IEEE Transactions on Nuclear Science, Vol NS-30, No. 6, December 1983

LET-DISTRIBUTIONS AND RADIATION DOSESDUE TO COSMIC RAYS

R. Silberberg, C. H. Tsao and J. H. Adams, Jr.

E. 0. Hulburt Center for Space ResearchCode 4154, Naval Research Laboratory

Washington, DC 20375

and

J. R. LetawSevern Communications Corporation

Severna Park, MD 21146

Abstract

A radiation transport calculation of allnuclides in cosmic rays has been carried out for

elements H to Ni. (The unattenuated flux at solanmin, outside the magnetosphere is /cmyear.) The computer code treats nuclear spallationreactions, ionization losses and geomagneticeffects. LET-distributions and radiation doses dueto cosmic rays can be calculated at any point inspacecraft and at various depths in any material.Results of sample calculations, including singleevent upsets, are presented. Hydrogenous material s

are shown to be more effective than aluminum forshielding against the high-LET components thatgenerate soft upsets.

1. Introduction

Heavy nuclei in cosmic rays are particularlydamaging due to their high rate of energy depositionor LET. Due to thei r high energy, they are highlypenetrating; and even after a nuclear collision, a

nuclear fragment generally emerges with nearly thesame energy per nucleon. Shielding is hencedifficult in view of the mass constraints forspacecraft.

Radiation transport or propagation calculationsof the flux of heavy nuclei are applicable to twoproblems: (1) soft upsets in microelectroniccomponents, and (2) radiobiological damage. As a

result of nuclear spallation reactions in shieldingmaterials, fragmented nuclei having decreased innuclear charge, can be below the threshold forgenerating soft upsets. Radiation dose and the RBEare also smaller for fragmented nuclei. On theother hand, the slowing down of nuclei by ionizationlosses increases their LET so that they become morelikely to cause soft upsets, as well as causingincreased radiobiological damage due to their higherLET (or rate of energy deposition) and the increasedRBE. The radiation transport calculations ofcosmic-ray nuclei designed for radio-biologicalinvestigations are therefore similar to those neededfor shielded microelectronic components.

The procedures of the propagation (or radiationtransport) calculations of cosmic ray nuclei aregiven in detail in our accompanying paper, "CosmicRay Transport in the Atmosphere; Dose a?dLET-Distributions in Materials," by Tsao et al .1,That paper also presents a discussion of errors anda comparison with available experimental data. (Ata depth of one nuclear interaction mean free path,the overall error is < 50 percent.)

Since the calculational procedures and pertinentreferences are given in our other paperl, thispaper is accordingly short and presents primarily

the results and discussion of the latter. Theprocedures we have developed permit the calculationof the radiation dose and the LET-spectrum of cosmicrays or solar flare particles Oincuding those due tospecific nuclides) at any point in spacecraft and at

various depths in any materia7.

2. Cosmic-Ray Energy Spectra

In Tsao et al.l, we presented data on thecosmic ray composition and radiation propagationequations. The differential fluxes given there had

to be integrated over the energy spectra.

Figure 1 shows the differential energy spectraof cosmic ray protons, helium and iron nuclei, at

sol r minimum and maximum, given in Adams etalY.C Analytic expressions for the energy spectraof protons, helium and of various classes of heavynuclei, are also given in Adams, et al.2.

DIFFERENTIAL COSMIC RAY S°ECTRA

1003 = =

10

10-

10-2(A

104

_ \

1o-F 101

0L0 105tKINETIC ENERGY (MeVINUC)

Fig. 1. The energy spectra of cosmic ray protons,helium and iron nuclei at solar minimum and maximum.

At sites with low geomagnetic cutoffs, abouthalf of the cosmic rays have energies above 103MeV/nucleon. Particles at such energies would

0018-9499/83/1200-4405$01.00O©1983 IEEE

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have effective ranges equal to several nuclearinteraction mean free paths. Hence, cosmic rays arehighly penetrating and difficult to shield against.The radiation propagation calculations that describecosmic rays must include partial cross sections ofnuclear interactions if the shielding thicknessapproaches the mean free path of iron nuclei.

3. Radiation Doses and LET-Distributions

A dose of 1 rad deposits 100 ergs/g or 10-2J/kg in biological tissue; it correspondsapproximately to the dose deposited by 3 x 10minimum ionizing particles/cm2. The technical termfor the above dose is absorbed dose = D = do/dm wherede is the mean energy imparted by ionizing radiationto matter of mass dm.

The doses from different kinds of radiation donot have the same biological effect. We must,therefore, define dose in a way that gives anequivalent biological effect. The dose equivalent,in units of rem, is H = DQ, where Q is the qual i tyfactor that weighs the absorbed dose with thebiological effectiveness of the charged particles ofa given kind. The quality factors Q that have beenin common use are those proposed inthe Report of the RBE Committee to the InternationalCommission on Radiological Protection and theInternational Commission on Radiation units andMeasurements .3

The differential LET spectrum of each nuclide oftype i is obtained from the differential energyspectrum:

Ji(S) = Ji(E) (dS/dE)-1 (1)

where S is the stopping power or rate of ionizationloss dE/dx. The absorbed dose rate from nuclide oftype i, with stopping power S > So is given by:

jmax

bi (s> so) =f Ji (S) S dS.

SJ(J

DOSE RATE AT THE SURFACE OF HNATER SPHERE (D = 30cm)

(I,0

00'a

co

w

0:C,)

-J

(9

z

LET (MeV/(g/cm2))

Fig. 2. 1dose ratesurface of

W 10

-~ 10° -a,

100

W/ 10 1-cc

m 1lo-'en

000

c 10-20

(9

Zj 10 -

(2)

If J is given in units of particles/cm2;sec, x ing/cm2 and E in units of 100 ergs, then D is givenin units of rad/sec.

For radiological purposes, the integral of Eq. 2is assumed to also contain the qu.ality factor Q(S)(as defined by the RBE committeef) which convertsdose to dose equivalent.

The LET spectra computed from Eq. (1) andcorresponding integral LET spectra are necessary forthe estimation of the rate of soft upsets inmicroelectronic components and the calculation ofbiological dose equivalents. The contributions ofvarious elements and groups of elements to theintegral LET spectrum are shown in Figures 2 and 3.

Figure 2 shows the integral LET spectrum of theabsorbed dose rate at the surface of a sphere ofwater, 30 centimeters in diameter, in units ofrads/year for various cosmic ray nuclides, at solarminimum, outside the earth's magnetosphere. Also theLET spectrum of the cosmic ray flux is readilyobtainable by our procedures and is presented inseveral figures by Tsao et al.1 With our computerprogram, the calculations can readily be carried outfor multi-layer structures, e.g. aluminum followed by

The LET-spectrum of the integral absorbedof groups of cosmic ray nuclides at thea sphere of water of 30 cm diameter.

DOSE RATE AT THE CENTER OF WATER SAHERE (D = 30 cM)

LET (MeV/(g/cm2))

Fig. 3. Same as Fig. 2, but at the center ofof water of 30 cm diameter.

105

sphere

water, or sets of various shielding thicknesses, eachassociated with a given solid angle. (Note that thesurface of the sphere is shielded on one side.) Fig.3 shows the corresponding integral LET spectrum atthe center of the sphere of water, 30 cm indiameter. We note that the attenuation of the dosedue to protons between the surface and the center isnegligible, and even the dose of cosmic-ray ironnuclei is attentuated only by a factor of about 3.

4. Attenuation of Cosmic Rays in HlydrogenousMaterial s

Hydrogenous materials have a considerably greatereffectiveness (per unit weight) for attenuatingcosmic rays, especially the high-LET component thatgenerates the single event upsets and has a higherrelative biological effectiveness. Table 1 displaysthe relative attenuation of cosmic-ray C and 0; Ne,Mg and Si; and Fe in aluminum, water and hydrogen.Table 1 was calculated using the fluxes at a time ofsolar minimum, outside the magnetosphere. Since the

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Table 1. Transmission of cosmic ray nuclei in Al, H20, and H2.*

C,O Ne,Mg,Si

Al H20 H2 Al H20 H2 Al H20 H2

0 1 1 1 1 1 1 1 1 1

10 0.77 0.64 0.2 0.72 0.56 0.1 0.58 0.33 0.01

20 0.59 0.41 0.04 0.52 0.32 0.01 0.34 0.11 0.00

30 0.45 0.26 0.01 0.38 0.18 - 0.20 0.04 -

*The attenuation rate of iron nuclei in pentane is - 1.5x greater than in H20 and in H2it is lOx that in Al. The mean free path of Fe in hydrogen is only - 2.2 g/cm2.

values given are ratios with respect to unshieldedvalues rather than absolute fluxes, they are nearlyindependent of solar modulation or geomagneticcutoff. It may be difficult to use hydrogen asshielding material. However, some hydrogen-richmaterials that can be maintained as a liquid, e.g.pentane, are more effective than water. Solidpolyethylene may be another possibility.

5. Dose Distribution in Biological Systems

In radiobiological dose calculations, the humanbody is frequently approximated by a spherical waterphantom, 30 cm in diameter. The dose calculations ofFigures 2 and 3 (shown in Sec. 3) were carried outfor such a phantom.

Figure 4 displays the annual dose equivalent inunits or rem/year due to cosmic-ray elements H, He,

10 DEPTH 0.1 g/cm2DEPTH IN 30-cm 1 g/cm2

WATER PHANTOM xxxxxxxxx 5 g/cm29 15g/cm2

9 ...... .... ....._5g =

04

U,

20

H He Li-B C-O F-S Cl-Mn Fe

ELEMENTS IN COSMIC RAYS

Fig9. 4. The annual dose equivalent due to sets ofcosmic-ray elements at various depths of a 30-cm waterphantom .

Li to B, C to 0, F to S, Cl to Mn and Fe at variousdepths within a sphere of water 30 cm in diameter,near solar minimum, outside the earth'smagnetosphere. We note the relatively rapiddepletion of high-LET nuclei like Fe by shielding.Yet, even at a depth of 15 cm ( at the center of thephantom), the heavy nuclei with Z > 6 in cosmic raysgenerate more radiobiological damage than the lighternuclei.

6. Single Event Upsets

The relationship between the rate of single eventupsets, the LET-spectrum of the cosmic ray flux,the critical charge of the device and the sensitivevolume is discussed in an accompanying paper by Tsaoet al.'

The upset rate u is related to the integralLET-spectrum N and Qc as follows:

0u[]

u=Ap N[Lmin (P)] C(p) dp0

(3)

where Ap is the mean projected area of thesensitive volume of a device and C(p) the path lengthdistribution function:

Lmin = 22.5 Q (pC)c

pp

(4)

where p is the Silicon density and p the chord length.

The close relationship between the application ofcosmic ray propagation calculations toradiobiological risks and single event upsets can beseen when comparing Fig. 3 and Fig. 5. In Fig. 5, adenotes helium nuclei, L the nuclei Li, Be, B; Mdenotes C , N, 0, F; Hi denotes nuclei with 10 < Z< 15, and H2 + H3 those with 16 < Z < 28. Theupper curve represents the sum due Ho alT nuclides.The former figure gave the annual dose rate ofvarious cosmic ray elements as a function of LET.Fig. 5 displays the upsets/kbit/day as a function ofQc for groups of cosmic ray elements in the

Nucleus:

Shields:(g/cm2)

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atmosphere at an altitude of 75,000 ft., at ageomagnetic cutoff rigidity of 1 GV/c, and asensitive volume 5 x 10 x 10 p3.

103

ALT = 75,000 FT.101o' RV= 1 GV

< 10° -

Wt 10o 3

10-4 P a L M H 2+H3

10-4 10-3 10-2 10-1 1 10

Qc ( pC)

Fig. 5. The daily upset rate per kilobit due toseveral groups of elements in cosmic rays as afunction of the critical charge. The labels L, M,H ., H2 + H3 refer to the respective chargeg oups of Z = 3-5, Z = 6-9, Z = 10-15 and Z = 16-26.

Acknowl edgements

This work is partially supported by DNA/DARPAunder the Single Events Radiation Effects Program.

References

1. C. H. Tsao, R. Silberberg, J. Adams, Jr., and J.R. Letaw, Cosmic Ray Transport in the Atmosphere:Dose and LET-Distributions in- Materials, in theseIEEE Proceedings, 1983.

2. J. H. Adams, Jr., R. Silberberg and C. H. Tsao,Cosmic Ray Effects on Microelectronics, Part I: TheNear-Earth Particle Environment, NRL Memo Report,4506, 1981.

3. RBE Committee Report, Health Physics, 9, 357-386,1963.