Results of a calculation which estimates the heavy primary secondary doses from cosmic ray interaction data are reported. The incident galactic cosmic ray heavy primary spectrum is represented as the sum of helium, nitrogen, magnesium, and iron components. The incident iron nuclei are allowed to fragment into lesser Z secondaries, which are assumed to travel in the same direction and start with the same energy per nucleon as the interacting primary. The total emergent particle energy spectra and dose are then presented for the galactic heavy primary spectrum incident on aluminum and tissue slabs. The importance of the fragmentation parameters assumed is also evaluated. The total dose from the heavy primaries and their secondaries is found to be reduced by only a factor of two in 20 g/sq cm of shielding

Curtis, S. B.

Wilkinson, M. C.

English

NASA Technical Reports Server

GALACTIC COSMIC RAY HEAVY PRIMARY SECONDARY DOSES*
M. C. Wilkinson (Boeing), S. B. Curtis (UCLRL - Berkeley)
The free space dose rates from the various components of the
galactic cosmic rays can be determined from the particle energy
spectra and energy loss data. Depth-dose profiles in material
shields or in body tissue are complicated by the nuclear cascade
set up in the material by the incident primaries. While consid-
erable work has been done on the proton induced particle cascade,
the heavy primary secondazy dose from the galactic cosmic rays,
which also fragment and cascade, has not been estimated.
In this paper we present the results of a calculation which
estimates the heavy primary secondary doses from cosmic ray inter-
action data. The incident galactic cosmic ray heavy primary spec-
trum is represented as the sum of helium, nitrogen (M group), mag-
nesium (light heavy), and iron (very heavy) components. The inci-
dent iron nuclei are allowed to fragment into lesser Z secondaries,
which are assumed to travel in the same direction and start with
the same energy per nucleon as the interacting primary. The total
emergent particle energy spectra and dose are then presented for
the galactic heavy primary spectrum incident on aluminum and tis-
sue slabs. The importance of the fragmentation parameters assumed
is also evaluated.
The total dose from the heavy primaries and their secondaries
is found to be reduced by only a factor of two in 20 g/cm 2 of
shielding.
*Work supported by NASw-1963
We present here a method for the cal-
culation of the secondary particles pro-
duced by heavy galactic primaries. The
galactic cosmic ray spectrum consists of
protons, helium and higher Z elements, all
with a similar energy spectrum, but of re-
duced intensity with increasing Z. As
these particles pass through matter, both
nuclear interaction and ionization reduce
the intensity and energy of the incident
spectrum. While the electromagnetic inter-
action for the particle energies of inter-
est are well understood, and their effects
readily calculated, the nuclear interac-
tions lead to complex cascades of secon-
dary partlcles. While a great deal is
known about the cascade products of pro-
ton induced reactions, the cascades in-
duced by the higher Z elements of the gal-
actic cosmic rays have received less atten-
tion.
The fraction of the yearly free space
dose resulting from the various components
of the galactic cosmic rays are shown in
Table I, as determined from the particle
energy spectra given in Reference i.
In Figure i, we show the depth-dose
profiles for the helium and higher Z par-
ticle groups under two assumptions: i) that
only electromagnetic interactions attenuate
the flux, and 2) that the particles suffer-
ing nuclear interaction are removed from
the beam (uncolllded particle dose only).
The wide range between these estimates in-
dicates a need for further analysis.
104
IO'S
10-4
Component
H (Z=l)
He (Z=2)
M (6<Z_9)
LH (I05ZS14)
VH (26<Z<28)
TABLE I
Yearly Dose
4.6
3.5
1.9
1.3
1.3
TOTAL: 12.6 rads/
year
- (LH)
\ |
I i : ) co- _Ilil ,J
I0 20 30 40 _0
GM/CM 2 - AL
Figure I: HEAVY PARTICLE GALACTIC DOSES
https://ntrs.nasa.gov/search.jsp?R=19720009964 2020-03-17T03:48:42+00:00Z
FORMULATION OF THE CALCULATION
Let _i (E,x) be the differential num-
ber flux of ions of type i at a point x in
the absorber. Then it is easy to show that
the relation between the incident flux and
the flux at a point in the absorber is
given by
S(E)
_i(E' ,xl=_i(E,Ols (E,)
neglecting nuclear interactions.
If we include nuclear interactions,
and change variables to energy per nucleon,
T, we have
(i) _i (r''x)=_i(T'O)x
S(T) _ _i (r) dt
S (T') exp-J
T
where S(T) is the stopping power of the ion
of type i and energy per nucleon T. If _
is energy dependent, then we have simply
exp[-_ix] for an attenuation factor. The
uncollided flux can then be determined at
points of interest in the absorber.
Now ions of type i produce secondary
ions of type J at points in the absorber
at the following rate
(2) d_J(T,
dx
where
_i(T,x)
ai(T)
Pij (T,T')
N
o
M =
_(T',x)=
No
,x)=_i(T,x)_-- aI(T)Pij(T,T')
is the energy spectrum of ions
of type i
is the interaction cross sec-
tion for ions of type i and
energy T
is the fragmentation parameter,
giving the probability for an
interaction of type i ions at
energy T to produce a secon-
dary ion of type J and energy
T'
Avogadro's number
the atomic weight of the ab-
sorber
the rate at which particles
of type J and energy T' are
being produced in the absorber
at point x
Particles of type J are slowed and
attenuated as they pass through the re-
mainder of the absorber and they emerge
with an energy related to their initial
energy T, and remaining path length in
the absorber, X-x, of
RJ (T)=RJ (Tf)+X-x
and with an intensity reduction of
S(T)
S(Tf) exp [-uj (X-x) ]
The emerging flux of type J particles pro-
duced by type i primaries is then
105
X
(3) _j(Tf,X)=? _i(T,x) X
O
S(T)
°i(T)PIj(T) S-_-f) x
exp[-uj (X-x)]dx
Now we apply these basic relations
to the problem of determining the final
penetrating energy spectrum of the gal-
actic heavy primaries and induced secon-
daries in an absorber. First, we con-
sider a maximum Z of 26, as only a small
number of higher Z particles are present
in the galactic cosmic ray flux. The
penetrating flux of 2_Fe particles at any
point in the absorberVcan be determined
by expression (i). Once _Pa (T,x) is
known, then the rate at whl6h lower ato-
mic number particles are being produced
at points in the absorber can be deter-
mined bv expression (2).
The total production rate of particles
of type j is given by the following sum
26
No (T)
_x--_(T'x)= Z ¢i (T 'X)M--_i (T) Pij
i=j+l
where _(T,x), the total flux of particles
of type-i, depends on both the incident
flux and the accumulated secondary flux.
To determine the penetrating flux of
particles, a computer program was devel-
oped to evaluate the expressions discussed
numerically. This program evaluates the
production rates of the secondaries at a
set of thickness points in the absorber for
a suitable energy grid. Then by sequential
transporting the highest Z element through
the absorber and determining the production
rates for all lower Z elements, we obtain
the final penetrating number energy spec-
trum.
BASIC ASSUMPTIONS USED IN THE CALCULATION
The preceding section has developed
the formations used in the calculation of
the secondary particles produced by the
heavy galactic primaries. Now we discuss
the basic assumptions used in this analy-
sis, and some of the resulting limitations
in the present calculations.
First we employ the straight ahead,
or one dimensional approximation. This
can be Justified by use of cosmic ray in-
teraction data as discussed in Reference 2
which shows that the heavy fragments emerg-
ing from the interaction site are strongly
peaked in the forward direction. It is
well known that the primary heavy parti-
cles suffer little angular deflection while
passing through matter.
Second, we use the energy independent
overlap cross section model used by Cleg-
horn, et al. (Reference 3) to fit his cos-
mic ray emulsion results. It was found
that cross sections were essentially inde-
pendent of energy in the energy range i00
MeV/nucleon to 30 GeV/nucleon. At energies
below i00 MeV/nucleon, the higher Z pri-
maries havea small range, but their cross ,C3
section will probably be underestimated
in this energyregion.
The fragmentation function, Po.(T,T')
represents the least well knownquantity
required in the calculation. Since the
energy dependenceof the secondaryfrag-
mentshas not yet beendescribed, wemake i_4the simple assumptionthat T=T', that is
the fragmentshave the samevelocity as
the primary ion. This assumptionis in
agreementwith an interaction model in
which the heavyprimary is stripped of
somefraction of its mass, and proceeds
on with unchangedvelocity. Twosets offragmentation parameterswere then used
10 -5
to explore the effects of various assump-
tlons on the final results. In the first
approximation, we have used a set of frag-
mentation parameters which assume one IH,
one 2He,and an equal probability of higher
Z fragments normalized to conserve Z in
the incident heavy primary. This approxi-
mation, when coupled to the equal velocity IC 6
approximation, leads to approximate con-
servation of energy, neglecting nuclear
binding energies and plon formation. The
second set of fragmentation parameters
are described in the paper by Curtis in
these Symposium proceedings.
Both sets of fragmentation parameters
are assumed to be independent of the pri- i0
0
mary particle energy, a conclusion that
is consistent with the results of Cleg-
horne.
Finally, the calculations have neg-
lected the interactions of primary and io-_
secondary ions with hydrogen. While the
I
results of Bertini's internuclear cascade
calculation can be applied to this prob-
lem by a proper transformation of rest
frames this has not yet been incorporated
in the calculation. The results given
for tissue thus neglect the fragmentation
induced by hydrogen. I0-4
RESULTS
Typical results of this calculational
method have been developed with the assump-
tions discussed. First, using the VH
group heavy particle spectrum presented
in Reference i, depth dose profiles for
a unidirectional beam of particles inci-
dent normally on a slab of water and alu-
minum are shown in Figures 2 & 3. The
total tissue dose, the 9_Fe (VH) dose,
and selected lower Z seCOndaries are
shown. For H20 , the two sets of fragmen-
tation parameters are represented by (i)
solid li_s and (2) dotted lines. We see
the expected rise and more gradual fall 1°-e
of the secondary dose components.
See I Frasmentatlon
Parameters
Set II Fragmentat£on
Parameeers
10 20 30 40 50
CM/CM 2 H20
Figure 2: HEAVY GALACTIC PRIMARY VH GROUP DOSE
60
26 Fe
70
i0 20 30 40 50 60 70
GM/CM 2 Aluminum
Figure 3: HEAVY GALACTIC PRIMARy VH GROUP
106
With the complete GCR spectra, as
represented by VH, LH, M and Helium com-
ponents, the results are as shown in Fig-
ure 4.
-r-
11 TM
He
l x
GMICM2_O
Figure 4: H_" GA_IC PRI_ T_ _SE
Meyer (Reference 4) has reviewed the
galactic cosmic ray data available up to
1969, and has presented an estimate of the
intensity of all the heavy primary compo-
nents below _ Fe. From this compilation
we have calculated the total depth dose
profiles in water for incident primaries
He to _.Fe9 and presented the results
n Figure°5.
,0-3
CONCLUSIONS
The results presented indicate the
general nature of the total depth-dose pro-
files we can expect in tissue and alumi-
num absorbers. Uncertainties in the frag-
mentation parameters lead to significant
changes in the total dose, as well as the
dose distribution among the secondary com-
ponents. Further work in defining the
fragmentation parameters and incorporation
of the hydrogen interaction results for
tissue would improve these dose estimates.
While only dose results are presented
in this paper, the penetrating particle
energy spectra are also calculated, and
can be used to examine the LET spectra for
further study of the biological implica-
tions of the galactic cosmic rays.
REFERENCES
i. S.B. Curtis and M.C. Wilkinson, "Study
of Radiation Hazards to Man on Extended
Missions" NASA CR-1037, May 1968
2. S.B. Curtis, W.R. Doherty, and M.C.
Wilkinson, "Study of Radiation Hazards
to Man on Extended Near Earth Missions",
NASA CR-1469, December 1969.
3. T.F. Cleghorne, P.S. Freler, C. J.
Waddington, Canadian Journal of Physics,
46, 5572 (1968).
4. P. Meyer, "Cosmic Rays in the Galaxy",
Annual Reviews of Astronomy and Astro-
physics, Vol. 7, Page i, 1969.
10-4
TOTAL DOSE
=<
10-5
6C
10-6
Figure 5:
10 20 30 40 50 60 10
GM/CM2 H20
HEAVY GALACTIC PRIMARY TOTAL DOSE
Separate Spectra, Excluding Proton Dose
107


Galactic cosmic ray heavy primary secondary doses

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