II

_ASA

_Te_chnical

__2987 _

_::=__ paper

I

June 1990

Improved Model for

Solar Cosmic Ray

Exposure in Manned

Earth Orbital Flights

i ,,:,4-:i' ::' :_

John W. Wilson, ........

John E. Nealy,

William Atwell,

Francis A. Cucinotta,

Judy Lo Shinn,

and Lawrence W. Townsend :

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NASA

Technical

Paper

2987

1990

National Aeronautics and

Space Administration

Office of Management

Scientific and Technical

Information Division

Improved Model for

Solar Cosmic Ray

Exposure in Manned

Earth Orbital Flights

John W. Wilson

and John E. Nealy

Langley Research Center

Hampton, Virginia

William Atwell

and Francis A. Cucinotta

Rockwell International

Space Transportation Systems Division

Houston, Texas

Judy L. Shinn

and Lawrence W. Townsend

Langley Research Center

Hampton, Virginia
• =

Z2
Abstract

A calculational model is derived for use in estimating Solar cosmic

ray exposure to critical body organs in low Earth orbit at the center of

a large spherical shield of fixed thickness. The effects of the Earth's

geomagnetic field and the astronauts' self-shielding are evaluated explicitly. The geomagnetic field model is an approximate tilted eccentric

dipole with geomagnetic storms represented as an impressed uniform

field. The storm field is related to the planetary geomagnetic index Kp.

The Shuttle geometry is introduced into the resultant computer code using the Shuttle mass distribution surrounding two locations on the flight

deck. The Shuttle is treated as pure aluminum and the astronaut as soft

tissue. Short-term average ftuence over a single orbit is calculated as a

function of the location of the lines of nodes or long-term averages over

all lines of nodes for a fixed inclination.

Introduction

Solar cosmic rays observed in low Earth orbit first

passed through the Earth's magnetic field. Those

particles that are able to penetrate the geomagnetic

field must further penetrate the walls of the spacecraft before exposing the human occupants. As a

result of interactions in the vehicle structure and the

bulk tissues of the astronauts' bodies, the composition of the rays is greatly altered. Any reasonable

estimate must account for geomagnetic effects, the

atomic and nuclear interactions, and the spacecraft

and human body geometry.

During times of increased solar activity, small

amounts of the solar plasma are ejected into interplanetary space. When this plasma interacts with the

Earth's magnetic field, large distortions of this field

result in geomagnetic storms. Since the energetic

solar flare particles often arrive during such geomagnetic disturbances, the penetration of the energetic

protons into the magnetospheric cavity can be vastly

different from that seen under quiet conditions.

In a previous report (ref. 1), we derived a simple

model for estimating exposure to the critical organs

of an astronaut within a large spherical shield using a

centered-tilted dipole model of the geomagnetic field

and an approximate geomagnetic storm field as an

impressed uniform field. In the present work, approximate expressions are derived for a tilted eccentric dipole model. Geomagnetic model parameters

are used to better approximate the recently calculated worldwide vertical cutoffs of Shea and Smart

(ref. 2) for the 1980 magnetic field parameters than

in the previous study (ref. 1). The average transmission factors of the approximate model agree well with

the transmission factors of Smart and Shea (ref. 3).

The approximate orbit-averaged transmission factors

are found as a function of location of the ascending

line of nodes, and dose is given for the worst-case

exposed orbit for various geomagnetic storm conditions. A comparison is made with earlier work.

A necessary requirement for space mission analysis is a reliable method of calculating the anticipated

dose distribution in the human body. In the case

of extraterrestrial radiations, a model is required for

evaluating the effects of the geomagnetic field in addition to the interaction with the spacecraft structure and the human body. Described herein are additional computer subroutines which calculate the

proton dose within the Shuttle averaged over five

major segments (upper limbs, lower limbs, upper

trunk, lower trunk, and skull) of the blood-forming

organs (BFO), ocular lens, and skin by treating the

human body and vehicle geometry in detail (refs. 4

and 5) but assuming isotropicity of the incident primary particles. The calculation uses an approximate

form of transport theory in which nuclear star effects are incorporated (refs. 1 and 6). The output

of the program is in terms of physical dose and dose

equivalent.

Geomagnetic Effects on Orbital

Environment

Charged particles arriving at some location within

the geomagnetosphere are deflected by the Lorentz

force ev × B which prevents penetration for some

directions of incidence and some energies. Such

phenomena were extensively studied by St6rmer

(ref. 7) for a dipole magnetic field which provides

the basis for classifying the orbital trajectories of

charged particles arriving at some location within

the field. As a part of StSrmer's theory, there exist allowed trajectories with no connection to asymptotic trajectories now recognized as trapping regions
associatedwithVanAllenradiation.Numericalsolutionsto thechargedparticleequationsof motionin

morerealisticgeomagneticfield modelswereintroducedby McCracken(ref.8) andfurtheradvanced

by SmartandShea(refs.2, 3, and9). Our purposeherewill not beto supplanthevastlydetailed

numericalworkbut to seeka simpleanalyticformto

reasonablyapproximatethemoregeneralnumerical

solutions.

The geomagneticfield can be reasonably

approximatedby a tilted dipole with moment

M = re331 500 nT displaced from the Earth's center

by 430 km or 0.068re where rc = 6378 km. The

tilt angle is 11.7 ° at 69 ° W longitude. The magnetic

quadrupole contributions are then about l0 percent

at the surface and decrease to 5 percent at 2re.

Higher-order moments are even smaller. The motion of charged particles in the geomagnetic field was

studied extensively by StSrmer. We outline his methods herein. In spherical coordinates, St5rmer showed

that the azimuth ¢ is an ignorable coordinate possessing an integral for the particles trajectory such

that

"7 (ZeM_ sin 0

cosw- mvrsin0 \ mvc / r 2 (1)

where m is the mass of the particle, Ze is the charge,

v is the velocity, c is the velocity of light, r is radial

distance from the center of the field, 0 is colatitude, "/

is an integration constant, and w is the angle between

the velocity vector and the azimuthal direction. The

allowed StSrmer regions consist of the space for which

icoswl_ 7 (ZeM_ sinO

mvr sin 0 \_] _g- <- 1 (2)

Further analysis of the condition in equation (2)

shows stable trapping regions as well as the

St6rmer main cone of transmission given for

"7= 2mv(ZeM/mve)l/2. The St6rmer main cone is

given (ref. 10) by the solid angle element

= 2 (1 + cos ) (3)

which contains the allowed directions of arrival for

particles of rigidity R (momentum per unit charge)

given by

M sin 4 0

R = (4)

c r2 [1 + (1- sin30cosw)l/2] 2

Henceforth we replace the colatitude 0 by the magnetic latitude Am and note that f_ varies from 0 to

2

47r reaching its half-value at w' = rr/2 including angles up to the vertical direction. The vertical cutoff

model is expressed as

a _ 4_ U [R - Rc (Am)] (5)

where the vertical cutoff rigidity from equation (4) is

M

Rc (,X.,)= 2 cos4 ),m (6)

and U(x) is the unit step function.

Not included in the above formalism are those

trajectories which are cut off by the shadow cast

by the solid Earth. The fraction of the solid angle

covered by the Earth's shadow is estinmted, assuming

that the curvature of the local trajectories is large

compared with the Earth's radius (ref. 10). Then

the solid angle fraction is

ftsh-- [l+c°s(sin-l!)147c 12 (7)

The corrected solid angle for the vertical cutoff model

is then

a = _shU [R - R c (_,n)] (8)

which leaves the local solid angle open to transmission of charged particles of rigidity R at altitude r

and geomagnetic latitude Am.

Spacecraft in low Earth orbit (LEO) are typically

in circular orbits which simplifies the analysis. The

orbit plane is inclined with respect to the equatorial plane. Since the Earth's angular momentum

(spin) and the spacecraft orbital angular momentum

are conserved, the angle between them is fixed and

equal to the inclination angle i. The magnetic axis

rotates with the Earth and therefore precesses about

the rotational axis within a 24-hour period. The geographic location of the ascending node likewise moves

around the geographic equator every 24 hours. The

inclination of the orbit plane relative to the magnetic

axis im likewise is periodic. If r/is the geographic coordinate of the ascending node line, then

cos im = cos i cos Om+ sin i sin 0m cos (r/- Cm - 90 °)

(9)

where Om and Cm are the magnetic north pole colatitude and longitude. The average transmission factor

around this orbit F is then

F(R,i,r/) = Qshi-_- _o TM U[R - RC(A)]d)_ ira - _,. flsh (i0) ira

where Am is the magnetic latitude with cutoff at R

as given by

Rc(),m) = n (11)
We notethat im goes through a maximum and

minimum orbit corresponding to qmax = Cm - 90 °

and Vmin = Cm + 90 ° for which im -= i + 0m and

ira = li- Oral, respectively, as we have shown elsewhere (ref. 1).

We may also calculate the long-term average over

many days of orbits by averaging equation (10) over

the node angle r1 as

1 fo" ira-Am 1 L" " -

-F(R,i) = -_ £_sh_ dn = - f2sh_m - Am do (12)

?_Ti2 71" _D2

where

cos im -- cos i cos 0m + sin i sin Ora cos ¢

and

(13)

o ] (A,,,<_I_- o._1)}

cos A m -- cos i cos 0m

?'A = c°s-1 [ s'_nisinO--'---_ (li - Oral< Am _<i + Ore)

n (Am > i + Ore)

Equation (12) may be rewritten as

(14)

ff(R'i)=_sh[(1---_) - --Trl_7r)_m dO]_ --zra (15)

where the last integral is approximated by a numerical quadrature. The results of equation (15) are

compared with the numerical calculations of Smart

and Shea for 400-kin (216-n.mi.)orbits at several inclinations in figure 1 for this centered dipole field

model with Om = 11.7 ° (tilt angle) and longitude

era =-69 ° (69°W).

An important correction to the centered dipole

field is the displacement of the geomagnetic dipole

430 km (232 n.mi.) from the Earth's center. Unfortunately, the formalism is very complicated, since the

distance r from the dipole center is no longer constant

even for a circular orbit. The offset dipole decreases

the cutoffs in the Atlantic hemisphere defined by the

meridinal plane normal to the tilt direction and increases the cutoffs in the remaining hemisphere over

the Pacific. We define two cutoff functions for centered dipole fields as

14.9

Rj()_m) = (7.+-_j)2 c°s4)%n

(16)

'- 1

g

._ .5

-- Present

- - Smart and Shea fief. 4)

-I 100 101 102

Rigidity, GV

(a) Orbit inclination, 20°.

" Present

- - Smart and Shea fief. 4)

JI

-I 100 101 10 2

Rigidity, GV

(b) Orbit inclination, 30°.

Present

Smart and Shea (ref. 4) - -

•_ .5

E:

#0

10-I 100 10 1 102

Rigidity, GV

(c) Orbit inclination, 40°,

-- Present

Smart and Shea fief. 4)

-1 i0 0 10 1 102

Rigidity, GV

(d) Orbit inclination, 50°.

Figure I. Dipole maximum and minimum cutoff model and

numerical simulation of exact geomagnetic field model.

where j=A, 5A=593km (320n.mi.) for the Atlantic hemisphere; j = P, 5p = -504 km (-272 n.mi.)

for the Pacific; Am is the usual magnetic latitude

which depends on the hemisphere; and r is the geocentric radius of the orbit. The value 14.9 GV

is found from the value of the dipole moment of

rea 31 500 nT, and 5j were chosen to match the minimum equatorial cutoff in the Atlantic region of Shea

and Smart (ref. 9) and the maximum cutoff in the

Pacific. The calculation of the orbit average transmission factor is as before except that the two hemispheres are considered separately as

[

ff(R,i,r]) = i_2sh _ra -- _A + ira _ )kp] (17)

Z Zrn im J

where

and

RA()_A) ----/{ (18)

Rp(,_p) = R (I9)

Similarly, the long-term average of equation (12) is

extended to each hemisphere as

if(R,i) = _ \ im / \ Zrn /

.4 P

(20)

where the integrals are evaluated as described for

equation (15). The average transmission factors

of equation (20) are compared with the numerical

calculations of Smart and Shea (ref. 3) in figure 2.

The pole's tilt angles (ref. 11) are given in table 1
alongwithsuitablychosenlongitudesandareshown

in relationto the verticalcutoffrigiditiesof Smart

andSheain figures3 and4.

o

•_ .5

E0 •

10 -1

Present (eq. (20))

Smart and Shea (ref. 3)

it

210oJ, ' / "" "" "

n

SM/"-

...... d._ _--_'-a , _ , J.,l • , ...... 1

100 10 1 102

Rigidity, GV

(a) Orbit inclination, 40°.

1

V

] Present (eq. (20))

] Smart and Shea (ref. 3)

_ .5

"_ q = 211°

[..

0 _" '_ ' • . ,,_',,.J....... I

10-1 100 10 1 10 2

Rigidity, GV

(b) Orbit inclination, 50°.

Figalre 2. Offset dipole model average transmission factors

with detailed calculations of Smart and Shea (ref. 3) and

maximum and nfinimum transmission factors.

Table 1. Geographic Locations of Offset Poles in

Present Calculations

Magnetic Longitude, [ Tilt,

pole era, deg ] Om, deg

North -69 I6

South 121 22

Earth is locally present, the plasma interacts with

the geomagnetic field in which the plasma pressure

performs work on the local geomagnetic field. The

initial impact produces hydromagnetic waves causing a general increase in geomagnetic intensity. As

plasma flow is established, it generates large electric

ring currents and a corresponding imprcssed magnetic storm field. In the initial phase (hydromagnctic

wave), the storm field is parallel to the equatorial

field after which the storm field reverses in the main

phase of the storm caused by ring currents within the

magnetopause and opposes the quiet field, to cause a

net decrease of the field strength. The main phase is

followed by slow recovery to the quiet field conditions

(ref. 11).

The magnetic storm model used here assumes a

uniform magnetic field impressed on the normal quiet

field (ref. 10). The storm field strength can be found

from the change in the horizontal field component

around the geomagnetic equator. We represent this

field by Hst. Typical values of//st in the main phase

range from substorm values -10 nT to severe storms

with -500 nT. On rare occasions, for very intense

storms, the storm field exceeds -1000 nT,

Magnetic disturbances have been observed for

many years, and various classification schemes for

such disturbances have been proposed. The planetary magnetic index /_p is based on magnetometer

measurements of 12 stations worldwide. The Kp index is related to a derived planetary index ap and

storm field strength by Bartels (ref. 11) given in

table 2.

Table 2. Relation of Magnetic Indices to Magnetic

Storm-Field Strength

Kp ap

0 0

1 4

2 7

3 15

4 27

5 48

6 80

7 132

8 207

9 400

lHstl,nT

0

8

14

30

54

96

160

264

414

8OO

During times of intense solar activity, the solar The vertical cutoff rigidity as given by equaplasma emitted in solar flares and subflares advances tion (16) is further modified to approximate the eloutward and arrives at 1 AU from the Sun. If the fects of geomagnetic disturbances. It was shown by
90 E

180 E

GM

270 E

Figure 3, Vertical cutoff contours in northern hemisphere showing location of North magnetic pole.

270 E

180 E

GM

90 E

Figure 4. Vertical cutoff contours in southern hemisphere showing location of South magnetic pole.

5
Kuhn, Schwamb, and Payne (ref. 10) that tile appropriate equation is

1__ cos4 Am + _- cos6 Am 1

Rc(Am)

(21)

for the centered dipole field. In the context of our

approximation of the offset-tilted dipole field, we get

t4,9 cos 4 Am 1 +

Rj(Am)= (r + bJ) 2 iiI _m 1

(22)

This vertical cutoff replaces equation (16) and applies

to storm conditions. Note that the cutoff is zero

whenever the result of equation (22) is negative. The

corresponding transmission factor on the worst ease

orbit Q/ ,,_ 211 °) is shown in relation to the quiet

field average transmission factors of Smart and Shea

(ref. 3) in figure 5.

Dose Estimation

In passing through tissue, energetic protons interact mostly through ionization of atomic constituents

by the transfer of small amounts of momentum to

orbital electrons. Although the nuclear reactions are

far less numerous, their effects are magnified because

of the large momentum transferred to the nuclear

particles and the struck nucleus itself. Unlike the

secondary electrons formed through atomic ionization by interaction with the primary protons, the radiations resulting from nuclear reactions are mostly

heavy ionizing and generally have large biological effectiveness. Many of the secondary particles of nuclear reactions are sufficiently energetic to promote

similar nuclear reactions and thus cause a buildup of

secondary radiations. The description of such processes requires solution of the transport equation.

The approximate solutions for the transition of protons in 30-era-thick slabs of soft tissue for fixed incident energies have been made (ref. 6). The results of

such calculations arc dose conversion factors for relating the primary monoenergetic proton fluence to

dose or dose equivalent as a function of position in a

tissue slab.

Whenever the radiation is spatially uniform, the

dose at any point X in a convex object may be

calculated (ref. 12) by

D(x) = Rn[zz(ft),E]¢(f_,E) d_ dE (23)

where Rn(z, E) is the dose at depth z for normal incident protons of energy E on a tissue slab, ¢(f't, E)

O

_ .5

F-

[

0

lO-i

Present

Smart and Shea (ref. 3)

nT Hst, ///' ////,,

#/"

. ---.,--_-:_r_.....".... i .... ,

I0 o 101 10 2

Rigidity, GV

(a) Orbit inclination, 30 °.

O

•:_ .5

o

1o-1

Present

Smart and Shea (ref. 3)

1

-1000 -_ Z /

Hst, n T .,. _"

4oo -_\ iii

-100 _#,,"

_Y , ,'

10 0 10 I 10 2

Rigidity, GV

(b) Orbit inclination, 40°.

Present

Smart and Shea (ref. 3)

rd,

Hst , n T j s _

•_ .5 -1000 -.. /Z/ "

.- 4oo -_ il/ z

0 ...... ,,,...I-- _," ....... I ........ I

10-1 10 0 10 1 I0 2

Rigidity, GV

(c) Orbit inclination, 50°.

Figure 5. Maximum transmission factor for various storm

fields and quiet time average transmission of Smart and

Shea. r/= 211°.

is the local differential proton fluenee along direction

Ft, and zx(ft) is the distance from the boundary
along12to point x. It has been shown that equation (23) always overestimates the dose but is an accurate estimate when the ratio of the proton beam

divergence due to nuclear reaction to the bodies' radius of curvature is small (ref. 12). Equation (23) is

a practical prescription for introducing nuclear reaction effects into calculations of dose in geometrically

complex objects such as the human body. The main

requirement is that the dose conversion factors for a

tissue slab be adequately known for a broad range of

energies and depths. The dose conversion factors for

tissue were derived in reference 6, and a correction

for an aluminum shield was found in reference 1. The

spacecraft geometry is taken as an aluminum sphere

of large radius.

Method for Shuttle Geometry

In the previous section, the calculation of astronaut exposure in the center of a large aluminum

sphere of arbitrary thickness was derived for a specific

orbit with either the quiet geomagnetic field or with

a geomagnetic disturbance. We denote that result by

Dsph(ts), and it has a different value for each critical organ for which exposure within the aluminum

sphere of thickness ts is evaluated. Within the context of assumed isotropic radiation, the exposure at

some location within the Shuttle is

_0 °C D = Dsph(ts) f(ts) dts (24)

where f(ts) describes the mass distribution of the

Shuttle structure assumed to be aluminum about

that particular location. Physically, f(ts) dts is the

solid angle fraction for which the areal density to the

Shuttle surface Iies between ts and ts +dts. The

cumulative distribution of areal density is given by

j_o ts

Fc(ts) = f(ts) dts (25)

and is shown for two locations in the Shuttle (ref. 5)

in figure 6. Also shown in figure 6 are the following

approximate functions:

fl(ts) =

0.176 (1 < ts < 2)

tS -- --

/

0.113 (2 < ts < 20)

t8 _ --

0.353 (20 < ts < 120)

tS -- --

(26)

and

0.303 (1 < ts < 6) }

t8 h --

f2(ts) = __0"147 (6 < ts < 132)

t8 -- --

(27)

where the functions are understood to be zero outside

of specified ranges. Formulas (24), (26), and (27) are

used in conjunction with the methods described in

previous sections to estimate Shuttle exposure in the

two locations referred to in reference 5 as dosimeter

location numbers 1 and 2 which comprise the most

and the least shielded locations in the Shuttle crew

compartment, respectively. The method can be easily expanded to include more astronaut organs and

other Shuttle locations.

100-

8O

V1

0,)

% 60

40

#.

2O

Dosimeter number 2 -7

/

- ,_

Dosimeter number 1

0 1 I I ,li''[ ' I I ailall i I , ltaHi

10 0 l0 I 10 2 10 3

Equivalent A1 thickness, T, g/cm 2

Figure 6. Mazs distribution of two locations on Shuttle flight

deck.

Results

The maximum exposure limits in force for the

Space Station Freedom (ref. 13) are shown in table 3. The dose and dose equivalent to critical body

organs for an aluminum shield 1 g/cm 2 thick are

shown in tables 4 through 7 for various storm conditions (Hst). The exposures are shown for a worstexposed orbit (r/ = 211 °) and the average over all

r/. The average is shown, since average transmission

factors are calculated by several groups, and one may

be tempted to use the transmission factor appropriate for the galactic cosmic ray background (refs. 14

and 15). It is clear from the results in tables 4

through 7 that such use of average cutoffs provides

exposure estimates which could be too small by a
factorof 2 to 10. Suchanunderestimatcis clearly

unacceptable.Furthermore, comparing the current

dose estimates with values for transmission factors

derived for a tilted concentric dipole field (ref. 1), we

see that the dose values of the current field model are

a factor of 3 to 5 higher. Tile eccentric field had two

effects which lower the cutoffs. The offset displaces

the South magnetic pole to lower latitudes and lowers the geomagnetic cutoff values over the Atlantic]

The methods derived herein allow evaluating exposures as a function of the location of the line of nodes

and should provide acceptable estimates of exposure.

Table 3. Ionizing Radiation Exposure Limits for Space

Station Freedom Astronauts

Exposure

interval

30 days

Annual

Career

Dose equivalent, cSv, for--

Blood-forming

Skin Eye organs

150

300

600

100

200

400

25

5O

al00 400

aDependent on gender and age at initial exposure.

Observing the levels of exposure in low inclination orbits (i _ 30°), a significant exposure could

clearly occur if particle arrivals coincided with a large

magnitude (Kp _ 9) magnetic disturbance. On the

basis of the present analysis, a more in-depth study

of potential solar flare exposure of the Space Station

Freedom seems warranted. Such a study should include a review of the history of major geomagnetic

disturbances in proximity to solar particle events, a

review of alternate geomagnetic storm models, and

a review of the specific Space Station Freedom shield

geometry.

The exposure for Shuttle flight in a 400-km

(216-n.mi.) orbit with a 50 ° inclination are shown

in table 8 for the February 23, 1956, solar event

spectrum as compiled by Foelsche et al. (ref. 16).

A magnetic storm was assumed to be in progress

with an impressed field of -100 nT. The results

shown in table 8 are for the long-tcrm, average geomagnetic cutoffs, since these arc directly comparable

with the work of other geomagnetic models (refs. 14

and 15). We note, however, that actual exposure

could be greatly different depending on the location

of the line of nodes at the time of arrival of the highenergy flare particles.

Concluding Remarks

The present code should be useful for assessing

the potential exposure in low Earth orbit missions if

the Solar spectrum and state of the geomagnetic field

are known.

It was shown For low inclination orbits (i _ 30 °)

that a significant exposure could occur if the particle's arrival coincided with a large magnitude (Kp

9) magnetic disturbance. On the basis of the present

analysis, a more in-depth study of potential solar

flare exposure of Space Station Freedom seems warranted. Such a study should include a review of the

history of major geomagnetic disturbances in proximity to solar particle events, a review of alternate

geomagnetic storm models, and specific Space Station Freedom shield geometry.

NASA Langley Research Center

Hampton, VA 23865-5225

April 17, 1990

L

8
Table 4. Skin Dose Behind Aluminum Shield 1 g/em 2 Thick During February 25, 1956, November 12 13, 1960, and August 4, 1972,

Events With Various Storm Fields

Skin dose, cGy, during

Feb. 1956 for Hst, nT, of Nov. 1960 for Hst , nT, of-- Aug. 1972 for Hst, nT, o_

Inclination,

deg - 100 -500 -900 - 100 -500 -900 - 100 -500 -900

30, max

30, avg

40, max

40, avg

50, max

50, avg

<0.I

<.1

2.9

.4

17.0

4.8

2.2

.3

19.0

5.4

31.0

13.0

12.0

2.6

28.0

9.8

39.0

18.0

0

0

6.3

.8

47.0

13.0

4.9

.5

53.0

15.0

89.0

36.0

34.0

7.1

79.0

28.0

111.0

51.0

0

O

19.0

2.3

140.0

39.0

15.0

1.6

170.0

47.0

280.0

110.0

100.0

22.0

240.0

86.0

340.0

160.0

Table 5. Skin Dose Equivalent Behind Aluminum Shield 1 g/cm 2 Thick During February 25, 1956, November 12-13, 1960, and August 4, 1972,

Events With Various Storm Fields

Skin dose equivalent, cSv, duringFeb. 1956 for Hst , nT, of- Nov. 1960 for Hst , nT, of-- Aug. 1972 for Hst , nT, of -

Orbit

inclination,

deg -100 -500 -900 -100 -500 -900 -100 -500 -900

301 max

30, avg

40, max

40, avg

50, max

50, avg

<0.1

<.1

4.3

.7

24.0

6.8

3.3

.4

27.0

7.7

44.0

18.0

17.0

3.7

39.0

14.0

54.0

25.0

0

0

8.9

1.1

68.0

18.0

7.0

.7

78.0

22.0

130.0

52.0

49.0

10.0

110.0

40.0

160.0

74.0

0

0

25.0

3.1

200.0

53.0

20.0

2.1

230.0

63.0

380.0

150.0

140.0

30.0

333.0

120.0

470.0

220.0

9
Table 6. BFO Dose Behind Aluminum Shield 1 g/cm 2 Thick During February 25, 1956, November 12-13, 1960, and August 4, 1972,

Events With Various Storm Fields

Orbit

inclination,

deg

30, max

30, avg

40, max

40, avg

50, max

50, avg

BFO dose, cGy, during -

Nov. 1960 for Hst, nT, of Aug. 1972 for Hst, nT, of -

- 100

<0.1

<.1

1.4

.3

4.6

1.5

Feb. 1956 for Hst, nT, of

- 500

1.0

.2

4.9

1.5

7.6

3.2

-900

3.3

.8

6.8

2.5

9.3

4.4

-100

0

0

1.3

.2

6.2

1.8

-5O0

.9

.1

6.7

2.0

11.0

4.4

-9OO

4.4

1.0

9.5

3.4

13.0

6.2

-tO0

0

0

2.5

.4

15.0

4.2

-500

1.8

.2

16.0

4.7

27.0

11.0

-900

10.0

2.3

24.0

8.8

33.0

16.0

Table 7. BFO Dose Equivalent Behind Aluminum Shield 1 g/cm 2 Thick During February 25, 1956, November 12 13, 1960, and August 4, 1972,

Events With Various Storm Fields

Orbit

inclination,

deg

30, max

30, avg

40, max

40, avg

50, max

50, avg

BFO dose equivalent, cSv, duringFeb. 1956 for Hst, nT, of Nov. 1960 for Hst, nT, of-- Aug. 1972 for Hst , nT, oK

-I00

<0.1

<:.1

2.3

.5

7.3

2.3

--5OO

1.7

.3

7.6

2.3

12.0

5.0

-900

5.1

1.2

10.0

3.9

14.0

6.9

-IOO

0

0

1.8

.3

8.5

2.5

-500

1.3

.2

9.2

2.7

15.0

6.1

- 9O0

6.1

1.3

13.0

4.7

18.0

8.6

-IO0

0

0

3.6

.5

21.0

6.0

-500

2.6

.3

23.0

6.7

38.0

15.0

-9OO

15.0

3.3

34.0

12.0

48.0

22.0

Table 8. Hi]man Exposure at Two Locations in Shuttle Crew Compartment for February 23, 1956,

Event With//st = -100 nT at 400 km and Orbit Inclination of 50 °

Location cGy

1 2.6

2 3.4

Exposure inBFO Skin Lens

cSv cGy cSv cGy cSv

4.9 4.0 6.8 4.1 7.6

5.9 6.0 9.4 6.0 10.0

10
References

1. Wilson, John W.; Khandelwal, Govind S.; Shinn, Judy L.;

Nealy, John E.; Townsend, Lawrence W.; and Cucinotta,

Francis A.: Simplified Model for Solar Cosmic Ray Exposure in Manned Earth Orbital Flights. NASA TM-4182,

1990.

2. Shea, M. A.; and Smart, D. F.: A World Grid of Calculated Cosmic Ray Vertical Cutoff Rigidities for 1980.0.

18th International Cosmic Ray Conference Conference

Papers, MG Sessions, Volume 3, Tata Inst. of Fundamental Research (Colaba, Bombay), 1983, pp. 415 418.

3. Smart, D. F.; and Shea, M. A.: Geomagnetic Transmission F_nctions for a 400 km Altitude Satellite. 18th International Cosmic Ray Conference--Conference Papers,

MG Sessions, Volume 3, Tata Inst. of Fundamental Research (Colaba, Bombay), 1983, pp. 419-422.

4. Billings, M. P.; and Yucker, W. R.: The Computerized

Anatomical Man (CAM) Model. NASA CR-134043, 1973.

5. Atwell, William; Beever, E. Ralph; Hardy, AIva C.; and

Cash, Bernard L.: A Racliation Shielding Model of the

Space Shuttle for Space Radiation Dose Exposure Estimations. Advances in Nuclear Engineering Computation

and Radiation Shielding, Volume 1, Michael L. Hall, ed.,

American Nuclear Soc., Inc., c.1989, pp. 11:1-1t:12.

6. Wilson, John W.; and Khandelwal, Govind S.: ProtonTissue Dose Buildup Factors. Health Phys., vol. 31, no. 2,

1976, pp. 115-118.

7. St6rmer, Carl: Periodische Elektronenbahnen im Felde

eines Elementarmagneten und ihre Anwendung auf

Briiches Modellversuche und auf Eschenhagens Elementarwellen des Erdmagnetismus. Z. Astrophys., Bd. 1,

1930, pp. 237 274.

8. McCracken, K. G.: The Cosmic-Ray Flare Effect, J. Geophys. Res., vol. 67, no. 2, Feb. 1962.

1. Some New Methods of Analysis, pp. 423-434.

2. The Flare Effects of May 4, November 12, and November 15, 1960, pp. 435 446.

3. Deductions Regarding the Interplanetary Magnetic

Field, pp. 447 458.

9. Shea, M. A.; Smart, D. F.; and Gentile, L. C.: The

Cosmic Ray Equator Determined Using the International

Geomagnetic Reference Field for 1980.0. 18th International Cosmic Ray Conference Conference Papers, MG

Sessions, Volume 3, Tata Inst. of Fundamental Research

(Colaba, Bombay), 1983, pp. 423-426.

10. Kuhn, E.; Schwamb, F. E.; and Payne, W. T.: Solar Flare

Hazard to Earth-Orbiting Vehicles. Second Symposium

on Protection Against Radiations in Space, NASA SP-71,

1965, pp. 429 434.

11. Johnson, Francis S., ed.: Satellite Environment Handbook,

Second ed. Stanford Univ. Press, 1965.

12. Wilson, John W.; and Khandelwal, G. S.: Proton Dose

Approximation in Arbitrary Convex Geometry. Nucl.

Technol., vol. 23, no. 3, Sept. 1974, pp. 298 305.

I3. Space Station Program Definition and Requirements, Section 3: Space Station Systems Requirements. SSP 30000,

Section 3, Revision F, Space Station Program Off., May

6, 1988.

14. Curtis, S. B.; Doherty, W. R.; and Wilkinson, M. C.:

Study of Radiation Hazards to Man on Extended Near

Earth Missions. NASA CR-1469, 1969.

15. Adams, James H., Jr.: Cosmic Ray Effects on Microelectronics, Part IV. NRL Memo. Rep. 5901 (Revised), Naval

Research Lab., Dec. 31, 1987.

16. Foelsche, Trutz; Mendell, Rosalind B.; Wilson, John W.;

and Adams, Richard R.: Measured and Calculated Neutron Spectra and Dose Equivalent Rates at High Altitudes;

Relevance to SST Operations and Space Research. NASA

TN D-7715, 1974.

11

Report Documentation Page

Nal*onal Ae ronaLl_lcs and

Space Admin_str ahon

1. ReportNAsANO.TP_2987 2. Government Accession No.

4. Title and Subtitle

Improved Model for Solar Cosmic Ray Exposure in Manned Earth

Orbital Flights

7. Author(s)

John W. Wilson, John E. Nealy, William Atwell, Francis A.

3. Recipient's Catalog No.

5. Report Date

June 1990

6. Performing Organization Code

8. Performing Organization Report No.

L-16759

10. Work Unit No.

199-22-76-01

11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Paper

14. Sponsoring Agency Code

Cucinotta, Judy L. Shinn, and Lawrence W. Townsend

9. Performing Organization Name and Address

NASA Langley Research Center

Hampton, VA 23665-5225

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, DC 20546-0001

15. Supplementary Notes

John W. Wilson, John E. Nealy, Judy L. Shinn, and Lawrence W. Townsend: Langley Research

Center, Hampton, Virginia.

William Atwell and Francis A. Cucinotta: Rockwell International, Space Transportation Systems

Division, Houston, Texas.

16. Abstract

A calcutational model is derived for use in estimating Solar cosmic ray exposure to critical

body organs in low Earth orbit at the center of a large spherical shield of fixed thickness. The

effects of the Earth's geomagnetic field and the astronauts' self-shielding are evaluated explicitly.

The geomagnetic field model is an approximate tilted eccentric dipole with geomagnetic storms

represented as an impressed uniform field. The storm field is related to the planetary geomagnetic

index Kp. The code is applied to the Shuttle geometry using the Shuttle mass distribution

surrounding two locations on the flight deck. The Shuttle is treated as pure aluminum and the

astronaut as soft tissue. Short-term average fluence over a single orbit is calculated as a function

of the location of the lines of nodes or long-term averages over all lines of nodes for a fixed

inclination.

17. Key V_rords (Suggested by Authors(s))

Solar flares

Geomagnetism

Dose equivalent

Nuclear reactions

18. Distribution Statement

Unclassified--Unlimited

Subject Category 93

: 19.UnclassifiedSecurity Classif, (of this report) 20.UnclassifiedSecurity Classif. (of this page) 21. No.12of Pages 22. A03Price

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