield were also determined using aP3S16 transport calculation.

ii

TRANSPORT STUDY OF NEUTRON AND PHOTON AllENUATlON THROUGH LITHIUM HYDRIDE AND TUNGSTEN SPHERICAL MEDIA

by John A. Peoples and Daniel Fieno Lewis Research Center

SUMMARY One-dimensional Sn transport theory and a point kernel line-of-sight method were

used to study (1) the attenuation of neutrons from a point uranium-235 fission source in 117-centimeter spheres of lithium hydride (LiH) and lithium-6 hydride (Li H), (2) the attenuation of monoenergetic 8.00-MeV point source photons through 14 centimeters of tungsten, (3) the attenuation of neutrons and secondary photons from a fast reactor with

6 a shield consisting of alternate layers of Li H and tungsten, and (4) the production of secondary gamma source strengths and distributions in the tungsten layers of the lami- nated shield.

The results of the study of neutron attenuation in the spheres of LiH and Li H showed that the two calculational methods can be made to agree provided that (1) at least a P3s16 30-group neutron transport calculation is used, and (2) the point kernel method uses neutron distributed removal cross sections for Li equal to 0.1000 square centimeter per gram and Li equal to 0.1156 square centimeter per gram.

that a P3SI6 16-group transport calculation was sufficient to give good agreement with the point kernel method only up to a radius of about 7 centimeters.

laminated layers of tungsten and Li H showed two effects. the point kernel neutron computation agreed with the P3s16 30-group transport calcula- tion within 40 percent at a radius of 117 centimeters. This agreement was obtained us- ing a neutron distributed removal cross section for Li of 0.1156 square centimeter per gram. Second, the total secondary gamma dose rates calculated by the point kernel method and a P3s16 16-group gamma transport computation were in agreement (within 10 percent) at the outer boundary of the shield.

of the shield, due to neutron absorption and inelastic scattering processes, were made using P1 and P3 elastic scattering orders and 30 and 17 neutron energy groups. The re- sults show that for this shield configuration the influence of group structure (30 against 17) on determining source strength and distributions is negligible. However, the elastic scattering order P 3 against P1 did show a variation in source strength for the tungsten regions being examined. The P 3 and P1 elastic scattering orders gave essentially the same secondary production in the reflector, while in the first and second tungsten layers the results differed by 10 and 20 percent, respectively.

6

6

6

The point source study of the attenuation of 8.00-MeV photons in tungsten showed

The calculation of the attenuation of both neutrons and secondary photons through the First, the calculation showed 6

6

The transport calculations of secondary gamma ray sources in the tungsten regions

TRANSPORT STUDY OF NEUTRON AND PHOTON ATTENUATION THROUGH LITHIUM

HYDRIDE AND TUNGSTEN SPHERICAL MEDIA

by John A. Peoples and Daniel Fieno Lewis Research Center

SUMMARY One-dimensional Sn transport theory and a point kernelline-of-sight method were

used to study (1) the attenuation of neutrons from a point uranium-235 fission source in 117-centimeter spheres of lithium hydride (LiH) and lithium-6 hydride (Li6H), (2) the attenuation of monoenergetic 8. OO-MeV point source photons through 14 centimeters of tungsten, (3) the attenuation of neutrons and secondary photons from a fast reactor with a shield conSisting of alternate layers of Li6H and tungsten, and (4) the production of secondary gamma source strengths and distributions in the tungsten layers of the lami­nated shield.

The results of the study of neutron attenuation in the spheres of LiH and Li 6H showed

that the two calculational methods can be made to agree provided that (1) at least a P 3S16 30-group neutron transport calculation is used, and (2) the point kernel method uses

neutron distributed removal cross sections for Li equal to 0.1000 square centimeter per gram and Li6 equal to 0.1156 square centimeter per gram.

The point source study of the attenuation of 8. OO-MeV photons in tungsten showed that a P 3S16 16-group transport calculation was sufficient to give good agreement with

the point kernel method only up to a radius of about 7 centimeters. The calculation of the attenuation of both neutrons and secondary photons through the

laminated layers of tungsten and Li 6H showed two effects. First, the calculation showed

the point kernel neutron computation agreed with the P 3S16 30-group transport calcula­tion within 40 percent at a radius of 117 centimeters. This agreement was obtained us­ing a neutron distributed removal cross section for Li6 of 0.1156 square centimeter per gram. Second, the total secondary gamma dose rates calculated by the point kernel method and a P 3S16 16-group gamma transport computation were in agreement (within 10 percent) at the outer boundary of the shield.

The transport calculations of secondary gamma ray sources in the tungsten regions of the Shield, due to neutron absorption and inelastic scattering processes, were made using P 1 and P 3 elastic scattering orders and 30 and 17 neutron energy groups. The re­sults show that for this shield configuration the influence of group structure (30 against 17) on determining source strength and distributions is negligible. However, the elastic scattering order P3 against P1 did show a variation in source strength for the tungsten regions being examined. The P3 and PI elastic scattering orders gave essentially the same secondary production in the reflector, while in the first and second tungsten layers the results differed by 10 and 20 percent, respectively.

INTRODUCTION

Nuclear reactors for space propulsion systems or auxiliary power systems require shielding to protect personnel or system components from neutrons and gamma rays. Shielding materials must be placed so that neutron and gamma doses are within pre- scribed limits in various regions around the reactor. Since reactor shields are heavy, it is important that the arrangement and thicknesses of the shield materials are at a minimum weight. Two methods of calculation that are useful in the preliminary design of the shield are one-dimensional Sn transport theory and the line-of-sight point kernel method.

tinuous angular distribution of particle velocities is represented by discrete angular di- rections. The Sn quadrature order, which is discussed throughout this report, is a pa- rameter related to the number of discrete angular directions. Increasing the quadrature order (Sa, S12, and S16) increases the number of discrete angular directions used in the problem. The elastic neutron or Compton scattering order (P1 and Ps) denotes the spherical harmonics expansion order of the scattering source in the Boltzmann transport equation. Both types of scattering are anisotropic, therefore a number of terms in the expansion are needed to approximate the source term.

The line-of-sight point kernel method concentrates the source region into a number of individual point sources and then traces a ray from each of these point sources to a receiver point keeping track of the distance and mass thickness (g/cm ) of each element encountered. Infinite medium buildup factors are used to calculate the gamma dose and a modified Albert Welton kernel is used to compute the fast neutron dose,

shield problems is studied. A one-dimensional multigroup Sn transport code (ref. 1) is used to determine energy-dependent neutron fluxes. The fluxes are then used to compute the source of secondary gamma rays due to neutron capture and inelastic scattering pro- cesses. The Sn method is also used to determine the photon fluxes. These fluxes can then be used to determine the neutron and gamma ray doses at given detector positions in a shield. The more approximate but less complicated line-of-sight point kernel code QAD (ref. 2) is also used to compute the neutron or gamma ray doses at given detector locations. The code QAD requires known distributions of either neutron or gamma sources, gamma ray buildup factors, and neutron removal cross sections. Although high-order transport calculations, such as the Sn method, may be needed to predict ac- curately the doses in a shield configuration, a simpler and faster computer code such as QAD is useful for determining the effect of perturbations in shield arrangements.

isotropic uranium-235 fission sources in spheres of lithium hydride (LiH) and lithium-6 hydride (Li6H). The Sn results for LiH were compared to Monte Carlo results. Trans-

2

The Sn transport method is a numerical iterative difference method in which the con-

2

In this report the application of these methods to a number of neutron and photon

The Sn approximation to the Boltzmann transport equation was studied using point

INTRODUCTION

Nuclear reactors for space propulsion systems or auxiliary power systems require

shielding to protect personnel or system components from neutrons and gamma rays. Shielding materials must be placed so that neutron and gamma doses are within pre­scribed limits in various regions around the reactor. Since reactor shields are heavy, it is important that the arrangement and thicknesses of the shield materials are at a minimum weight. Two methods of calculation that are useful in the preliminary design of the shield are one-dimensional Sn transport theory and the line-of-sight point kernel

method.

The Sn transport method is a numerical iterative difference method in which the con­tinuous angular distribution of particle velocities is represented by discrete angular di­

rections. The Sn quadrature order, which is discussed throughout this report, is a pa­rameter related to the number of discrete angular directions. Increasing the quadrature order (88, 812, and S16) increases the number of discrete angular directions used in the problem. The elastic neutron or Compton scattering order (P 1 and P 3) denotes the

spherical harmonics expansion order of the scattering source in the Boltzmann transport equation. Both types of scattering are anisotropic, therefore a number of terms in the expansion are needed to approximate the source term.

The line-of-sight point kernel method concentrates the source region into a number of individual point sources and then traces a ray from each of these point sources to a receiver point keeping track of the distance and mass thickness (g/cm2) of each element encountered. Infinite medium buildup factors are used to calculate the gamma dose and a modified Albert Welton kernel is used to compute the fast neutron dose.

In this report the application of these methods to a number of neutron and photon shield problems is studied. A one-dimensional multigroup Sn transport code (ref. 1) is used to determine energy-dependent neutron fluxes. The fluxes are then used to compute the source of secondary gamma rays due to neutron capture and inelastic scattering pro­cesses. The Sn method is also used to determine the photon fluxes. These fluxes can then be used to determine the neutron and gamma ray doses at given detector positions in a shield. The more approximate but less complicated line-of-sight point kernel code

QAD (ref. 2) is also used to compute the neutron or gamma ray doses at given detector locations. The code QAD requires known distributions of either neutron or gamma sources, gamma ray buildup factors, and neutron removal cross sections. Although high-order transport calculations, such as the Sn method, may be needed to predict ac­curately the doses in a shield configuration, a simpler and faster computer code such as QAD is useful for determining the effect of perturbations in shield arrangements.

The 8n approximation to the Boltzmann transport equation was studied using point

isotropic uranium-235 fission sources in spheres of lithium hydride (LiH) and lithium-6 hydride (Li6H). The Sn results for LiH were compared to Monte Carlo results. Trans-

2

6 port calculations were d s o performed for Li H because it is a shield material of inter- est. The effect on the calculated dose rates of varying the Sn quadrature order (n = 8, 12, and 16) and the elastic scattering order from P1 to P 3 were also studied. The effect of neutron energy group structure was determined by varying the number of groups from 17 to 30. All of the Sn calculations included a sufficient number of mesh intervals to en- sure accurate f lux calculations. A number of calculations using the line-of-sight point kernel code QAD was also made to determine this code's usefulness in predicting neutron doses in these media.

The Sn transport method was also used to study the attenuation of photons in a sphere of tungsten using a point isotropic photon source having a monoenergetic energy of 8 MeV. This calculation was performed using 16 energy groups, a quadrature order of 16, and a scattering order of 3.

A P$16 transport calculation with 30 energy groups was made to compute the neu- tron dose of a fast reactor with a shield consisting of alternate layers of tungsten and

6 Li H. Calculation of the secondary gamma ray sources in the tungsten regions of this shield, due to neutron absorption and inelastic scattering processes, was also studied using P1 and P3 elastic scattering orders. gamma ray sources of this reactor was calculated using P1S16 and P3SI6 order. Calcu- lations of these doses for the distributed neutron and gamma ray sources were also made using the QAD code.

The gamma ray dose from the secondary

COMPUTER PROGRAMS AND NUCLEAR DATA

Computer Programs

Three computer programs were used to generate the necessary group-averaged mi- croscopic and macroscopic cross sections. GATHER I1 (ref. 4), and GAMLEG (ref. 5): GAM I1 is a B3 code for the calculation of flux weighted multigroup neutron cross sections; GATHER I1 is used to calculate cross sections for the thermal neutron group; and GAMLEG is used to produce multigroup photon cross sections,

photon fluxes through the various shielding materials. This program also calculated, for the case of the tungsten laminated shield, neutron absorption and inelastic reaction rates necessary to determine the secondary photon source strength and distribution.

A line-of-sight point kernel code QAD (ref. 2) was used to calculate neutron and photon dose rates. The QAD code employs infinite medium buildup factors for gamma doses and the Albert-Welton kernel for the hydrogenous material of the shield with an appropriate removal cross section for the other constituents for computing fast neutron doses.

These programs were GAM I1 (ref. 3),

A one-dimensional Sn transport program (ref. 1) was used to determine neutron and

3

port calculations were aiso performed for Li6H because it is a shield material of inter­est. The effect on the calculated dose rates of varying the Sn quadrature order (n = 8, 12, and 16) and the elastic scattering order from P 1 to P 3 were also studied. The effect of neutron energy group structure was determined by varying the number of groups from 17 to 30. All of the Sn calculations included a sufficient number of mesh intervals to en­sure accurate flux calculations. A number of calculations using the line-of-sight point kernel code QAD was also made to determine this code's usefulness in predicting neutron doses in these media.

The Sn transport method was also used to study the attenuation of photons in a sphere of tungsten using a point isotropic photon source having a monoenergetic energy of 8 MeV. This calculation was performed using 16 energy groups, a quadrature order of 16, and a scattering order of 3.

A P 3S16 transport calculation with 30 energy groups was made to compute the neu­tron dose of a fast reactor with a shield consisting of alternate layers of tungsten and Li6H. Calculation of the secondary gamma ray sources in the tungsten regions of this

shield, due to neutron absorption and inelastic scattering processes, was also studied using P 1 and P 3 elastic scattering orders. The gamma ray dose from the secondary

gamma ray sources of this reactor was calculated using P 1 S16 and P 3S16 order. Calcu­lations of these doses for the distributed neutron and gamma ray sources were also made using the QAD code.

COMPUTER PROGRAMS AND NUCLEAR DATA

Computer Programs

Three computer programs were used to generate the necessary group-averaged mi­croscopic and macroscopic cross sections. These programs were GAM II (ref. 3), GATHER II (ref. 4), and GAMLEG (ref. 5): GAM II is a B3 code for the calculation of flux weighted multigroup neutron cross sections; GATHER II is used to calculate cross sections for the thermal neutron group; and GAMLEG is used to produce multigroup photon cross sections.

A one-dimensional Sn transport program (ref. 1) was used to determine neutron and photon fluxes through the various shielding materials. This program also calculated, for the case of the tungsten laminated Shield, neutron absorption and inelastic reaction rates necessary to determine the secondary photon source strength and distribution.

A line-of-sight point kernel code QAD (ref. 2) was used to calculate neutron and photon dose rates. The QAD code employs infinite medium buildup factors for gamma doses and the Albert-Welton kernel for the hydrogenous material of the shield with an appropriate removal cross section for the other constituents for computing fast neutron doses.

3

Energy Group Structure

~ --

1 . 4 9 2 ~ 1 0 ~ to l,000X107 16 1.000 to 9 . 0 4 8 ~ 1 0 ~ 17 9.048 to 8.187 18 8. 187X106 to 7.408 19 7.408 to 6.703 20 6.703 to 6.065 21 6.065 to 5.488 22 5.488 to 4.966 23 4.966 to 4.493 24 4.493 to 4.066 25 4.066 to 3. 329 26 3. 329 to 2.725 27 2.725 to 2.019 28 2.019 to 1.353 29 1.353 to 8. 2O8X1O5 30

.- - - . .

Two neutron energy group splits were used to describe the neutron spectra: one of 30 groups and another of 17 groups. The energy boundaries of the group structure are presented in table I. Group split A is used to give a detailed description of the high- energy part of the neutron spectrum and the resonance energy range of tungsten where some of the secondary gammas are produced by neutron absorption. Groups 2 to 10 of group split A correspond to GAM-I1 fine groups covering the energy range from about 4 to 10 MeV where most of the neutron dose was expected to occur. Group B is less de-

_- ~ ..____

to 2.024 8. 2O8X1O5 to 4 . 0 7 6 ~ 1 0 ~ 4.076 2.024 to 8 . 6 5 2 ~ 1 0 ~ 8 . 6 5 2 ~ 1 0 ~ to 1.930 1.930 to 3 . 3 5 5 ~ 1 0 ~ 3 . 3 5 5 ~ 1 0 ~ to 9. 611X102 9. 611X102 to 3.536 3.536 to 1. 301 1.301 to 4. 785X101 4.785X101 to 1.760 1.760 to 5 . 0 4 3 ~ 1 0 ~ 5. O43X1O0 to 1.445 1.445 to 1.125 1.125 to 4. 140X10-1 4. 140X10-1 to 1. OOOX10-3

__._. - - . -~ --

TABLE I. - NEUTRON GROUP SPLIT

(a) Group split A

4

OUP

- 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 -

Group

9

(b) Group split B _- _ _ ~

eV eV

1 . 4 9 2 ~ 1 0 ~ to 8. 187X106 10 3. 355X1O3 to 5. 829X102 8. 187X106 to 5.488 11 5. 829X102 to 1.013 5.488 to 3.012 12 1.013 to 2. 902X1O1 3.012 to 1. 353 1 3 2.9O2X1O1 to 1.068 1.353 to 9 . 0 7 2 ~ 1 0 ~ 14 1.068 to 3.O59X1O0 9 . 0 7 2 ~ 1 0 ~ to 4.076 15 3. O59X1O0 to 1.125 4.076 to 1.111 16 1.125 to 4. 140x10-1 1.111 to 1 . 5 0 3 ~ 1 0 ~ 17 4. 140X10-1 to 1. OOOx10-3 1 . 5 0 3 ~ 1 0 ~ to 3 . 3 5 5 ~ 1 0 ~

-

- - -__ _ _ _ _

Energy Group Structure

Two neutron energy group splits were used to describe the neutron spectra: one of 30 groups and another of 17 groups. The energy boundaries of the group structure are

presented in table 1. Group split A is used to give a detailed description of the high­energy part of the neutron spectrum and the resonance energy range of tungsten where some of the secondary gammas are produced by neutron absorption. Groups 2 to 10 of

group split A correspond to GAM- II fine groups covering the energy range from about 4 to 10 MeV where most of the neutron dose was expected to occur. Group B is less de-

TABLE I. - NEUTRON GROUP SPLIT

(a) Group split A

Group Bmmdary energy ~~e;;:--- Gr=;J ~dary energy Values,-1 eV eV

-- ---- -- ---

I 1. 492x10 7 to 1. OOOxlO 7 16 8.208x105 to 4. 076x105

2 1.000 to 9.048)(106 17 4.076 to 2.024

3 9.048 to 8.187 18 2.024 to 8. 652x104

4 8. 187x106 to 7.408 19 8. 652x104 to 1. 930

5 7.408 to 6.703 20 1. 930 to 3. 355x103

6 6.703 to 6.065 21 3. 355x103 to 9. 611x102

7 6.065 to 5.488 22 9.611X102 to 3.536

8 5.488 to 4.966 23 3.536 to 1. 301

9 4.966 to 4.493 24 1. 301 to 4. 785X101

10 4.493 to 4.066 25 4.785x101 to 1. 760

11 4.066 to 3.329 26 1. 760 to 5.043)(100

12 3.329 to 2.725 27 5.043x100 to 1. 445

13 2.725 to 2.019 28 1.445 to 1. 125

14 2.019 to 1. 353 29 1. 125 to 4. 140xlO-1

15 1. 353 to 8. 208X105 30 4. 140xlO-1 to 1. 000xlO- 3 ----"------- -

(b) Group split B --~ --.~--- :1--- ------ ------

Group Boundary energy values, Group Bound:ry _~:~gy values, I eV

1 1. 492x10 7 to 8. 187X106 10 3. 355x103 to 5. 829x102

2 8. 187X106 to 5.488 11 5.829X102 to 1. 013

3 5.488 to 3.012 12 1. 013 to 2. 902x101

4 3.012 to 1. 353 13 2.902x101 to 1. 068

5 1. 353 to 9. 072X105 14 1. 068 to 3.059x100

6 9. 072x105 to 4.076 15 3.059x100 to 1. 125

7 4.076 to 1. 111 16 1.125 to 4. 140xlO- 1

8 1.111 to 1. 503x104 17 4. 140x10-1 to 1. 000xlO- 3

9 1. 503x104 to 3. 355X103

4

----------------___ 11 __ 11_11 Ifill I I I II 11 •• 111 ••• 11111111 II I ,., I

Group

1 2 3 4 5 6 7

TABLE n. - GAMMA GROUP SPLIT

(a) Group split A

Boundary energy value, e V

8. 25X1O6 to 7. 75X106 7.75 to 6.75 6.75 to 5.50 5.50 to 5.00 5.00 to 4.50 4.50 to 4.00 4.00 to 3.50 3.50 to 3.00

Group

9 10 11 12 13 14 15 16

Boundary energy value, e V

3. OOX106 to 2. 6Ox1O6 2.60 to 2.20 2.20 to 1.80 1.80 to 1.35 1.35 to 9 . 0 0 ~ 1 0 ~ 9 . 0 0 ~ 1 0 ~ to 4.00 4.00 to 2.60 2.60 to 1.00

Group

(b) Group split B

hundary energy value, eV

8. OOx106 to 5. 5OX1O6 5.50 to 5.00 5.00 to 4.50 4.50 to 4.00 4.00 to 3.50 3.50 to 3.00 3.00 to 2.60

:roup

8 9

10 11 12 13 14

3oundary energy value, eV

2. 6OX1O6 to 2 . 2 0 ~ 1 0 ~ 2.20 to 1.80 1.80 to 1. 35 1.35 to .90

.90 to .40

.40 to .260

.260 to .10

tailed and was used in the interest of reducing computer run time. The thermal group of both group structures (A and B) extends from 0.001 to 0.414 electron volt.

were used. Group split A was used in the calculation of the 8.00-MeV monoenergetic point gamma source. Group split B was used in the gamma transport calculation through the laminated shield. Group splits A and B differ only in that the first group of group split B was divided into three groups to provide a more adequate group structure for the point source calculation.

For the analysis of photon attenuation, the two energy group splits shown in table II

Secondary Photon Spectra

The use of tungsten as a shield against primary photons is highly effective; however, in the neutron flux field of a reactor this material gives rise to a considerable source of secondary gamma radiation. These secondary photons are a consequence of neutron ab- sorptions and inelastic scattering interactions with the tungsten nuclei. The secondary photon spectra for tungsten absorptions and inelastic scattering events are given in

5

TABLE II. - GAMMA GROUP SPLIT

(a) Group split A

Group Boundary energy value, Group Boundary energy value,

eV eV

1 8. 25X106 to 7. 75x106 9 3. 00X106 to 2. 60x106

2 7.75 to 6.75 10 2.60 to 2.20

3 6.75 to 5.50 11 2.20 to 1. 80

4 5.50 to 5.00 12 1. 80 to 1.35

5 5.00 to 4. 50 13 1. 35 to 9. 00x105

6 4.50 to 4.00 14 9. 00x105 to 4.00

7 4.00 to 3.50 15 4.00 to 2.60

8 3.50 to 3.00 16 2.60 to 1. 00

(b) Group split B

Group Boundary energy value, Group Boundary energy value,

eV eV

1 8. 00x106 to 5. 50X106 8 2. 60x106 to 2. 20x106

2 5.50 to 5.00 9 2.20 to 1. 80

3 5.00 to 4. 50 10 1. 80 to 1. 35

4 4.50 to 4.00 11 1. 35 to .90

5 4.00 to 3.50 12 .90 to .40

6 3.50 to 3.00 13 .40 to .260

7 3.00 to 2.60 14 .260 to .10

tailed and was used in the interest of reducing computer run time. The thermal group of both group structures (A and B) extends from 0.001 to 0.414 electron volt.

For the analysis of photon attenuation, the two energy group splits shown in table II were used. Group split A was used in the calculation of the 8. OO-MeV monoenergetic point gamma source. Group split B was used in the gamma transport calculation through the laminated shield. Group splits A and B differ only in that the first group of group split B was divided into three groups to provide a more adequate group structure for the point source calculation.

Secondary Photon Spectra

The use of tungsten as a shield against primary photons is highly effective; however, in the neutron flux field of a reactor this material gives rise to a considerable source of secondary gamma radiation. These secondary photons are a consequence of neutron ab­sorptions and inelastic scattering interactions with the tungsten nuclei. The secondary photon spectra for tungsten absorptions and inelastic scattering events are given in

5

TABLE III. - SECONDARY PHOTON SPECTRA

FOR TUNGSTEN

Energy group, Mev

Absorption spectra, MeV/absorption

8.00 to 5.50 5.50 to 5.00 5.00 to 4.50 4.50 to 4.00 4.00 to 3. 50 3.50 to 3.00 3.00 to 2.60 2.60 to 2.20 2.20 to 1.80 1. 80 to 1. 35 1.35 to .90 .90 to .40 .40 to .26 .26 to .10

0.720 .320 .260 .200 .750 .750 .580 .580 .650 .450 .500 .490 .120 . 00

Inelastic spectra, MeV/inelastic scattering

0.002 .002 .002 .002 .002 .005 .020 .030 .060 .700

1.000 .050 .050 . 00

~

table III. These spectra were derived from the data of reference 6. No secondary pho- ton sources other than tungsten were considered in this study.

Dose Conversion Factors

Two sets of neutron flux conversion factors were used: (1) the Hurst single scatter factors presented in reference 7, and (2) the first collision factors given in reference 8. These neutron dose conversion factors are listed in table IV for the two energy group splits A and B. The gamma flux conversion factors to rad per hour, shown in table V, were calculated using the photon energy absorption coefficients obtained from reference 9.

6

TABLE ID. - SECONDARY PHOTON SPECTRA

FOR TUNGSTEN

Energy group, Absorption spectra, I Inelastic spectra, I Mev MeV/absorption MeV/inelastic scatterin~

8.00 to 5.50 0.720 0.002 5.50 to 5.00 .320 .002 5.00 to 4.50 .260 .002 4.50 to 4.00 .200 .002 4.00 to 3.50 .750 .002 3.50 to 3.00 .750 .005 3.00 to 2.60 .580 .020 2.60 to 2.20 .580 .030 2.20 to 1. 80 .650 .060 1. 80 to 1. 35 .450 .700 1. 35 to .90 .500 1. 000 .90 to .40 .490 .050 .40 to .26 .120 .050 .26 to .10 .00 .00

table III. These spectra were derived from the data of reference 6. No secondary pho­ton sources other than tungsten were considered in this study.

Dose Conversion Factors

Two sets of neutron flux conversion factors were used: (1) the Hurst single scatter

factors presented in reference 7, and (2) the first collision factors given in reference 8.

These neutron dose conversion factors are listed in table IV for the two energy group

splits A and B. The gamma flux conversion factors to rad per hour, shown in table V,

were calculated using the photon energy absorption coefficients obtained from reference 9.

6

__ •• ___ • ____ •••• _---_ ••••• _--_. __ ._. __ • ___ 1

TABLE IV. - NEUTRON FLUX 1’V W S E CUNVKHS’IUN

1

Group

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15

First collision conversion,

rad/hr

.eutron/( cm2) (sec)

2. O O X ~ O - ~ 1.80 1.76 1.73 1. 69 1.62 1.58 1.55 1.44 1.40 1.35 1. 30 1.19

8.28 9.9ox10-6

(a) Group split A

3urst conversion, mrep/hr

ieutron/(cm 2 )(sec)

3roup

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17

;roup

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

(b) Group split B

Fir st collision conversion,

rad/hr 2 ieutron/( cm )( sec)

Fir st collision conversion, rad/hr

neutron/(cm 2 )(sec)

2. O O X ~ O - ~

1.70 1.48 1.08 8. 4OX1Om6 6.40 3. 61 I . 1 8 ~ 1 0 - ~

0

Hurst conversion, meP/hr

ieutron/( cm2)(se c)

6. 50X10-3 3.20

0

7

Group

1

2

3

4

5

6

7

8

9 10

11

12

13

14

15

TABLE IV. - NEUTRON FLUX TO DOSE CONVERSION

First collision

conversion,

rad/hr

neutron/( cm2)(sec)

2.00xlO- 5

1. 80

1. 76

1. 73

1. 69

1. 62

1. 58

1. 55

1. 44

1. 40

1. 35

1. 30

1.19 9.90XlO-6

8.28

(a) Group split A

First collision

mrep/hr conversion,

rad/hr

Bur" ronv.n'=. ~ G<oup

neutron/( cm2)(sec)

neutron/( cm2)( sec) -

1. 60XlO- 2 16 6.30xlO- 6

17 5.04

18 2.88

19 1.44

20

21

22

23 24

25

26 1. 40xlO- 2 27

1. 25 28

1. 08 29 8.80xlO- 3 30

(b) Group split B

Group First collision conversion,

rad/hr

neutron/( cm2)(sec)

1 2.00Xl0- 5

2 1. 70

3 1. 48

4 1. 08

5 8.40xlO- 6

6 6.40

7 3.61

8 1. 18Xl0-7

9 0

10

11

12

13

14

15 16

17

0

Hurst conversion,

mrep/hr

neutron/( cm2)( se c)

6.50Xl0- 3

3.20

0

7

11111111l11l1l111llllIIl II Ill I IIIIII

Group Gamma conversion, Group Gamma conversion,

photon/( cm2)(sec) photon/( cm2)(sec) rad/hr rad/hr

7. 828x10-6 7.250 6.430 5.712 5.345 4.895 4.513 4.102

9 10 11 12 13 14 15 16

Group

11 12 13 14

Group

1 2 3 4 5 6 7

3. 697X10-6 3.222 2.913 2.472 1.883 1.105 5. 886X10-7 3.240

Gamma conversion, rad/hr

photon/( cm2)( sec)

6. 510X10-6 5.712 5.345 4.895 4.513 4.102 3.697

Gamma conversion, rad/hr

photon/( cm2)( sec)

3. 322X10-6 2.913 2.472 1.883 1.105 5. 886X10-7 3.240

POINT SOURCE ANALYSIS

Neutron Attenuation - Lithium Hydride Spheres

The LiH medium was used to examine the effect on neutron dose of varying the Sn quadrature order, the elastic scattering order, and energy group structure. Since high- order Sn transport problems require longer computer running times, it is worthwhile to

puter run time.

Li H with densities of 0.750 and 0.6614 gram per cubic centimeter, respectively. ures 1 and 2 show the results on neutron dose rate of a P3 17 group transport calcula- tions with varying quadrature order from S16 to S8 in 117-centimeter radii sphere of LiH and Li H. These data indicate that the transport results for dose rate have con- verged at an Sn order of 16 for neutron penetrations up to 117 centimeters. Decreasing the Sn order to 12 or even 8 decreases the calculated neutron dose rate at the 117-

' investigate the effect of lower order calculations on dose in an effort to conserve com-

The study used a point uranium-235 fission source of neutrons in spheres of LiH and 6 Fig-

6

8

I1I111I11111111111111111111111111111

TABLE V. - GAMMA FLUX TO DOSE CONVERSION

(a) Group split A

Group Gamma conversion, Group Gamma conversion,

rad/hr rad/hr

photon/( cm2)(sec) photon/( cm2)(sec)

1 7. 828XlO-6 9 3.697xI0-6

2 7.250 10 3.222 3 6.430 11 2.913 4. 5.712 12 2.472 5 5.345 13 1. 883 6 4.895 14 1.105 7 4.513 15 5. 886Xl0-7

8 4.102 16 3.240

(b) Group split B

Group Gamma conversion, Group Gamma conversion,

rad/hr rad/hr

photon/( cm2)(sec) photon/( cm2)(sec)

1 6. 510XlO-6 8 3. 322xl0- 6

2 5.712 9 2.913 3 5.345 10 2.472 4 4.895 11 1. 883 5 4.513 12 1.105 6 4.102 13 5. 886Xl0-7

7 3.697 14 3.240

POINT SOURCE ANALYSIS

Neutron Attenuation - Lithium Hydride Spheres

The LiH medium was used to examine the effect on neutron dose of varying the Sn quadrature order, the elastic scattering order, and energy group structure. Since high­order S transport problems require longer computer running times, it is worthwhile to n

, investigate the effect of lower order calculations on dose in an effort to conserve com-

puter run time. The study used a point uranium-235 fission source of neutrons in spheres of LiH and

Li6H with densities of 0.750 and 0.6614 gram per cubic centimeter, respectively. Fig­ures 1 and 2 show the results on neutron dose rate of a P 3 17 group transport calcula­

tions with varying quadrature order from S16 to S8 in 117-centimeter radii sphere of LiH and Li6H. These data indicate that the transport results for dose rate have con­verged at an Sn order of 16 for neutron penetrations up to 117 centimeters. DecreaSing the Sn order to 12 or even 8 de creases the cal culated neutron dose rate at the 117-

8

L c

7 10-8 c

L

e N-

E u

L al

al + n

e

c

t \ '8

1 - 100 120

I 80

I - I I I I I 60

Radius, cm

Figure 1. - Variation of neutron dose rate through lithium hydride sphere as function of Sn order (n - 8, 12 or 16). Point

40 0 20 10-13

uranium-235 fission source; 17 neutron energygroups; elastic scattering order Pp

9

If I

1 20

_I 1 40

\\ ~ ,

~ ~ ~ ~ ,~ ,

~, , '\-"

"~ ~,

~, "~, ~~ "\ ,

~'\ ~~ " ~,

'\, n

\16 '\ 1~

1 I I 60 80 100 120

Radius, cm

Figure 1. - Variation of neutron dose rate through lithium hydride sphere as function of Sn order (n • 8, 12 or 16). Point uranium-235 fission source; 17 neutron energy groups; elastic scattering order P3.

9

10

u e;: c e "5 '" c:

-::;. .... ..c: =a E

N-E u

c:: ~ :::;J

'" c:

'" ~ :::;J

s: .... '" 0-

'" E '" ~

"CI X

N

~ ...

10

10-8

10-9

10-10

10-13 L--__ L--_-----,JL--_-----' __ ---c'c--_------'-__ ~-----'---80 100 o

Radius, cm

Figure 2. - Variation of neutron dose rate through Iithium-6 hydride sphere as function of Sn order (n = 8, 12 or 16). Point uranium-235 fission source; 17 neutron energy groups; elastic scattering order P3·

120

TABLE VI. - RELATIVE FLUX VALUES FOR VARYING S,, AND ELASTIC SCATTERING ORDERS THROUGH

A LITHIUM HYDRIDE MEDIUM WTTH 17 NEUTRON ENERGY GROUPS

Radius, r = 20 c m Radius, r = 70 c m calculation

order

'3%

'3'12

'3'16

p1s16

Radius, r = 117 c m ~~ ~

Group 4 Group 7

5 . 0 3 9 ~ 1 0 - ~ 4 . 8 2 1 ~ 1 0 - ~

5.206 4.950

5.177 4.969

5.420 3.167

Group 1

8.342X10-'

8.566

8.601

1 . 0 3 8 ~ 1 0 - ~

Group 1 Group 4

1 . 2 6 8 ~ 1 0 - ~ ~ 1.32x10-11

1.462 8. 31

1.569 8.85

1.917 8.067

5. 150X10-11

6.482

6.885

3.975

1 . 1 6 3 ~ 1 0 - ~ ~ 1 . 9 4 7 ~ 1 0 - ~ ~ 1. O O O X ~ O - ~ ~

1.437 2.348 1.200

1.592 2.583 1.311

1.925 2.522 8. 30

centimeter position of the sphere by as much as 10 to 25 percent. The Sn quadrature coefficients used for this study were moments-modified ordinates and weights.

Table VI shows the relative flux values for this ser ies of transport calculations at vari- ous radii through the spherical medium. At a radius of 117 centimeters, the flux values for the three representative neutron groups are not completely converged at s16.

The next consideration was the determination of the effect on dose when the elastic scattering order is varied. The Sn quadrature order was held constant at 16 while the elastic scattering order was changed from P3 to Ply again with the point fission source in LiH. The P1s16 17-group transport calculation w a s then compared with the P3s16 computation and the data plotted in figure 3. At 110 centimeters, the P3S16 calculations show a resulting dose rate almost twice the value of the PIS16 computation. Calcula- tions with higher order elastic scattering were not performed because the GAM I1 cross section code is limited to a P3 scattering order computation. However, reference 10 shows that for deep (120-cm) penetration of neutrons in water, the dose values have con- verged at the P3 scattering order.

A comparison was made between a 17- and 30-group structure (see table I) problem. A dose rate was computed with the 30 broad neutron groups and the same point fission source in a LiH sphere using a P3S16 transport calculation. figure 3. At 116 centimeters, near the outer boundary of the LiH sphere, the 30-group dose rate calculation gave results more than twice that of the corresponding 17-group computation.

in part, to the cross-section averaging procedure used by the GAM-IT computer code. GAM-I1 generates an infinite medium flux spectrum for given input source spectrum and material composition. This flux spectrum is then used to average the 99 GAM-II fine

Although the doses may have converged, the fluxes may not be completely converged.

Finally, the effect of varying neutron group structure on dose rate was examined.

The results are shown in

The large difference in the doses with 30 energy groups and 17 energy groups is due,

11

TABLE VI. - RELATIVE FLUX VALUES FOR VARYING Sn AND ELASTIC SCATTERING ORDERS THROUGH

A LITHIUM HYDRIDE MEDIUM WITH 17 NEUTRON ENERGY GROUPS

[Boundary energy values: 14.92 to 8.187 MeV for group 1; 3.01 to 1.35 MeV for group 4;

and 0.407 to 0.111 MeV for group 7.]

S ~ RadiUS, r = 20 em RadiUS, r = 70 em RadiUS, r - 117 em

ealeul'!.tion I I--order Group 1 Group 4 Group 7 Group 1 Group 4 Group 7 Group 1 Group 4 Group 7

P3S8 8.342><10-8 5.039><10-6 4.821><10-6 1.268X10-11 7.32X10- 11 5.750x1O- 11 1. 163X10-14 1. 947X10- 14 1. 000x1O -14

P 3S12 8.566 5.206 4.950 1.462 8.31 6.482 1. 437 2.348 1. 200

P 3S16 8.601 5.177 4.969 1.569 8.85 6.885 1. 592 2.583 1. 317

P 1S16 1. 038x1O-7 5.420 3.167 1. 977 8.067 3.975 1. 925 2.522 8.30

centimeter position of the sphere by as much as 10 to 25 percent. The Sn quadrature coefficients used for this study were moments-modified ordinates and weights.

Although the doses may have converged, the fluxes may not be completely converged. Table VI shows the relative flux values for this series of transport calculations at vari­ous radii through the spherical medium. At a radius of 117 centimeters, the flux values for the three representative neutron groups are not completely converged at S16'

The next consideration was the determination of the effect on dose when the elastic scattering order is varied. The S quadrature order was held constant at 16 while the n elastic scattering order was changed from P 3 to P l' again with the point fission source in LiH. The P 1 S16 17-group transport calculation was then compared with the P 3S16 computation and the data plotted in figure 3. At 110 centimeters, the P 3S16 calculations show a resulting dose rate almost twice the value of the P 1 S16 computation. Calcula­tions with higher order elastic scattering were not performed because the GAM II cross section code is limited to a P 3 scattering order computation. However, reference 10 shows that for deep (120-cm) penetration of neutrons in water, the dose values have con­

verged at the P 3 scattering order. Finally, the effect of varying neutron group structure on dose rate was examined.

A comparison was made between a 17- and 30-group structure (see table 1) problem. A dose rate was computed with the 30 broad neutron groups and the same point fission source in a LiH sphere using a P 3S16 transport calculation. The results are shown in figure 3. At 116 centimeters, near the outer boundary of the LiH sphere, the 30-group dose rate calculation gave results more than twice that of the corresponding 17-group computation.

The large difference in the doses with 30 energy groups and 17 energy groups is due, in part, to the cross-section averaging procedure used by the GAM-II computer code. GAM-II generates an infinite medium flux spectrum for given input source spectrum and material composition. This flux spectrum is then used to average the 99 GAM-II fine

11

- 30groups --- P$16 17 groups --- PIS16 17 groups

Figure 3. - Dose rate variation with elastic scattering order (P1 or P3) and neutron energy group structure through lithium hydride sphere for a point source of uranium-235 fission neutrons.

12 12

_ .. L ____ L 60

Radius, cm

P3S16 30 groups --- P3S16 17 groups --- P1S16 17 groups

80 100

Figure 3, - Dose rate variation with elastic scattering order (PI or P3) and neutron energy group structure through lithium hydride sphere for a point source of uranium-235 fission neutrons.

120

I

Radius, 140-cm LPH sphere (density, 0.66138 g$m2) --- 140-cm UH sphere (density, 0.7% glcm 1

I- \\

t 2

E-

10-5 L\ \ \

0 1 2 3 4 5 6 7 8 I"

Energy, E, MeV

Figure 4. - Neutron spectrum through spheres of lithium hydride and lithium-6 hydride. Point uranium-235 fission source; u) neutron groups; P$16 S, transport.

13

I

I

10-9

Radius, cm

90 , " , ,

--- 140-cm Lj6H sphere (density, O. 66138 g/~m2) - - - 140-cm LiH sphere (density, 0.750 g/cm )

................ -------........ .................. ,

.........

"

o 2 3 4 5 6 7 8 9 10 11 12 13 14 Energy, E, MeV

Figure 4. - Neutron spectrum through spheres of lithium hydride and Iithium-6 hydride. Point uranium-235 fission source; 30 neutron groups; P3S16 Sn transport.

13

group structure so that cross sections for various broad group energy structures can be obtained. The spectrum in the LiH far from the source becomes much harder (i. e., the average energy of the spectrum increases) than even the uranium-235 fission spectrum. Thus, averaging over infinite medium spectra may be inappropriate for these calcula- tions. However, it is expected that the more detailed 30-group split is less sensitive than the corresponding 17-group split to the method of averaging the neutron cross sec- tions. This hardening effect is shown in figure 4 for the point uranium-235 fission spec-

6 t rum calculations in spheres of LiH and Li H. The differential neutron number (neutrons/(MeV)(sec)) is plotted as a function of energy at various positions in spheres of LiH and Li H for the two energy group splits. From these figures the distinct flat- tening of the spectral curves is seen at the 90- and 120-centimeter positions. The aver- age energies of these spectra at various positions are given in table Vn.

6

TABLE VII. - AVERAGE ENERGIES OF NEUTRONS IN LiH

AND Li6H FOR A POINT ISOTROPIC FISSION

SOURCE (30 GROUPS)

Radius, cm

0

20

60

90

120

Average energy, E, MeV

Li H

2.00

1.82

2.67

3.64

4 .20

Li6H

2.00

1 .91

2.99

4 .13

4 .67

Figure 5 is a comparison of a 30-group P3S16 transport calculation and a QAD point kernel computation of neutron dose through LiH with Kam's Monte Carlo results (ref. 11). Though the Sn transport differs with the Monte Carlo results at 90 centimeters, the Sn data do f a l l within the three sigma er ror bar of the Monte Carlo calculation. The differ- ences between the s, and Monte Carlo results can be due to differences in the fine group neutron cross sections used by these two methods, the inadequacy of the GAM I1 cross- section averaging process, too few broad neutron groups used for the Sn calculation and to the choice of the moments-modified S, quadrature set.

sections for natural lithium and the following modified Albert- Welton coefficients (ref. 12):

The QAD data shown in figure 5 are the result of using two neutron removal cross

14

group structure so that cross sections for various broad group energy structures can be

obtained. The spectrum in the LiH far from the source becomes much harder (i. e., the

average energy of the spectrum increases) than even the uranium-235 fission spectrum.

Thus, averaging over infinite medium spectra may be inappropriate for these calcula­

tions. However, it is expected that the more detailed 30-group split is less sensitive

than the corresponding 17 -group split to the method of averaging the neutron cross sec­

tions. This hardening effect is shown in figure 4 for the point uranium-235 fission spec­

trum calculations in spheres of LiH and Li 6H. The differential neutron number

(neutrons/(MeV)(sec» is plotted as a function of energy at various pOSitions in spheres

of LiH and Li 6H for the two energy group splits. From these figures the distinct flat­

tening of the spectral curves is seen at the 90- and 120-centimeter pOSitions. The aver­

age energies of these spectra at various pOSitions are given in table VIT.

TABLE VII. - AVERAGE ENERGIES OF NEUTRONS IN LiH

AND Li6H FOR A POINT ISOTROPIC FISSION

Radius,

em

0

20

60

90

120

SOURCE (30 GROUPS)

Average energy,

LiH

2.00

1. 82

2.67

3.64

4.20

2.00

1. 91

2.99

4.13

4.67

Figure 5 is a comparison of a 30-group P 3S16 transport calculation and a QAD point

kernel computation of neutron dose through LiH with Kam's Monte Carlo results (ref. 11).

Though the Sn transport differs with the Monte Carlo results at 90 centimeters, the Sn

data do fall within the three sigma error bar of the Monte Carlo calculation. The differ­

ences between the Sn and Monte Carlo results can be due to differences in the fine group

neutron cross sections used by these two methods, the inadequacy of the GAM II cross­

section averaging process, too few broad neutron groups used for the Sn calculation and

to the choice of the moments-modified Sn quadrature set.

The QAD data shown in figure 5 are the result of using two neutron removal cross

sections for natural lithium and the following modified Albert-Welton coefficients

(ref. 12):

14

0 Monte Carlo calculations (ref. 11) - Sn transport results for P3S16

QAD calculations 30 neutron groups

A Lithium rem Val cross section = 0.08763 cm l g

B Lithium re oval cross section =

-- -- s

0.1oOO cm 7 l g

u 120

I I 80 100

I 60

Radius, cm

I I I I 40 20

I

Figure 5. - Comparison of 30-group P3S transport, QAD, and Monte Carlo calculations of the neutron dose rates in l i th ium hydride sphere for a point source of uranium-% fission neutrons.

15

10-7

u <l>

'" Vi

'" e "5 10-8 <l>

'" ~ .s:: ;:; g

N-

E ~ ",-

e 10-9 "5 <l>

'" <l>

~ :::l

~

~ <l>

E 10-10 <l>

is -0 X

N

~ ...

I 20

I 40

I 60

Radius, cm

o Monte Carlo calculations (ref. 11)

Sn transport results for P3S16 3D neutron groups

---- QAD calculations

80

A Lithium rem~val cross section =

0.08763 cm /g B Lithium re~oval cross section =

0.1000 cm /g

100

Figure 5. - Comparison of 3D-group P3S16 transport, QAD, and Monte Carlo calculations of the neutron dose rates in lithium hydride sphere for a point source of uranium-235 fission neutrons.

120

15

10-7

lo-!

Sn transport (single scatter dose conversion, ref. 8)

cross section = 0.11% cm*/g) 0 QAD results (Lithium removal

I I 1 I 0 20 40 60 80 100 120

10-13 I Sphere radius, cm

Figure 6. - Comparison of 30-group P SI6 tr!nsport and QAO neutron dose rates through l i thium-6 h y d r i d (density, 0.66138 g/cm3) for a point source of uranium-235 fission neutrons.

16

U '" '" c: e ::; '" c: -.... .s: 'i3 E

N-

E ~

c:-e ::; '" c:

'" u .... '" 0

'" .... 8. '" 1;; .... ~ 0 -c x

N

'f& ....

16

10-8

10-9

10-10

10-11

10-12

--- 5n transport (single scatter dose conversion, ref. 8)

o QAD results (lithium removal cross section = 0.1156 cm2/g)

Sphere radius, cm

Figure 6. - Comparison of 3D-group P3S16 transport and QAD neutron dose rates through lithium-6 hydride (density, 0.66138 g/cm3) for a point source of uranium-235 fission neutrons.

9 2 a1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.29x10 mrep/(hr-W)cm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.290 ~ 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.830 CY^........................................... 0.580

Curve A uses the slab removal cross section for lithium of 0.0876 square centimeter per gram obtained from reference 12. Curve B uses a distributed removal cross section of 0.100 square centimeter per gram obtained by fitting the removal cross section for lith- ium to the Sn transport data. Reference 13 presents a more detailed discussion for ob- taining distributed neutron removal cross sections for lithium and lithium-6.

neutron attenuation in a sphere of Li H. The good agreement established between the Sn transport and the QAD calculation is the result of correcting the neutron removal cross section for lithium. A correction was made to the distributed removal cross section (0.100 cm /g) determined in the preceding LiH study to account for the difference in density between natural lithium and lithium-6. Since the overall scattering cross sec- tions for lithium and lithium-6 are quite similar, this density correction to the neutron removal cross section has proved to be adequate. The value used in the QAD calculation of figure 6 to represent the distributed removal cross section for lithium-6 was 0.1156 square centimeter per gram.

Figure 6 shows the results of an Sn transport and QAD calculation of point source 6

2

Photon Attenuation - Tungsten Sphere

The Sn transport calculations were made for a point monoenergetic photon source of 8.00 MeV in an 18-centimeter tungsten sphere. The tungsten density was taken as 19.3 grams per cubic centimeter. compared, at various positions through the tungsten, with the moments method results reported by Goldstein and Wilkens (ref. 14). same results as the moments method. The Sn transport calculation used to study this problem had 16 photon energy groups (see table IT), an Sn order of 16, and P3 and P1 Compton scattering orders. The energy group spacing of 16 was considered detailed enough in the high-energy region to be adequate for this photon study.

are shown in figure 7. Good agreement is found between the two methods up to approxi- mately 7 centimeters of tungsten. At this point, the P3s16 transport calculation begins to diverge from the moments method.

The photon dose rates calculated by this method were

The point kernel code (QAD) gives the

The dose rates generated by the two calculational method (moments and transport)

17

· .7. 29x109 mrep/(hr-W)cm2

0.290 0.830 0.580

Curve A uses the slab removal cross section for lithium of 0.0876 square centimeter per gram obtained from reference 12. Curve B uses a distributed removal cross section of 0.100 square centimeter per gram obtained by fitting the removal cross section for lith­ium to the Sn transport data. Reference 13 presents a more detailed discussion for ob­taining distributed neutron removal cross sections for lithium and lithium-6.

Figure 6 shows the results of an Sn transport and QAD calculation of point source neutron attenuation in a sphere of Li6H. The good agreement established between the Sn transport and the QAD calculation is the result of correcting the neutron removal cross section for lithium. A correction was made to the distributed removal cross section (0.100 cm2/g) determined in the preceding LiH study to account for the difference in density between natural lithium and lithium-6. Since the overall scattering cross sec­tions for lithium and lithium-6 are quite similar, this density correction to the neutron removal cross section has proved to be adequate. The value used in the QAD calculation

of figure 6 to represent the distributed removal cross section for lithium-6 was 0.1156 square centimeter per gram.

Photon Attenuation - Tungsten Sphere

The S transport calculations were made for a point monoenergetic photon source of n

8.00 MeV in an 18-centimeter tungsten sphere. The tungsten density was taken as 19.3 grams per cubic centimeter. The photon dose rates calculated by this method were compared, at various positions through the tungsten, with the moments method results reported by Goldstein and Wilkens (ref. 14). The point kernel code (QAD) gives the same results as the moments method. The Sn transport calculation used to study this problem had 16 photon energy groups (see table II), an Sn order of 16, and P 3 and P 1 Compton scattering orders. The energy group spacing of 16 was considered detailed enough in the high-energy region to be adequate for this photon study.

The dose rates generated by the two calculational method (moments and transport) are shown in figure 7. Good agreement is found between the two methods up to approxi­mately 7 centimeters of tungsten. At this point, the P 3S16 transport calculation begins to di verge from the moments method.

17

Moments method and point kernel (QADI results --- 16-Group transport

A '3'16 p1s16

I 16

1 I 12 14

I 1 I 1 2 4 6 8 10

Radius, cm

Figure 7. - Comparison of dose rates calculated by Sn transport and moments methods for 8.M-MeV point source in tungsten sphere.

18 18

c­o 15 .s:: c. a>

~ 10-8

~

~ a>

rt; L­

a> ~ -c x

N

'f& 10-9 ....

--- Moments method and pOint kernel (QAD) results

16-Group transport A P3S16

B P1S16

10-10 '--__ '----__ '--1 __

o 2 4 1 6

1 8

Radius, cm

1 10

1 12

1 14

1 16

Figure 7. - Comparison of dose rates calculated by Sn transport and moments methods for 8. OQ-MeV point source in tungsten sphere.

LAMINATED SHIELD ANALYSIS

Radius

The final portion of this study examines a spherical reactor-laminated shield com- bination. A 2.5-megawatt (thermal power) fast reactor was enclosed in a 471 laminated

6 tungsten-Li H shield. The reactor core and reflector composition are given in table VIII. This reactor configuration was chosen because the neutron and photon atten- uation problems are similar to those that might be encountered in a typical space power reactor shield (ref. 15).

Element

TABLE VIII. - SIZE AND COMPOSITION OF

REACTOR AND SHIELD ~

Regi

1

~~

2

Inner, cm

0 ~~

18.00

29.00

36.62

46.78

54.40

56.94

Outer, 7 18.00 I U-233

W

0 ~ i ?

I 29.00 W I Li7

48.781w I

54.40 H I Li6} Li6H

11' 1 :i6} Li6H

ktom density, atom/( b)( cm)

0.009357 .026849 .004686 .018897

0.06022 -002 34 3

0.056837 .056837

0.0632

0.056837 .056837

0.0632

0.056837 .056837

19

LAMINATED SHIELD ANALYSIS

The final portion of this study examines a spherical reactor-laminated shield com­bination. A 2. 5-megawatt (thermal power) fast reactor was enclosed in a 41T laminated tungsten-Li6H shield. The reactor core and reflector composition are given in table VIII. This reactor configuration was chosen because the neutron and photon atten­uation problems are similar to those that might be encountered in a typical space power reactor shield (ref. 15).

TABLE Vlll. - SIZE AND COMPOSITION OF

REACTOR AND SHIELD

Region Radius Element Atom density,

atom/(b)( em) Inner, Outer,

em em

1 0 18.00 U-233 0.009357

w .026849 Li7 .004686

0 .018897 -

2 18.00 29.00 W 0.06022 Li7 .002343

l 3 29.00 36.62 H } Li6H 0.056837

Li6 .056837

l 4 36.62 46.78 W 0.0632

5 46.78 54.40 H }Li6H 0.056837

Li6 .056837

,- 6 /54.40 56.94 w 0.0632

I 7 56.94 117 H }Li6H 0.056837

Li6 .056837

19

teflector - - -

~

D

-i6H 4

w __.

L 40

Li6H -

Sn transport results for

QAD results P3S16 30 neutron groups

A I r / p = 0.0876 cm2/g B z r / p = 0.1156 cm2/g

---

1. L 50 60

Radius, cm

1 - I I 1 I 110 100 70 80 90

Figure 8. - Comparison of neutron dose rates in laminated shield for 30-group P$16 transport computation and QAD calculation for the model fast reactor.

20

104

L. 102 .c "a E ",'

E '" v> 0 "C

C e "'5

101 '" z

10-2

20

Reactor core Reflector U6H W U6H W

I

Sn transport results for P3S 16 30 neutron groups

QAD results

I

A £r/p = 0.0876 cm2/g B £r/p = 0.1156 cm2/g

U6H

I I I ~I

I 1 --I: L 1 I

0 10 20 30 40 50 60 70 80 90 100 110 120 Radius, cm

Figure 8. - Comparison of neutron dose rates in laminated shield for 3O-group P3S16 transport computation and QAD calculation for the model fast reactor.

Neutron Dose Analysis

The initial portion of this analysis will be concerned with the neutron dose rate from the model reactor-laminated shield. From the point source study, it was decided to use a P3s16 30-group transport calculation for the laminated shield.

computations of the neutron dose in the laminated shield. The dotted curves A and B are QAD calculations for two values of the neutron removal cross section for lithium. Curve A uses the lithium slab removal cross section of 0.0876 square centimeter per gram. These data show that by using this value for removal cross sections the results may differ from the Sn transport data by as much as a factor of 6 at a radius of 117 cen- timeters in the shield. Curve B utilizes the removal cross section for lithium of 0.1156 square centimeter per gram as determined in the preceding point source analysis. These results show that the QAD and Sn transport calculations differ by only 50 percent at a radius of 117 centimeters. moval cross section used for tungsten was 0.0110 square centimeter per gram.

Figure 8 is a comparison of a 30-group P3S16 transport calculation and two QAD

For both of these QAD calculations, the neutron re-

Secondary Gamma Source Analysis

The final analysis of this study will examine the major contributor to the dose rate emanating from this shield. The secondary gammas produced by tungsten neutron ab- sorptions and inelastic scatterings result in dose rates several orders of magnitude greater than the dose from the primary core gammas. The tungsten reflector used in this reactor configuration is thick enough to significantly reduce the importance of the primary gammas and these will warrant no further discussion. Other possible sources of secondary gammas such as Li H will also be neglected.

The calculational procedure used to determine the dose rates from these secondary sources is as follows:

source neutron)) is first determined for the tungsten regions by an Sn neutron transport calculation. The results are then used to evaluate a total photon source strength and spatial distribution for each tungsten region.

Sn transport calculation to determine the dose of these secondary gammas through the remainder of the shield.

order (P1 or P3) influenced the total number of absorptions and inelastic scattering events calculated for the tungsten regions. A variation in energy group structure was

6

(1) The total number of absorptions and inelastic scattering (events/(cm 3 )(sec/

(2) These computed strengths and distributions are then used by either QAD or the

From the Sn transport calculations it was found that a variation in elastic scattering

21

II

Neutron Dose Analysis

The initial portion of this analysis will be concerned with the neutron dose rate from

the model reactor-laminated shield. From the point source study, it was decided to use

a P 3816 30-group transport calculation for the laminated shield. Figure 8 is a comparison of a 30-group P 3816 transport calculation and two QAD

computations of the neutron dose in the laminated shield. The dotted curves A and B are QAD calculations for two values of the neutron removal cross section for lithium. Curve A uses the lithium slab removal cross section of 0.0876 square centimeter per gram. These data show that by using this value for removal cross sections the results may differ from the 8n transport data by as much as a factor of 6 at a radius of 117 cen­timeters in the shield. Curve B utilizes the removal cross section for lithium of O. 1156 square centimeter per gram as determined in the preceding point source analysis. These results show that the QAD and 8n transport calculations differ by only 50 percent at a radius of 117 centimeters. For both of these QAD calculations, the neutron re­moval cross section used for tungsten was 0.0110 square centimeter per gram.

Secondary Gamma Source Analysis

The final analysis of this study will examine the major contributor to the dose rate emanating from this shield. The secondary gammas produced by tungsten neutron ab­sorptions and inelastic scatterings result in dose rates several orders of magnitude

greater than the dose from the primary core gammas. The tungsten reflector used in this reactor configuration is thick enough to significantly reduce the importance of the primary gammas and these will warrant no further discussion. Other possible sources of secondary gammas such as Li 6H will also be neglected.

The calculational procedure used to determine the dose rates from these secondary sources is as follows:

(1) The total number of absorptions and inelastic scattering (events/(cm3)(sec/ source neutron)) is first determined for the tungsten regions by an 8n neutron transport calculation. The results are then used to evaluate a total photon source strength and spatial distribution for each tungsten region.

(2) These computed strengths and distributions are then used by either QAD or the 8n transport calculation to determine the dose of these secondary gammas through the remainder of the shield.

From the 8n transport calculations it was found that a variation in elastic scattering order (P 1 or P 3) influenced the total number of absorptions and inelastic scattering events calculated for the tungsten regions. A variation in energy group structure was

21

6xg-3 PIS16 17 group; P3s16 17 groups All curves coincided

2 -

I 18 20 22 24 26 28

Radius, cm (a) Reflector (18.0 to 29.0 cm).

- P$16 17 and 30 groups coincided 8r-5 30

I 48

Radius, cm (b) Tungsten shell 1 (36.62 to 46.78 cm). 6 ~ 1 0 - ~

- P3S16 17 and 30 groups coincided

--- P1s16 17 groups 4 -

2 -

0 I I I I I 1 54 55 56 57

Radius, cm

(c) Tungsten shel l 2 (54.40 to 56.94 cm).

Figure 9. - Relative distr ibution of absorptions in tungsten regions of model fast reactor and shield.

22 22

4

2

O~----~-----L----~----22 24 26 28

u ; 6

"" E ~ C o

~ 4 ~ .c '" Q)

> ~ 2 Q)

0::

4

2

18 20

38

Radius. em

(a) Reflector (l8. 0 to 29.0 em).

--- P3S16 17 and 30 groups coincided

--- P1S16 17groups

40 42 44 46 Radius. cm

(b) Tungsten shell 1 (36.62 to 46. 78 cm).

-- P3S 16 17 and 30 groups coincided

--- P1S16 17 groups

O~~--~-----L----~---56 57 54 55

Radius. cm

(c) Tungsten shell 2 (54.40 to 56.94 em).

30

48

Figure 9. - Relative distribution of absorptions in tungsten regions of model fast reactor and shield.

also studied. Changing the total number of energy groups from 17 to 30 had little effect on either the secondary gamma source strength or distribution.

actions in the reflector, first tungsten region, and in the final tungsten region for P3s16 (17- and 30-group) and a P3s16 (17-group) transport calculations. As can be seen from these figures, the relative distributions for both absorptions and inelastic scattering events a re for the most part the same for either the 30-group neutron structure or the

Figures 9 and 10 show the relative distribution of absorptions and inelastic inter-

4x1V3 PIS16 17 groups

P3516 30 groups

18 20 22 24 26 30 28

1 6 ~ 1 0 - ~ r

1.6

1.2

. 8

. 4

Radius, cm

(a) Reflector (18 to 29 cm).

----

I U 42 44 46

I 40

I 38

Radius, cm

(b) Tungsten shel l l(36.60 to 46.78 cm).

I 48

I Radius, cm

(c) Tungsten shel l 2 (54.40 to 56.94 cm).

Figure 10. - Relative distribution of inelastic scattering events in tungsten regions of the model fast reactor and shield.

23

I

also studied. Changing the total number of energy groups from 17 to 30 had little effect on either the secondary gamma source strength or distribution.

Figures 9 and 10 show the relative distribution of absorptions and inelastic inter­actions in the reflector, first tungsten region, and in the final tungsten region for P 3816 (17- and 30-group) and a P 3816 (17-group) transport calculations. As can be seen from these figures, the relative distributions for both absorptions and inelastic scattering events are for the most part the same for either the 30-group neutron structure or the

VI u ~ .!!! Q)

.~ Q)

>

~ Q)

""

12

8

4

036

I 38

Radius, cm

(a) Reflector (18 to 29 cm).

I 40 42

Radius, cm

1. 6x10-6 (b) Tungsten shell 1 (36.60 to 46. 78 cm!.

1.2

.8

.4 54

- - - - P3S 16 17 groups --- P3S16 30 groups - - P1S16 17 groups

I I 55 56 Radius, cm

(e) Tungsten shell 2 (54.40 to 56. 94 em!.

Figure 10. - Relative distribution of inelastic scattering events in tungsten regions of the model fast reactor and shield.

23

I

Group Energy boundaries, eV

1 14.920~10~ to 8.187~10~

3 5.488 to 3.012 4 3.012 to 1.353 5 1.353 to 9.072~10~ 6 9.072~10~ to 4.076 7 4.076 to 1.11

2 8.187 to 5.488

I

Region 6 (tungsten)

'r l-l I I I I I I I I I I I

1 0 ~ 7 ' 1 7 1 1 6 1 1 5 ' 1 4 13 12 11 10 9 8 7 6 5 4

1 L L I 3 2 1

Energy groups (Scale does not represent eigher equal energy or lethargy intervals)

Figure 11. - Absorptions as function of energy group w i th in two tungsten shells as determined by P1S16 and P3s16 transport calculations for model fast reactor.

24

c e ::; '" c

'" ~ ::> 0 V'> ---=-u ~

M-

E u

"5i c 0

~ ~ .c

-..$.-

24

11111111 I 11111111. II I

Group Energy boundaries, eV

1 14. 920xl06 to 8. 187x106

2 8. 187 to 5.488 3 5.488 to 3. 012 4 3.012 to 1. 353 5 1.353 to 9. 072x105

6 9. 072x105 to 4. 076 7 4.076 to 1.11 8 1. 11 to 1. 503xl04 9 1. 503xl04 to 3. 355xl03

10 3. 355Xl~ to 5.829xlOZ 11 5. 820xlu- to 1.013 12 1.013 to 2. 902x101

13 2. 902x101 to 1. 068 14 1. 068 to 3. 059x100

15 3. 059x100 to 1. 125 16 1. 125 to 4. 14xlO-1 17 4. 14xlO-1 to 1. OOxlO-3

Region 4 (tungsten)

10-4

10-5

Region 6 (tungsten)

10-7L--L __ ~~ __ -L __ L-~ __ -L __ L--L __ ~~L--L--~~--~--~~

17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 Energy groups (Scale does not represent eigher equal energy or lethargy intervals)

Figure 11. - Absorptions as function of energy group within two tungsten shells as determined by PIS16 and P3S16 transport calculations for model fast reactor.

17-group structure. The P1 and P3 elastic scattering order gives essentially the same secondary production in the reflector, in the first tungsten layer they differ by about 10 percent, and in the final tungsten layer the difference amounts to about 20 percent.

of neutron energy for the reflector and two tungsten regions of the laminated shield for the 17 neutron energy group split. the absorptions take place in energy groups 6 to 12 (907 keV to 29 eV) with the maximum occurring in group 8 (111.1 to 15 keV). tion of the inelastic scattering events take place in energy groups 3 to 7 (5.49 to

Figures 11 and 12 show the absorptions and inelastic scattering events as functions

From figure 11 it can be seen that a large portion of

From figure 12 it can be seen that a large por-

4.08 meV).

10-2

10-6

'3'16

calculation-, - 17-group

\ \

id, Region 6 (tungsten) I

4 I I I I I I I

17 t o 10 9 8 7 6 5 4 3 2 1 Energy groups (Scale does not represent either

equal energy or lethargy intervals)

Figure 12. -Tungsten inelastic scattering events as funct ion of energy group w i th in two tungsten shells for model fast reactor.

25

I

17 -group structure. The P 1 and P 3 elasti c scattering order gives essentially the same secondary production in the reflector, in the first tungsten layer they differ by about 10 percent, and in the final tungsten layer the difference amounts to about 20 percent.

Figures 11 and 12 show the absorptions and inelastic scattering events as functions of neutron energy for the reflector and two tungsten regions of the laminated shield for the 17 neutron energy group split. From figure 11 it can be seen that a large portion of the absorptions take place in energy groups 6 to 12 (907 keV to 29 eV) with the maximum

occurring in group 8 (111. 1 to 15 keV). From figure 12 it can be seen that a large por­tion of the inelastic scattering events take place in energy groups 3 to 7 (5.49 to

4.08 meV).

P3S16 17-group calculation,

\ \ ,

Region 4 (tungsten)

\

Region 6 (tungsten)

10-6 '----_=--=----:-:-__ -'--~----::-----'---_=__~---'-__=__'______:;___'____::_-'-----c::__'____:_-' 17 to 10 9 8 7 6 5 4 3 2

Energy groups (Scale does not represent either equal energy or lethargy intervals)

Figure 12. - Tungsten inelastic scattering events as function of energy group within two tungsten shells for model fast reactor.

25

Secondary Gamma Dose Analysis

The variation in source strength and source distribution due to the changing of elas- tic scattering order and, to a small degree, neutron group structure, can be seen more clearly when the dose rates resulting from the use of these sources are compared. Us- ing the absorption and inelastic gamma spectra shown in table TII enables the determina- tion of the gamma dose rates by an Sn photon transport calculation. Table M shows the total secondary dose rate at the periphery of the laminated shield and the individual con- tributions to the total dose from the reflector and each of the tungsten regions. F'ig- ure 13 is a plot of the secondary gamma dose rates from each of the tungsten regions throughout the laminated shield. These data a re generated using a P3S16 14-group transport calculation. The secondary source strength and source distributions for each of these regions were generated by a P3S16 17-group neutron transport calculation.

The total sec- ondary gamma dose rates calculated by QAD are in good agreement with the Sn transport calculation. However, the gamma dose contribution from the reflector, as calculated by the Sn transport method and the QAD code, differs considerably. Since both codes used the same secondary source strengths and source distributions, the difference must lie

The QAD results are also given in table M for comparison purposes.

TABLE M. - SECONDAFtY GAMMA DOSE RATES FOR THE TUNGSTEN REFLECTOR

AND TUNGSTEN SHIELD COMPONENTS (DETECTOR LOCATED AT 117 CM)

Radiation I Dose rates, rad/hr at detectox lose rate fo: detector at 117 cm, r ad/hr

Total dose

Source generation calculation

'1'16 (17 group)

'3'16 (17 group)

'3'16 (30 group)

Gamma transport calculation

'1'16 (14 group)

QAD

Region 2

type r Region 4 Region 6

24.230 10.440

10.170 9.680

34.567 20.145

54.712 tnelastic

tnelastic 28.660 12.880

10.490 9.330

39.705 22.308

62.013

Absorption 0.304 helasti c 1 .050

helastic

40.314 25.780

44.792 27.207

39.426 25.810

-

66.094

71.999

55.236

28.230 13.370

31.400 14.810

27.510 13.260

11.780 12.360

12.840 12.300

11.600 12.500

QAD

helastic

helastic 30.390 14.460

12.890 12.350

43.831 26.908

10.739

26

. . .

Secondary Gamma Dose Analysis

The variation in source strength and source distribution due to the changing of elas­tic scattering order and, to a small degree, neutron group structure, can be seen more clearly when the dose rates resulting from the use of these sources are compared. Us­ing the absorption and inelastic gamma spectra shown in table III enables the determina­tion of the gamma dose rates by an Sn photon transport calculation. Table IX shows the

total secondary dose rate at the periphery of the laminated shield and the individual con­tributions to the total dose from the reflector and each of the tungsten regions. Fig­ure 13 is a plot of the secondary gamma dose rates from each of the tungsten regions

throughout the laminated shield. These data are generated using a P 3S16 14-group transport calculation. The secondary source strength and source distributions for each

of these regions were generated by a P 3S16 17 -group neutron transport calculation. The QAD results are also given in table IX for comparison purposes. The total sec­

ondary gamma dose rates calculated by QAD are in good agreement with the Sn transport calculation. However, the gamma dose contribution from the reflector, as calculated by the Sn transport method and the QAD code, differs considerably. Since both codes used the same secondary source strengths and source distributions, the difference must lie

TABLE IX. - SECONDARY GAMMA DOSE RATES FOR THE TUNGSTEN REFLECTOR

AND TUNGSTEN SHIELD COMPONENTS (DETECTOR LOCATED AT 117 CM)

Source Gamma Radiation Dose rates, rad/hr at detector Dose rate for Total

generation transport type detector at dose

calculation calculation Region 2 Region 4 Region 6 117 cm,

rad/hr

P 1S16 P 1S16 Absorption 0.167 24.230 10.170 34.567 54.712

(17 group) (14 group) Inelastic .025 10.440 9.680 20.145

QAD Absorption 0.555 28.660 10.490 39.705 62.013

Inelastic .098 12.880 9.330 22.308

P 3S16 P 3S16 Absorption 0.304 28.230 11. 780 40.314 66.094

(17 group) (14 group) Inelastic .050 13.370 12.360 25.780

QAD Absorption 0.552 31. 400 12.840 44.792 71. 999 Inelastic .097 14.810 12.300 27.207

-

P 3S16 P 3S16 Absorption 0.316 27.510 11. 600 39.426 65.236

(30 group) (14 group) Inelastic .050 13.260 12.500 25.810

QAD Absorption 0.551 30.390 12.890 43.831 70. 739 1

Inelastic .098 14.460 12.350 26.908

26

Reflector

I I ?il 20 25

Li6H I

I 35

1

\ \ \ \

\,

W

I I 40 45

Radius, cm

Dose rate Absorption gamma ---- Inelastic gamma

0 Reflector contribution 0 First tungsten shell contribution A Second tungsten shell contribution

Li6H

A I 65 70 VllO 115 120

I €4

Figure 13. - Secondarygamma dose rates from tungsten reflector and first and second tungsten shields with P3S16 14-group photon transport calculation for model fast reactor.

27

Core Reflector

15 20 25 30 35

\ \ \ \ \ \ \ \ \ \ r';l \ \

w

40

\ \ \ \ \ \ \ \ , , , ,

\ \

45 50 Radius, cm

\ q

\ \ o

\

w

55

Dose rate Absorption gamma Inelastic gamma

o Reflector contribution o First tungsten shell contribution l!. ~econd tungsten shell contribution

--0 __ --0._-_0

------0

60 ~65-----7Li~~I~-0----1~15----~120

Figure 13. - Secondary gamma dose rates from tungsten reflector and first and second tungsten shields with P3S16 14-group photon transport calculation for model fast reactor.

27

in the calculation of the transport of the photons through the laminated shield. The dif- ference could be attributed, in part, to the following:

(1) The P3 elastic scattering order used in the Sn transport method may not be high enough to accurately calculate the deep attenuation of the secondary photons in the re- flector.

is questionable. (2) For the reflector secondaries, the use of a water buildup factor in the QAD code

CONCLUDING REMARKS

A study was made of point neutron and gamma sources in spherical media and a spherical reactor laminated shield using the point kernel (QAD) and discrete ordinates (S,) methods. The Sn method was limited by the available computer to the following: a scattering order of 3, a quadrature order of 16, and 30 groups. From the neutron point fission source study, the following conclusions may be drawn:

1. Based on the agreement with the Monte Carlo results for natural LiH, an Sn transport calculation of the order P3S16 with 30-neutron groups will yield adequate dose rates for neutron penetrations up to 90 centimeters in LiH and Li H.

parameters in the Sn transport calculation affected the computed dose:

6

2. From the study of the point fission source in LiH, it was found that various

a. Reducing the Sn quadrature order from 16 to 12 or 8 resulted in a calculated dose rate that was lower by 10 and 25 percent, respectively, at an LiH thickness of 117 centimeters.

b. Lowering the elastic scattering order from P3 to P1 resulted in a reduction of the calculated neutron dose rate by a factor of 2.5 at 117 centimeters.

c. Changing the neutron group structure from 30 to 17 reduced the computed dose rate by a factor of 2 at 117 centimeters. 3. The point kernel code QAD can be made to yield adequate dose rates by giving

careful consideration to the neutron removal cross section. The slab removal cross sections for the various elements did not give good results when hydrogenous mixtures of these elements were examined. The distributed neutron removal cross sections that were found to give the best results were Li in LiH (0.1000 cm /g) and Li in Li H (0.1156 cm2/g).

of tungsten, the following conclusions were found:

P3s16 16-group transport calculation agreed with the moments method.

2 6 6

From the study of the transmission of photons from a point source through a medium

1. Up to approximately 7 centimeters of tungsten, a photon dose rate computed by a

2. At 14 centimeters of tungsten, the transport calculation gave dose rates approxi-

28

in the calculation of the transport of the photons through the laminated shield. The dif­ference could be attributed, in part, to the following:

(1) The P 3 elastic scattering order used in the Sn transport method may not be high enough to accurately calculate the deep attenuation of the secondary photons in the re­

flector. (2) For the reflector secondaries, the use of a water buildup factor in the QAD code

is questionable.

CONCLUDING REMARKS

A study was made of point neutron and gamma sources in spherical media and a spherical reactor laminated shield using the point kernel (QAD) and discrete ordinates (Sn) methods. The Sn method was limited by the available computer to the following: a scattering order of 3, a quadrature order of 16, and 30 groups. From the neutron point fission source study, the following conclusions may be drawn:

1. Based on the agreement with the Monte Carlo results for natural LiH, an Sn transport calculation of the order P 3S16 with 30-neutron groups will yield adequate dose

rates for neutron penetrations up to 90 centimeters in LiH and Li6H. 2. From the study of the point fission source in LiH, it was found that various

parameters in the Sn transport calculation affected the computed dose: a. Reducing the Sn quadrature order from 16 to 12 or 8 resulted in a calculated

dose rate that was lower by 10 and 25 percent, respectively, at an LiH thickness of 117 centimeters.

b. Lowering the elastic scattering order from P 3 to P 1 resulted in a reduction of the calculated neutron dose rate by a factor of 2.5 at 117 centimeters.

c. Changing the neutron group structure from 30 to 17 reduced the computed dose rate by a factor of 2 at 117 centimeters.

3. The point kernel code QAD can be made to yield adequate dose rates by giving careful consideration to the neutron removal cross section. The slab removal cross sections for the various elements did not give good results when hydrogenous mixtures of these elements were examined. The distributed neutron removal cross sections that were found to give the best results were Li in LiH (0.1000 cm2/g) and Li6 in Li6H

(0.1156 cm2/g). From the study of the transmission of photons from a point source through a medium

of tungsten, the following conclusions were found: 1. Up to approximately 7 centimeters of tungsten, a photon dose rate computed by a

P 3S16 16-group transport calculation agreed with the moments method. 2. At 14 centimeters of tungsten, the transport calculation gave dose rates approxi-

28

mately 40 percent lower than the moments method.

puted a photon dose rate only one-half that of the moments method.

showed that the QAD dose rate computation agreed with the P3s16 30-group transport calculation within 40 percent at a radius of 117 centimeters. This agreement was ob- tained by using the neutron removal cross-section lithium-6 of 0.1156 square centimeter per gram.

the laminated shield, the following conclusions were obtained

tion to generate photon secondary source strengths and distributions in all the regions of the shield.

2. A P1 elastic scattering order neutron transport calculation was sufficient to gen- erate the secondary gamma source strength and distribution in the reflector region.

3. In the last tungsten region, the secondary source strength and distribution com- puted by a neutron transport calculation using a P1 elastic scattering order differed con- siderably from that of the P3 order.

The total secondary gamma dose rates calculated by the QAD point kernel method agreed to within 10 percent with the Sn transport results. However, the secondary dose calculated by the two methods differed considerably for the reflector. This difference can be attributed, in part, to (1) the elastic scattering order of three used in the Sn cal- culation being insufficient to accurately calculate deep transport of photons, and (2) the use of a water buildup factor in the QAD line-of-sight code to describe the laminated media of the shield.

3. Again at 14 centimeters of tungsten, a P1S16 16-group transport calculation com-

The study of the neutron penetration from the reactor through the laminated shield

In the analysis of the secondary gamma sources produced in the tungsten layers of

1. The 17 neutron energy group split was adequate for a neutron transport calcula-

-.

Lewis Research Center, National Aeronautics and Space Administration,

Cleveland, Ohio, August 14, 1968, 129-02-04-14-22.

REFERENCES

1. Fieno, Daniel: Transport Study of the Real and Adjoint Flux for NASA Zero Power Reactor (ZPR- 1). NASA TN D- 3990, 1967.

2. Malenfant, Richard E. : QAD A Series of Point-Kernel General-Purpose Shielding Programs. Rep. No. LA-3473, Los Alamos Scientific Lab., Apr. 1967.

29

I

mately 40 percent lower than the moments method. 3. Again at 14 centimeters of tungsten, a P 1 S16 16-group transport calculation com­

puted a photon dose rate only one-half that of the moments method. The study of the neutron penetration from the reactor through the laminated shield

showed that the QAD dose rate computation agreed with the P 3S16 30-group transport calculation within 40 percent at a radius of 117 centimeters. This agreement was ob­tained by using the neutron removal cross-section lithium-6 of O. 1156 square centimeter per gram.

In the analysis of the secondary gamma sources produced in the tungsten layers of the laminated Shield, the following conclusions were obtained:

1. The 17 neutron energy group split was adequate for a neutron transport calcula­tion to generate photon secondary source strengths and distributions in all the regions of the shield.

2. A P 1 elastic scattering order neutron transport calculation was sufficient to gen­erate the secondary gamma source strength and distribution in the reflector region.

3. In the last tungsten region, the secondary source strength and distribution com­puted by a neutron transport calculation using a P 1 elastic scattering order differed con­Siderably from that of the P 3 order.

The total secondary gamma dose rates calculated by the QAD point kernel method agreed to within 10 percent with the Sn transport results. However, the secondary dose calculated by the two methods differed considerably for the reflector. This difference can be attributed, in part, to (1) the elastic scattering order of three used in the Sn cal­culation being insufficient to accurately calculate deep transport of photons, and (2) the use of a water buildup factor in the QAD line-of-sight code to describe the laminated media of the shield.

Lewis Research Center, National Aeronautics and Space Administration,

Cleveland, Ohio, August 14, 1968, 129-02-04-14-22.

REFERENCES

1. Fieno, Daniel: Transport study of the Real and Adjoint Flux for NASA Zero Power Reactor (ZPR-1). NASA TN D-3990, 1967.

2. Malenfant, Richard E.: QAD: A Series of Point-Kernel General-Purpose Shielding Programs. Rep. No. LA-3473, Los Alamos Scientific Lab., Apr. 1967.

29

3. Joanou, G. D.; and Dudek, J. S.: GAM-II. A B3 Code for the Calculation of Fast- Neutron Spectra and Associated Multigroup Constants. Rep. No. GA-4265, General Dynamics Corp., Sept. 16, 1963.

4. Joanou, G. D.; Smith, C. V.; and Viewig, H. A.: GATHER-TI: An IBM-7090 FORTRAN-TI Program for the Computation of Thermal-Neutron Spectra and Asso- ciated Multigroup Cross-Sections. Rep. No. GA-4132, General Dynamics Corp., July 8, 1963.

5. Lathrop, K. D. : GAMLEG - A Fortran Code to Produce Multigroup Cross Sections for Photon Transport Calculations. Rep. LA-3267, Los Alamos Scientific Lab., Mar. 11, 1965.

6. Celnik, J. ; and Spielberg, D. : Gamma Spectral Data for Shielding and Heating Cal- culations. Rep. No. UNC-5140, United Nuclear Corp. (NASA CR-54794), Nov. 30, 1965.

7. Goldstein, Herbert: Fundamental Aspects of Reactor Shielding. Additon- Wesley Publ. Co., Inc., 1959.

8. Anon. : Protection Against Neutron Radiation up to 30 Million Electron Volts. Hand- book 63, National Bureau of Standards, Nov. 22, 1957, p. 7.

9. Astin, A. V. : Physical Aspects of Irradiation. Handbook 85, National Bureau of Standards, Mar. 31, 1964.

10. Mynatt, F. R.; Greepe, N. M.; and Engle, W.' W.; Jr.: On the Application Of Di s cr et e - Or dinat e s Transport The o r y to Deep - P enet r ation Fast- Neutron- Dose Calculations in Water. Trans. Am. Nucl. Soc., vol. 9, no. 2, Nov. 1966, pp. 366- 368.

11. Kam, Francis B. D. ; and Clark, Francis H. S. : Fission Neutron Attenuation and Gamma-Ray Buildup Factors for Lithium Hydride. July 1967, pp. 433-435.

Nucl. Appl., vol. 3, no. 7,

12. Blizard, Everett P.; and Abbott, Lorraine S., eds: Shielding. Vol. 111, Part B of Reactor Handbook. Second ed., Interscience Publ., 1962.

13. Lahti, Gerald P: Fission Neutron Attenuation in Lithium 6, Natural Lithium Hy- dride, and Tungsten. NASA TN D-4684, 1968.

14. Goldstein, Herbert; and Wilkins, J. Ernest, Jr. : Calculations of the Penetrations of Gamma Rays. Rep. NDA-15C-41, Nuclear Development Assoc., Inc. (AEC Rep. NYO-3075), June 30, 1954.

15. Lahti, Gerald P. ; Lantz, Edward; and Miller, John V. : Preliminary Considera- tions for Fast-Spectrum, Liquid-Metal Cooled Nuclear Reactor Program for Space-Power Applications. NASA TN D-4315, 1968.

30 NASA-Langley, 1969 - 24 E-4503 I

3. Joanou, G. D.; and Dudek, J. S.: GAM-II. A B3 Code for the Calculation of Fast­Neutron Spectra and Associated Multigroup Constants. Rep. No. GA-4265, General

Dynamics Corp., Sept. 16, 1963.

4. Joanou, G. D.; Smith, C. V.; and Viewig, H. A.: GATHER-II: An IBM-7090 FORTRAN-II Program for the Computation of Thermal-Neutron Spectra and Asso­

ciated Multigroup Cross-Sections. Rep. No. GA-4132, General Dynamics Corp.,

July 8, 1963.

5. Lathrop, K. D.: GAMLEG - A Fortran Code to Produce Multigroup Cross Sections

for Photon Transport Calculations. Rep. LA-3267, Los Alamos Scientific Lab.,

Mar. 11, 1965.

6. Celnik, J.; and Spielberg, D.: Gamma Spectral Data for Shielding and Heating Cal­

culations. Rep. No. UNC-5140, United Nuclear Corp. (NASA CR-54794), Nov. 30,

1965.

7. Goldstein, Herbert~ Fundamental Aspects of Reactor Shielding. Additon-Wesley

Publ. Co., Inc., 1959.

8. Anon.: Protection Against Neutron Radiation up to 30 Million Electron Volts. Hand­

book 63, National Bureau of Standards, Nov. 22, 1957, p. 7.

9. Astin, A. V.: Physical Aspects of Irradiation. Handbook 85, National Bureau of

Standards, Mar. 31, 1964.

10. Mynatt, F. R.; Greene, N. M.; and Engle, W: W.; Jr.: On the Application Of

Discrete-Ordinates Transport Theory to Deep-Penetration Fast-Neutron-Dose

Calculations in Water. Trans. Am. Nucl. Soc., vol. 9, no. 2, Nov. 1966, pp. 366-368.

11. Kam, Francis B. D.; and Clark, Francis H. S.: Fission Neutron Attenuation and

Gamma-Ray Buildup Factors for Lithium Hydride. Nucl. Appl., vol. 3, no. 7, July 1967, pp. 433-435.

12. Blizard, Everett P.; and Abbott, Lorraine S., eds~ Shielding. Vol. III, Part B of

Reactor Handbook. Second ed., Interscience Publ., 1962.

13. Lahti, Gerald P: Fission Neutron Attenuation in Lithium 6, Natural Lithium Hy­

dride, and Tungsten. NASA TN D-4684, 1968.

14. Goldstein, Herbert; and Wilkins, J. Ernest, Jr.: Calculations of the Penetrations

of Gamma Rays. Rep. NDA-15C-41, Nuclear Development Assoc., Inc. (AEC

Rep. NYO-3075), June 30, 1954.

15. Lahti, Gerald P.; Lantz, Edward; and Miller, John V.: Preliminary Considera­

tions for Fast-Spectrum, Liquid-Metal Cooled Nuclear Reactor Program for

Space-Power Applications. NASA TN D-4315, 1968.

30 NASA-Langley, 1969 - 24 £-4503

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