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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
ORNVA 1787
Conf.651101-49
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CALCULATED FLUXES OF LESS THAN 50-MeV NEUTRONS DIFFUSING BENEATH THE
SHIELD OF A MESON PRODUCTION FACILITY*
TEC 21 1965
W. E. Kinney
Oak Ridge National Laboratory
Oak Ridge, Tennessee

RMTASDD FOR ANNOUNCEMENT
IN NUCLEAR SCIENCE ABSTRACTS
Introduction:
In a facility for producing mesons in large quantities, protons of high
energy, e.g. 800 MeV, impinge on a target and the mesons are produced as a
result of intranuclear processes. Lower energy protons and neutrons also
result from the nuclear interactions. These radiations present a hazard to
personnel as well as to equipment and so adequate shielding must be provided.
Approximate methods have been used to estimate the fluxes of secondary
particles coming through the shiela, , but no such methods exist for esti-
mating with much confidence the flux of neutrons which are born beneath the
shield and diffuse into experimental areas behind it, thus producing an
"earthshine" analogous to skyshine.
A Monte Carlo calculation was performed in an attempt to estimate the
effect of the earthshine in an idealized but useful shield configuration.
This is a difficult problem to solve by straightforward Monte Carlo because
of the large numbers of mean free paths the neutrons must traverse. Some
crude biasing techniques were employed in an effort to improve the results.
In this paper the methods used in the calculation are discussed and some
results and conclusions are presented.
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Methods
The idealized problem is illustrated in Fig. 1. An isotropic point
source of neutrons is located 5 ft above the surface of a semi-infinite
L
can insentire ,
medium of SiO2 and 5 ft from the face of a semi-infinite slab of iron,
*Research sponsored by the U. S. Atomic Energy Commission under contract
with the Union Carbide Corporation.
viewing
*
;
.1:
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ORNL-DWG 64-1116-lli
FIELD
POINTS
i
5
w
- 10 ft -
Fe
Plu) = (***) * (***) ; x = LARGEST OF 1+1 RANDOM NUMBERS
WEIGHT = oto la..)"
The Idealized Calculational Model Indicating the Biased Source
Distribution and Weight.
Fig. 1
SiO2

...
loss
cos
ZE=4 Hou (med
5 ft
0.5
SOURCE-
1.0
LEGAL NOTICE
This report was prepared as an account of Government sporsorod work. Noither the United
States, por the Commission, nor any person acting on behalf of the Commission:
A. Makes any warranty or representation, expressed or implied, with rozpoc
racy, complotones, or usofulness of the loformation contained in this report, or that the we
of any information, apparatus, mothod, or process diaclosed in this roport may not Infringe
privately owned rights; or
B. Assunor any liabilities with rospect to the use of, or for dumyces resulting from the
use of any information, appartus, method, or procesi dicioned in this report.
As used in the above, "person acting on behalf of the Commission" includes may .
ployee or contractor of the Commission, or employee of such contractor, to the extent that
such employoe or contractor of the Commission, or employee of such contractor properes,
disseminates, or provides access to any information pursuant to his employd wat or contract
with the Commission, or his employment with such contractor.
.
.
10 ft thick, resting on the Sioa.
The SiO2 density was assumed to be .
1.8 g/cm3
Neutrons and their resulting secondaries of energy greater than 50 MeV
are transported through the configuration by means of NTC, a high-energy
nucleon transport code. Nuclear interactions are treated by a subroutine
4.
version of Bertini's Intranuclear cascade code* which is itself a nucleon
transport code on an intranuclear scale. Secondaries of üll energies up to
a large fraction of the incident nucleon energy result from the interactions.
Neutrons below 50 MeV are put on a tape to be used as sources for the low-
energy neutron transport calculation. Nucleons above 50 MeV are transported
until they disappear from the system by interaction, by escape, or, in the
case of protons, by slowing down. After a nuclear interaction, the residual
nucleus is left with excitation energy which is gotten rid of by evaporation
processes. So, in addition to the above direct-interaction secondaries,
there are evaporation secondaries of energy below 50 MeV. The evaporation
neutrons are added to the source tape for the low-energy calculation.
The low-energy 'transport is done by 05R,' a general-purpose Monte Carlo
neutron transport code. This code rather than NTC must be used below 50 MeV
since below this energy the model for nuclear interactions becomes of doubtful
validity and neutron elastic scattering, which is neglected in NTC, becomes
an important mechanism for energy loss.
A 01
Neutrons were started from the source point with 400-MeV energy. It
was felt that the most important source neutrons for producing secondaries
which would reach the vicinity of the field points would be those emitted
near the line which joins the source and the intersection between the
nea
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rear slab face and the earth and which lies in a plane perpendicular to the
slab. Accordingly, the source neutrons were highly biased about this direction
by picking up, the cosine of the angle between the above-mentioned line and
the direction or emission, from the distribution
Plu) = (2) (+),
where u is the largest of n+1 ranaon numbers. A value of 32 was used for n.
This gives an average cosine of 0.945. Since the source is assumed to be
isotropic, a weight must be associated with the source neutrons to compensate
.
for the source biasing.
The weight is easily seen to
nl \ l te
In addition to the source biasing, neutrons were started always at the
SiO2 interface. Those neutrons whoses paths lay through the iron simply had
their weights multiplied by the iron attenuation factor ezh, where £ is the
iron cross section for nuclear interaction and t is the distance the neutron
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traveled in the iron.
One further biasing technique was employed in an effort to direct neutrons
toward the field points. The intranuclear cascade secondary nucleons were
biased according to their direction of emission. There was computed the
cosine of the angle between the direction of emission and the line joining
the collision site with the point at which the rear slab face and earth
intersection meets the plane perpendicular to the slab and containing the
source. If the cosine was between 0.5 and 1.0, the secondary was accepted.
If the cosine lay between 0 and 0.5, the secondary was accepted with prob-
ability 0.1 but with its weight multiplied by 10. If the cosine was negative,
the secondary was accepted with probability 0.05 but with 20 times its weight.
Nine batches of 2000 primary neutrons each were run. The 2000 neutrons
produced approximately 5400 neutrons of energy less than 50 MeV. About one
hour of IBM 7090 time was required to run each batch.
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In an attempt to save time in running the low-energ" calculation, most
of the neutrons on the source tape were discarded as being too far from the
field points ever to contribute significant).y to the flux. Only neutrons
born at a distance greater than about 6 1/2 ft from the front face of the
slab and at a depth less than 5 ft in the earth were run in 05R. Approxi-
mately 450 out of the 5400 neutrons satisfied these conditions for each
batch.
O5R was run on the CDC-1604 computer and required approximately 15
min to run the neutrons to 1 keV and write their histories on magnetic
tape.
Estimates of the fluxes were made by statistical estimation from each
collision point using the 05R collision tape. The total contribution to the
flux from each neutron was computed to see how many significant contributors
there were to each field point. Approximately ll min was required to estimate
the fluxes at each field point. Field points were located on the earth sur-
face in a plane perpendicular to the iron slab and containing the source
point at distances of 0, 5, and 10 ft behind the slab.
Results
Although fluxes were estimated in energy intervals over the range
i keV to 50 MeV, nearly all the contribution was in the I keV to 1 MeV
range. The statistics were so poor that it does not seem worthwhile to
--
tabulate any but these results. Table I gives the fluxes at the three
field points.as estimated from each of the nine batches and the number
of neutrons contributing greater than 1% of the flux. Generally, one
neutron was responsible for at least 40% of the flux. The average of
the nine batches yields 2.7 x 10-10, 3.6 x 1c-11 and 1.4 x 10-11(neutrons/
cm?:)/(source neutron).::for the flux at 0, 5, and 10 ft, respec cively.
---
imertinimo
c tar
in conta
obowy
now,
time to
smanandam meminta
:: Table I
Fluxes in the 1-key to l-MeV Energy Region and the Number of
Neutrons Contributing Greater Than 1% at 0, 5, and 10 ft
Behind the Shield for Nine Independent Batches
5 ft
-
-
Oft
Number
Contributing
>1%
Number
Contributing
10 ft
Number
Contributing
>1%
Batch
Flux
Flux
>1%
Flux
1.5(-11
5.7(-11)
1.11-10)
6.41-21)
9.30-11)
4.61-10)
4.5(-11)
4.81-10)
4.5(-10)
9.51-10)
6.0(-12)
5.21-11)
9.21(-13)
1.5(-12)
1.91-11)
dเก่า)
3.7(-13
01-12
Nu Furacana
1.21-10)
5.71-11)
2.01-11
1.3(-22)
3.31(-ií)
9
3.6(-21)
1.4(-11)
Avg. 2.7(-10)
*5.7(-11) = 5.7 x 10-11.
The uncollided flux at 5 f't is 3.9 x 10-15. A very crude but conservative
estimate of the flux of neutrons greater than 50 MeV at Oft gives on the
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order of 10-11(neutrons cm2 Mev”?)/(source neutron), or a total flux of
~10** (neutrons/cm^)/(source neutron).
If one considers the radiation hazard of the earthshine and assumes that
~1015 neutrons/sec are produced due to, say, 1 mamp of beam (6.25 x 2015
protons/sec), then one gets ~105 neutrons cm 2 sec 1 at O ft behind the shield.
The average whole-body dose of neutrons of this energy is ~10*8 rads neutronº?
cm?, so that one has 10-3 rads /sec = 3.6 r/hr, which is orders of magnitude
above the recommended dose to personnel of 7.5 mr/nr for a 40-hr week.
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Conclusions
This estimate must clearly be regarded as a first attempt at finding a
solution to the earthshine problem for neutrons of energy below 50 MeV.
, immat
Only those few neutrons which the analog process brought near the field
points contributed significantly to the fluxes, often only one or two making
up most of the flux.
mwanamitin
The flux estimates are no doubt low, but even so, a radiation hazard
exists for the test configuration assuming a source of 1015 neutrons/sec.
A more effective biasing technique must be used in the future for deep
penetration problems of this type to direct more of the high-energy secon-
daries toward the points of interest.
References
1. H. B. Knowles, p. 333 in Minutes of the Conrerence on Proton Linear
Accelerators Held at Yale University, October 21-25, 1963, TID-7691.
2. R. N. wallace, Muci. Inst. Methods 18/19, 405 (1962).
3. W. E. Kinney, "The Nuclear Transport Code, NTC" ORNL-3610, August, 1964.
4. H. W. Bertini, Phys. Rev. 131, 1801 (1963).
5. R. R. Coveyou et al., "05R, A General Purpose Monte Carlo Neutron Trans-
port Code," ORNL-3622, February, 1965.
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DATE FILMED
1 / 19 /66








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