NASA Technical Paper 3495

HZETRN: Description of a Free-Space Ion andNucleon Transport and Shielding ComputerProgram

John W. Wilson, Francis F. Badavi, Francis A. Cucinotta, Judy L. Shinn, Gautam D. Badhwar,

R. Silberberg, C. H. Tsao, Lawrence W. Townsend, and Ram K. Tripathi

(NASA-TP-349_) H_ETRN: DESCRIPTION N95-28530

OF A FREE-SPACE 10N AND NUCLEON

TRANSPORT AN_ SHIELDING COMPUTER

PRCGRAM (NA3A. Langley Research Unclas

Center) 148 p

HI/q3 0049768

May 1995

https://ntrs.nasa.gov/search.jsp?R=19950022109 2020-04-19T23:39:56+00:00Z

NASA Technical Paper 3495

HZETRN: Description of a Free-Space Ion andNucleon Transport and Shielding ComputerProgram

John W. Wilson

Langley Research Center • Hampton, Virginia

Francis F. Badavi

Christopher Newport University ° Newport News, Virginia

Francis A. Cucinotta and Judy L. Shinn

Langley Research Center ° Hampton, Virginia

Gautam D. Badhwar

Johnson Space Center • Houston, Texas

R. S ilberberg

Universities Space Research Association • Washington, D.C.

C. H. Tsao

Naval Research Laboratory ° Washington, D.C.

Lawrence W. Townsend

Langley Research Center • Hampton, Virginia

Ram K. Tripathi

Christopher Newport University • Newport News, Virginia

National Aeronautics and Space AdministrationLangley Research Center • Hampton, Virginia 23681-0001

I

May 1995

Available electronically at the following URL address: http://techreports.larc.nasa.gov/itrs/ltrs.html

Printed copies available from the following:

NASA Center for AeroSpace Information

800 Elkridge Landing Road

Linthicum Heights, MD 21090-2934

(301) 621-0390

National Technical Information Service (NTIS)

5285 Port Royal Road

Springfield, VA 22161-2171

(703) 487-4650

Contents

Abstract...........................................................................

1. Introduction.....................................................................

2. Derivation of Boltzmann Equation .................................................... 3

3. Transport Formalism .............................................................. 5

4. Approximation Procedures .......................................................... 6

4.1. Neglect of Target Fragmentation .................................................. 6

4.2. Space Radiations .............................................................. 7

4.3. Velocity-Conserving Interactions ................................................. 8

4.4. Decoupling Target and Projectile Flux ............................................. 8

4.5. Back Substitution and Perturbation Theory ......................................... 10

5. Galactic Ion Transport ............................................................ 11

5.1. Derivation of GCR Heavy Ion Transport Equation ................................... 11

5.2. Numerical Procedure .............. _ ........................................... 14

5.3. Error Propagation ............................................................. 15

5.4. Numerical Algorithms ......................................................... 16

6. Stopping Power ................................................................. 17

7. Nuclear Database ................................................................ 19

8. Environmental Mode ............................................................ .29

9. HZETRN Benchmarking .......................................................... 31

10. HZETRN Computational Results ................................................... 31

11. Concluding Remarks ............................................................ 33

Appendix A--HZETRN Description ................................................... 34

Appendix B--HZETRN Computer Code Sample Output .................................... 40

References ....................................................................... 70

Figures .......................................................................... 75

iii

Abstract

The high-charge-and-energy (HZE) transport computer program

HZETRN is developed to address the problems of free-space radiation

transport and shielding. The HZETRN program is intended specifically

for the design engineer who is interested in obtaining fast and accurate

dosimetric information for the design and construction of space mod-

ules and devices. The program is based on a one-dimensional space-

marching formulation of the Boltzmann transport equation with a

straight-ahead approximation. The effect of the long-range Coulomb

force and electron interaction is treated as a continuous slowing-down

process. Atomic (electronic) stopping power coefficients with energies

above a few A MeV are calculated by using Bethe's theory including

Bragg's rule, Ziegler's shell corrections, and effective charge. Nuclear

absorption cross sections are obtained from fits to quantum calcula-

tions and total cross sections are obtained with a Ramsauer formalism.

Nuclear fragmentation cross sections are calculated with a semiempir-

ical abrasion-ablation fragmentation model The relation of the final

computer code to the Boltzmann equation is discussed in the context of

simplifying assumptions. A detailed description of the flow of the com-

puter code, input requirements, sample output, and compatibility

requirements for non- VAX platforms are provided.

1. Introduction

During the last 40 years, propagation of galactic ions through extended matter and determination of

the origin of these ions have been the subject of many studies. Peters (ref. 1) used the one-dimensional

equilibrium solution, without including ionization energy loss and radioactive decay, to show that the

light ions have their origin in the breakup of heavy particles. Davis (ref. 2) showed that one-dimensional

propagation is simplistic and that leakage at the galactic boundary must be taken into account. Ginzburg

and Syrovatskii (ref. 3) argued that the leakage can be approximated as a superposition of nonequilib-

rium one-dimensional solutions. The solution to the steady-state equations was given as a Volterra

equation by Gloeckler and Jokipii (ref. 4), which was solved to the first order in the fragmentation cross

sections by ignoring energy loss. This provided an approximation of the first-order solution that

included ionization energy loss and was only valid at relativistic energies. Lezniak (ref. 5) gave an over-

view of the cosmic ray propagation and derived a Volterra equation that included the ionization energy

loss and evaluated only the unperturbed term. The previous discussion indicates, that for a long time,

the main interest of cosmic ray physicists was to achieve first-order solutions in the fragmentation cross

sections where path lengths in the interstellar space are on the order of 3 to 4 g/cm 2. Clearly, higher

order terms cannot be ignored in accelerator or space shielding transport problems. (See refs. 6-9.)

Besides this simplification, previous cosmic ray models have neglected the complicated three-

dimensional nature of the fragmentation process.

Several approaches to the solution of high-energy heavy ion propagation that include ioniza-

tion energy loss have been developed (refs. 6-19) during the last 20 years. All but one (ref. 6) have

assumed the straight-ahead approximation and velocity-conserving fragmentation interactions. Only

two (refs. 6 and 9) have incorporated energy-dependent cross sections. The approach by Curtis,

Doherty, and Wilkinson (ref. 14) for a primary ion beam represented the first-generation secondary

fragments as a quadrature over the collision density of the primary beam. Allkofer and Heinrich

(ref. 15) used an energy multigroup method in which an energy-independent fragmentation transport

approximation was applied within each energy group after which the energy group boundaries were

moved according to continuous slowing-down theory. Chatterjee, Tobias, and Lyman (ref. 16) solved

the energy-independent fragment transport equation with primary collision density as a source and

neglected higher order fragmentation. The primary source term extended only to the primary ion range

from the boundary and the energy-independent transport solution was modified to account for the finite

range of the secondary fragment ions.

Wilson (ref. 7) derived an expression for the ion transport problem to the first-order (i.e., first-

collision) term and gave an analytical solution for the depth-dose relationship. The more common

approximations used in solving the heavy ion transport problem were examined further by Wilson. (Seeref. 6.) The effect of conservation of velocity on fragmentation and on the straight-ahead approximation

was found to be negligible for cosmic ray applications. Solution methods for representation of the

energy-dependent nuclear cross sections were derived. (See ref. 6.) Letaw, Tsao, and Silberberg(ref. 17) approximated the energy loss term and the ion spectra by simple forms for which energy deriv-

atives were evaluated explicitly. The resulting ordinary differential equations in terms of position were

solved analytically. This approximation results in the decoupling of motion in space and a change in

energy. In Letaw's formalism, the energy shifts were replaced by an effective attenuation factor. Wilson

(ref. 8) added the next higher order (i.e., second-collision) term. This term was found to be very impor-

tant in describing 2°Ne beams at 670A MeV. The three-term expansion was modified to include the

effect of energy variation of the nuclear cross sections. (See ref. 9.) The integral form of the transport

equation was also used to derive a numerical marching procedure to solve the cosmic ray transportproblem. (See refs. 6 and 12.) This method could accommodate the energy-dependent nuclear cross sec-

tions within the numerical procedure. Comparison of the numerical procedure with an analytical solu-tion of a simplified problem (refs. 12 and 13) validated the solution technique to approximately

1-percent accuracy. Several solution techniques and analytical methods have also been developed for

testing future numerical solutions of the transport equation. (See refs. 18 and 19.) More recently, an ana-

lytical solution for the laboratory ion beam transport problem has been derived with a straight-ahead

approximation, velocity conservation at the interaction site, and energy-dependent nuclear cross

sections. (See ref. 10.)

From an overview of these past developments, the applications are divided into two categories: a

single-ion species with a single energy at the boundary and a broad host of elemental types with a broadcontinuous energy spectrum. Techniques, which will represent the spectrum over an array of energy

values, require vast computer storage and computation speed to maintain sufficient energy resolutionfor the laboratory beam problem. In contrast, analytical methods (ref. 6), which are applied as a march-

ing procedure (ref. 12) have similar energy resolution problems. This is a serious limitation because a

final (i.e., production) high-charge-and-energy (HZE) computer code for cosmic ray shielding must be

thoroughly validated by laboratory experiments; some hope exists of having a single code which can bevalidated in the laboratory. (See refs. 9, 10, 20, and 21.) More recently, a Green's function has been

derived which has promise for a code which can be tested in the laboratory and used on space radiation

protection applications. (See ref. 22.)

In this paper, the starting point is the derivation of the general Boltzmann equation. By using stan-

dard assumptions to derive the straight-ahead equation in the continuous slowing-down approximation

and the assumption that heavy projectile breakup conserves velocity, the Boltzmann equation is simpli-fied. A numerical procedure is derived with the coupling of heavy ions to the nucleon fields. Numerical

stability and error propagation are discussed. The environmental model required as input to the HZE

transport computer program HZETRN is briefly discussed. Atomic and nuclear models used to obtain

the transport coefficients are discussed. Monte Carlo results are compared with the numerical proce-

dures and database. Sample results for solar minimum and maximum periods are provided. Detailed

descriptions of the flow of the computer code, input requirements, sample output, and compatibility

requirements for non-VAX platforms are provided. This program, which is designated LAR-15225, isavailable through NASA's software technology transfer center COSMIC (Computer Software Manage-ment and Information Center) at 382 E. Broad Street, University of Georgia, Athens, GA 30602.

2. Derivation of Boltzmann Equation

Because the volume of any material is mostly electrons, the interaction of energetic ions passing

through any material is primarily with these electrons. The cross section for the interactions of electrons

is G at = 10 -16 cm 2 . The long range of the nuclear Coulomb field also presents a sizable cross section of

Gc = 10-19 cm 2 to the passing ion. Ion collisions are dominated by these two processes, but individual

collisions have little effect on the passing ions.

Although most collisions in the material are Coulomb collisions with orbital electrons and nuclei,

the rare nuclear reactions are of importance because of the significant energy transferred in the reaction

and the generation of new energetic particles. The transfer of kinetic energy into new secondary radia-

tions occurs through several processes such as direct knockout of nuclear constituents, resonant excita-

tion followed by particle emission, pair production, and possible coherent effects within the nucleus.

Through these processes, a single particle incident on a shield may attenuate through energy transfer to

electrons of the media or generate a multitude of secondaries which cause an increase in exposure. The

process that dominates depends on energy, particle type, and material composition.

The relevant transport equations are derived on the basis of conservation principles by considering a

region of space filled with matter described by appropriate atomic and nuclear cross sections. In

figure 1, a small portion of such a region enclosed by a sphere of radius 8 is shown. The number of par-

ticles of type j leaving a surface element 82 d_ is given as x+ 8_, f_, E 82 d_, where

)x, _, E is the particle flux density, } is a vector to the center of the sphere, f_ is normal to the sur-

face element, and E is the particle energy. The projection of the surface element through the sphere cen-

ter to the opposite side of the sphere defines a flux tube through which pass a number of particles of

type j given as #j/_ - 8_, _, E)82 d_, which would equal the number leaving the opposite face if the

tube defined by the projection were a vacuum. The two numbers of particles differ by the gains and

losses created by atomic and nuclear collisions as follows:

x+8_,_,E _52d_ = x-8_,_,E 82d_

+82 dr2 k _,_,E,E' _k k+l_,_,E" d_'dE"

k

8(2.1)

-'9" --), ) are the media macroscopic cross sections. The cross sectionwhere %. (E) and _jk X_,_, E, E'

l _-_' ) -_'cjk _, f2, E, E' represents all those processes by which type k particles moving in direction f_ with

energy E' produce a type j particle in direction f_ with energy E. Note that there may be several reac-

tions that could produce this result, and the appropriate cross sections of equation (2.1) are the inclusive

ones. The second term on the right side of equation (2.1) is the source of secondary particles integrated

[ -"over the total volume 28 82 d_), and the third term is the loss through nuclear reaction integrated over

the same volume. The expansion of the terms of each side and retention of the terms to order 83 explic-

itly result in

+25 k _,f_,E,E k x,f_,E" d dE"

k

- x, _'), +26Oj (E) E O (6 4) (2.2)

which can be divided by the cylindrical volume 26 / 62 d_) and written as

fi.V x,n,E = k _,a,E,E Ok x,f_,E' dfi dE'-oj(E) x,f_,E +O(6/ (2.3/

k

for which the last term O (6) approaches zero in the limit as 6 _ 0. Equation (2.3) is recognized as the

time-independent form of the Boltzmann equation for a dual-species tenuous gas. Atomic collisions pre-

serve the identity of the particle, and both terms on the right side of equation (2.3) contribute. The dif-

ferential cross sections for the atomic processes have the approximate form

fl, fl E,E' = N_-_oat(E')6 fl._ -1 k6 E+e n-E' (2.4)' _ Jn

n

where n labels the electronic excitation levels and e n represents the corresponding excitation energies,which are small (1 to 100 eV) compared with the particle energy E. The atomic terms can then be

written as

Z_ at/-4 -4, ') / _ -4, )d_ _jat d_j/_ -4 )O)k _,_,E,E #Dk x,_,E" 'dE'- (E) x,_,Ek

/ 0,('- x, k'-_,= '_-_0 at (E+gn) x, _, E+£ n ojat (E) Ei-...., ,In

tl

Z _ja _j( ) Z 0j( _ -4 )]_ t(E)d_j( )a Fo_t(el x, a, e o_a x',fi, e= t(E) _¢,_,E + en_-E L jn/1 /1

= Sj (E) l_j X, _"_, E (2.5)

because the stopping power is

= _'_0 at (2.6)Sj(E) _ j.(e)%tl

and the atomic cross section is

_jat (E) = z__'_oatjn(E) (2.7)/1

Equations (2.5)-(2.7) permit the rewriting of equation (2.3) in the usual continuous slowing-down

approximation as

,4 ) Es, )] )x.,a.V _c,a,E --_ (E) x,n,E + oj (E) E

i o,( ,)= k _,_,E,E ¢_k x,_,E' dE' (2.8)

k

where the cross section of equation (2.8) now contains only the nuclear contributions.

4

3. Transport Formalism

The Boltzmann equation (2.8), as derived in section 2, can be rewritten as

•V Aj_E_(E)+_(E) _x,fl,E = de'd_'_k E,E,n,_J_k_,x,_,E' (3.1)k

)where x, f2, E is the flux of ions of type j with atomic mass Aj at x_ with motion along f_ and

energy E in units ofA MeV, _j (E) is the corresponding macroscopic cross section, S. (E) is the linear

I )energy transfer (LET), and %'k E, E, f_, _' is the production cross section for type j particles with

energy E and direction _ by collision of a type k particle of energy E" and direction . The term that

contains S. (E) on the left side of equation (3.1) is the result of the continuous slowing-down approxi-

mation. The solutions of equation (3.1) are unique in any convex region for which the inbound flux of

each particle type is specified everywhere on the boundary surface. If the boundary is given as the loci->

of a two-parameter vector function 7(s, t) for which a generic point on the boundary is given by F,

then the boundary condition is specified by requiring the solution of equation (3.1) to meet

for each value of f_ such that

) )F,_,E = F, fLE (3.2)

_2.n F <0 (3.3)

where n F is the outwardly directed unit normal vector at the boundary surface at point F, and gtj is

the specified boundary condition.

The fragmentation of the projectile and target nuclei is represented by the quantity

Ski E, E', _, a'), which is composed of three functions

ojk E,E,fl, fi' = Ok(E)mjk(e) k E,E',n, fi' (3.4)

where mjk(E') isthemultiplicity(i.e.,averagenumber) of typej particlesbeingproduced by a co]li-

, i , _ )sion of type k of energy E , and fj_ E, E, fL _' is the probability density distribution for producing

particles of type j of energy E in the direction _ from the collision of a type k particle with energy E'-.->,

moving in the direction _ . For an unpolarized source of projectiles and targets, the energy angle distri-

bution of reaction products can be a function of energies and cosine of the production angle relative to

the incident projectile direction. The secondary multiplicities mjk (E) and secondary energy angle dis-

tributions are the major unknowns in ion transport theory.

Information on the multiplicity mjk (E) was obtained in the past through experiments with galactic

cosmic rays (GCR) as an ion source, and the fragmentation of the ions on target nuclei was observed in

nuclear emulsion. (See ref. 23.) Such data are mainly limited by not knowing precisely the identity of

the initial or secondary ions and by relatively low-counting rates of each ion type. The heavy ion accel-eration by machine reduces the uncertainty because high-counting rates can be obtained with known ion

5

types. In addition, accelerator experiments provide information, which was not previously available, for

the spectral distribution _ E, E, f_, _' . (See ref. 24.)

The spectral distribution function consists of two terms that describe the fragmentation of the

projectile and the fragmentation of the struck nucleus as follows (refs. 25 and 26):

ojk E, E, _, = o k (E) (E E, E, f_, + (E E, E, f_, (3.5)

where vj_ and fj_ depend only weakly on the target and v)_ and fj_ depend only weakly on the projec-

tile. Although the average secondary velocities associated with i4, are nearly equal to the projectile

velocity, the average velocities associated with fir are near zero. Experimentally,

F m 13' fj_(E, E', f_, _'3 = _2_(ojp 32] 4_-E exp 2(oP)2 j

= L2n:(_'_)2J "_exp-_f_d2mE-f_d2mE)l 2(4) 2 1 (3.6,

9 9,where p and p are the momenta per unit mass ofj and k ions, respectively, and

I2 m )2] 3/2 I- j_2 -1fjT(E, E', _, _')= x(aj T ,4_-E exp 2( ajr)2j (3.7,

where a P and o T are related to the rms momentum spread of secondary products. These parametersJK J

depend only on the fragmenting nucleus. Feshbach and Huang (ref. 27) suggested that the parameters

olx.e and O.TjKdeoend_ on the average_ s0uare_ momentum of the nuclear fragments as described by Fermirr_otion. A precise formulation of these ideas in terms of a statistical model was obtained by Goldhaber.

(See ref. 28.)

4. Approximation Procedures

4.1. Neglect of Target Fragmentation

)The use of equations (3.5)-(3.7) in the evaluation of the source term x, _, E of equation (3.1)results in

x, _, E = dE' ' _ -_ .....ok(E)¢ k x,_,E' -_k (E) k E,E,_, + T T E,E,K_,_

k

__1(_c,_,E)+_y(_c,_,E) (4.1)

where as before, the superscripts P and T refer to the fragmentation of the projectile and the target,

respectively. The target term is

_Y(x_' f_'E)-> = E [2r_(ojT)2lk Imq3/2 ,_exp I-mE) tfd_'_EdE'vT(E"°k(E')¢k(_C'_"E')(4"2)(O)k--_T'2 jk

6

whichisnegligiblysmallfor

Thus,for calculatingthefluxathighenergy,

(4.3)

(4.4)

4.2. Space Radiations

Space radiations have the convenient property of being nearly isotropic. This fact, coupled with the

forward-peaked spectral distribution, leads to a substantial simplification in the source term as follows:

(4.5)

If ¢_ x_, _', E' is assumed to be a slowly varying function of f_, an expansion about the sharply

peaked maximum of the exponential function is possible. Such an expansion is made by letting

--)r

fi+ (cos0 l)fi+ '= - e_sm0 (4.6)

where

--) --),

cos0 = _. Xq (4.7)

and

-_ ---),

_x_

e¢ = fiXfi'(4.8)

The flux may be expanded as

/ / /1 e °sin0 +Ck _c,_',E' = _k x,_,E" _ _ _+ ¢_k x,_,E" • [(cosO-1)f_+ ... (4.9)

Substitution of equation (4.9) into equation (4.5) and simplification result in

3/2 I_( 2__ 2,___mE,)21_exp 2(t_JPk)2 J

(4.10)

7

The leading term of equation (4.10) is clearly a good approximation of the source term whenever

_'--0_ x,_,E'2mE _

_>> ddkl_X,_,E,) (4.11)

The leading term is equivalent to assuming that secondary ions are produced only in the direction of

motion of the primary ions. For space radiations, which are nearly isotropic, equation (4.11) is easily

met, and neglection of higher order terms in equation (4.10) results in the usual straight-ahead approxi-

mation. If radiations are highly anisotropic, then equation (4.11) is not likely to apply. Validity of

straight-ahead approximation was studied empirically by Alsmiller et al. (refs. 29 and 30) for proton

transport.

4.3. Velocity-Conserving Interactions

Customarily, in cosmic ion transport studies (ref. 31), fragment velocities are assumed to be equal

to the fragmenting ion velocity before collision. The order of approximation resulting from such an

assumption is derived with the assumption that the projectile energy E' is equal to the secondary energy

plus a positive quantity E,

E' = E + e (4.12)

where E is assumed to contribute to equation (4.10) only across a small range above zero energy.

Substitution of equation (4.12) into equation (4.10) and expansion of the integrand result in

;_ x, ta,e = _o k(E)v_ (e) ¢_ x, u, ek xmE

+ _ AlrcmE - _--_ 2mE•-_ ... (4.13)

I,_',_/[o_}2/mE _<1, the assumption of velocity conservation at those energies for which mostBecause

nuclear reactions occur is inferior to the straight-ahead approximation but may be adequate for space

l, )radiations where variation of Ok x, _, E with energy is sufficiently smooth. That is

e_

4.4. Decoupling Target and Projectile Flux

Equation (3.1) can be rewritten with equation (4.1) as

=k k

where the differential operator is given by

: •v @ _-Esj(E) +oj(E)

(4.14)

(4.15)

8

and the integral operator Fjk = F._ + Fj_ is given by

l )f I 'F.kCpk _x, fi, E = dE' dfi' _. k E, E , fi, a J,k(x, f_ , E' (4.16)

By defining the flux as the sum of two terms,

x, f2, E = _x,f2, E + _c, _, E (4.17)

which permits the following separation:

--> -> P _ E} (4. 18)

k k

_:,_,E = _,E + _,E (4.19)z_, jk'Vk \ , z__ jk'Vk\ ,k k

As noted in connection with equations (4.1)-(4.4), the source term on the right side of equation (4.19) issmall at high energies. Assume that

x, _, E = 0 (4.20)

for E ,> _k /m. As a result of equation (4.20) and the fact that the ion range is small compared with

its mean free path at low energy,

I_*PI},_,E)=_" FP_P( _c _,E) (4.21)z_ jk"Vk \ ,k

) -> _'F Te_P( _ O, E (4.22)x, f2, E = z_ jkVk \ ,

k

The advantage of this separation is that, once equation (4.21) is solved, equation (4.22) can be solved in

closed form. The solution of equation (4.22) is accomplished by noting that the inwardly directed flux

_f must vanish on the boundary so that

,f(_,fi, E)=Z_EE_,dE , AjPj(E) fdE,,d_Tk(E,,E,,,_,fi, )k 5(e)5(e)

x _ {x_+ [-R. (E)-Rj (E')]fi, _', E"} (4.23)

where E r = Rj -l [d + R. (E) ] with d being the projected distance to the boundary.

The use of equations (3.5) and (3.7) in equation (4.23) yields

TI_--> I _EE'dE' AJP'(E•) I2 (-_)213/2 [(a--_-k/2 ]_j x, f2, E = m 2_exp mE"

I_(E)_(E)

x ;f {_: + [-Rj (E) -R. (E')]fi} (4.24)

where

_f (_) = Z_dE'df_ Ok(E)_T (E')_PI_c,_", E') (4.25)k

9

andoj T has been assumed to be a slowly varying function of projectile type k and projectile energy E. Ifthe range of secondary type j ions is small compared with their mean-free-path lengths and the mean

free paths of the fragmenting parent ions lk , then

(4.26)

and the integral of equation (4.24) may be simplified as

dOj(_,fi, E) = Aj _f(_)_E_, I ra 13/2 l- mE" lSj(E----_ 12rc(_jT)} ] 2_' exp (_T)21 dE' (4.27)

which can be reduced into terms of known functions. Thus,

_ 1 f-)V3 mE(4.28)

in terms of the incomplete gamma function. Equation (4.28) can be shown to be equivalent to

a 'I' F" 11=Sj_E)_f(x_)_--_ _erfc -_erfc| iT-L-_I

m= m= / 1+ I_I _---_._12 exp 1- I _-_-k12] - _]_I'_-j_ 12 exp [ - }( cjjT 121

At points sufficiently far from the boundary such that

R -! (d) >> T(_j_)2] m

(4.29)

(4.30)

equation (4.28) may be reduced to

_(._,fi, E) A. 2_1 {12 I m_l l mE I mE) 1}-erfc _ _T 2 exp - _TT'2 (4.31)

which is the equilibrium solution because the target fragment spectrum is the difference between the

collision source and collision losses. The solution of equation (4.21) is examined in section 4.5.

4.5. Back Substitution and Perturbation Theory

One approach to the solution of equation (4.21) results from the fact that the multiple charged ions

tend to be destroyed in nuclear reactions. Thus,

Fj_ - 0 (j _>k)

This means that there is a maximumj such that

,l )B]_] x,_,E = 0

(4.32)

(4.33)

10

where J is the maximumj. Furthermore,

and in general,

_,EBj-N*Y- N ' =

N-I

Fy_,,,;_k,j_k x,a,ek=l

(4.34)

(N < J - 1) (4.35)

Note that equations (4.34) and (4.35) constitute solvable problems. The singly and doubly charged ionssatisfy

J

1, 1_1 x, _'2, E + l,k# k x, f2, E (4.36)k=2

Equation (4.36), unlike equations (4.33)-(4.35), is an integral-differential equation that is difficult to

solve directly. Equation (4.35) is solvable by perturbation theory, and the resultant series is known toconverge rapidly for intermediate and low energies. (See refs. 10 and 32-34.) Note that equations (4.33)

and (4.35) are also obtained from perturbation theory as applied to equation (4.21) at the outset. Thus,

the perturbation series is expected to converge after the first J plus a few terms.

5. Galactic Ion Transport

5.1. Derivation of GCR Heavy Ion Transport Equation

In this section, the methods of previous nucleon transport studies (ref. 32) are expanded by combin-

ing analytical and numerical tools. The galactic cosmic ray ion transport problem is transformed to an

integral along the characteristic curve of that particular ion, and the perturbation series (ref. 32) is

replaced by a simple numerical procedure. The resulting method reduces the difficulty associated with

the low-energy discretization and the restriction to a definite form for the stopping power. The resulting

numerical procedure is simple and is not computationally intensive.

Here, the straight-ahead approximation is used, and the target secondary fragments are neglected.

(See refs. 6 and 8.) For multiple charged ions, the transport equation can be written as

OE sj(E) +(_ ,j(x, e) = _kak%(x,e) (5.1)k>j

where #j (x, E) is the flux of ions of type j with atomic mass Aj at x moving along the X-axis atenergy E in units of A MeV, o. is the corresponding macroscopic nuclear absorption cross section,- J .

Sj(E) is the change in E per unit distance, and m.. is the multiplicity of ionj produced by ion k in ajKcollision. The corresponding transport equation for the light ions is

g_ _e sJ (e) + _ (e) ,j _k (e, K) *k(x, e') dE'k

The quantities mjk .and cj are assumed to be energy independent in equation (5.1) but are fully energydependent in equatmn (5.2).

The range of the ion is given as

(5.3)

11

Thesolutiontoequation(5.1)is foundsubjecttotheboundaryspecificationatx = 0 and arbitrary E as

(:l)j(0, E) = Fj (E) (5.4)

Usually, Fj (E) is called the incident beam spectrum.

From Bethe's theory,

A Z 2_p J

_j (e) = -_-_ Sp (e) (5.5)J p

which holds for all energies greater than --100A keV, provided that the ion effective charge is used, andleads to

z? z 2

=J p

The subscript p refers to proton. Equation (5.6) is accurate at high energy and only approximately true at

low energy because of electron capture by the ion (which effectively reduces its charge), higher order

Born corrections to Bethe's theory, and nuclear stopping at the lowest energies. Herein, the

parameter v. is defined as

_R.(E) = vkR k (E) (5.7)

so that

z 2J

V. "_- --

J A.J

(5.8)

Equations (5.6)-(5.8) are used in the subsequent development, and

neglected. The inverse function of Rj (E) is defined as

the energy variation in vj is

E = Rj-1 [Rj(E)] (5.9)

For the purpose of solving equation (5.1), the following coordinates are used:

-qj= x- Rj (E) (5.10)

_j-x + l_(E) (5.11)

where 'l]j varies along the particle path, and _j is constant along the particle trajectory. The new fluencefunctions are defined as

xj(nj, j)=_3j(e),j(x,e) = (5.12)

_k (T_j,_j) = Zk (nk, _k )(5.13)

where

_j+rlj = _k+rlk (5.14)

_lj-_j = Vk_.(nk- _k) (5.15)

12

and rj = R. (E). By this coordinate mapping, equation (5.1) becomes

V.

k

(5.16)

where oj is assumed to be energy independent for simplicity of formalism. There is a small variationin _; (=20 percent) that is accounted for in the code. (See ref. 35.) Equation (5.16) is solved by using

line integration with an integrating factor (ref. 12), which results in

Then,

where

By defining

then

Furthermore,

Xj (rlj, _j)

,j(nj, _) 1

= exp I- 1_ (_j + rlj)lXj(-_j,_ j)

1

+ nj)Jk

• Vk+V j , Vk-V j

, _k-_ , vk+vj

: exp(-_.x)gy(0, rj+x) + dzexp(-_z) Zr_,c_k_-,V , x-z,r,+_-,zk

= exp (-_.h) _j (x, rj + h)

;o / /+ dzexp(-a..z)Zm:kok vj exp[-ok(h-z)]_ k x, rk+_z+h-zj .t Vk V k

k

qlj(x +h,_) = exp(-(_h)gtj(x,_ +h)

+ dz exp (-(_jz)Zn_k(_k_.lllk x +h-z,r kk

Equation (5.20) clearly shows that

Iltk (x + h - Z, rk) = exp[-Ok(h-z)]llf k (x, rk + h ) + O ( h - z)

which, after substitution into equation (5.21), yields

%(x+h,r)

13

(5.17)

(5.18)

(5.19)

(5.20)

(5.21)

(5.22)

(5.23)

which is correct to order h 2. This expression can be further approximated by

_j(x + h, t)) = exp (-_h) lltj(x, t) + h)

+Zn_k_k_klexp(-_h)-exp(-_kh)l ( +v---_Jhl (5.24)k ok_ vk x,r k vk )

which is accurate to O [ (v k - v,) h]. Equation (5.24) is the basis of the GCR transport computer codeGCRTRN. (See refs. 12, 13, and 36.) The nucleon transport equation (5.2) is solved by adding the heavy

ion collision source of nucleons to the BRYNTRN computer code (ref. 33) to create HZETRN, which

effectively solves equation (5.2) by adding a heavy ion collision source of nucleons to the right side of

the equation. Equation (5.24) provides the propagation algorithm for the heavy ions. The corresponding

propagation procedure for the light ions (refs. 33, 37, and 38) is

_t (x + h, r) = e-ah_ll (x, r + h) + e-°h_o Odz_r r dr'jr(r + z, r'+ z) V (x, r'+ h) (5.25)

with the order of h 2.

The following quantities are of interest:

1. The integral fluence is

Cj(x, >E)

2. The energy absorbed per gram is

= Ce) (x, r) dr (5.26)

Dj (x, > E) = _EAjqIj [x, 1_ (E) ] dE (5.27)

3. The dose equivalent is

Hj (x, > E) : A.J_ E QF_IIj [x, 1_ (E) ] dE(5.28)

where QF is the quality factor. These quantities are not recommended for use in shield design for pro-tection from GCR but give some relative measure of their biological importance.

5.2. Numerical Procedure

The secondary particle production term of the propagation algorithm for the nucleons in

equation (5.25) has been further reduced to a form that can be numerically integrated with ease. Details

of the form and its validity are discussed in reference 33. For the heavy ions, the secondary production

term (i.e., the second term on the right side of equation (5.24)) does not involve any integration; how-

ever, the interpolation of the transformed fluence function is based on the independent variable r k,

which is different from the range of ions r: of type j given on the left side of the equation. To circum-vent the problem, the equation is further modified by using the definition of Sj (E), with E given in unitsof A MeV; then

A (Ej/Aj) 1 AF_ 1Sj (E) = 7Sj(F_/Aj) - Ax - A. A-_ = Sj (Ej) (5.29)J J

with

Sj(ET) = Z2S (Ej/Aj) (5.30)

14

whereSp

where

is the proton stopping power, and Ej is the energy in MeV of the ions of typej. Then

j(E) = (5.31)3

E = E./A.jj (5.32)

By rewriting equation (5.19) as

vj(x, 9) -_-3j(E),j(x,e) = _:s(E),j(x, e)

the new fluence function can be defined as

(5.33)

with r = rp = vjrj, where

Equation (5.24) becomes

v_(x,,) - v: (e), (x,e) _=vj (x,9) (5.34)

(5.35)

' -_h , (e-_ "h-e-_Jkh_vk ,_lj(x+h,r) = e _j(x,r+v.h) +Zr_k(y k t_k-t_) " )_lk(x,r+vjh)k

(5.36)

so that there is now only one definition of range that is related to energy. The equation can be solved bysetting up the proton range grid r and marching the solution from x = 0 by steps of h to the desiredthickness.

5.3. Error Propagation

When considering how errors are propagated in the use of equation (5.36), the error is introduced

locally by calculating Wj (x, r + vjh) across the energy range grid. By limiting the analysis to the first

term of equation (5.36), the error is defined at each range grid r i such that

-%h ,_lj (x + h, ri) = e Wj (x, ri + v.h) (5.37)

The truncation error e i is introduced in the interpolation procedure for the value Wj, int and

_@ (x, ri + v.h) = Wj, int (X, ri + vjh) +Ei(h) (5.38)

After the ruth step from the boundary, the numerical solution is

m-1

-%h ,' he t (h) (5.39)_Fj(mh, ri) = e _tj, int[(m-1)h'ri+_ h] + Z e-_(m-l)

/=0

Suppose 0 < e t (h) < e (h) for all I; then the propagated error is bounded by

m-1 m-1

Eprp (m) = E e-%(m-l)hel(h) <-E(h) Z e-Oj(m-l)h (5.40)

I=0 l=O

15

Notethat

m-I

'( )_-_ e-t_mhe_jhl = -h"_. 1 - e -_mh (5.41)

1=0 Y

because hoj <_1. Clearly, the propagated error on the ruth step is bounded by

e.(h ) ( e-t_mh )eprp (h) < -ff_.\ 1 - (5.42)J

where e (h) is the maximum error per step. With the increasing value of m, the propagated error grows

with each step to a maximum value of e (h)/hc.. Because the increase in the value of h is limited bythe perturbation theory, the reduction of the locaJl truncation error is the only viable approach left for

reducing the propagated error to a desired level. The same consideration can be applied to the second

term of equation (5.36) as the terms are similar in nature. The issue of error propagation in HZETRN is

further studied by Shinn and Wilson. (See ref. 39.)

5.4. Numerical Algorithms

The error analysis of section 5.3 results in the conclusion that, to effectively reduce the level of

propagated error, the local truncated error must be reduced. Three numerical algorithms are involved in

solving equations (5.25)-(5.28) and (5.36): interpolation, integration, and grid generation. The choice ofgrid distribution that is interrelated to the interpolation and integration methods can increase the

efficiency of the code if the number of grids can be reduced.

The interpolation method in HZETRN is the third-order Lagrange's method, which was used suc-

cessfully in improving BRYNTRN. (See ref. 37.) With the four neighboring interpolation grids (data

points) placed on both sides of the interpolated point, the error will tend to be the smallest in the middle

interval of all the data points if the grid distribution is rather uniform. (See ref. 40.) The choice of amuch higher order Lagrange's method will substantially decrease the efficiency of the computer code

because there are more than 10 interpolation calls for each energy point at each step. Other interpolation

methods such as a cubic spline were considered but discarded. In general, the splines are more accurate;

however, their characteristically large oscillations can result in erroneous solutions.

The procedure for numerical integration that was used in the improved BRYNTRN (ref. 37) is also

used here in HZETRN. The procedure is based on the compound quadrature formulation summing over

all the subintervals between the grids with the midpoint evaluated by making use of the improved inter-polation procedure mentioned previously. A simple numerical method such as Simpson's rule is used to

integrate for the subintervals.

Three considerations dictate how the grids should be distributed. The first is the shape of the input

spectrum. Because the GCR fluences are several orders of magnitude greater at the lower energies

(refs. 41-43), a logarithmic scale is used for the energy or range coordinate as was done in reference 37.

The second is the choice of the interpolation method, which requires that the four neighboring grids be

as uniformly spaced on a logarithmic scale as possible so that the interpolation error can be minimized.

Because the interpolation is performed on the range grid rather than on the energy grid, a uniform griddistribution on a logarithm of range r is desired. The third is the code efficiency, which increased almost

quadratically with the decrease in the number of grid points. With the uniform grid points on a logarith-

mic scale r as the basic structure, the distribution can be modified further to reduce the number of points

in the region in which the data are not propagating through the steps. For BRYNTRN, this region

occurred below rmin + h (i.e., =1 g/cm 2) because rmin _ 1 and h is assumed to equal 1 g/cm 2. (See

ref. 37.) This also applies to HZETRN, although the interpolation is now at rmi n + vjh, where vj isalways equal to or much greater than 1; because in propagating a distance h, all ions with energy below

rmi n + h are slowed to energies below the first energy grid point.

16

6. Stopping Power

In passing through a material, an ion loses the greater fraction of its energy to electronic excitation

of the material. Although a satisfactory theory of high-energy ion-electron interaction is available in the

form of Bethe's theory utilizing the Born approximation, an equally satisfactory theory for low energies

is not available. Bethe's high-energy approximation of the energy loss per unit length (i.e., stoppingpower) is given by

tS - In C

e mv 2 ( 1 - [32) I t(6.1)

where Z is the projectile charge, N is the number of target molecules per unit volume, Zt is the numberof electrons per target molecule, m is the electron mass, v is the projectile velocity, 13 = v/c, c is the

velocity of light, C is the velocity-dependent shell correction term (ref. 44), and I t is the meanexcitation energy given by

Zt In (It) = __rf n In (En) (6.2)tl

where fn are the electric dipole oscillator strengths of the target, and E n are the corresponding excita-tion energies. The sum in equation (6.2) includes discrete and continuum levels. Molecular stopping

power is reasonably approximated by the sum of the corresponding empirically derived atomic stoppingpowers for which equations (6.1) and (6.2) imply that

Zln(l) = ZnjZj In(L) (6.3)J

where Z and I pertain to the molecule, Z. and I. are the corresponding atomic values, and nj are thestoichiometric coefficients. This additive _le (e_. (6.3)) is usually called Bragg's rule. (See ref. 45.)

As an input to HZETRN, the high-energy cutoff for the incident GCR spectrum is usually taken to

be far beyond the minimum stopping power of =2A GeV, where Bethe's theory starts to overestimate

and worsens as the energy increases. This overestimation can be corrected by considering that the field

of the incoming ion projectile is perturbed by the neighboring polarized atoms. In HZETRN the approx-imate correction for the polarization effect (i.e., density effect) is based on the work of Sternheimer.

(See ref. 46.) In reference 46, the polarization effect corrections for various elements and compoundswere evaluated and fitted by the expressions

8 = 0 (x < x0) (6.4a)

8=lnlq2+C+a(xl-x)m (Xo<X<Xl) (6.4b)

8 = In 1]2 + C (x >Xl) (6.4c)

where _5is the density effect correction used in the stopping-power formula, 11 = P/moC, p is themomentum, m ° is the rest mass of the charged particle, c is the velocity of light, and

x = (lOgl0e)In r I = 0.43429 In r I

The quantities a, m, x ° , and x 1 are constants that must be evaluated for each material; C is given by

C = -2 In (I/hVp- 1) (6.5)

17

whereI is the mean ionization potential; the plasma energy hVp of the material is

hVp = h(ne2/nme) 1/2 (6.6)

where n is the electron density in electrons/cm 3, m e is the rest mass, and e is the charge of an electron.

For compounds and mixtures, the effective mean ionization potential can be determined by

1 nlnl = nZ ilnl i (6.7)

t

where n.!

potential.

is the electron density for the ith element, and I i is the corresponding atomic ionization

Reference 46 suggests that, for some practical applications, the use of only the asymptotic density

effect correction (eq. (6.4c)) may be adequate for all charged particle energies. In reference 47

Armstrong and Alsmiller compared the stopping-power differences between correct expressions and an

asymptotic formula for several elements and compounds. The results indicated an overestimation of at

most 6 percent when using the asymptotic formula. Therefore, only the asymptotic formula is used in

HZETRN. Equation (6.1) with polarization effect modification becomes

4_NZ_Zte4 F 2my2 1- _2 C 8S e = my 2 {In t (i _--_) I -_-_} (6.8)

The use of equation (6.8) in conjunction with the asymptotic formula of equation (6.4c) does not

involve any evaluation of the constants a, m, x o , and x I for the material considered. A comparison of

equations (6.1) and (6.8) for different materials is discussed by Shinn et al. (See ref. 48.)

The electronic stopping power for protons is adequately described by equation (6.8) for energies>500 keV for which the shell correction C makes an important contribution up to 10 MeV. (See ref. 49.)

For proton energies <500 keV, charge exchange reactions alter the proton charge over much of its path

so that equation (6.8) is understood to be an average over the proton charge states. Normally, an averageover the charge states is introduced into equation (6.8) so that the effective charge is the rms ion charge

and not the average ion charge. At any ion energy, charge equilibrium is established very quickly in all

materials. By utilizing the effective charge in equation (6.8), only modest improvement results at ener-

gies <500 keV, which presumably indicates the failure of this theory based on the Born approximation.

(See refs. 49 and 50.)

The electronic stopping power for alpha particles requires terms in equation (6.8) of higher order in

projectile charge Z because of corrections to the Born approximation. The alpha stopping power cannot be related to thPeproton stopping power through their effective charges. Parametric fits to experi-

mental data are given by Ziegler in reference 51 for all elements in both gaseous and condensed phases.

The electronic stopping powers for heavier ions are related to the alpha stopping power through

their corresponding effective charges. HZETRN uses the effective charges suggested by Barkas

(ref. 52) of

Z* = Z E1 -exp(-125_/Zp 2/3)_ (6.9)

where Z in equation (6.9) is the atomic number of the ion.P

18

At sufficientlylowenergies,theenergylostbyanioninanuclearcollisionbecomesimportant.Thenuclearstopping-powertheoryusedin HZETRNisa modificationof thetheoryof Lindhard,Scharff,andSchiott.(Seeref.53.)Thereducedenergyisgivenas

32.53ApAtEE = (6.10)

ZpZt (Ap+ At) ( Z2p/3 + Z t2/3 '1/2fl

where E is in units of A keV, and Ap and A t are the atomic masses of the projectile and the target,respectively. The nuclear stopping power in reduced units (ref. 51) is

Srl

1.59e 1/2 (e < 0.01)

1"7el/2 in(e+el) (0.01 <e< 10)1 + 6.8e + 3.4e 3/2

In (0.47e) ( 10 < e)2e

(6.11)

and the conversion factor to units of (eV-atoms/cm2)/10 !5 is

8.426ZA tA p[=

(ap+ at)(Z2p/3+ Z2/3) 1/2

The total stopping power S. is obtained by summing the electronic and nuclear contributions. OtherJ . .

processes of energy transfer such as Bremsstrahlung and pair producuon for stopping massive ions areunimportant.

For energies greater than a few A MeV, Bethe's equation is adequate if the appropriate corrections

to Bragg's rule (refs. 54-56), shell corrections (refs. 44, 49, and 50), and an effective charge are

included. Electronic stopping power for protons is calculated from the parametric formulas of Andersen

and Ziegler (ref. 49) with some modifications. (See ref. 9.)

Because alpha stopping power is not derivable from the formula for proton stopping power by using

the effective charge at low energy, the parametric fits to empirical alpha stopping powers given by

Ziegler (ref. 51 ) are used. Physical state and molecular binding effects are most important for hydrogen(ref. 54); water stopping power was approximated by using the condensed phase parameters for hydro-

gen and the gas phase experimentally derived parameters for oxygen. Electronic stopping powers for

ions with a charge greater than 2 are related to the alpha stopping power by the effective charge of equa-

tion (6.9). Figures 2(a), 2(b), and 2(c) show the transport coefficient ranges and stopping powers for five

different charge values Z, as calculated by HZETRN for aluminum, water, and liquid hydrogen targets,

respectively.

7. Nuclear Database

The nuclear cross sections for neutron and proton interactions are described extensively in refer-

ences 10 and 33. The heavy ion absorption cross sections _abs are currently derived from

r f "_ 7E 2

"'2'al/3+A}/3-LO.200+A_,l+aTl-O.292exp_-_--_)cos(O.229E°'45')J, (1 5E -|) ("7.1)_ffabs = "*'0 t,. p +

which for r 0 = 1.26 fm were fit to the quantum mechanical nuclear cross sections calculated inreference 57.

In this section, the heavy ion fragmentation mechanism is described by abrasion-ablation formal-

ism. In the abrasion-ablation fragmentation model, the high-energy projectile nuclei collide with

19

stationary target nuclei. In the abrasion step, those portions of the nuclear volumes that overlap are

sheared away by the collision. The remaining projectile piece, called "a prefragment," continues its tra-

jectory with essentially its precollision velocity. As a result of the dynamics of the abrasion process, the

prefragment is highly excited and subsequently decays by the emission of nuclear particles. This step is

the ablation stage. Final deexcitation is through gamma emission. The resultant isotope is the nuclear

fragment whose cross section is measured. The abrasion process can be analyzed with classical geomet-

ric arguments (refs. 11, 36, and 58) or methods obtained from formal quantum scattering theory. (See

refs. 59 and 60.) The ablation stage can be analyzed with geometric arguments (ref. 11) or more sophis-

ticated methods based on Monte Carlo or intranuclear cascade techniques. (See refs. 61-64.) Predictions

of fragmentation cross sections on hydrogen targets are made with the approximate semiempirical

parameterization formulas of references 65 and 66. The fragmentation cross sections for other heavier

targets are generated by the NUCFRG series of semiempirical fragmentation codes, in particular, the

second version NUCFRG2 as described in reference 67.

The amount of nuclear material stripped away in the collision of two nuclei of radius Rp and R r is

taken as the volume of the overlap region times an average attenuation factor. (See refs. 36 and 67.) The

relevant formula for the constituents in the overlap volume in the projectile is given by

Aab r = FAp [ 1 - exp (-CT/_.) ] (7.2)

where C r is the chord length at maximum overlap density of the intersecting volume of the projectile

and the target _, is the nuclear mean free path, and the expression for F depends on the nature of the col-

lision (i.e., peripheral versus central) and the relative sizes of the colliding nuclei.

From reference 61, for R T > Rp,

P= 0.125 (Mv)1/2( 1_ 2)( _--_)2- 0.125 I0.5 (IAV)1/2( 1_ 2)+ 1]( __._)3_._t _t

(7.3)

and

F = 0.75 (1 -v) 1/2 -0.125 [3 (1 -v) 1/2_ 1] (7.4)

with

gpv = _ (7.5)

Rp + R T

b (7.6)- Rp+R T

and

1 RT

v Rp(7.7)

Equations (7.3) and (7.4) are valid when the collision is peripheral (the two nuclear volumes do not

completely overlap). In this case, the impact parameter b is restricted such that

RT-Rp<-b<-RT+ R P (7.8)

2O

If the collision is central, then the projectile nucleus volume completely overlaps the target nucleus vol-

ume (b < R r - Re), and all the projectile nucleons are abraded. In this case, equations (7.3) and (7.4) arereplaced by

P = -1 (7.9)

and

F = 1 (7.10)

and there is no ablation of the projectile because it was destroyed by the abrasion.

For a peripheral collision with Rp > R T, equations (7.3) and (7.4) (ref. 63) become

P = O'125(l'tv)_/2(_-2)(_v_)Z-o'125{O'5(v_l/2(l-2) [('/v' (1-1"t2)'/2-11 [(2-_a)!'tl'/2}/_J-)3 (7.11)

and

(L_--_) 2 ¢ (l-v) 1/zF = 0.75(1 -v) 1/2 _0.125 3_t

where the impact parameter is restricted such that

For a central collision

[ 1 - (1 -la2) 3/21 [ 1 - (1 -la) 21 1/2} (_"_) 3p3 (7.12)

Rp - R T < b < Rp + R T

( b < Rp - RT) with Rp > R T, equations (7.11) and (7.12) become

p_-I_,, - _, '_- _l I, - (_)_l '_

(7.13)

(7.14)

and

F = [1- (1-_2)3/2] 1- (7.15)

The charge ratio of the nuclear matter removed by the collision is assumed to be that of the parent

nucleus. The spectators in the overlap region are assumed loosely bound to the remaining prefragment

and are lost in a preequilibrium emission process. (See ref. 67.)

The surface distortion excitation energy of the projectile prefragment following abrasion of them nucleons is calculated from the clean-cut abrasion formalism of reference 58. For this model, the col-

liding nuclei are assumed to be uniform spheres with radii R i (i = P, T). In collision, the overlappingvolumes shear off so that the resultant projectile prefragment is a sphere with a cylindrical hole gougedout of it. The excitation energy is then determined by calculating the difference in surface area between

the distorted sphere and a perfect sphere of equal volume. This excess surface area AS is given inreference 61 as

AS = 47tRp2 [1 +P- (1 -F) 2/3] (7.16)

where the expressions for P and F differ and depend upon the nature of the collision (i.e., peripheral

versus central) and the relative sizes of the colliding nuclei, which were given in previous equations.

The excitation energy associated with surface energy is known to be 0.95 MeV/fm 2 for near-

equilibrium nuclei so that

t

Es = 0.95AS (7.17)

21

for smallsurfacedistortions.Whenlargenumbersof nucleonsareremovedin theabrasionprocess,equation(7.17)is expectedto beanunderestimateof theactualexcitation.Thisrequirestheintroduc-tionof anexcessexcitationfactor(refs.11and36)in termsof thenumberof abradednucleonsAab r as

A3

f = 1 + 5Aabr+_ [1500 - 320 (Ap- 12)] A3ab----Zr (7.18)p p

which approaches 1 when the impact parameter is large but increases the excess excitation when manynucleons are removed and grossly distorted nuclei are formed by the collisions. (See ref. 11 .) The quan-

tity in the brackets accounts for light nuclei having greater excitation energy than heavier nuclei for thesame fraction of mass removed (ref. 67) and is limited to values between 0 and 1500. The total excita-

tion energy is then

Es = E_ (7.19)

which reduces to equation (7.17) for small Aab r. Also, the assumption is that 100 percent of the frag-ments with a mass of 5 are unbound, 90 percent of the fragments with a mass of 8 are unbound, and

50 percent of the fragments with a mass of 9 (9B) are unbound. (See ref. 11 .)

A secondary contribution to the excitation energy is the transfer of kinetic energy of relative motionacross the intersecting boundary of the two ions. The rate of energy loss of a nucleon when it passes

through nuclear matter (ref. 68) is taken as 13 MeV/fm, and the energy deposit is assumed to be sym-

metrically dispersed about the azimuth so that 6.5 (MeV/fm)/nucleon at the interface is the average rate

of energy transfer into excitation energy. (See ref. 36.) This energy is transferred in single-particle colli-

sion processes, and the energy is transferred to excitation energy of the projectile for half of the eventsand leaves the projectile excitation energy unchanged for the remaining half of the events. (See ref. 11.)

The first estimate of this contribution uses the length of the longest chord C 1 in the projectile surface

interface. This chord length is the maximum distance traveled by any target constituent through the pro-

jectile interior. The number of other target constituents in the interior region can be found by estimating

the maximum chord C t transverse to the projectile velocity, which spans the projectile surface inter-face. (See ref. 36.) The total excitation energy from excess surface and spectator interaction is then

' I 1 1.5) 1 (7.20)Ex = 13C 1 I+_(C t-

where the second term contributes only if C t > 1.5 fm. Also, the effective longitudinal chord length forthese remaining nucleons is assumed to be one third of the maximum chord length.

The decay of highly excited nuclear states is dominated by heavy particle emission. In the presentmodel, a nucleon is assumed to be removed for every 10 MeV of excitation energy. The number of

ablated nucleons is

E+E_ s x (7.21)

Aabl 10

In accordance with the previously discussed directionality of the energy transfer, E x has two values

EX

E' forP =1x x 2

10 for Px =

(7.22)

where Px and Px are the corresponding probabilities of occurrence of each value in collisions.

22

ThenumberAAof nucleonsremovedthroughtheabrasion-ablationprocessisgivenasafunctionoftheimpactparameteras

AA = Aab r (b) + Aab I (b) (7.23)

The cross section for the removal of AA nucleons is estimated as

O (AA) = _/b2 - b2) (7.24)

where b 2 is the impact parameter for which the volume of the intersection of the projectile contains

Aabr nucleons and the resulting excitation energies release an additional Aab I nucleons at the rate of1 nucleon for every 10 MeV of excitation such that

tAabr (b2) + AabI (b2) = AA - ,_ (7.25)

similarly, for b 1

1Aab r (bl) + Aab 1 (bl) = AA + _ (7.26)

In the previous discussion, the assumption of straight-line trajectories makes the impact parameter b

the distance of closest approach. This assumption makes the abrasion-ablation model a high-energy

heavy ion fragmentation model; thus, Coulomb corrections due to low-energy trajectories must be

added to the standard abrasion-ablation model. Equations (7.24)-(7.26) can be combined and rewritten

(ref. 58) as

(7.27)

Equation (7.27) is retained in NUCFRG2 as written. However, b is no longer taken to be the dis-

tance of closest approach as used in equation (7.27) but is redefined in the following discussion.

The equations of motion in the nuclear Coulomb field are given by energy conservation as

1 .2 12 ZpZTe2

Et°t = 2 I'tr + 2-_r 2 + _r (7.28)

where Etot is the total kinetic energy in the center-of-mass system at great relative distances, r is the rel-ative distance between the charge centers with time derivative f, g is the reduced mass, I is the angular

momentum, Zp and Z r are the atomic numbers of the projectile and target nucleus, respectively, and eis the electronic charge. The angular momentum is given as

12 = 2btEtotb2 (7.29)

With the use of equation (7.29) and/- = 0, equation (7.28) becomes

Etotb2 ZpZTe2

Et°t - r 2 + --r(7.30)

which can be written as

b2 = r(r-rm) (7.31)

23

where

rm

ZpZre2

Etot(7.32)

Note that r is the distance of closest approach for the zero impact parameter. For a given AA,

equation (7.3m2) is used in NUCFRG2 to calculate the distance of closest approach and equation (7.31) isused to calculate the impact parameter, which permits extrapolation backward in time along the

Coulomb trajectory to the initial impact parameter. (See ref. 69.) This calculated value of b is used in

equation (7.27) to evaluate the cross section. Note that the effect of the Coulomb trajectory is to move

the separation at impact r to smaller impact parameters b and thus reduce the cross sections, especially

at low energy.

A second correction to the trajectory calculation comes from the transfer of kinetic energy into

binding energy in the release of particles from the projectile. The total kinetic energy in passing through

the reaction zone is reduced from the initial energy E i to the final energy Ef

Ef = E i- 10AA (7.33)

by assuming that 10 MeV is the average binding energy. The kinetic energy used in the closest approach

calculation is the average

1 1Eto t = _ (E i + Ef) = E i - _ (IOAA) (7.34)

As given by equation (7.34), Eto t is obviously very crude and equation (7.34) can be refined further.

The distribution of charge Z F of final projectile fragments of mass A F are strongly affected bynuclear stability. The charge distribution for a given c(AA) as described by Rudstam (ref. 70) is

a(AF, ZF) = Flexp/_ R ZF_SAF+ TA 2 3/2)O (AA) (7.35)

where R = 11.8/A D, D = 0.45, S -- 0.486, T = 3.8 x l0 -4 , and F 1 is a normalizing factor such that

ZO (A F, ZF) = c (AA) (7.36)

zr

The Rudstam formula for a(AA) was not used because the AA dependence is too simple and breaks

down for heavy targets (refs. 11, 36, 71, and 72) and was replaced by equation (7.27) in the

abrasion-ablation fragmentation model.

The charge of the removed nucleons AZ is calculated according to charge conservation

Zp = ZF + AZ (7.37)

and is divided between the nucleons and hydrogen and helium isotopes according to the following four

rules:

1. The abraded nucleons are those removed from that portion of the projectile in the region of over-

lap with the target. (See ref. 67.) Therefore, the abraded nucleon charge is assumed to be proportional to

the charge fraction of the projectile nucleus as

Zabr = ZPAabr/A P (7.38)

24

This, of course,ignoresthe chargeseparationcausedby the giant dipole resonancemodelofreference63.Thechargereleasein theablationstageis then

Zab I = AZ-Zab r (7.39)

which simply conserves the remaining charge.

2. The alpha particle is known to be unusually tightly bound in comparison with other nucleon

arrangements. Because of this unusually tight binding of the alpha particles, the helium production is

maximized in the ablation process. (See refs. 11 and 36.) The number of alpha particles is

Net = [Int (Zabl/2), Int (Aabl/4) ] min (7.40)

where Int(x) denotes the integer part of x. The remaining isotopes are likewise maximized from the

remaining ablated mass and charge in the order of decreasing binding energy. (See ref. 69.) The number

of protons N produced is given by charge conservation as

Np = Zab 1 -ZZiNi (7.41)i

where i ranges over all ablated particles of mass 2, 3, and 4. Similarly, mass conservation requires the

number of neutrons N produced to be

N n = Aab I - Alp - ZA iN i (7.42)

3. The calculation is performed for AA = 1 to AA = Ap - 1, for which the cross section associated

with AA > Ap - 0.5 is omitted. These are, of course, the central collisions for which the projectile is

assumed to disintegrate into single nucleons if rp < r r. Then

Np = Zp (7.43)

Nn = Ap - Zp (7.44)

Other collision products such as the energetic target fragments and mesonic components are ignored.

The peripheral collisions with AA < 0.5 are also ignored. Most important in these near collisions is the

Coulomb dissociation process. (See ref. 73.)

4. The description of the nuclear radius is given by

R = 1.29(R2rms - R2) (7.45)

where Rrms is the rms radius of the nucleus charge distribunon and R is the radius of the proton chargeP

distribution. The improvements to the abrasion-ablation model as implemented in NUCFRG2 and com-

parison with experiments are further described in references 74 and 75.

Finally, the electromagnetic (EM) dissociation cross-section contributions to the nuclear database

as implemented in NUCFRG2 must be considered. In electromagnetic dissociation, the virtual photon

field of the target nucleus interacts electromagnetically with the constituents of the projectile to cause

excitation and eventual breakup. The electromagnetic dissociation model implemented in NUCFRG2 islimited to single nucleon (proton or neutron) removal processes.

25

The total electromagnetic cross section for one nucleon removal resulting from electric dipole (El)

and electric quadrupole (E2) interactions is written

Gem = GEl+GE2

= [ [NE1 (E) OEI (E) + NE2 (E) GE2 (E) ] dE.1

(7.46)

where the virtual photon spectra of energy E produced by the target nucleus (ref. 76) are given for the

dipole field by

12 2 1 1 22 2 K 2NEI(E) = _Z _-_I_KoKI-_ 13 (K 1- o/1 (7.47)

and for the quadrupole field by

-1-_2B4(K2-K2)I12Z2otl[-2(1-132)K2+_(2-132)2KoK 1 27 ,- \ 'NE2(E) = E_ 13 [_

(7.48)

The terms GEl (E) and GE2 (E) are the corresponding photonuclear reaction cross sections for the

fragmenting projectile nuclei. The terms K 0 and K 1 in the expression for NE1 and Ne2 are modifiedBessel functions of the second kind and are also functions of the parameter _. The latter is

2r_Ebmin (7.49)= y13hc

where E is the virtual photon energy, bmi n is the minimum impact parameter below which the collision

dynamics are dominated by nuclear interactions rather than by EM interactions, 13 is the speed of the tar-

get measured from the projectile rest frame as a fraction of the speed of light c, h is Planck's constant,

and y is the usual Lorentz's factor from special relativity y = (1 -132) -1/2. The minimum impact

parameter is

7ta° (7.50)bmi n = (1 +Xd) bc+ 2---n

where x d = 0.25 and

a0 -ZeZre 2

moV2

(7.51)

allows for trajectory deviation from a straight line. (See ref. 77.) The critical impact parameter for

single-nucleon removal is

bc = 1.34 [a 1/3 + A1T/3 - 0.75/Ap1/3 + ATI/3)J (7.52)

with Ap and A T being the projectile and target nucleon numbers, respectively.

The photonuclear cross sections aEl (E) and ae2(E) are Lorentzian shaped and somewhat

sharply peaked in energy. Therefore, photon spectral functions can be taken outside of the integral of

equation (7.46) to yield the approximate form (ref. 76) of

dE(Iem= NEI (EGDR) fGEI (e) ME + NE2 (EGQR) E2QRfGE2 (E) -E_ (7.53)

26

andE___ are the energies at the peaks of the E1 and E2 photonuclear cross sections,where EGD R tJt_K

respectively. These integrals of photonuclear cross sections, integrated over energy, are evaluated with

the following sum rules (ref. 76):

N pZpt"

/oE, (e) de-- 60A----_d

(7.54)

and

_%2 (E) dE 0.22fZpap2/3 (7.55)

In equations (7.54) and (7.55), N v is the number of neutrons, Z e is the number of protons, and Ap

is the mass number of the projectile nucleus. The fractional exhaustion of the energy-weighted sum rule

in equation (7.55) (ref. 68) is

0.9 (A t ,> 100)f = 0.6 (40<Ap< 100)

0.3 (40 < Ap)

(7.56)

In equation (7.53), EGD R and EGQ R are the energies at the peaks of the E1 and E2 photonuclearcross sections, respectively. For the dipole term (ref. 68),

EGDR = 2-_l_\ l+u l+e+u )J(7.57)

with

3J Apt/3 (7.58)U __ ...--3Q

and

R o = roAlp/3 (7.59)

where e = 0.0768, Q' = 17 MeV, J = 36.8 MeV, r0 = 1.18 fm, and m* is 0.70 of the nucleon mass.

For the quadrupole term,

63 (7.60)EGQ R - All3

Finally, the single-proton or single-neutron removal cross sections are obtained from a em

(eq. (7.53)) by using proton- and neutron-branching ratios gi (i = p, n). Then

o (i) = git_em (i = p or n) (7.61)

The proton-branching ratio has been parameterized by Westfali et al. (ref. 68) as

gp= min IA_-pe,1.95 exp(-0.075Z/,) 1(7.62)

27

where Zp is the number of protons, and the minimum value of the two quantities in brackets is to betaken. This parameterization is satisfactory for heavier nuclei (Zp > 14); however, for light nuclei, the

following branching ratios are used instead:

gp _--- 0.5 (Zp < 6)0.6 (6 _<Zp < 8)

0.7 (8 <Zp< 14)

(7.63)

For neutrons, the branching ratio is

gn = 1 - gp (7.64)

Figure 3 shows the absorption cross section as a function of energy for six different projectile

charge numbers Zp, as calculated by HZETRN for aluminum, water, and liquid hydrogen targets. The

importance of the target size on the systematic variation of the absorption cross section with projectilemass is clearly seen. Small target nuclei preferentially fragmentize heavy ions, which is important to

shield performance. (See ref. 78.)

Among the best known fragmentation cross sections are those for carbon ion beams on carbon tar-

gets. Measurements have been made at four energies (250A MeV in ref. 79, 600A MeV in ref. 80, and1.05A and 2.1A GeV in ref. 81) and are compared in figure 4 with the results from NUCFRG2 cross-

section calculation. The effects of the Coulomb trajectory are clearly apparent on the lighter mass frag-

ments of lithium and beryllium which exhibit a change in slope below 100A MeV. Such Coulomb

effects will be even more important for projectile and fragments of greater charge. Figure 5 shows the

results of very-low-energy (11.7A MeV) oxygen projectiles onto a molybdenum target (ref. 82) where

Coulomb effects are very important. The resulting charge removal cross sections seem well represented

by NUCFRG2 calculation even at low energies. The process whereby a nucleon is exchanged between

the oxygen projectile and the target nucleus is referred to as "exchange poles." As shown in figure 5,

the addition of exchange poles to the model will bring charge removal cross sections into agreement as

can be judged by the proton exchange pole (neutron removal) contribution for proton exchange.

Figure 6 shows three projectile-target combinations for which two groups of experimenters havetaken measurements at nearly the same energy (1.55A GeV in ref. 83 and 1.88A GeV in ref. 84). On the

basis of NUCFRG2 calculations, very small cross-section differences are expected to exist at these high

energies. (See fig. 4.) Cross sections NUCFRG2 tend to favor the data of Westfall et al. (ref. 84) and lie10 to 50 percent above that of Cummings et al. (See ref. 83.) Perhaps the most encouraging result of the

comparison with the data of Cummings et al. is that trends in NUCFRG2 below aluminum measure-

ments (Z F = 13) of Westfall et al. appear in reasonable agreement with the results of Cummings et al.

down to neon fragments (Z F = 10). The NUCFRG2 fragmentation cross sections below neon remainsuntested.

To better quantify the comparison of results shown in figure 6, X2 analysis is used. The test data of

the fragmentation model in NUCFRG2 are compared with the experimental data of Cummings et al.(ref. 83) and Westfall et al. (ref. 84) and shown in table I for iron projectiles on three targets. Shown in

table I are the total X2 values and the average X2 contributions per degree of freedom n. Clearly, the

data for producing aluminum fragments in the experiments of Westfall et al. show large systematic

errors, which are nearly the sole contribution to the X 2 values. The elimination of the aluminum data

from the experiments of Westfall et al. is shown in the table as the values in parentheses. By excludingthe aluminum data, the model then shows good agreement with the data of Westfall et al. for carbon and

copper targets. The greater discrepancy for the lead targets surely results from the simplified nuclearmatter distribution; the use of a diffusive surface model rather than the uniform sphere model is recom-

mended. When comparing the model with the data of Cummings et al., similar trends are shown with

28

targetmass,buttheoverallagreementwiththedataof Cummingsetal. is inferiortotheagreementwiththedataofWestfalletal.aswaspreviouslynotedin thediscussionof figure6.

Table I. X2 Analysis of Iron Fragmentation Model

NUCFRG2-Westfall a NUCFRG2-Cummings

Shield + target Z 2 X2/n X2 X2/n

Fe + C 50.2 (16.0) 5 (1.8) 48.3 3.7

Fe + Cu 200.6 (22.9) 20 (2.5) 78.1 6.0

Fe + Pb 177.4 (56.2) 18 (6.2) 83.1 6.7

aAIl values in parentheses exclude Westfall's aluminum cross section.

The Z 2 analysis has been used to compare how well the results of one experimental group compare

with the results of another. Such a comparison is shown in table II. Again, the values in parentheseseliminate the aluminum data contribution of Westfall et al. What is clear from table II is that the model

represents the two sets of experimental data better than either experimental data set represents the other.

This is the best that can be hoped for within the present experimental uncertainty.

Table II. X 2 Analysis of Iron Fragmentation Experiments

Westfalla-Cummings Cummings-Wesffall a

Shield + target X 2 X2/n X2 X2/n

Fe + C 85.6 (43.3) 8.6 (4.8) 54.6 (33.6) 5.5 (3.7)

Fe+Cu 424.4 (108.4) 42.4 (12.0) 160.3 (69.4) 16.0 (7.7)

Fe + Pb 348.8 (79.5) 34.9 (8.8) 143.4 (55.8) 14.3 (6.2)

aAll values in parentheses exclude Westfall's aluminum cross section.

Figures 7(a), 7(b), and 7(c) show the fragmentation cross sections as calculated by NUCFRG2 as a

function of projectile and fragment mass numbers at four different projectile energies for aluminum,

water, and liquid hydrogen targets, respectively. It is difficult to interpret the data directly in terms of

shield performance. However, the ion fragmentation at lower energies is clearly most effective for

complex target nuclei as can be seen by comparing the aluminum cross sections at 25A MeV infigure 7(a) with those of liquid hydrogen in figure 7(c). In contrast at high energies, the hydrogen target

distributes the mass of the fragments more broadly than the aluminum targets as seen by comparing the

results at 2400A MeV in figures 7(a) and 7(c). The water target displays both of these characteristics

simultaneously.

8. Environmental Model

Calculations and measurements show that HZE ions in GCR particle fluxes vary inversely with

solar activity. This dependency indicates that, at maximum solar activity, the GCR particle flux is at a

minimum, and at minimum solar activity, the GCR particle flux reaches a maximum. This process of

flux variation results from the shielding of the inner part of the solar system by the magnetic fields that

are being carried away from the solar surface by the solar wind and varies periodically during an 11- to

13-year cycle. This shielding process is particularly effective in low-energy GCR particles. Calculations

have shown that, for energies of 100A MeV or less, the GCR particle flux variation between solar mini-mum and solar maximum is a factor of 10 or more. At GCR particle energies above a few hundred

A MeV, the effect of solar modulation on GCR particle flux gradually decreases and above approxi-

mately 10A GeV becomes negligible.

29

A numericaldescriptionof theprevioussolarmodulationmustbesuppliedasaninputto theenvi-ronmentalmodelof anyspaceradiationtransportcomputercodeincludingHZETRN.Theenvironmen-tal modelof BadhwarandO'Neill is usedin HZETRN.(Seeref. 42.)Thismodelisbasedon fittingmeasureddifferentialenergyspectraof 1954-1989to stationaryFokker-Planckequationsolutionstoestimatethe diffusion coefficientor the equivalentdecelerationparameter_ in units of MV.Reference42showsthat,independentof energy,thisapproachfits theavailabledatawithinanerrorof+10 percent rms. By using the calculated diffusion coefficient, the GCR spectra of hydrogen, helium,

carbon, oxygen, silicon, and iron are estimated. The spectra of the remaining elements were scaled tothe previous elements by following reference 43. The environmental model data (i.e., solar maxima-

minima) available in HZETRN are for the years 1958-1959, 1970-1971, 1981-1982, and 1989 solarmaxima and 1965, 1977, and 1986-1987 solar minima.

Based on the model of reference 42 used in HZETRN, figure 8 shows the predicted fluxes of 1977

solar minimum and 1981 solar maximum as a function of energy for five different charge groups.Figure 9 shows the flux ratio of the 1981 solar maximum compared with the 1977 solar minimum for

five different charge groups in the energy range of 0.1 to 106 MeV. As discussed previously, the two

spectra are essentially identical at energies above 50A GeV, while at lower energies, the ratio can be

1:10 or less depending on the ion type.

Solar flare occurrence is correlated with solar activity and the most important events seem to occur

during the ascending or descending phase of the solar cycle. The four solar particle events (SPE) of

February 1956, November 1960, August 1972, and October 1989 are widely used to estimate flare-

shielding requirements. Fitted fluence energy spectra of these four events (refs. 85-88), King's-fittedspectrum of 1972, and Webber's fit (ref. 89) are as follows:

1. February 1956

( 0) (._p(>E) = 1.5xl09exp - _5 +3xl08exp 3-20 J

2. November 1960

_p(>E) = 7.6xl09exp(-E_10)+3.9xl08exp( - E-100180J

3. August 1972

( E:!oo ¢p(>E) = 6.6x108exp 30 J

4. October 1989

P(E)__e (>E) = 8.65 x l01° exp 59.261J

5. August 1972 (King spectrum)

_e (>E) = 7.9 x 109 exp( E2_6.5-30_j

6. Webber spectrum with 100 MV rigidity

F239.1 - P (E) 1Cp(>E) = 1.0x 109 expL 1"-00

where E is the energy in MeV, P(E) = _/E(E+ 1876) is the rigidity, and Op(>E) is the protonintegral fluence in protons/cm 2. Figure 10 shows the fitted spectra. The flare of October 1989 produced

3O

thegreatestnumberof protons less than 4 MeV, and the flare of August 1972 produced the greatest

number of protons between 4 and 150 MeV. The February 1956 flare produced approximately one tenth

as many protons greater than 10 MeV as the 1972 and 1989 flares, but it delivered far more protons of200 MeV or greater than the three other flares. The November 1960 flare exhibited intermediatecharacteristics.

9. HZETRN Benchmarking

In this section, the subject of HZETRN validation is addressed. Ideally, validation should be accom-

plished with detailed transport data obtained from carefully planned and controlled experiments; unfor-

tunately, such data are scarce. Although useful for comparative purposes, the atmospheric propagation

measurements (ref. 36) used previously are clearly not definitive because they consist of integral flu-

ences of as many as 10 different nuclear species combined into a single datum. Although limited quan-tities of HZE dosimetry measurements from manned space missions (e.g., Skylab) are available

(ref. 90), numerous assumptions about the relationship between the dosimeter location and spacecraft

shield thickness and geometry must be made to estimate astronaut dose with GCR codes. Because manyof these assumptions may involve inherently great uncertainties (i.e., factors of 2 or greater), differences

in results are difficult to attribute to the particular assumptions or approximations that may have been

used in the analysis. Without definitive GCR transport measurements with which to compare code pre-dictions, other methods of validation must be considered. One such method is to compare HZETRN

with limited available proton transport Monte Carlo results. (See ref. 87.)

In reference 87 comparisons of the results obtained for a hypothetical problem with four differentproton transport codes are presented. The hypothetical problem was to determine the dose, as a function

of depth in water, resulting from a typical solar flare proton spectrum normally incident on a semi-

infinite slab shield which is followed by the slab of water. The water was assumed to be 30 g/cm 2 thick.

The solar proton spectrum was taken to be exponential in rigidity (Webber spectrum of section 8) with a

characteristic rigidity of 100 MV and was normalized to 109 protons/cm 2 with energy >30 MeV. TheNucleon Transport Code (NTC) (ref. 9 I) is used here and compared with HZETRN.

Figures 11 (a) and 11(b) show the total dose in gray (Gy) and total dose equivalent in sievert (Sv) for20 g/cm 2 shields of aluminum and iron, respectively, followed by 30 g/cm 2 of water. For both shields,

the code correlation is good. At water depths >20 g/cm 2, HZETRN predictions are slightly greater thanNTC because of the 400-MeV cutoff in the NTC calculation. (See ref. 37.)

Figures 12(a) and 12(b) show the secondary neutron dose in gray (Gy) and secondary neutrondose equivalent in sievert (Sv) for 20 g/cm 2 shields of aluminum and iron, respectively, followed by

30 g/cm 2 of water. For both shields, the code correlation is only fair, which results partly from the gridcoarseness of the Monte Carlo secondary neutron prediction runs and current limitations in the neutron

transport database and elastic scattering propagation. (See ref. 33.)

Other comparisons of HZETRN with analytic functions are reported in references 35, 39, and 75.

10. HZETRN Computational Results

In this section results from applying HZETRN to different targets and environmental periods (i.e.,

solar minimum or maximum) are presented to provide a sufficiently broad database for code testing.The emphasis is on information that can be extracted directly from a typical execution of HZETRN.

Therefore, environmental periods of the 1977 solar minimum and 1981 solar maximum and target mate-

rials of aluminum, water, and liquid hydrogen are used. Although HZETRN-calculated dose equivalentresults are based on the International Commission on Radiological Protection ICRP-26 and ICRP-60

(refs. 92 and 93) quality factor recommendations, only the dose equivalent results for ICRP-60 are

shown here. The calculations include the following results for skin dose and blood-forming organ(BFO) dose:

31

1. Flux contributions from carbon, oxygen, calcium, and iron ions at different energies

2. Total and individual ions, dose and dose equivalent contributions for skin (0-cm surface dose),

and BFO (5-cm-depth dose) at different depths

3. Flux contributions, total dose and dose equivalent contributions for skin (0 cm), and BFO (5 cm)

at different linear energy transfers (LET)

shortcomings of the HZETRN calculations are as follows:

All secondary particles from HZE interactions are presently assumed to be produced with a

velocity equal to that of the incident particle; this is conservative for neutrons produced in HZE

particle fragmentations

2. Meson contributions to the propagating radiation fields are neglected

3. Target fragments in HZE reactions are neglected

4. Angular dependence, especially in neutron propagation is neglected

These data are not all conservative and probably account for the 15- to 30-percent underestimation

of the exposure. As discussed in references 94 and 95, the main sources of uncertainty are the input

nuclear fragmentation model and the incident GCR spectrum. Taken together, they could easily impose

an uncertainty factor of 2 or more in the astronaut risk estimate. This is especially true for track struc-

ture dependent biological models. (See refs. 78 and 96.)

Figures 13-16 show the flux of carbon, oxygen, calcium, and iron ions in aluminum targets for the1977 and 1981 solar periods at depths of 0, 10, 20, and 30 g/cm 2 in the energy range of 10-2A to

105,4 MeV. Similarly, figures 17-24 show the flux for water and liquid hydrogen targets. In all figures

the effect of solar minimum and solar maximum periods are demonstrated through a reduction in the

magnitude of the particular ion flux during solar maximum. Figures 13-24 demonstrate that lighter

target materials such as liquid hydrogen have better attenuation characteristics than heavier target

materials such as aluminum for all target depths.

Figure 25 shows skin dose, Gy and dose equivalent, Sv, when using ICRP-60 quality factorsin aluminum, water, and liquid hydrogen targets for the 1977 and 1981, 1982 solar periods at depths of

0 to 30 g/cm 2. Only a modest gain in protection is displayed by aluminum shielding. A water shield

shows substantially better attenuation characteristics. Liquid hydrogen has excellent shielding charac-teristics. These results are demonstrated more clearly in figure 26, which shows skin dose, Gy, and dose

equivalent, Sv, when using ICRP-60 quality factors in aluminum, water, and liquid hydrogen targets forthe 1977 and 1981 solar periods at depths of 0 to 30 g/cm 2. In figure 26, the effect of the atomic and

nuclear properties of the target is demonstrated by increases in skin doses for larger target nuclei.

Figures 27-29 show skin dose, Gy, and figures 30-32 show dose equivalent, Sv, when using

ICRP-60 quality factors for six different charge groups in aluminum, water, and liquid hydrogen targetsfor the 1977 and 1981 solar periods at depths of 0 to 30 g/cm 2. The better attenuation properties of the

liquid hydrogen target versus aluminum target at all target depths are shown for the given charge groups

for both solar epochs.

Figures 33-40 show the attenuation behavior of GCR in aluminum, water, and liquid hydrogen at

the 5-cm-BFO depth. The dosimetric characteristics of different target materials as a function of target

depth are similar to those in figures 13-32, except here an additional attenuation exists in all databecause of an additional 5 g/cm 2 of water.

Figures 41-49 show skin flux and dosimetric characteristics of GCR components in aluminum,

water, and liquid hydrogen targets for the 1977 and 1981 solar periods for the LET range of 1 to105 MeV/cm of water at depths of 0, 10, 20, and 30 g/cm 2. The presence of the primary components of

Major

1.

32

GCRfromprotontoironisclearlydemonstratedasinflectionsinall figures. The attenuation character-

istics of lighter targets such as liquid hydrogen versus heavier targets such as aluminum are shown at all

depths and LET ranges.

Figures 50-58 show 5-cm-BFO flux and dosimetric characteristics of GCR components in alumi-

num, water, and liquid hydrogen targets for the 1977 and 1981 solar periods for the LET range of 1 to105 MeV/cm of water at depths of 0, 10, 20, and 30 g/cm 2. As before, the dosimetric characteristics of

different target materials as a function of target depth are similar to those in figures 41-49, except herean additional attenuation exists in all figures because of an additional 5 g/cm 2 of water. As in

figures 41-49, the presence of the primary components of GCR from proton to iron is clearly demon-

strated as inflections, and the attenuation characteristics of lighter targets such as liquid hydrogen versus

heavier targets such as aluminum are shown at all depths and LET ranges.

The use of the HZETRN code and the control of the options to generate a typical output are

discussed in appendix A. A complete sample output with the options of appendix A is provided in

appendix B.

11. Concluding Remarks

The study of free-space radiations is essential for estimation of the risk factors for long-duration

manned space flights. The estimates of galactic cosmic ray (GCR) ion flux inside a space module can be

made by calculating quantities such as energy and linear energy transfer (LET) spectra. The estimation

of doses and LET spectra by numerical predictive techniques, such as HZETRN, is essential for any

long-duration manned space mission.

This paper reports the progress in computer code development for space radiation studies and shield

design for future NASA space programs; the HZETRN code is a state-of-the-art fast computational tool

available for a design engineer to obtain answers to some of the radiation questions that arise in plan-

ning any mission. However, major uncertainties in nuclear cross sections, environmental models, and

astronaut risk affect the overall accuracy of the predictions of any analytical-computational technique.

These uncertainties have a major impact on the proposed shield design for any mission and the subse-

quent mission cost. Much work remains to accurately resolve the problems with nuclear cross-section

calculations, environmental model development, and risk estimate methods.

NASA Langley Research Center

Hampton, VA 23681-0001

February 14, 1995

33

Appendix A

HZETRN Description

A1. Program Structure

The main program and each subroutine or function module begins with a brief description of its pur-pose. The program has 8358 lines, is written in FORTRAN 77, and was developed on a VAX 4000

scaler minicomputer under the VMS operating system; in its current version, the program requires

463 blocks (237 056 bytes) of storage space. However, the program is essentially platform and operating

system independent. The complete computer code consists of a main program HZETRN, 63 subroutines,

and 37 function modules. Table AI provides a list of the subroutines and function modules in the order

in which they appear in the program. The overall structure of HZETRN is shown in figure A1, which

includes input requirements and output options.

Table AI. HZETRN Program Modules

Program Program Program

No. module Type a No. module Type a No. modu/e "/}rpe a

1 MATTER S 35 DENSEFF F 69 FB F

2 DMETRIC S 36 ATOPA S 70 SLOPE F

3 PRPGT S 37 ACOEF F 71 ELSEC F

4 OD F 38 CCOEF F 72 XTOT F

5 TS F 39 ATOPN S 73 XTOTLM F

6 F2 S 40 BUILD F 74 XSEC F

7 FRAG F 41 SNF F 75 ABSEC F

8 XSECFRG F 42 TEXP F 76 LZEVAP S

9 YIELDX S 43 TSQR F 77 ASIGM S

10 YIELDN S 44 RMAT F 78 XTEST S

II YIELDA S 45 SIONA F 79 SPLCN S

12 YIELDT S 46 ZEFF F 80 SPLIN S

13 PXN S 47 RTIS F 81 PRPLI S

14 YIELD1 S 48 MGAUSS S 82 FD S

15 YIELD2 S 49 IUNI S* 83 LITEST S

16 YIELD3 S 50 IBI S* 84 TBARLI S

17 YIELD4 S 51 QXZII4 F* 85 LIFRAG S

18 NAND F 52 QXZII5 S* 86 RADIUS F

19 YIELDH S 53 QXZII6 S* 87 XLISEC F

20 YIELDLI S 54 QXZII7 S* 88 LKOSPC S

21 YIELDEM F 55 SUTPAR S* 89 E3MAX F

22 BESSEL F 56 QXZ060 S* 90 WDKO S

23 GEODA S 57 QXZ061 S* 91 LQESPC S

24 BSEACH S 58 QXZ062 S* 92 WQE F

25 DELTA S 59 QXZ063 F* 93 DERF F

26 FPOFB S 60 QXZ 111 S* 94 GCRFLUX S

27 LIMIT S 61 QXZII2 S* 95 FBERT S

28 GEOFR S 62 QXZII9 S* 96 BERTINI S

29 RADLI F 63 PHTOINT S 97 RANFT S

30 EOFS S 64 PHI F 98 FDNP S

31 CROSS0 S 65 PHTOD S 99 Q60 F

32 QOFS F 66 ELSPEC S I00 SFBERT S

33 ATOE S 67 XPP F

34 ATOPP S 68 XNP F

a S--subroutine module.

F--function module.

S --subroutine module taken from LaRC-NASA mathematical library (N2-3D).

F*--function module taken from LaRC-NASA mathematical library (N2-3D).

34

A2. HZ_.TRN Input Requirements

The complete program is composed of the HZETRN source code (HZEALH20. FOR in the COSMIC

library) and three input data files. In the current version, HZEALH20. FOR requires the following inputfiles:

1. ATOMIC. DAT

2. NUCLEAR. DAT

3. JSCCOSMC. DAT

The following isa briefdescriptionof each fileand how tosetup the inputflagsifany are required.

1. FORTRAN code HZEALH20. FOR is set up to transport galactic cosmic ray (GCR) particles in

free space (geomagnetic cutoffs are ignored) through a given thickness of the aluminum shield followed

by a given depth of water. Besides the setting of array dimensions for the energy grid points and isotope

fragment number, which are defined in the PARAMETER statement throughout the code as II:45 and

IJ:59, respectively, the only changes to the code required for any mn are in the MAIN module and

subroutine MATTER. In addition the user has the option of changing the isotope table that is used to rep-

resent the transported particle fields of the GCR particles in the shield or target material in function TS.

a. In the MAIN module, the following two integer variables must be defined:

(1) IPRGCR, which specifies the extent (1, 2, or 3) of printed information, with 2 being a goodchoice for most calculations

(2) IYEAR, which specifies the year in the solar cycle to be used (solar maxima for the years

1958, 1970, 198l, and 1989 and solar minima for the years 1965, 1977, and 1986)

b. In subroutine MATTER, the following arrays and variables must be defined:

(1) Dimension of array XAL, which specifies the depth in the aluminum shield where dosimetric

quantities are to be calculated and printed. The depth within the aluminum shield is deter-

mined by summing the elements of array XAL. For example, if XAL has a dimension of 3 and

is defined in the data statement as DATA XAL/5,5, 10/, the transport calculation results

will be printed for the following depths of the shield material:

(a) Depth 1: XAL ( 1 ) = 5 g/cm 2

(b)Depth 2:XAL (i) +XAL (2) :5 + 5:10 g/cm 2

(c)Depth 3: XAL (1 )+XAL (2 )+XAL (3 ) :5 +5 + 10: 20 g/cm 2

(2) Dimension of array XWAT. The discussion in paragraph 1.b.(1) also applies to the array XWAT

forwaten

Note that for the shield and target material the particle fields are transported and calculated by

default in steps of H--2 g/cm 2 throughout the program, and the discussion in para-

graphs 1 .b.(1) and l.b.(2) refers only to the depths for which data are to be printed.

(3) Variables NTOTI and NTOT2 must be equal to the dimensions of XAL and XWAT arrays,

respectively. For example, if XAL has dimension 3 and XWAT has dimension 5, then NTOT1

and NTOT2 are defined by

DATA NTOTI,NTOT2/3,5/

35

(4) The following physical properties of the shield and target material are included: NAT is the

number of elements in the shield or target--NAT= 1 for aluminum, NAT=2 for water, DN is theoverall density of the shield or target in g/cm 3, ATRG is the atomic mass number of each ele-

ment of the shield or target, ZTRG is the atomic charge number of each element of the shield

or target, and DENSTRG is the number of atoms/g of each element of the shield or target.DENSTRG is calculated from

DENSTRG(I): [N0*R(I) ]/SUM[R(I)*ATRG(I) ]

where NO is the Avogadro number taken as 6. 023E23 atoms/gram-atom, R ( I ) is the num-

ber of atoms/molecule, and ATRG ( I ) is the mass in gram/gram-atom of the Ith element in

the shield or target. For a simple material like aluminum, DENSTRG becomes

DENSTRG(1):(6.023E23*I)/(I*27.0):2.23E22(_rAI)

For a compound material like water, DENSTRG becomes

DENSTRG (I) : (6. 023E23"2 )/ (2"1. 008+1"16.0) =6.68E22 (forH)

DENSTRG (2) : (6. 023E23 *i )/ (2*I. 008+1"16.0 ):3.34E22 (forO)

Note that only 3 significant figures are retained for compatibility with the generated data files.

Also, note that arrays ATRG, ZTRG, and DENSTRG currently have a dimensional limit of 5.

For a more complex material with NAT>5, the dimensions of ATRG, ZTRG, and DENSTRG

must be adjusted appropriately.

(5) The transport of chosen particles in the shield or target is represented by a user-provided iso-

tope table that is defined in function TS. The arrays APRO and ZPRO in common block PROJ

contain the mass and charge numbers of transported isotopes. The isotope table can bechanged by choosing a different table or, if more or less than 59 isotopes are needed, by

adjusting variable IJ=59 in the PARAMETER statement throughout the codes to reflect a

larger or smaller isotope table.

2. ATOMIC. DAT is the energy, range, and stopping-power database for water and aluminum. For

any other material, the source code will automatically generate a file called NEWRMAT. DAT during exe-

cution. This file should be appended to the ATOMIC. DAT master data file for future transport runs.Note that DENSTRG format is E 12.3, which permits only three significant figures.

3. NUCLEAR. DAT is the absorption and fragmentation cross-section database for water and alumi-

num. For any other material, the source code will automatically generate a file called NEWNUC 59. DAT

during execution. This file should be appended to the NUCLEAR. DAT master data file for future trans-

port runs. Note that DENSTRG format is El2.3, which permits only three significant figures.

4. JSCCOSMC. DAT is the environmental model database taken from references 42 and 43 for the

solar maxima for the years 1958, 1970, 1981, and 1989 and solar minima for the years 1965, 1977, and1986.

A3. Compiler Dependencies

Besides the usual compiler-dependent OPEN and REAL* 8 statements, which must be checked bythe HZEALH20. FOR code user, the source code has one compiler-dependent feature in subroutine

QXZ061, which must be modified if this code is to be run on a non-VAX platform. In QXZ061,

36

variablesTHIRD and SIXTH are defined in OCTAL format and must be modified to conform with a

non-VAX compiler octal number format. Besides these trivial changes, the rest of the source code

should run on any platform with a FORTRAN compiler.

A4. Program Execution

To provide the users of HZEALH20. FOR with a detailed description of a typical run, the following

input conditions are used to generate the sample output given in appendix B:

1.IPRGCR:2

2. IYEAR=4 (1977 solar minimum)

3. XAL (3) =5, 5, 10 (aluminum depths of 5, 10, and 20 g/cm 2)

4. XWAT( 5 ) : 1,1,1,1,1 (water depths of 1, 2, 3, 4, and 5 g/cm 2)

The sample output is divided into 36 blocks (A ..... Z and AA ..... JJ). Each block includes a brief

description of the flow of the program and how to interpret the output.

Block A prints the values of the physical properties (mass, charge, density, etc.) of the target mate-

rial, which in almost all cases is water. These quantities are used in the function RTIS. In RTIS the

input data file ATOMIC. DAT is accessed to see if it contains the energy, range, and stopping power of

the chosen target material. This is accomplished by comparing the supplied physical properties of the

target with those available in ATOMIC. DAT. If the physical properties are the same, then the energy,

range, and stopping-power arrays are loaded from ATOMIC. DAT. If ATOMIC. DAT does not have the

information for the target of interest, then a host of other subroutines and functions are called to gener-

ate the appropriate energy, range, and stopping-power arrays. This new information is written into the

file NEWRTIS. DAT. The user has the responsibility to append NEWRTIS. DAT to ATOMIC. DAT after

the program execution for future use. The user is then informed that all appropriate arrays in RTIS are

initialized, and the message RTIS IS INITIALIZED is printed.

Next, the user is informed that the 1977 solar minimum is chosen as the environmental model.

The program searches the input data file JSCCOSMC. DAT to load and scale the flux arrays inHZEALH20. FOR for later transport calculations.

Then, the program reads the physical properties (same quantities as previously read in RT I S) of theshield material from subroutine MATTER. The subroutine MATTER, as discussed previously, is the only

module that the user has to modify to accommodate new shield and target materials. Once the shield

material information is read from MATTER, the information concerning the transported particle field

absorption and fragmentation cross sections for the shield material is read from the input data file

NUCLEAR. DAT. This is accomplished by calling function TS. In TS, as in RTIS, the physical proper-

ties of the aluminum shield material are compared with those available in NUCLEAR. DAT. If the phys-

ical properties are the same, then the absorption and fragmentation cross-section arrays are loaded fromNUCLEAR. DAT. If NUCLEAR. DAT does not have the information for the shield material of interest,

then a host of other subroutines and functions are called to generate the appropriate cross-section arrays.

This information is written into the file NEWNUC 5 9. DAT. As in RTIS, the user has the responsibility to

append NEWNUC 5 9. DAT to NUCLEAR. DAT for future runs. The user is then informed that all appro-

priate cross-section arrays are initialized and the message MATERIAL FOR TS 1 FOUND ONNUCLEAR. DAT FILE is printed.

The physical properties of the shield material are used in function RMAT to load energy, range, and

stopping-power arrays for the shield material from input data file ATOMIC. DAT. RMAT is identical to

RTIS, except that it is designed to calculate or load the energy, range, and stopping-power arrays forshield material rather than for target material. As in RT I S, if the ATOM I C. DAT does not have the infor-

mation for the shield material, a new file called NEWRMAT. DAT is generated which will have to be

37

appended to ATOMIC. DAT for future runs. Finally, when all appropriate arrays in RMAT are initialized,

the message RMAT IS INITIALIZED is printed.

Block B contains the depth values of the shield material in g/cm 2 at which transported quantities are

printed. The first depth value corresponds to the free-space boundary or x= 0 g/cmC The quantities for

the transported particles are atomic mass, atomic charge, integral flux for a given isotope in particles/

cm2-yr, dose in cGy, and dose equivalent in cSv according to the International Commission on Radio-

logical Protection ICRP-26 and ICRP-60 guidelines are printed for charge Z = 0 to Z = 2 8. Note that dose

and dose equivalent can be easily converted to engineering units by the following:

1 rad = 1 centiGray (cGy) = 0.01 Gy

1 rem = 1 centiSievert (cSv) = 0.01 Sv

Then, the minimum and maximum energy, A MeV, and range, g/cm z, that were used to calculate the

previous flux quantities are printed.

Block C prints the cumulative integral flux and dosimetric values at the depths of the shield material

that correspond to the same depths as block B. The cumulative transported quantities are grouped into

six charge groups of Z = 0, Z= 1, z=2, 3 <Z<l 0, 1 l<Z<2 0, and 2 l<Z<2 8. The units for integral flux,

dose, and dose equivalents are the same as for block B.

Then, the total cumulative integral flux and dosimetric values for all six charge groups are printed.

Block D contains the depth values of shield material at which transport quantities are calculated and

stored. The depth increment is set by default to H-- 1 g/cm 2. The printing of depth values stops when the

first depth of the shield material as defined in subroutine MATTER is reached.

Blocks E, H, and K are similar to block B.

Blocks F, I, and L are similar to block C.

Blocks G and J are similar to block D. At this stage, calculations for the aluminum shield material

are complete and the program begins to read information for the target material.

Block M prints the values of the physical properties (mass, charge, density, etc.) of the target mate-

rial, as defined in subroutine MATTER. These quantities are used in function RMAT. As described in the

second half of block A, these physical properties are compared with those available in the input data file

ATOMIC. DAT, and the appropriate arrays for energy, range, and stopping power are either loaded from

ATOMIC. DAT or calculated and stored in NEWRMAT. DAT. As in block A, the user has the responsibil-

ity to append NEWRM.AT. DAT to ATOMIC. DAT after the program execution for future use.

Blocks N, Q, s, U, W, and Y are similar to block B.

Blocks O, R, T, V, ×, and Z are similar to block C.

Block P is similar to block D. At this stage, calculations for the water target material are complete

and the program begins the stopping-power calculations for the shield and target materials.

Block AA is the start of the printed transported quantities as a function of stopping power S =LET. It

contains the depth values of the shield material in g/cm 2, at which the transported quantities are calcu-

lated. The first depth value corresponds to the free-s_ace boundary at x= 0 g/cm 2. The printed quantities

for the transported particles are LET in MeV/(g/cmZ), integral flux at a given LET in particles/cm 2 yr,

dose in cGy, and dose equivalent in cSv to ICRP-26 and ICRP-60 guidelines.

Blocks BB, CC, and DD are similar to block AA. The printed quantities in blocks AA ..... DD are

LET-related quantities in the shield material.

Block EE prints the transported quantities as a function of LET for the target material at a target

depth of x= 0 g/cm 2.

Blocks FF, GG, HH, II, and JJ are similar to block EE.

38

i I (E'vir°nmentInput _ Energy grid 1options Shield material

Shield thickness

Atomic & nuclearJ f Energy loss databaseinteractions _ [ Cross-section databasek

[_"--''-o'Yu_a'l(propagation | _ Stepsize 1algorithm J

[ D°simetric 1 f Quality factor specificationquantities _ [ Alternate risk estimate approach specificationsubroutinek

(Fluxes

Output k Alternate risk estimatesoptions -_

LET spectra

1Designates semiflexible inputs.

Figure A1. Computational structure of HZETRN.

39

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68. Westfall, G. D.; Wilson, Lance W.; Lindstrom, P. J.; Crawford, H. J.; Greiner, D. E.; and Heckman, H. H.: Fragmentation of56

Relativistic Fe. Phys. Rev. C, vol. 19, no. 4, Apr. 1979, pp. 1309-1323.

69. Wilson, John W.; Chun, Sang Y.; Badavi, Francis E; and John, Sarah: Coulomb Effects in Low-Energy Nuclear

Fragmentation. NASA TP-3352, 1993.

70. Rudstam, G.: Systematics of Spallation Yields. Zeitschriftfur Naturforschung, vol. 21a, no. 7, July 1966, pp. 1027-1041.

72

71. Townsend, Lawrence W.; Wilson, John W.; Norbury, John W.; and Bidasaria, Hari B.: An Abrasion-Ablation Model

Description of Galactic Heavy-lon Fragmentation. NASA TP-2305, 1984.

72. Townsend, L. W.; Wilson, J. W.; and Norbury, J. W.: A Simplified Optical Model Description of Heavy Ion Fragmentation.

Canadian J. Phys., vol. 63, no. 2, Feb. 1985, pp. 135-138.

73. Norbury, John W.; and Townsend, Lawrence W.: Electromagnetic Dissociation Effects in Galactic Heavy-Ion

Fragmentation. NASA TP-2527, 1986.

74. Townsend, Lawrence W.; Wilson, John W.; Tripathi, Ram K.; Norbury, John W.; Badavi, Francis F.; and Khan, Ferdous:

HZEFRGI: An Energy-Dependent Semiempirical Nuclear Fragmentation Model. NASA TP-3310, 1993.

75. Wilson, John W.; Chun, Sang Y.; Badavi, Forooz F.; Townsend, Lawrence W.; and Lamkin, Stanley L.: HZETRN: A Heavy

Ion/Nucleon Transport Code for Space Radiations. NASA TP-3146, 1991.

76. Bertulani, Carlos A.; and Baur, Gerhard: Electromagnetic Processes in Relativistic Heavy Ion Collisions. Phys. Rep.,

vol. 163, nos. 5 & 6, June 1988, pp. 299-408.

77. Aleixo, A. N. E; and Bertulani, C. A.: Coulomb Excitation in Intermediate-Energy Collisions. Nucl. Phys., vol. A505,

no. 2, Dec. 11, 1989, pp. 448-470.

78. Kim, A.; Wilson, J. W.; Thibeault, S. A.; Nealy, J. E.; Badavi, F. F.; and Kiefer, R. L.: Galactic Cosmic Radiation Shield

Performance Studies. NASA TP-3473, 1994.

79. Kidd, J. M.; Lindstrom, P. J.; Crawford, H. J.; and Woods, G.: Fragmentation of Carbon Ions at 250 MeV/Nucleon. Phys.

Rev. C, vol. 37, no. 6, June 1988, pp. 2613-2623.

80. Webber, W. R.; Kish, J. C.; and Schrier, D. A.: Individual Isotopic Fragmentation Cross Sections of Relativistic Nuclei in

Hydrogen, Helium, and Carbon Targets. Phys. Rev. C, vol. 41, no. 2, Feb. 1990, pp. 547-565.

81. Olson, D. L.; Berman, B. L.; Greiner, D. E.; Heckrnan, H. H.; Lindstrom, P. J.; and Crawford, H. J.: Factorization of

Fragment-Production Cross Sections in Relativistic Heavy-lon Collisions. Phys. Rev. C, vol. 28, no. 4, Oct. 1983,

pp. 1602-1613.

82. Lefort, Marc: Mass Distribution in Dissipative Reactions--The Frontier Between Fusion and Deep Inelastic Transfers.

Deep-Inelastic and Fusion Reactions With Heavy Ions, W. von Oertzen, ed., Lecture Notes in Physics, Springer-Verlag,

vol. 117, 1980, pp. 25-42.

83. Cummings, J. R.; Binns, W. R.; Garrard, T. L.; Israel, M. H.; Klarmann, J.; Stone, E. C.; and Waddington, C. J.: Determina-

tion of the Cross Sections for the Production of Fragments From Relativistic Nucleus-Nucleus Interactions. 1.

Measurements. Phys. Rev. C, third ser., vol. 42, no. 6, Dec. 1990, pp. 2508-2529.

84. Westfall, G. D.; Wilson, Lance W.; Lindstrom, P. J.; Crawford, H. J.; Greiner, D. E.; and Heckman, H. H.: Fragmentation of

Relativistic 56Fe. Phys. Rev. C, vol. 19, no. 4, Apr. 1979, pp. 1309-1323.

85. Wilson, John W.: Environmental Geophysics and SPS Shielding. Workshop on the Radiation Environment of the Satellite

Power System, Walter Schimmerling and Stanley B. Curtis, eds., LBL-8581 (Contract W-7405-ENG-48), Univ. of

California, Sept. 15, 1978, pp. 33-116.

86. Alsmiller, R. G., Jr.; and Scott, W. W.: Comparisons of Results Obtained With Several Proton Penetration Codes, Part 2.

NASA CR-95141, 1968.

87. Alsmiller, R. G., Jr.; and Scott, W. W.: Comparisons of Results With Several Proton Penetration Codes. NASA CR-88880,

1967.

88. Nealy, John E.; Simonsen, Lisa C.; Sauer, Herbert H.; Wilson, John W.; and Townsend, Lawrence W.: Space Radiation

Dose Analysis for Solar Flare of August 1989. NASA TM-4229, 1990.

89. King, Joseph H.: Solar Proton Fluences for 1977-1983 Space Missions. J. Spacecr. & Rockets, vol. 11, no. 6, June 1974,

pp. 401-408.

90. Benton, E. V.; Henke, R. P.; and Peterson, D. D.: Plastic Nuclear Track Detector Measurements of High-LET Particle

Radiation on Apollo, Skylab and ASTP Space Missions. Nucl. Track Detect., vol. 1, no. 1, 1977, pp. 27-32.

91. Kinney, W. E.: The Nucleon Transport Code, NTC. ORNL-3610, U.S. Atomic Energy Commission, Aug. 1964.

92. Recommendations of the International Commission on Radiological Protection. ICRP Publ. 26, Pergamon Press, Inc.,1987.

73

93. Recommendations of the International Commission on Radiological Protection. ICRP Publ. 60, Pergamon Press, Inc.,

1964.

94. Townsend, Lawrence W.; Wilson, John W.; and Nealy, John E.: Space Radiation Shielding Strategies and Requirements for

Deep Space Missions. SAE Tech. Paper Ser. 891433, July 1989.

95. Townsend, L. W.; and Wilson, J. W.: An Evaluation of Energy-Independent Heavy Ion Transport Coefficient

Approximations. Health Phys., vol. 54, no. 4, Apr. 1988, pp. 409-412.

96. Wilson, J. W.; Kim, M.; Schimmerling, W.; Badavi, E F.; Thibeault, S. A.; Cucinotta, F. A.; Shinn, J. L.; and Kiefer, R.:

Issues in Space Radiation Protection: Galactic Cosmic Rays. Health Phys., vol. 68, no. 1, 1995, pp. 50--58.

74

Z

X

Figure 1. Transport of particles through spherical region.

75

fq

E

d

105

104

103

102

101

100

10-1

10-2

10-3

/.-•". Charge Z

,_-"1

..... 2

5

14

...... 22

10-2 10 -1 100 101 102 103 104 105

Energy, A MeV

¢q

Eo

o 102

.=.e_e'L

O_

105 Charge Z

• . . • .... " ° . . - .... 2

l°4F..;/ "\.,. __.... 154

/- _, , \ .. - ..... 22

F ",L \ ", \

101_

100

10-2 10 -1 100 101 102 103 104 105

Energy, A MeV

(a) Range and stopping power in aluminum.

Figure 2. Linear energy transfer (LET).

76

105

104

103

102

E 101d=_ 1oo

10-1

10-2

10-3

10 -4

10-2

Charge Z

/// __-77___//,/ ---

//,( ..... 14

" ///;: " ..... 22/,..,

• I_l IlVl III1 I I III I I ill I I III I I III I I III

10 -1 10 0 101 10 2 10 3 10 4 105

Energy, A MeV

t"q

105

104

10 3

i,..7

lo2

101

10 0

10-2

Charge Z

• . . . . . . . .....

\ ----- 5- 14

/ \ \ ., ... " ..... 22

.- _-.. \ \ .

.. \. "\ ............

_ "', \, _ .........

_ "', \,

_ "', \

i i Ill i I lll i i Ill i i lil i i III i i Ill t I III

10 -1 10 0 101 10 2 10 3 10 4 10 5

Energy, A MeV

(b) Range and stopping power in water.

Figure 2. Continued.

77

10 5

104

10 3

10 2

t"q

E.._ lO 1

10 0

lO -I

/

/

/.-• " Charge Z

/: 1t.

..... 2

5

]4

...... 22

10 -1 100 101 102 103 104 105

Energy, A MeV

t'q

E

10 3

lO2

$

101

105 E " " ....... "

104 . /" -._. _ \'."

_-"--_ . , \, ,. ......

i " ..........."',,, \'\, \'-_ .........

",, \,\

I00

10 -2

I f rll I I ill f i ill _ J ill i i t_l I J ttl t i lit

10 -1 I00 I01 102 103 104 105

Energy, A MeV

Charge Z

1

2

5

14

22

(c) Range and stopping power in liquid hydrogen.

Figure 2. Concluded.

78

10 I

10 3

101

10-2b_

Charge Zp

O 1

12] 2

O 6A 8

IX 20

D 26

i I i i I i i i i i i t i i I

102 103 104

Energy, MeV

(a) Aluminum target.

10 o

oE 10-1

10 -2

101

Charge Zp

O 1

[] 2

@ 6A 8

Ix 20

I'_ 26

102 103 104

Energy, MeV

(b) Water target.

100

l0 l

10 -2 J a i J I i J J i I i L , , [

101 102 103 104

Energy, MeV

Charge Zp

O 1

12] 2

O 6A 8

Ix 20

D 26

(c) Liquid hydrogen target.

Figure 3. Absorption cross section Oab s.

79

Ed

L)

200 --

150 --

100 --

50--

OOA[] Experimental data

NUCFRG2 calculation

OB

[]

aLiA

© oC0

0 0

+ 25

°Be

, i i l lllll I , , _,,,,I i j , ,,,,,I , i , ,,,,,I010 101 102 103 104

Energy, A MeV

Figure 4. Charge-removal cross sections for carbon on carbon.

103• Experimental data (ref. 82)

[] NUCFRG2 calculation

101 I I I I I I0 2 4 6 8 10 12

Charge ZF

Figure 5. Charge-removal cross sections for 11.7A-MeV oxygen projectile on molybdenum target.

8O

e_

E

_9

_9

¢-,

E

250 --

200--

150 --

100--

50--

C) Cummings et al., 1.55A GeV

_- Westfall et al., 1.88A GeV

[] NUCFRG2 calculation

o

[]

I I I I I10 15 20 25 30

Charge Z F

(a) Carbon target.

e-_

E

O

o

E(D

300

250

200

150

100

50

Q) Cummings et al., 1.55A GeV

Jr Westfall et al., 1.88A GeV

[] NUCFRG2 calculation

[]

[]

[]

[]

I I I I 1 I0 5 10 15 20 25 30

Charge Z F

(b) Copper target.

Figure 6. Charge-removal cross sections for 1.88A-GeV iron projectile.

81

e_

E

O

o

o

o

600

500

400

300

200

lOO

O Cummings et al., 1.55A GeV

Jr Westfall et al., 1.88A GeV

[] NUCFRG2 calculation

[]

i[]

[]I I I I5 10 15 20

Charge Z F

(C) Lead target.

Figure 6. Concluded.

I25

I30

82

AI (E = 25 MeV)AI (E = 150 MeV)

t ,

AI (E = 600 MeV) AI (E = 2400 MeV)

(a) Four energy levels in aluminum.

Figure 7. Fragmentation cross sections.

83

H20 (E = 25 MeV)

%

H20 (E = 150 MeV)

H20 (E = 600 MeV) H20 (E = 2400 MeV)

(b) Four energy levels in water.

Figure 7. Continued.

84

LH 2 (E = 25 MeV)

_,_711.....

LH 2 (E = 150 MeV)

LH 2 (E = 600 MeV) t "

,_' ,'i_,,_' _

LH 2 (E = 2400 MeV)

(c) Four energy levels in liquid hydrogen.

Figure 7. Concluded.

85

106 _-

105

103i

102

lO1¢..q

100

10_1

"_10 -2

lO, t-,_ /..- ,,_', ,, \-= .,/ ..'" ",X', \ \

_:Charge Z _.',_ \; 1- .'¢', "', \

10-3_ ..... 2

_ 3 -<Z< 10 "'" "X "

10 -4 _ • ,11 <_Z_<20 ,,_,

10 -51-1- ...... 21 _<Z<28

10-'61" I I ll1 t I in[ I J ttl i i tll ) t ill t t Itl t I tit

10 -1 100 101 102 103 104 105 106

Energy, A MeV

(a) GCR ion flux for 1977 solar minimum.

10 6 =

105

lO.

_,_ 10 3

_ 10 2

ca<, 101

o 10 0

-_,o-1_-'..<.:._•-',.'\ '\ \-_ _,<-'..-- _z '..-_,,- \lo-2 - ... - .-,,,, ", \_-" ld

!o-3 ..... 2 "'.._,',, ,3_<Z<iO .x_,\ ',

10 -4 11 <Z<20 ,_

...... 21 <Z<28 \10-5 - ,

10 -6 ) I II1 t I tll J I )ll I I ill ) t tll I J ttl t I ill

10 -1 100 101 102 103 104 105 106

Energy, A MeV

(b) GCR ion flux for 1981 solar maximum.

Figure 8. Differential fluence spectra.

86

Figure9.

O

u

100

10-1

f Charge Z

1

..... 2

----- 3 <Z< 10

11 -<Z<20

...... 21 <Z_<28

10-2 J _ _1 _ i _1 _ a l_l i a ill i t ill i i Jtl J i iJl

10 -I 100 101 102 103 104 105 106

Energy, A MeV

GCR ion flux ratio of 1981 solar maximum to 1977 solar minimum.

¢q

...r

A

t-

1011 -

1010

109

i

x

..... No_. 1960 -'\ I,', \

Oct. 1989 i'll ', \

107 i i _Jl _ J _1 _ _1'. J_ _ _1\ , , ,_1

10 -1 10 0 101 10 2 10 3 10 4

Energy, A MeV

108

Figure 10. Integral fluence spectra of important solar particle events.

87

,i

10-2

QE-

10-1 _ 0 HZETRNNTC

10-3 I I t I I I I I I I

0 6 12 18 24 30

Water depth, g/cm 2

t-

O'*

O

[-

!0 0 O HZETRN

I NTC

10-1

10 -2

10 -3 1 I

0

I I I I I I I I I

6 12 18 24 30Water depth, g/cm 2

(a) Aluminum shield on water. 20 g/cm 2 AI; 30 g/cm 2 water.

Figure 11. Total dose and total dose equivalent.

88

@

10-1

10 -2

10-3

0

- © HZETRN

-- NTC

O

%_o

i I J I J I a f

12 18 24 30Water depth, g/era 2

100 _

10-1..gc-

O

_ 10_2

O HZETRN

NTC

10 -3 I I J I I I I I I I

0 6 12 18 24 30

Water depth, g/cm 2

(b) Iron shield on water. 20 g/cm 2 Fe; 30 g/cm 2 water.

Figure 11. Concluded.

89

10-2

lo-3O

0 HZETRN

NTC

_0

10 -4 t I , I I I I I I I

0 6 12 18 24 30Water depth, g/cm 2

]

@

10-1 O HZETRNNTC

10-2

0 0 0 0 !

10-3 i I

0 6

0 0 0 0 00 0

0 0 0

l I I I I I I I

12 18 2 24 30Water depth, g/cm

(a) Aluminum shield on water. 20 g/cm 2 AI; 30 g/cm 2 water.

Figure 12. Secondary neutron dose and dose equivalent.

9O

10 -2 _

10 -30

© HZETRN

NTC

_O

I I I J I I 1 I I

6 12 18 24 30Water depth, g/cm 2

10-1

o

10_2,..,t

0

0 HZETRN

NTC

O

o LO

OO

OO

0 0 0 0

1 o

10 -3 I I I I j I a I I I

0 6 12 18 24 30Water depth, g/cm 2

(b) Iron shield on water. 20 g/cm 2 Fe; 30 g/cm 2 water.

Figure 12. Concluded.

91

103

102

>

< lO1¢-q

•_ 10 0¢-,

10-1

Depth, g/cm 2

0

..... 10

..... 20

,'" 30

_ /

10-2

10-2

n , all n i iii i i l,l I i ill i i ill i I iii i ,'!i,l

10 -1 100 101 102 103 104 105

Energy, A MeV

(a) 1977 solar minimum.

103

10-2

10-2 10 -1 100 101 102

Energy, A MeV

Depth, g/cm 2

0

..... 10

20

30

103 104 105

(b) 1981 solar maximum.

Figure 13. GCR energy flux for carbon ion in aluminum.

92

;>

IO1

E

.6•_ 100

,4

10-1

103

Depth, g/cm 2

0

10102 20

30

10-2 _ , ,,I _ , ,Jl _ J _1 , ,Jtl , J J,I , J _1 _ _.,,1

10 .2 10-1 100 101 102 l03 104 105

Energy, A MeV

(a) 1977 solar minimum.

103

102

;>

<, 101I'M

"6"_ 100

10-1

Depth, g/cm 2

0

..... 10

----- 20

30

t

"1/////

,2"- -- - ";'/"

10-2 J t_,l i a,,I , I Jll , J ,,I , ,J,I t J ,,I I rlll

10 -2 10-1 100 101 102 103 104 105

Energy, A MeV

(b) 1981 solar maximum.

Figure 14. GCR energy flux for oxygen ion in aluminum.

101

lOo

0

10-1

E

•_ 10 .2e_

10-3

10 -4

10 -2

Depth, g/cm 2

0

..... 10

20

30

| J JJl I I III ! ! ill I I Ill l I Ill I ) I_ I I 111

I0 -1 10 0 101 10 2 10 3 10 4 10 5

Energy, A MeV

(a) 1977 solar minimum.

100

10-1

Eo

o

•_ 10 .2

10-3

101 _

1 /

//,,"

Depth, g/cm 2

0

..... 10

20

30

10-4 i ,,ll , i !nl i _l,l t , J,l , _ rill, ii,l i ,ill

10-2 10-1 100 10 i 102 103 104 105

Energy, A MeV

(b) 1981 solar maximum.

Figure 15. GCR energy flux for calcium ion in aluminum.

94

102

101

< 1o°¢.q

._ 10 -1

10-2

10-3

10-2

Depth, g/cm 2

0

..... 10

2O

30

:-- -._-

J n _ll i i ill i I ill J J ill i _ ill f J ill J q'll]

10 -1 100 101 102 103 104 105

Energy, A MeV

(a) 1977 solar minimum.

102

101

<, 100¢,q

"6._ 10 -1

10-2

10-3

10-2

Depth, g/cm 2

0

..... 10

----- 20

30

/

s I

,,\,ill

10 -1 10 0 101 10 2 10 3 10 4 10 5

Energy, A MeV

(b) 1981 solar maximum.

Figure 16. GCR energy flux for iron ion in aluminum.

95

103

102

_ 101

E10 0

"_ 10_ I

10.2

10-3 , i ill i i ill i i ill i illi i i ill t i ill l i ill

10-2 10 -1 100 10 ! 102 103 104 105

Energy, A MeV

Depth, g/crn 2

0

10

20

30

(a) 1977 solar minimum.

103

102

_ 101

<,E

10 0

"_ 10_ !

10 .2

10-3

Depth, g/cm 2

0

..... 10

----- 20

30

i _ i,l i i ,il i , iii i I III I I Ill I I It] I } III

10-2 10-1 100 101 102 103 104 105

Energy, A MeV

(b) 1981 solar maximum.

Figure 17. GCR energy flux for carbon ion in water.

96

10 2

101

100

"6

"_ 10-I

10-2

103 -

',\

\

Depth, g/cm 2

0

10

20

30

10-3 J i III I , Ill , I ,il i JlJl , J Ill i J ,il i , Ill

10-2 10-! 100 101 102 103 104 105

Energy, A MeV

(a) 1977 solar minimum.

103

102

_ 101

<t.,,i _

10 0

"_ 10_ 1

10 -2

I I II1 I I III I I II1 I 1 Ill I I II1 I I II1 I I Ill

10 -1 100 101 102 103 104 105

Energy, A MeV

10-3

10-2

Depth, g/cm 2

0

10

20

30

(b) 1981 solar maximum.

Figure 18. GCR energy flux for oxygen ion in water.

97

10 o

>

10-1

E

-_ 10 .2

101 _

I10-2 10-1 104 10 5

Depth, g/cm 2

0

10

20

30

100 101 102 103

Energy, A MeV

(a) 1977 solar minimum.

101 _

10 0 /'_

-..... ,/-/ ,,,\,,_

,o_.y.. ":il10--41 , ,,,I i ,,,I ,, ,,I , ,ill i ,,,I , ,,,I i _,sll

10-2 10-1 10 0 101 10 2 10 3 10 4 10 5

Energy, A MeV

Depth, g/cm 2

0

10

20

30

(b) 1981 solar maximum.

Figure 19. GCR energy flux for calcium ion in water.

98

lO 1

>_ 10 0

<i

¢'-I

_10 -1

"_ 10 .2

10-3

102 - Depth, g/cm 2

0

..... 10

20

30

\\

10-4_ I I Ill I ' ,,I .... I , , ,,I .... I .... I , },,,I

10-2 lO-I 10 0 101 102 10 3 10 4 10 5

Energy, A MeV

(a) 1977 solar minimum.

102

101

>o 100

<,t"-I

10 -1

"_ 10 -2

[.r.,

10-3

Depth, g/cm 2

0

..... 10

20

30

_ / \,\,

I I II1 1 J Ill I I II1 1 I Ill I I Ill I I III I Iklll

10-I 100 101 102 103 104 105

Energy, A MeV

(b) 1981 solar maximum.

Figure 20. GCR energy flux for iron ion in water.

99

103_

102

;>o101

¢",1

10 0

_lO-I

u,

10-2

10-3

10-2

Depth, g/cm 2

0

..... 10

20

30

s

'l

\\

I I Ill I i _ll _ I ill I L Ill J _ _ll i t ill I _lal

10 -1 100 101 102 103 104 105

Energy, A MeV

(a) 1977 solar minimum.

103

102 !

>o 101

<¢..1 _

Eu 100

_10-1

K

IT.

10--2

10--3

10--2

\.I I I1[ I I IlL i i liD i i |1[ i I iiI i i iii i i_,lli

10 -1 100 101 102 103 104 105

Energy, A MeV

Depth, g/cm 2

0

10

20

30

(b) 1981 solar maximum.

Figure 21. GCR energy flux for carbon ion in liquid hydrogen.

100

10 3

102

K:; lO1

< lO0eq

"alO -1

lO -2

10-3

10 -4 _ _ ,,I j _J,I

10-2 10-1 10 0

_ Depth, g/cm 2

- 0

10

20

30

.------ /./././ \,,\,',,,\

_-1-/" /" k. \,',,,\

/ \\,,,

-/ \\i

\

I II1 I I I1[ I I II1 I I Ill I I III

101 102 103 104 105

Energy, A MeV

(a) 1977 solar minimum.

103

10 2

1o1

<, 10 0

_ 10 -1

_ 10 .2

10-3

10--4i , J J,I , J,,I , J,_l I i_Jl ,

10 -2 10-1 100 101 10 2

Energy, A MeV

/ \\'/

\I III I I III I IIII

103 104 105

Depth, g/cm 2

0

10

20

30

(b) 1981 solar maximum.

Figure 22. GCR energy flux for oxygen ion in liquid hydrogen.

101

101

10 o

10-1

e_,lO -2

_ 10.3

_ 10 -4

10-5

10-6

10-2

Depth,0g/cm2

..... 10

----- 20

.... 30

z / •

/ / \ \ ',--_-/ / \ \

/ '\ \/"

.... i \

I J II1 I I III I I III I I I|1 I I II1 I I Ill I _1 Ill

10 -1 100 101 102 103 104 105

Energy, A MeV

(a) 1977 solar minimum.

101

10 o

10-1

,10-2

"d 10 .3

e._

-4

10-5

Depth, g/cm 2

0

10

20

30

/i

/

/

/ \

/ \

\

\

/" \10-6 ",'-,-._r', ,,,I , i,,l i l lll , i,,l i ,t,l p',, ,,I

10-2 10 -1 100 101 102 103 104 105

Energy, A MeV

(b) 1981 solar maximum.

Figure 23. GCR energy flux for calcium ion in liquid hydrogen.

102

102

101

100

_,_10 -1>o

10-2<

10-3o

_ 10--4

"_ 10-5e_

10 _5

10-7

10-8

10-9 i

10 -2

_ _sl • -_

J

Depth, g/cm 2

0

10

20

x

/ \ ',j

- \J

J j

j" \

j- \

30

i Ill I I I11 I I ltl I I III i i III I i 111 I i Ill

10-1 100 101 102 103 104 105

Energy. A MeV

(a) 1977 solar minimum.

102

101

.-. 100

;_10 -1

10-2

_'E 10-3

_-_10 -4c.J

_ 10 -5

_10-6

Depth, g/cm 2

0

- 10

- 20

30

.- J \

.JJ f - - "---_

10 -7 .._

10-8 >-._.-/_

10-9 J , J,I , , ,,I , J JJl J , JJl , , ,,I J

10-2 10-1 10 0 101 10 2 10 3

Energy, A MeV

xx

x

\

\x

\

\

\

i ill i n Ill

104 105

(b) 1981 solar maximum.

Figure 24. GCR energy flux for iron ion in liquid hydrogen.

103

i0 o

1o-1_3

10-2

0

1977 solar min.

..... 1981, 1982 solar max.

l I i I i I L I ,

6 12 18 24

Shield depth, g/cm 2

I

30

,,.$

@

101

10 o

10-1

10-2

1977 solar min.

..... 1981, 1982 solar max.

t I i I J I i I t I

6 12 18 24 30

Shield depth, g/cm 2

Figure 25.

(a) In aluminum.

GCR skin dose and dose equivalent.

104

o£O

10o

10-1

10-2

0

1977 solar rain.

..... 1981, 1982 solar max.

J I I I I I i I t I

6 12 18 24 30Shield depth, g/cm 2

O

t_

101 _

100

10 -1

10-2

1977 solar min.

..... 1981, 1982 solar max.

f I J I J I i I 1 I

6 12 18 24 30Shield depth, g/cm 2

(b) In water.

Figure 25. Continued.

105

10 o

1o-1O

10-2

0

1977 solar min,

..... 1981, 1982 solar max.

K I i I I I t I i I

6 12 18 2 24 30Shield depth, g/cm

¢0

¢P_J

0

101

100

10-1

10-2

I 1977 solar rain.

..... 1981, 1982 solar max,

i I I I i I s I e I

0 6 12 18 24 30Shield depth, g/cm 2

(c) In liquid hydrogen.

Figure 25. Concluded.

106

O

r_

101 _

10 o

10-1

10-2

0

AI

..... H20

LH 2

---,..,..

I i I J I I I t I

6 12 18 24 30Shield depth, g/cm 2

e-

101 _

100

10-1

10-2

0

AI

..... H20

_____ LH 2

I I I I I I I N I

6 12 18 2 24 30Shield depth, g/cm

(a) 1977 solar minimum.

Figure 26. GCR skin dose and dose equivalent in aluminum, water, and liquid hydrogen.

107

101-

10 0

i0 -1

10-2

0

A!

..... H20

_____ LH 2

I I t I i I t I I I

6 12 18 2 24 30Shield depth, g/cm

101 -

10 0

-._

0

_ 10-1

10-20

\

AI

..... H20

__ _ __ LH 2

I I I I I

6 12 18 2Shield depth, g/cm

I I I

24 30

(b) 1981 solar maximum.

Figure 26. Concluded.

108

100

0

10-1

10-2

10-3

10-4

10-50

I t I I I I I t I

6 12 18 24 30

Shield depth, g/cm 2

(a) 1977 solar minimum.

Charge Z

0

1

2

3 -<Z< 10

11 <Z<20

21 <Z<28

10 0 -

@

10-1

10-2

10-3

10-4

10-5

____ ...........................

_2£_L S 22 "

J

fI I t

6I J I I I I I

12 18 24 30

Shield depth, g/cm 2

Charge Z

0

1

2

3<Z_<I0

11 _<Z_<20

21 <Z<28

(b) 1981 solar maximum.

Figure 27. GCR skin dose for six charge Z groups in aluminum.

109

100

10 -1

10 -2

10-3

10 -4

10-5

0

Ja l i

6

I. t I I I

12 18 24

Shield depth, g/cm 2

I

30

(a) 1977 solar minimum.

Charge Z

0

1

2

3 <Z< 10

11 <Z_<20

21 <Z<28

i0 o

10-1

10-2

@

10-3

10-4

10-5

0

_.____._ ..........................

=-"-_7.

6

I I i I J I i I

12 18 24 30

Shield depth, g/cm 2

(b) 1981 solar maximum.

Figure 28. GCR skin dose for six charge Z groups in water.

Charge Z

0

1

2

3<Z_< 10

11 <Z<20

21 <Z<28

110

C,

10-1 _ .................................

10- - \ ",. "'-_ --_..

10-3

10-4

\

\

\

\

\

k

\

\

\

\

,..

\

I i I i I J\ I i I

6 12 18 24 30

Shield depth, g/era 2

10-5 i

0

(a) 1977 solar minimum.

Charge Z

0

1

2

3 <Z< 10

11 <Z<20

21 -<Z_<28

10-1

0

10-2

10-3

10-4

10 -5 J I

0 6

N

\

\

N

N

\ "•

\ ".,

\

\

\

\

I \ I I

12 18 24

Shield depth, g/cm 2

i I

30

Charge Z

0..... ]

2

3_<Z_<lO

...... ll_<Z_<20

21 <Z_<28

(b) 1981 solar maximum.

Figure 29. GCR skin dose for six charge Z groups in liquid hydrogen.

111

100 -

10-1 _ _ ¢-. _ ----.-

(I]

10 -2

"3

N 10 .3@

10--4

Charge Z

0

..... 1

2

3<Z<IO

...... 11 <Z<-20

21 <Z<28

10-5 I I i I i I I I I I0 6 12 18 24 30

Shield depth, g/cm 2

(a) 1977 solar minimum.

Figure 30.

100

"V-" -':'-'" _ _-- "-- ..........

10 -2

•_ Charge Z

N 10_ 3 0..... 1

23<_Z_<IO

!0--4 kJ 11 -<Z< 2021 <_Z<28

10 .5 I i I t I t I I I t I0 6 12 18 24 30

Shield depth, g/cm 2

(b) 1981 solar maximum.

GCR skin dose equivalent for six charge Z groups in aluminum.

112

10 o

10 -1

oO

lO-2

N 10.3@

10-4

10-51

0

i

I

- c I

Charge Z

0

1

2

3 <Z< 10

I1 <Z<20

21 <Z_<28

I i I I I i I I I

6 12 18 24 30

Shield depth, g/cm 2

(a) 1977 solar minimum.

10o

10-1

_ 10.2e-,

"3

N 10 .30

10--4

10-5

0

Figure 31.

.............

Charge Z0

..... 1

2

3_<Z_< 10

...... 11 <Z_<20

21 <Z<28

i I I J I J I I I I

6 12 ! 8 24 30

Shield depth, g/cm 2

(b) 1981 solar maximum.

GCR skin dose equivalent for six charge Z groups in water.

113

10 0

10-1

lO-2o

m

gN 10 -3O

10--4

.... __ ......

-__-" z._ "_--

\

10 -5 I I i I i I

0 6 12 18

Shield depth, g/cm 2

\

\

\

\

\

\

\

\

i I _ "1

24 30

(a) 1977 solar minimum.

Charge Z

0

1

2

3 <Z< I0

11 <Z<20

21 _<Z<28

_10-3@

10o

10 -1 .I", .x ,,,"\'.

o_ .- . _ .-... - ..........10 -2 "---- ----. ----- _ \_ -.-,_,

\

10 -4

\

\

\

\

i I

6

\

\

N.

\

10 -5 1 I t 1 l I i

0 12 18 24

Shield depth, g/cm 2

\

\1

30

Charge Z

0

1

2

3<Z<IO

11 <Z_<20

21 <Z<28

(b) 1981 solar maximum.

Figure 32. GCR skin dose equivalent for six charge Z groups in liquid hydrogen.

114

I0 0

lO-I©

10-20

1977 solar rain.

..... 1981, 1982 solar max.

i I J I i I t I i

6 12 18 _ 24Shield depth, g/cm 2

I

3O

.5

o

101 _

10o

10-1

10-2

1977 solar min.

..... 1981, 1982 solar max.

I I I I i I i I i I

0 6 12 18 24 30Shield depth, g/cm 2

Figure 33.

(a) In aluminum.

GCR 5-cm-BFO dose and dose equivalent.

115

O

¢2

10 0 -

10 -1

10-2

0

1977 solar rain.

..... 1981, 1982 solar max.

i I t I i I

12 18 2 24Shield depth, g/cm

I

30

101

_. !00ra_

0"

_ 10-1

10 -2 I I

0 6

1977 solar min.

..... 1981, 1982 solar max.

I L I i I i I

12 18 24 302

Shield depth, g/cm

(b) In water.

Figure 33. Continued.

116

10o

m-1@

t_

10 -2

0

1977 solar min.

..... 1981, 1982 solar max.

J I t I i I t I

6 12 18 24

Shield depth, g/cm 2

I

30

101

> 10 0

°_

@

t21 10-1

10-2_

1977 solar min.

..... 1981, 1982 solar max.

I J I I I i I i I

6 12 18 24 30Shield depth, g/cm 2

(c) In liquid hydrogen.

Figure 33. Concluded.

117

@

101

100

10 -1

AI

..... H20

LH 2

10-2 I I I I i I i I J I

0 6 12 18 2 24 30Shield depth, g/cm

101 A1

I ..... H20

----- LH 2

10 0

10 -1

10 -2

0

I I I I I I I I I

12 18 24 306 Shield depth, g/cm 2

(a) 1977 solar minimum.

Figure 34. GCR 5-cm-BFO dose and dose equivalent in aluminum, water, and liquid hydrogen.

118

O

101

10 o

10 -1

10-2i

0

AI

..... H20

__ _ __ LH 2

-.-......

i I i I i I i I

12 18 24 30Shield depth, g/cm 2

101 _

_, 100

..>Q,,

0

_ 10-1

10-2

0

A1

..... H20

__ _ __ LH 2

I I I I I I I I I I

6 12 18 2 24 30Shield depth, g/cm

(b) 1981 solar maximum.

Figure 34. Concluded.

119

10o

10-I

10-2

10-3

10 -4

10-5

0

...................................

_ 2212

I I I I I I i I t J

6 12 18 24 30

Shield depth, g/cm 2

(a) 1977 solar minimum.

Charge Z

0

1

2

3 <Z< 10

11 <Z<_20

21 <Z_<28

100

O

10-I

10-2

10-3

10-4

10-5

Charge Z

0

1

2

3 <Z<_ 10

11 <Z<20

21 <Z_<28

J I J I m I I I i I

0 6 12 18 24 30

Shield depth, g/cm 2

Figure 35.

(b) 1981 solar maximum.

GCR 5-cm-BFO dose for six charge Z groups in aluminum.

120

10 o

10 -1

10-2 i

0

_ 10-3

10 -4

10-5

0

t 1 _ I I I I I _ I

6 12 18 24 30

Shield depth, g/cm 2

(a) 1977 solar minimum.

Charge Z

0

1

2

3<Z<10

11 <Z<20

21 <Z<28

10 0 -

0

10-1

10-2

10-3

10-4

10-5

" - Charge Z

"_ . 0

..... |

----- 2

3<_Z<_IO

...... 11 _<Z_<20

21 _<Z_<28

_

i I i I J 1 J I J I

0 6 12 18 24 30

Shield depth, g/cm 2

(b) 1981 solar maximum.

Figure 36. GCR 5-cm-BFO dose for six charge Z groups in water.

121

10 0

C,

I0-1

10-2

10-3

10--4

\

\ ". ,

\ • ,

\ ".

10 -5 J 1 I

0 6

\

\ ".

\I I I ,_A I I I

12 18 24 30

Shield depth, g/cm 2

(a) 1977 solar minimum.

Charge Z

0

1

2

3<Z<lO

11 <-Z<20

21 <Z<28

100

10-1

10-2

10-3

10-4

10-50

Figure 37.

\

\ - , --o

\ .

\ ".

\

,N, , , .

\\h ""I i I t A I i "-I

6 12 18 24 30

Shield depth, g/cm 2

Charge Z

0

1

2

3 <Z< 10

11 <Z<20

21 <Z_<28

(b) 1981 solar maximum.

GCR 5-cm-BFO dose for six charge Z groups in liquid hydrogen.

122

10 0 _

_. 10 -1

.,..r

o

_ 10-2

10-3

0

:--:':-7::%[--- - ...................

_...¢_ ..-- . .

""_ ,_...

I I I I i I J I i I

6 12 18 24 30Shield depth, g/cm 2

(a) 1977 solar minimum.

---h

Charge Z

0

1

2

3 <Z< 10

11 -<Z_< 20

21 -<Z<28

10 0 _

._>

t2r

@

10-1

10-2

- . . . . .

_- :._ _________ _ -.--

10-3 f I I I

0 24 30

/

I I I I I I

6 12 18 2Shield depth, g/cm

Charge Z

0

1

2

3 _<Z< 10

11 -<Z<20

21 <Z<28

(b) 1981 solar maximum.

Figure 38. GCR 5-cm-BFO dose equivalent for six charge Z groups in aluminum.

123

10 0

_, 10 -1

ID

::1

E

_ 10-2

10-3

0

1

_--. _--._-. ---_ 2"-... "-_ . . 3_<Z<IO

•.. ...... 11 -<Z<20

21 _<Z_< 28

i I i I J I J I i I

6 12 18 24 30Shield depth, g/cm 2

(a) 1977 solar minimum.

10 o

_. 10 -1

10 -2

Charge Z

e_. " - . • 0

_ " . 3_<Z_<IO

.__ -_ . ..... II _<Z<_2021 _<Z<_28

J

10 -3 I I I I I I I I t I0 6 12 18 24 30

Shield depth, g/cm 2

(b) 1981 solar maximum.

Figure 39. GCR 5-cm-BFO dose equivalent for six charge Z groups in water.

12,4

100 I' -

\-. ...........................

"5 10-2 \ "'". "'_-N

10-3

10 .--4 A I J

0 6

O

\\

\

\

I i

12

• ",,

\

\ -

\ "

\

I J\ I i I

18 24 30

Shield depth, g/era 2

(a) 1977 solar minimum.

Charge Z

0

1

2

3_<Z<lO

11 _<Z< 20

21 <Z<28

10 o

10-1

r._

J

•5 10 -2

O

10-3

.\

::

\ ". _..

"''', ...

\

\

N

\

\ •

t I L I i I "h I t "'1

6 12 18 24 30

Shield depth, g/cm 2

Charge Z

0

1

2

3 <Z< 10

lI<Z<20

21 <Z<28

(b) 1981 solar maximum.

Figure 40. GCR 5-cm-BFO dose equivalent for six charge Z groups in liquid hydrogen.

125

"7

t'q

¢

109

108

107

106

105

lo4

103

102

100 101

\

\

102 103

LET, (MeV-cm2)/g

10 4

(a) 1977 solar minimum.

Depth, g/cm 2

0

..... i0

20

30

105

-7

t",l

,_J

109

108

107

106

105

1o4

Depth, g/cm 2

0

..... 10

_--- 20

30

103

100 101 102 103 104 105

LET, (MeV-cm2)/g

(b) 1981 solar maximum.

Figure 41. GCR skin integral flux LET spectra in aluminum.

126

.7"2"

¢q

E

g,-3A

109

108

107

106

105

104

103

102

10 o 101 102 103 104

LET, (MeV-cm2)/g

(a) 1977 solar minimum.

Depth, g/cm 2

0

..... 10

----- 20

30

105

"7

t'q

g.LO.3A

e

109

108 I

107_ "_z-._,. _.106 •

105

o4:_

-10 2 J , Ill I i III 1 t ill i\xlxa_tl

I00 101 102 103 104

LET, (MeV-cm2)/g

Depth, g/cm 2

0

..... 10

----- 20

30

I I Ill

105

(b) 1981 solar maximum.

Figure 42. GCR skin integral flux LET spectra in water.

127

"7

.d

109

108

107

106

105

104

103

102

10 o 101 102 103

LET, (MeV-cm2)/g

104

(a) 1977 solar minimum.

Depth, g/cm 2

0

..... 10

20

30

105

"7

t"q

E

G

Ae

109

108

107

106

105

104

103

102

100

, ..,, , ... , ',,,\101 102 103 104

LET, (MeV-cm2)/g

Depth, g/cm 2

0

..... 10

20

30

i I11

10 5

(b) 1981 solar maximum.

Figure 43. GCR skin integral flux LET spectra in liquid hydrogen.

128

D

O

10-1

10-2

10-3

10 o

,°°I

'\ \', \

}:ii,101 102 103 104

LET, (MeV-cm2)/g

(a) 1977 solar minimum.

Depth, g/cm 2

0

..... 10

----- 20

30

i i Ill

105

@

10 o

10-1

10 3I "\:fi"\

100 101 102 103

LET, (MeV-cm2)/g

_,1

104

(b) 1981 solar maximum.

Depth, g/cm 2

0

..... 10

----- 20

30

Figure 44. GCR skin dose LET spectra in aluminum.

129

10 o

10-1

10-2

10-3

100 101 10 2 10 3 10 4

LET, (MeV-cm2)/g

(a) 1977 solar minimum.

Depth, g/cm 2

0

..... 10

----- 20

30

J I ItJ

10 5

1o0 _-

o

10-1

10-2

10-3

100

\.', ",\

101 10 2 10 3

LET, (MeV-cm2)/g

Ill

104

(b) 1981 solar maximum.

Depth, g/cm 2

0

..... 10

20

30

Figure 45. GCR skin dose LET spectra in water.

130

_2@

t_

i0 0

i0-I

10 -2

10-3

10o

\ \ ", \

101 102 103 104

LET, (MeV-cm2)/g

(a) 1977 solar minimum.

Depth, g/cm 2

0

..... 10

20

30

I I I II

105

@

10 o

i0-I

10-2

10-3

I0 0

',.?,, "',,, \'_. \.., "'. , .\

) i ,,l",, ,"),,I t ,',,1 ,\

101 10 2 10 3

LET, (MeV-cm2)/g

Depth, g/cm 2

0

..... 10

20

30

104 105

(b) 1981 solar maximum.

Figure 46. GCR skin dose LET spectra in liquid hydrogen.

131

O')

t_cO

"2

101 [-

100

10-3

30-2

100

Depth, g/cm 2

0

10

20

30

-_-Z-.

.,?:, \

101 302 103 104

LET, (MeV-cm2)/g

(a) 1977 solar minimum.

_D

_D

@

101 -

300

Depth, g/cm 2

0

..... 10

20

30

10-I

I

\\',,\10 -2 [ I R iI , , IiI , J J II 'J\\_ J II

300 103 102 103 104

LET, (MeV-cm2)/g

(b) 1981 solar maximum.

Figure 47. GCR skin dose equivalent LET spectra in aluminum.

132

101

10-2

10 o

;_ 10 0

..a

13"

O

_ 10-1

Depth, g/cm 2

0

..... 10

----- 20

30

...... '--(5,:,\

, ,,,, , ,,,, , ,,,, ",2\':,,,_,101 10 2 10 3 10 4

LET, (MeV-cm2)/g

(a) 1977 solar minimum.

_r

.2-i

O

r_

101

10 o

Depth, g/cm 2

0

..... 10

----- 20

30

10-1 --12\2-g;-----

100 101 102 103 104

LET, (MeV-cm2)/g

(b) 1981 solar maximum.

Figure 48. GCR skin dose equivalent LET spectra in water.

133

..r

o

o"

@

_2

101

10 0

10-1

10-2

10 -3 I

10 o

Depth, g/cm 2

0

..... 10

20

30

• _ x x

"\.. _. ', \

- \

\ \ ',I I II t I I II I I 'r II _ I. I _1 II

101 10 2 10 3 10 4

LET, (MeV-cm2)/g

(a) 1977 solar minimum.

.,..r

o

_r8

101

100

10-1

10-2

10-3

100

Depth, g/cm 2

0

..... 10

----- 20

30

_ \ -\ ', \

_ "\ ', \

1 I , 11 I , I"'__ I I ii_l I", I I

101 102 103 104

LET, (MeV-cm2)/g

(b) 1981 solar maximum.

Figure 49. GCR skin dose equivalent LET spectra in liquid hydrogen.

134

10 9

10 8

10 7

"7

_,_ 10 6E

o

g-10 5

....3

10 4

10 3

10 2

10 0 101 102 103

LET, (MeV-cm2)/g

10 4

(a) 1977 solar minimum.

Depth, g/cm 2

0

..... 10

20

30

105

10 9

10 8

10 7

"7

_,_ 10 6

105

A

10 4

Depth, g/cm 2

0

..... 10

----- 20

30

10 3

10 2

10 o

Figure 50.

101 102 103 104 105

LET, (MeV-cm2)/g

(b) 1981 solar maximum.

GCR 5-cm-BFO integral flux LET spectra in aluminum.

135

10 9

10 8

10 7

"7

_ 10 6

&

_105

e

lO 4

lo3 x,_,,,\,02 _, , ,,,, ,'_x',",\, ,,,'

100 101 102 103 104 105

LET, (MeV-cm2)/g

Depth,_cm 2

0

..... 10

20

30

(a) 1977 solar minimum.

109

108

-_._ -- _ _

107

104 1 '_x_',_k

102[ - _l , i ,ll , i i,I I',I,,X,I , t J ,1

100 101 102 103 104 105

LET, (MeV-cm2)/g

Depth, g/cm 2

0

10

20

30

(b) 1981 solar maximum.

Figure 51. GCR 5-cm-BFO integral flux LET spectra in water.

136

10 9

10 8'

10 7

_,_ 10 6E

_105,dA

e

10 4

103

102

100

Depth, g/crn 2

0

..... 10

_X,, 20

_. 30

X\', \

I I I I I I 1 I II I I I _ I i II

101 102 103 104 105

LET, (MeV-cm2)/g

(a) 1977 solar minimum.

10 9

10 8

107

_,_ 10 6

105A

e

10 4

103

10 0 101 10 2 10 3 104 10 5

LET, (MeV-cm2)/g

Depth, g/cm 2

0

..... 10

20

30

(b) 1981 solar maximum.

Figure 52. GCR 5-cm-BFO integral flux LET spectra in liquid hydrogen.

137

10 0

10-1

10-2

Depth, g/cm 2

0

..... 10

----- 20

30

,\,

\\,,'\'\ ,,

10-3

100 101 102 103 104

LET, (MeV-cm2)/g

(a) 1977 solar minimum.

O

100

10-1

10-2

10-3I I I [

10 0 10 4101 102 103

LET, (MeV-cm2)/g

Depth, g/cm 2

0

..... I0

----- 20

30

(b) 1981 solar maximum.

Figure 53. GCR 5-cm-BFO dose LET spectra in aluminum.

138

i0o

10-1

10-2

10-3100 101 102 103 104

LET,(MeV-cm2)/g

(a) 1977solarminimum.

Depth,g/cm20

..... 10203O

100-

10-1

10-2

Depth,g/cm20

..... 102030

"'_-.._ . ..\.'-_ .

"\'\ "-.

10-3 , _ 11 , , , ,I , ,_,lx"k'_. _ , ,I

100 101 102 103 104

LET, (MeV-cra2)/g

(b) 1981 solar maximum.

Figure 54. GCR 5-cm-BFO dose LET spectra in water.

139

L9

@

10 0

10-1

10-2

10-3

10 0

Depth, g/cm 2

0

..... 10

20

\,,_,\ ",,,,,,,,, ,\,101 10 2 10 3 104

LET, (MeV-cm2)/g

(a) 1977 solar minimum.

10 o

10-1

L_

O

10-2

10-3

10o

Figure 55.

Depth, g/cm 2

0

..... 10

----- 20

30

"'\"\\'""'",I , il , , \',,'I. "x ,'h,l \,_

101 102 103

LET, (MeV-cm2)/g

, ill

10 4

(b) 1981 solar maximum.

GCR 5-cm-BFO dose LET spectra in liquid hydrogen.

140

e_

001F_ Depth, g/cm 2/

....... ....- '°°r-,._----__ ........ --. \ ---2o

... -____.....\-.. _ ..... 30

iI,

10 -2 _ , _ ,I , , , ,I , II

100 101 102 103 104

LET, (MeV-cm2)/g

(a) 1977 solar minimum.

>

=

_a

1o 0

10 -1

Dep_,g/cm 2

0

..... 10

----- 20

30

_--LZ ....

|0 -2 I , I II I I , I I i I I I' I1\11_' I [ I I

100 101 102 103 104

LET, (MeV-cm2)/g

(b) 1981 solar maximum.

Figure 56. GCR 5-cm-BFO dose equivalent LET spectra in aluminum.

141

"d

O

10 o

10-1

10 -2

10 0 101 102 103 104

LET, (MeV-cm2)/g

Dep_,_cm 2

0

10

20

30

(a) 1977 solar minimum.

10 0

r_

0

10-2

10 o

Figure 57.

Depth, g/cm 2

0

..... 10

----- 20

30

-.\,N

101 102 103 104

LET, (MeV-cm2)/g

(b) 1981 solar maximum.

GCR 5-cm-BFO dose equivalent LET spectra in water.

142

o_

Q

10 o

10-1

10-2

100

x x

101 10 2 10 3 10 4

LET, (MeV-cm2)/g

Depth, g/cm 2

0

10

20

30

(a) 1977 solar minimum.

O

100 -

10-1

Depth, g/cm 2

0

..... 10

_--- 20

30

\x

--i\.

\ - \

10 -2 I I I ]1 t t 3-. t

100 101 102 103 104

LET, (MeV-cm2)/g

(b) 1981 solar maximum.

Figure 58. GCR 5-cm-BFO dose equivalent LET spectra in liquid hydrogen.

143

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May 1995 Technical Paper4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

HZETRN: Description of a Free-Space Ion and Nucleon Transport andShielding Computer Program WU 199-45-16-11

6. AUTHOR(S)

John W. Wilson, Francis F. Badavi, Francis A. Cucinotta, Judy L. Shirm,Gautarn D. Badhwar, R. Silberberg, C. H. Tsao, Lawrence W. Townsend,and Ram K. Tdpathi

7. PERFORMING ORGAI_IZATION NAME(SI AND ADDRESS(ES)

NASA Langley Research CenterHampton, VA 23681-0001

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L-17417

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NASA TP-3495

11. SUPPLEMENTARY NOTES

Wilson, Cucinotta, Shirm, and Townsend: Langley Research Center, Hampton, VA; Badavi and Tripathi: Christopher NewportUniversity, Newport News, VA; Badhwar: Johnson Space Center, Houston, TX; Silberberg: Universities Space Research Asso-ciation, Washington, D.C.; Tsao: Naval Research Laboratory, Washington, D.C. Software and documentation are available asLAR-15225 through COSMIC, 382 E. Broad Street, University of Georgia, Athens, GA 30602.

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13. ABSTRACT (Maximum 200 words)

The high-charge-and-energy (HZE) transport computer program HZETRN is developed to address the problems offree-space radiation transport and shielding. The I-IZETRN program is intended specifically for the design engineerwho is interested in obtaining fast and accurate dosimetric information for the design and construction of spacemodules and devices. The program is based on a one-dimensional space-marching formulation of the Boltzmarmtransport equation with a straight-ahead approximation. The effect of the long-range Coulomb force and electroninteraction is treated as a continuous slowing-down process. Atomic (electronic) stopping power coefficients withenergies above a few A MeV are calculated by using Bethe's theory including Bragg's rule, Ziegler's shell correc-tions, and effective charge. Nuclear absorption cross sections are obtained from fits to quantum calculations andtotal cross sections are obtained with a Ramsauer formalism. Nuclear fragmentation cross sections are calculatedwith a semiempirical abrasion-ablation fragmentation model. The relation of the final computer code to theBoltzmann equation is discussed in the context of simplifying assumptions. A detailed description of the flow ofthe computer code, input requirements, sample output, and compatibility requirements for non-VAX platforms areprovided.

_14.SUBJECT TERMS

Space radiation; Heavy ions; Shielding

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