A simple code for use in analyses of gamma radiation effects in laminated materials is described. Simple and good geometry is assumed so that all multiple collision and scattering events are excluded from consideration. The code is capable of handling laminates up to six layers. However, for laminates of more than six layers, the same code may be used to incorporate two additional layers at a time, making use of punch-tape outputs from previous computation on all preceding layers. Spectrum of attenuated radiation are obtained as both printed output and punch tape output as desired

Wan, C. C.

English

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A SIMPLECODEFORUSEINSHIELDING
ANDRADIATIONDOSAGEANALYSES
C. C. Wan
Hughes Aircraft Company
ABSTRACT
A simple code for use in analyses of gamma radiation effects
in laminated niaterials is described in this note. Simple and good
geometry is assumed so that all multiple collision and scattering
events are excluded from consideration. Buildup factors may be
applied to the results of this simplified analysis, when available,
to arrive at improved estirnates of energy deposition and attenuated
intensity for actual materials.
The code proper is capable of handling laminates up to six
layers. However, for laminates of more than six layers, the same
code may be used to incorporate two additional layers at a time,
making use of punch-tape outputs from previous computation on
all preceding layers.
Spectrum of attenuated radiation may be obtained as both
printed output and punch tape output as desired. This code is
written in "Extended Basic" language, compatible with the GE 265
Time Sharing system.
I. Theoretical Fundamentals
Energy deposition resulting from inter-
action between photons (X-rays, gamma rays)
and matter has been discussed in some detail
in Reference (I). The basic results, obtained
for simple and good geometry in a one-dimen-
sional representation, are
Attenuated spectrum at depth x:
[ oX]Ix(El = Io I(E) . exp 0-(El d
(ll
Energy deposited at depth x:
q(x) = Io f Oa(E ) . (Ix/Io) dE (Z)
O
whe re x
dm
= depth into the material, in cm.
= P dx = differential mass depth
in gm/sq cm.
P = density of material, in gm/cc.
E = energy level, in KeV
I = fluence, in cal/sq cm,
o
incident on the surface of the
first layer
I(E) = spectrum of the incident
radiation, function of E,
normalized to unity for E
ranging from 0 to infinity
= mass attenuation and mass
absorption coefficients
To circumvent the need for a detailed defin-
ition of incident energy spectrum, Planckians
expressed in terms of equivalent blackbody
temperatures, in KeV units, are used as a
convenient means to segregate engineering
estimates of shielding and thermomechanical
effects completely from specific identification
of spectral contents of the primary source,
i.e., bomb types, etc. Therefore, the
quantity I(E) may be thought of as
I(E) = Ei Ii . P(E/Ei)
_(E), _ (E)
a
387
https://ntrs.nasa.gov/search.jsp?R=19720010001 2020-03-17T03:49:31+00:00Z
where I. = fluence weighting factor for
1 the i-th equivalent black body,
with _iI. = 1, and
1
P(_) : normalized Planckian, as
shown in Figure 1.
Since I o appears in both expressions displayed
above, no loss of generality will result if I o
is set equal to unity, corresponding to a
fluence of 1 calorie per square centimeter.
Thus a normalized dose Q(x) may be defined
as
Q{x} = q(x}/I °
which is a unique property of the material in
question when subjected to an incident spec-
trum associated with a specific equivalent
blackbody temperature, or with a particular
combination of spectra associated with a
number of black bodies of different equivalent
temperatures. The attenuated spectrum is of
course given by the ratio Lx(E)/I o, or simply
Ix(E), since I o = 1.
When materials of various thicknesses
are placed one after another, either as close-
ly spaced laminates or as a series of material
layers with air spaces in between, the above
computation process can be applied to each
layer in succession. The attenuated spectrum
from the first layer becomes the incident
spectrum for the next layer, and so on. Thus,
the entire series of computation may be made
by means of a simple loop; the number of
layers that may be accommodated becomes
strictly a question of the size of machine
storage available.
The mass absorption coefficients and the
mass attenuation coefficients are both com-
plicated functions of energy level, which have
been tabulated by several agencies. For
definiteness, the following source data are
used -- these data are not always consistent
with each other, but they represent the best
information available at this time. Logarith-
mic interpolation is used throughout for
establishing pertinent values associated with
each energy level of concern.
(I) Photon Cross Sections from 0. 001 to
1 00 MeV for Elements 1 through 100,
Los Alamos Scientific Laboratory
Report LA-3753, November 15, 1967.
(z) Analytical Approximations for X-ray
Cross Sections, Sandia Laboratory,
Report SC-RR-66-45Z, February
1967.
(3) X-ray Attenuation and Absorption
Coefficients, The Boeing Company,
Report D2-125065-1, September
1966.
A new edition of itern (1) is in press, and
will be scanned for necessary updating when
published. Values to be used can be com-
posites based on all three of the above ref-
erences, a sample of which is shown on the
next page, for the element copper.
For compounds, both coefficients may
be approximated by proportional weighting
in accordance with their atomic abundancy.
Since the mass coefficients have already been
referred to unit mass densities, this implies
that
= Ni _X i AX i 1
where Axi is the atomic weight of the ele-
ment X i. The molecular formula of the
compound in question is of course
For heterogeneous mixtures of several com-
pounds, the attenuation problem involved is
far more complex than can be correctly
handled by the present simplified approach.
However, for an engineering estimate, it
will be assumed that they behave like com-
pounds with the same proportion of various
elements by weight.
II. Description of the Code "ENEDEP"
The code written in the Extended Basic
language for use on the GE-265 Time Shar-
ing system is named ENEDEP (ENErgy
DEPosition). It is capable of handling lami-
nations up to six layers of different materials.
Various combinations of source temperature
(equivalent blackbody temperature) and inci-
dent fluence can be processed in series for
the same material configuration. The output
of this code provides:
(1) Identification of layer material by
name, its density and thickness.
(z) Depth, mass depth, energy deposi-
tion per unit mass and local radia-
tion intensity in tabular form.
(3) Attenuated spectrum at the back
side of the last material layer, in
tabular form and/or in punch tape
form as desired to be selected by
appropriate control indices.
Input data requirement,
possible modification to accomodate mater-
ials with a large number of edges in their
mass absorption coefficients, and a sample
388
problem are discussed in the following
sections.
IlL Input Data
input data for executing the ENEDEP
code must be presented in the following
format:
lZ00 DATA N, M
N index for printout and punch tape
input selection:
0 no attenuated spectrum informa-
tion at all
1 tabulated attenuated spectrum,
punched tape output optional
punched tape input and tabulated
attenuated spectrum with optional
punched tape output
M
Z000*
integer, denoting the number of
layers, not greater than 6.
DATA X(1) N(1), :
x(I) Thickness of the I-th layer, in
mils
N(I) Number of printout desired in the
l-th layer, integer
*ZOO0 is a typical line number, which
may be any number greater than
1 ZOO, followed by tape input
containing
2010, "AAAAAAAAAA", W(I), J(I),:
"AAAAAAAAAA" alpha-numeric
string of ten characters, being
the name of the material of the
l-th layer
W(I) Density of the material in the
I-th layer, in gm/cc
J(I) Number of sets of mass atten-
uation and mass absorption co-
efficients, integer, not Treater
than 35
*ZOlO is a typical line number; for
materials with no edges between
0.5 KeV and Z00 KeV, there will
be ZZ sets of coefficients on this
prepared tape; for materials with
edges, add two sets for each edge.
9900
S.
i
DATA S I, Pl' Sz' Pz' .........
Incident fluences, in cal/sq cm
(equal to 1 for most cases)
Pi Equivalent blackbody temperature,
in KeV units
The usual requirement calls 1or five
sets of S, P combinations, namely, 1, 1,
1,2, I, 4, I, 7, I, 15. However, any
other combinations pertinent to a par-
ticular problem can be used.
On the prepared tape, in addition to what is
explained above under "Z010", there will be
other lines of material properties coefficients,
specified in triplets, giving:
E(j) Energy coordinate, in KeY
F(j) Mass attenuation coefficient, o
G(j) Mass absorption coefficient, aa
IV. Materials With More than Six Layers
When the material under consideration
has more than six layers, the first six
layers will be processed as indicated above,
using an index N = 1 and obtain a punch tape
output. This tape is then read into a new
problem, with the following important
modifications:
lZ00 DATA Z, Z
Only two more layers may be treated,
due to storage limitation in the GE-Z65
Time Sharing system.
Line 9900 must be modified to read as
follows:
9900 DATA S, P
S, P here must be the same set of
parameters pertaining to the punch tape
data being read in as tape input.
On occasions, more than 35 entries may
be required to provide an adequate repre-
sentation of the mass attenuation and mass
absorption coefficients of one or more
materials. In such cases, the dimensional
statement in line 20 must be revised accord-
ingly, an example of this may be seen in
section V. Due to limitation in the size of
data storage capacity, the number of layers
of materials may also be adjusted. Thus a
typical modification of line Z0 may have the
following form:
Z0 E(4, 4Z), F(4, 4Z), G(4, 4Z)
V. Sample Problem
To illustrate the usage of the ENEDEP
code, a six layer laminate consisting of the
following materials is analyzed:
Quartz 0.013 grn/cm z 2 mils
Silicon 1.07 grn/cm Z 180 mils
Z
Quartz O. 01 5 gin/cm Z mils
.389
Platinum 0. 0022 gm/cm 2 0. 04 mils
Gold 0.002 gm/cm 2 0.04 mils
2.0 grn/cm 2 100
Bi2Te 3 n-dls
Due to the high Z-number associated with
the materials in the last three layers, 42
entries are required for each of these
layers. Therefore, the main program is
modified to handle only four layers, each
with provision for 42 entries. The main
program would have tO be recycled three
times to complete the analysis required
for all six layers, inpu t data for the first
four layers used in the first cycle, results
for the first four layers, input data for the
fifth layer with tape input of attenuated
spectrum from the first four layers, out-
put for the fifty layer, input data for the
sixth layer with tape input of attenuated
spectrum from the first-five layers, a_d
output for the sixth layer are displayed in
succession at the end of this paper. A
summary of results for the entire range
of equivalent blackbody temperature from
1 to 16 KeV is displayed in Figures 2 and 3.
VI. Concluding Remarks
A simple code for determining energy
deposition dosage and attenuated fluence in
material laminates induced by gamma ray
radiation is presented. The average run-
ning time for one set of fluence and equiva-
lent blackbody temperature is approximately
80 seconds (computer time). This code
therefore provides a very convenient and
economical tool for parametric studies in
shlelding problems and energy deposition
analyses.
1)
REFERENCE
Leipunskii, O. L., Novozhilov, B. V., and Sakhrov, V. N. :
The Propagation of Gamma Quanta in Matter, International
Series of IVfonographs on Nuclear Energy, Division X, Reactor
Design Physics, Volume 6, Pergamon Press, New York, 1965.
COPPER
Z - 29; A - 63,54; p - 8.94: J = 28
Note: Values are given in floating poin% format; powers of
ten are shown after the letter E.
j Phton Energy Attenuation Absorption
(re,V)
I 0.5000 E 00 0.1120 E 05 0.1120 E O5
2 0.6OO0 m 00 0.7007 E 04 0.7007 E 04
3 0,8000 E O0 0,3333 E 04 0,3333 E 04
4 0,9320 E 00 0,2237 E 04 0.2237 E 04
5 0,9320 E 00 0,1646 E 05 0,1646 E 05
6 O,i000 E 03. 0,1358 E 05 0.1358 E 05
7 0,1100 E Ol 0,1046 E 05 0.i046 E 05
8 o._00 _ Ol o.11ooE 05 0.]a00E 05
9 o.].50oE oi o.525oE 04 0.5250E o4
i0 0,2000 E Ol 0,2400 E 04 0,2400 E 04
11 0.3000 E Ol o.780o E 03 0.7800 E 03
12 0.4000 E 03.. 0.3500 E 03 0.3500 E 03
13 0.5000 E Ol 0,1900 E 03 O.1900 E 03
14 0,6000 E Ol 0.IIi0 E 03 O'.1108 E 03
15 0,8000 E Ol 0,5400 E 02 0,5383 E 02
16 0,8980 E Ol 0,4100 E 02 0.4083 E 02
17 0,8980 E O1 0,2960 E 03 0,2958 E 03
18 0,i000 E 02 0.2240 E 03 0.2238 E 03
19 0,1500 E 02 0.7600 E 02 0,7580 E 02
20 0,2000 E 02 0.3300 E 02 0.3284 E 02
21 0,3000 E 02 0.1060 E 02 0.1044 E 02
22 0,4000 E 02 0,4570 E O1 0,4422 E Ol
23 0.5000 E 02 0.2410 E 01 0.2268 E 01
24 0,6000 E 02 0,1490 E Ol 0,1354 E Ol
25 0.8o0o E 02 0.7080 E O0 0.5826 E O0
26 0,I000 E 03 0,4250 E O0 0,3083 E O0
27 0.1500 E 03 0.2080 E 00 0.1083 E O0
28 0,2000 E 03 0,33480 E OO 0,6055 E-OI
TABLE i. WEIGH_'D ATTENUATION AND ABSORPTION COEFFICIENTS3
390
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3 4 5 6 7
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FIGURE I. NORMALIZED PLANCKIAN
ARF-._ uN_R cc_9v£ = /
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O _ 4 & 8 Io s2 Id_ tit,
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391


A simple code for use in shielding and radiation dosage analyses

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