The computer program, MCFLARE, uses Monte Carlo methods to simulate solar flare occurrences during an interplanetary space voyage. The total biological dose inside a shielded crew compartment due to the flares encountered during the voyage is determined. The computer program evaluates the doses obtained on a large number of trips having identical trajectories. From these results, a dose D sub p having a probability p of not being exceeded during the voyage can be determined as a function of p for any shield material configuration. To illustrate the use of the code, a trip to Mars and return is calculated, and estimated doses behind several thicknesses of aluminum shield and water shield are presented

Karp, I. M.

Lahti, G. P.

English

MCFLARE code to calculate probable flare doses encountered on interplanetary missio

NASA Technical Reports Server

Probable solar flare doses encountered on an interplanetary mission as calculated by the MCFLARE code

I_OBABLE SOIAR FLARE DOSES ENCOU_r_ED ON AN INTerPLANETARY MISSION AS CALCLW_ATED BY THE MCFIARE CODE
Gerald P. Lahti and Irving M. Karp
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio
The computer program, MCFLARE, uses Monte Carlo methods to simulate solar
flare occurrences during au interplanetary space voyage. The total biological
dose inside a shielded crew compartment due to the flares encountered during
the voyage is determined. The computer program evaluates the doses obtained
on a large number of trips having identical trajectories. From these results,
a dose D_ having a probability p of not being exceeded during the voyage
can be de_ermined as a function of p for any shield material configuration.
The user of the code selects any number of solar flares considered to be
representative of the ones that will occur during future solar active periods
(these flares are generally selected from the flares that occurred during the
last solar active period 1956 to 1962). The flares are assumed to occur dur-
ing these periods. The dose at a distance of 1 AU from the Sun from each of
these flares behind any shield configuration investigated is input to the
MCFIARE code. The code accounts for the dependence of the dose received from
a flare on the distance from the Sun according to a (i/r) _ variation, where
r is the distance from the Sun and the exponent _ can be assigned. From
trajectory parameters, which are input to the computer program, the distance
from the Sun as a function of time during the trip is calculated.
To illustrate the use of the code, a trip to Mars and return is calcu-
lated, and estimated doses behind several thicknesses of aluminum shield and
water shield are presented.
INTRODUCT ION
The protons emitted by solar flares are the
most hazardous source of space radiation encount-
ered on an interplanetary space voyage which rapid-
ly traverses the Van Allen belts. To define shield-
ing requirements for biological protection from
solar flare protons encountered in manned inter-
planetary missions, a computer program MCFLARE
(ref. l) has been prepared which uses Monte Carlo
methods to simulate solar flare occurrences during
the trip and records the total associated biological
doses for the trip behind various shield material
configurations.
A set of flare events, considered to be repre-
sentative of those that will occur during future
solar active periods, is required. Presently, this
set is selected from the flares that occurred dur-
ing the last solar active period from 1956 to 1962.
The flares are assumed to occur randomly during the
trip. The doses behind the various shield config-
urations investigated have to be evaluated for each
flare, at a distance of 1 AU from the Sun, by using
another computer code such as one of those described
in Refs. 2 or 3. (Ref. 4 presents doses from solar
flare proton spectra behind two shield materials as
calculated by using Ref. 2.) These dose values are
input to the computer program MCFIARE. This pro-
gram provides for including the dependence of the
magnitude of the dose received from the flare on
the distance r from the Sun. This dependence is
taken to be of the form (ro/r) _, where r o is the
distance between the Sun and the Earth, and the ex-
ponent _ can be any arbitrarily selected value.
The Monte Carlo sampling procedure (analogous
to particle transport Monte Carlo) is used to de-
termine when flares are encountered on the trip,
which of the input flares occur, and the total dose
obtained from all flares encountered during the
trip behind each shield configuration. The comput-
er program tallies the doses obtained for a large
number of trips having identical trajectories and
from this, the distribution of doses incurred on
the mission for each shield configuration is ob-
tained. Each dose distribution determines a dose
Dp having the probability p of not being exceed-
ed as a function of p.
METHOD OF ANALYSIS
Any N flare events can be selected as repre-
sentative of the flare activity that will occur
during the space voyage. The doses from each flare
at a distance of 1 AU from the Sun behind one or
more shield material configurations investigated
are input to the computer. Each flare is assumed
to occur randomly on the average of once during the
solar active period Tref, which is of the order of
2000 days or 52_Years.
Monte Carlo Method to Determine Occurrences
of Flares During Trip
Inasmuch as flares are assumed to occur ran-
domly in the solar active period, the probability
of any flare occurring in the time interval dt is
(N_ref)dt m _ dt. Then the probability of no
flare occurring for time t is e-_ t and the
probability of a flare occurring in dt at time t
is e-_t_ dt.
In the Monte Carlo method, this probability of
flare occurrence in the time interval dt at time
t is equated to the probability of selecting a
random number in an interval d_ about _. If a
random number set uniformly distributed in the in-
terval (O,1) is selected, then the probability of
selecting a random number in d_ about _ is d_.
Equating these two probabilities, one gets
e-_t_ dt = d_
f e-_t'_ dt' =_0 _ d_'
t =-_ in(l - _)
S_
https://ntrs.nasa.gov/search.jsp?R=19720009992 2020-03-17T03:49:51+00:00Z
Inasmuch as both _ and i - _ are uniformly
distributed in the interval (0,i) an equivalent ex-
pression for t which results in the same exponen-
tial distribution is
t = - _ln _ (1)
By selecting a random number from a uniformly dis-
tributed set in the interval (O,1) the time be-
tween flare events is obtained from Eq. (1).
When an event has occurred, a particular flare
of one of the N is also selected by random num-
bers. The ith flare occurs when a new random
number occurs in the interval
i-l<_<i
N N i = l, 2, . .., N (2)
Dose values input to the code are calculated
by using the methods of Ref. 2, or 5, for each rep-
resentative flare using the solar flare proton in-
tensity and spectral shape as observed at the
Earth. The code permits an effect of the distance
from the Sun on the dose (or intensity) received
from a flare of the form (ro/r) _ where r o is the
distance from the Sun to the Earth, r is the dis-
tance of the spacecraft from the Sun during the
flare, and _ is an exponent that is assigned.
The code evaluates r for any time during the
trip by calculating the mission trajectory from in-
put parameters describing the two transfer ellipses
and the total trip time. The first ellipse is the
trajectory from the Earth to the planet and the
second describes the return trip.
The calculation proceeds as follows: Select-
ing a random number and using Eq. (1) determines
the time in the mission when a flare occurs. Se-
lecting another random number and using Eq. (2) de-
termines the particular flare which occurs. Know-
ing the time in the mission (and, hence, distance
from the Sun) and the particular flare, the dose
received through each shield configuration is
tallied. The duration of the flare event is then
added to the time in the mission when the flare
occurred to give the time when the event is over.
From a new random number and Eq. (1), the time
elapsed until the next flare occurs is calculated,
and so on. This procedure is repeated until the
total trip time has elapsed. The total dose from
all flare events encountered on the trip is deter-
mined for each of the shields considered.
Selection of Dp
This procedure is repeated for a large number
M of trips of identical trajectory. The code di-
vides the dose range into dose intervals that are
1 dose unit wide and tabulates the number of trips
A(D) during which doses that lie within each dose
interval are encountered. The cumulative fraction
of the total trips that encounter doses less than
the upper dose bound of each interval is also tab-
ulated (this is an estimate of the probability p
that a dose equal to the upper dose bound will not
be exceeded). From this tabulation, for any spec-
ified p, a dose Dp which has the probability p
of not being exceeded on the trip can be selected
for any shield. The standard deviation of this
value from the true value is shown in Ref. 1 to be
(3)
where M is the number of trips in the group in-
vestigated, and f(Dp) is the dose probability
density at D O (which is calculated from the tab-
ulated outputS. If A(Dp) is the number of trips
contained in the interval in which Dp occurs,
f(Dp) is approximately given by
A(Op)
f(Dp) = --
M
If A(D) is a widely fluctuating value in the vi-
cinity of Dp, averaged values of A(D) can be hand
calculated from the tabular computer output;
f(D_) is obtained from the averaged value of
A(D_). Note that for a given p, because f(Dp!
is independent of the number of trips, ODp varies
inversely as _/M.
To reduce the uncertainty associated with Dp
for a given number of trips, the code is written
so that the trips constitute a stratified sample
for the time-to-first-flare selected in accordance
with the exponential distribution exp[-(Nt/Tref_.
ILLUSTRATIVE EXAMPLE
An interplanetary trip to Mars and return has
been evaluated in order to illustrate details of
the method and to present some representative
shield requirements for such a mission. Water and
aluminum were the shield materials considered.
Selection of Flare Events
The flare occurrences during the last solar
active period 1956 to 1962 are assumed to be repre-
sentative of those that will occur during a future
active period. Webber in Ref. 5 has compiled a
record of these flares, their time-integrated
proton intensities, and spectra. From these rec-
ords, the 20 largest flares, based on proton inten-
sity_ were selected (the effect of neglecting the
rest of the flares is small for shields considered
here). These flares are listed in table I which
presents the integrated flux of protons having
energies greater than 50 MeV and some constants A
and Po associated with each flare. The spectral
shape of each flare is assumed to vary as
N > E = A exp -
Po
325
where N > E is the total number of protons per
square centimeter with energies greater than E.
The values of Po were obtained from Webber's
compilation, and the values of A were calculated
to be consistent with flux values of N > 50 MeV.
It has been observed that some of the flares
tend to occur in clusters. Table I indicates that
such clusters occurred in August 1958, July 1959,
November 1960, and July 1961. These four clusters
were selected as representative of the clustered
flare events that may occur and were assumed to be
events of 12-, 8-_ i0-, _id S-day durations, re-
spectively. The other nine single flares were each
assumed to have a duration of 2 days. During fu-
ture solar active periods, each of the four clust-
ered events and each of the nine single flare
events are assumed to occur randomly with a fre-
quency of once during the active period (taken to
be 2000 days).
TABLE I. - FLARES (FROM SOLAR ACTIVE PERIOD 1956 TO 1962)
SELECTED AS REPRESENTATIVE OF THO5E THAT WILL
OCCUR DURING FUTURE ACTIVE PERIODS
[Integral flux above 30 MeV, and spectral constants A and Po for
each flare are tabulated. ]
Flare N > 30 MeV Po A,
date protorm/cm 2 protons/cm 2
2-23-56 1. @<109 195 3.4)<109
1-20-57 2_<108 61 1.t_<109
8-29-57 1.2)<108 56 8.@<109
10-20-57 _b<107 127 3.3x108
3-23-58 2.5_108 64 1.1><109
7-7-58 2. _<10 8 62 1.2)<109
8-16-58 4)<107 64 1.7",<109 ]
8-22-58 7)<107 56 5.@<109 _ Clustered flare event
8-28-58 1.1><108 51 1.2><10103
5-10-59 9.6:<108 84 1.7"x1010
6-13-59 8. _< 107 a48 1.2";<1010
1.0<1010 ]
7-10-597_14-59 1" @<109.3x109 10480 2.6x1010 I Clustered flare event
7-16-59 9.1)<108 105 8.9><109 )
9-3-60 3.5><107 127 2.3)<108
11-12-60 I,31109 124 8.9x109
11-15-60 7.2×108 114 5.9><109 fClustered flare event11-20-60 4. _<107 118 3.4><109
7-12-61 4)<107 56 2"9x109 lClastered flare event
7-18-61 3><108 102 3.1><109 J
aEstimated.
Doses For Selected Flare Events
Table lip resents the doses obtained behind
various shield thicknesses from each of these 15
events. These doses were calculated by using the
Lewis Proton Shieldimg Code, described in Hef. 2,
and are representative of doses received at the
center of a spherical crew compartment having the
given shield thicknesses when the vehicle is lo-
cated at a distance of l AU from the Sun.
.Table II(a) presents the rem doses behind the water
shield, and table II(b) the rem doses behind the
aluminum shield, The data presented in this table
are input to the computer code MCFLARE.
Trajectory
The trajectory selected for the trip is one
that requires $58 days for the complete mission
(and happens to be one that results in near mini-
mum vehicle weight for a departure date in 1983).
The outward journey from Earth to Mars requires
280 days, then there is a _O-day stay at Mars, then
a 236-day return trip during which the vehicle ap-
proaches within 0.5 AU of the Sun.
TABLE U. - REM DOSES FROM SELECTED FLARE EVENTS BEHIND
VARIOUS THICKNESSES OF WATER AND ALUMINUM SHIELD AT
1 ASTRONOMICAL UNTF FROM SUN
(a) Rein dose behlr, d water shield
Shield thlckmess,
_/cm 8
rem
4_,10 27,75 20,79 13.05 9.05
1,07 .88 .19 .07 I .01
.43 .If, .07 .08 .O1
1.20 .88 .42 .81 .12
1.12 .40 .18 ._ .04
1.26 .48 .22 .Oa .04
1.03 .35 .17 .0_ .04
11,80 4.28 1.67 1.86 .87
.co .80 .10 .04 .86
49.59 23.86 13.78 6.11 3,55
,84 ,46 .29 .15 .86
48.34 26.49 18.78 8.80 4,85
5,48 8.6"/ 1.57 .71 .39
Co) Rem d_e eehtnd atumlmm shield
8-23-58
1-80-57
8-88-57
10-80-57
3-83-58
%7.58
Aug. 1958 duster
5-10-59
6-13-59
July I959 cluster
8-3-5O
Nov. 1980 cluater
J_/y 1981 c/uater
8ateld t_ckne_,
g/cm 2
10I 1,180I 20I4oI  150
Dose,
re_
58.°° [57.20 12°.77 1o._ i 14.1e.
2.11 I .8_ I .48 .24 .15
.gO ! .50 P .19 .10 .0_
1.73 ! 1.00 r .68 .38 .25
8.20 I .89 I .50 .25 .17
2,48 I 1.01 [ .56 .28 ,19
2.12 [ .83 [ .45 .24 .17
18.28 [ 8.0#6 I 5.36 8,58 1.68
1.85 I .49 [ .86 .14 .10
78,42 140.36 [25,18 12.79 8.12
1.86 I .71 [ .48 .2e .17
21.89 ] 61.17 )_,69 18._ 9,_
8.27 [ 8.42 [ 2.22 1.44 ,_
Flare date
11.15 9.26 1.23-58
• 18 .10 1-80-57
.06 .05 8-29-57
• 18 ,14 10-80-57
.12 .11 3-23-58
• 14 .12 7-7-56
.13 .11 Aug. 1958cluste]
1.18 .93 5-10-59
.08 .06 6-13-59
5.86 4.59 July 1959 cluate]
• 13 .10 5-3-eo
7.17 5.51 Nov, l_Ocb_g_e:
• 66 .52 July 1961 cluate]
Discussion of Results
Figure 1 shows the distribution of dose ob-
tained for a large number of identical trips. The
figure presents the rem dose distribution behind
_0 g per square cm of water shield obtained from a
computer run of AO 000 trips. The effect of dis-
tance on dose was assumed to vary as (i/r) 2.
In Fig. l(a), A(D), the number of trips on
which a dose between D - 1 and D has been en-
countered, is plotted against D. A smoothed
curve of this distribution A(D) (obtained by av-
eraging seven values centered about each A(D)) is
also shown as a dashed line in this figure.
In Fig. l(b)_ p(D) the probability of not ex-
ceeding Eany dose D is shown plotted against D
D
1
p(D) = _ _ A(i)
i=l
where M is the number of trips considered in a
computer run. For the case of Fig. l(b),
D
1 E A(i)p(V) _o ooo
i=l
326
If Dp is defined as that dose which has a
probability p of not being exceeded, then from
Fig. l(b), D0.99 for the group of 40 000 trips,
occurs in the dose interval between 93 and 94 rem
and is Selected as the upper bound of the interval,
namely, 94 rem.
The dose probability density function f(D) is
approximately equal to A(D)/M. At a D0.99 of
94 rem_ the value of f(D), evaluated by using the
smoothed value of A(D), is
f(Do.99) = 26= O. 00065/rem
_0 000
and the standard deviation from Eq. (3) is
°DO 9^ = 0.77 rem.
• _here is a 97.7 percent confidence that the
true dose D8.99 is less than D0.99 + 2oD0.99;
is less than 95.5 rem.
Table III presents values of D0.99 deter-
mined by using the computer code for rem doses be-
hind various thicknesses (expressed as g/cm 2) of
aluminum shield and water shield. These values
are presented for both the ease where the dose re-
ceived from a flare event is assumed to vary as
(l/r) 2 (considered representative of what might be
a solar proton diffusion model in space) and for
the case where there is no effect of distance
(i.e., distance effect, g(r) = 1). Also shown in
the table are the values of OD^ ^^ associated
U._ .
vith each D0.99 and the correspondzng values of
D0.99 + 2O'D0.$9.
,f
/
t"
/
./
¢'
/
/m
30 1() 511 60 _ 80 _ 1_ 11o
(8) CIJ_U_IIVE PRO_B&_ (If IRIP _ICOO_m[RING DOSEI_$S _ D.
Figure 1. - C_lu_.
TABLE IIL - VALUES OF D0.99 AND CORRESPONDING STANDARD
DEVIATION BEHIND VARIOUS THICKNESSES OF WATER AND
ALUMINUM DETERMINED FROM GI_)UP OF 40 O0O TRIPS
(&) Rein dose behind water shield
Distance C_anflty
effect,
g(r)
aDo. 99
DO. 99 + 2aD0. 99
1 D0.99
aDo. 99
DO.99 + 3aDo. 99
Shield thickness,
g/cm3
10161
354 130
2.0 1.3
358 141.6
165 90
1.7 1.0
168.4 9_i
30130140
Dcee,
rein
94 55 37
.77 ,44 .31
95. 5 55.9 37.6
63 35 23
.57 .35 .2
64.1 35.5 23.4
('o) Rem dose behind aluminum shield
Distance
effect,
s(r)
I/r 2
_t_
D0.99
aDo. 99
DO. 09 + 2aD0. 9_
DO. 99
aDo. 99
DO 99 + 2o D
" 0.99!
Shield thickness,
101151.1301 401 I 80
Dose,
fez
3'/8 i 213 146 87 62 48 39
3.3 1.8 1.4 .7_ .$4 .42 .31
382._ 216.3 148.8 88.5 63.1 48.8 39.6
250 138 94 58 40 31 25
2._ 1. .91 .5| .31 .2_ .32
354.4 141 95.8 59.2 40.6 31.5 25.4
327
In _'ig. 2 the values of D0-99 + 2o])0 99 are
plotted against shield thickness. In Fig. "2(a),
the rem dose is plotted against water shield thick-
ness for cases of g(r) = 1/r 2 and g(r) = i.
Figure 2(b) is a similar plot of the rem dose be-
hind the aluminum shield. From curves such as
Fig. 23 one can select a shield thickness such that
on a given mission, there is a probability p of
not exceeding an accumulated dose Dp.
These curves indicate how much more effective
water is as a shield material than aluminum for
shielding against solar flare protons on the basis
of grams per square centimeter of material neces-
sary to maintain a given dose level inside the
crew compartment. Also shown for this mission is
that a 1/r 2 distance effect on dose received
from a flare can have an appreciable effect on
shield requirements when the mission trajectory
brings the vehicle to within 0.5 AU of the Sun.
This result indicates a need for information re-
garding the effect of position from the Sun on ra-
diation encountered from a flare.
COMPUTPR PROGRAM
Complete data input instructions for the com-
puter program MCFLARE are presented in Ref. 1.
The version of the code presented is operational
on the Lewis Research Center IBM 709A-II/70&4 com-
puter system. Execution times for the examples
discussed previously in this report were about
2 minutes per group of AO 000 trips. The MCFLARE
code is available from the Radiation Shielding In-
formation Center of 0akRidge National Laboratory
as code package CCC-93.
!
2O 30 40
WATERSHIELDTHICKNESS,_cm2
(A) REMDOSEBEHINDWATERSHIrlD
Figure2. - Valuesof DO.99+ 2%0 99 for various
thicknessesof waterandaluminu_shields,and
for casesofdistance ffectvaryingas l/r _ and
noeffectofdistance.Numberoftrips, 40000.
REFERENCES
i. Lahti, Gerald P.; Karp, Irving M.; and Rosenbaum, Burt M.: MCFLARE, A
*'^_ _ Code to _m_=_._ _-_^_ _7_o,._ Evcnts and Estimatc _-
able Doses Encountered on Interplanetary Missions. NASA TN D-4511,
1968.
2. Hildebrand, R. I.; and Renkel, H. E.: The Lewis Proton Shielding Code.
NASA TMX-52166 , 1966.
5. Kinney, W. E.: The Nucleon Transport Code, NTC. Rep. ORNL-5610, Oak
Ridge National Lab., Aug. 196A.
_. Scott, W. Wayne: Estimate of Primary and Secondary Particle Doses Be-
hind Aluminum and Polyethylene Slabs due to Incident Solar-Flare
and Van Allen Belt Protons. Rep. 0RNL-RSIC-18, Oak Ridge National
Lab., July 1967.
5. Webber, W. R.: An Evaluation of the Radiation Hazard Due to Solar-
Particle Events. Rep. D2-90469, Boeing Co.; Dec. 1965.
328


Probable solar flare doses encountered on an interplanetary mission as calculated by the MCFLARE code

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