March 2017

NASA/TP-2017-219590

3DHZETRN: Inhomogeneous Geometry Issues 

John W. Wilson 

Old Dominion University, Norfolk, Virginia 

Tony C. Slaba 

Langley Research Center, Hampton, Virginia 

Francis F. Badavi 

Old Dominion University, Norfolk, Virginia 

https://ntrs.nasa.gov/search.jsp?R=20170002588 2017-08-31T15:13:40+00:00Z
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March 2017

NASA/TP-2017-219590

3DHZETRN: Inhomogeneous Geometry Issues 

 

John W. Wilson 

Old Dominion University, Norfolk, Virginia 

Tony C. Slaba 

Langley Research Center, Hampton, Virginia 

Francis F. Badavi 

Old Dominion University, Norfolk, Virginia 
Available from:

NASA STI Program / Mail Stop 148

NASA Langley Research Center

Hampton, VA 23681-2199

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iii 

Contents

Abstract .......................................................................................................................................................... 1

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

3D Marching Procedures ................................................................................................................................ 2

Geometry/Material Selection .......................................................................................................................... 3

Spherical Geometries ...................................................................................................................................... 3

Complex Geometries ...................................................................................................................................... 7

Conclusions .................................................................................................................................................... 9

Acknowledgements ........................................................................................................................................ 9

References .................................................................................................................................................... 10
iv 

Figures 

1. Geometric relations of quantities useful in solving equation (1). The symbol 

n is a unit normal vector. .......... 3

2. A 30 cm diameter ICRU sphere within a 7.41 cm thick aluminum shell with a 1 m void (referred to as "orig. 

geom." in subsequent figures and tables). ............................................................................................................ 4

3. A 30 cm diameter ICRU sphere within a 7.41 cm thick aluminum shell (referred to as "void removed" in 

subsequent figures and tables). ............................................................................................................................. 4

4. The effects on the particle fields at the top and bottom of the sphere induced by removing the void in Fig. 2. .. 4

5. A 30 g/cm2 diameter ICRU sphere within a 20 g/cm2 thick aluminum shell in g/cm2 scale (referred to as 

"g/cm2

 geom." in subsequent figures and tables). ................................................................................................. 5

6. A 30 g/cm2 diameter ICRU sphere made of equivalent aluminum within a 20 g/cm2 thick aluminum shell 

(referred to as "eq. Al geom." in subsequent figures and tables). ......................................................................... 5

7. 3DHZETRN results of fluence vs. kinetic energy for detectors at the top and bottom of an ICRU tissue 

sphere within an aluminum shell for the configuration depicted in Figs. 2, 3, 5, and 6. ...................................... 6

8. Neutron fluence ratios for the approximate geometries (Figs. 3, 5, and 6) relative to solutions of the original 

geometry (Fig. 2). ................................................................................................................................................. 6

9. Complex geometry used in the current study: ICRU tissue sphere shielded by an aluminum cylindrical shell 

with internal components (referred to as "orig. geom." in subsequent figures and tables). .................................. 7

10. Fluence spectra in complex geometry for detectors at the top and bottom of the geometry configuration 

depicted in Fig. 9 and related approximate geometries. ....................................................................................... 8

11. Neutron fluence ratios in complex geometry for the approximate geometries relative to solutions of the 

original geometry. ................................................................................................................................................ 8
v 

Tables 

1. Dose and dose equivalent at top and bottom of tissue sphere contained within an aluminum shell represented 

with various levels of approximation. .................................................................................................................. 7

2. Relative differences (%) between values in Table 1 for geometry with void region compared to values for 

various levels of approximation. .......................................................................................................................... 7

3. Dose and dose equivalent in complex geometry at top and bottom of tissue sphere contained within an 

aluminum shell represented with various levels of approximation. ...................................................................... 9

4. Relative differences (%) between values in Table 3 for geometry with void region compared to values for 

various approximate geometries. .......................................................................................................................... 9
1 

Abstract 

Historical methods for assessing radiation exposure inside complicated geometries for space 

applications were limited by computational constraints and lack of knowledge associated with 

nuclear processes occurring over a broad range of particles and energies. Various methods were 

developed and utilized to simplify geometric representations and enable coupling with simplified 

but efficient particle transport codes. Recent transport code development efforts, leading to 

3DHZETRN, now enable such approximate methods to be carefully assessed to determine if past 

exposure analyses and validation efforts based on those approximate methods need to be revisited. 

In this work, historical methods of representing inhomogeneous spacecraft geometry for radiation 

protection analysis are first reviewed. Two inhomogeneous geometry cases, previously studied 

with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric 

approximation. Fluence, dose, and dose equivalent values are computed in all cases and 

compared. It is found that although these historical geometry approximations can induce large 

errors in neutron fluences up to 100 MeV, errors on dose and dose equivalent are modest (<10%) 

for the cases studied here. 

Introduction 

Traditionally, radiation protection meant isolating a sensitive material from the radiation source by 

shielding materials, distance, or time. For space operations with ubiquitous sources and mission dependent duration 

of exposure, radiation protection meant surrounding the sensitive materials to the extent possible with appropriate 

choice of shield materials. Many space system components are relatively open structures and offer little protection 

except over a restricted solid angle, leaving the pressure vessel and micrometeoroid bumper as the first line of 

inherent protection for space operations [Beever and Ruslino 1965, Slaba et al., 2011]. As a result of the high launch 

costs, minimizing the associated added weight of shield material is imperative to control mission costs [Shavers et 

al. 2003, Wilson et al. 2004], and consequently, there is a long history of developing engineering design strategies 

and methods for space operations [Krumbein et al. 1962, Robins 1965, Celnik et al. 1965, Atwell et al. 1979, 1987, 

Adamczyk et al. 2011, Walker et al. 2013, Simon et al. 2014]. 

 Prior research identified radiations trapped within the Earth’s magnetic field and solar particle events as the 

main concerns for protecting the astronauts and equipment from deleterious effects, so that protecting against 

moderate energy protons and energetic electrons became the focus of shield design and evaluation [Schaefer 1957, 

Foelsche 1962, Keller 1962]. As such, the atomic interactions were viewed as a primary driver of shielding design 

with optimization methods based on the scaling of atomic parameters [Krumbein et al. 1962], representing the range 

of penetration in units of mass per unit area (areal density). As attention turned to longer duration missions in deep 

space, it became apparent that the galactic cosmic rays might be the limiting factor [Foelsche 1959] (see 

Introduction of Wilson et al. [1991] for a review and Wilson et al. [1996] for a prospectus). In this case, the 

biological response to multiply charged ions of high energy and the means of reducing their effects with shielding 

was highly uncertain [Wilson et al. 1991]. Mitigation of radiation exposure from such ions remains a focus of 

current NASA radiation protection research (for background see Wilson et al. 1996). 

 The usual approach to shield design has been to first represent the spacecraft using combinatorial geometry 

(combinations of base objects as boxes, ellipsoids, cylinders etc.) and evaluate the average areal density (g/cm2

) of 

material in units of equivalent aluminum (eq. Al) within each given solid angle element of an equally divided unit 

sphere [Robins 1965, Liley and Schaedle 1965, Langley and Billings 1972, Atwell et al. 1987] and analyzing the 

transmission properties of each such sector. Various computer programs were developed to estimate the dose behind 

varying amounts of aluminum as given for each angular sector of the shield [Raymes 1965, Liley and Schaedle 

1965, Simpson et al. 1965] and culminated in development of the HZETRN computer code [Wilson et al. 1991, 

2005, 2006, Slaba et al. 2010, 2011]. Since the dose is reduced dramatically with increasing areal density of 

aluminum it was found that only the regions of minimal shielding contributed significantly to the dose [Keller 1962] 

and the most efficient shields are spherically symmetric [Wilson et al. 1993]. The first anthropomorphic model 

(Computerized Anatomical Man, CAM [Kase 1972]) was in units of equivalent aluminum to easily integrate into 

existing software [Atwell 1975]. Only later was the buildup factor method developed to more accurately represent 

dose and dose equivalent at a location in tissue behind an aluminum shield [Wilson and Kandelwal 1976, Wilson et 

al. 1991]. Additional work was done later to incorporate detailed voxel tissue phantoms [Slaba et al. 2009]. Since 

even isotropic sources of space radiation produce an anisotropic interior field within spacecraft, the orientation of 

the astronaut within a structure can produce differing organ exposures by a factor of two or more with changing 
2 

astronaut orientation [Wilson et al. 1993]. All of these past methods provided only one-dimensional (1D) 

approximations appropriate to each sector used in defining the geometric relations of the environment to dose or 

dose equivalent within an organ. Clearly, the angular dependence of secondary radiations produced in the shield will 

alter the solution within a given sector by diffusive losses from that sector that are not fully balanced by diffusion 

from adjacent sectors [Wilson et al. 2015a-c, Slaba et al. 2015]. 

 Recently, an approach based on the straight-ahead/bi-directional approximations in HZETRN was extended 

into a three-dimensional (3D) code in which nuclear reactions within adjacent sectors are effective in modifying the 

fluence spectra along an adjacent ray [Wilson et al. 2015a,b]. Herein, this 3DHZETRN code will be used to evaluate 

the veracity of earlier work based on HZETRN (or other 1D codes) in which lateral diffusion is assumed balanced 

among adjacent sectors. In the present study, this 3DHZETRN code is used to examine the effects of differing 

geometric representations by evaluating the effects on dose, dose equivalent and spectral distributions within an 

International Commission on Radiation Units and Measurements (ICRU) tissue sphere [ICRU 1993] embedded 

within an aluminum structure. 

3D Marching Procedures 

The relevant transport description is the coupled linear Boltzmann equations derived on the basis of 

conservation principles [Wilson et al. 1991] for the flux (or fluence) density j

(x,,E) of a type j particle. In the 

continuous slowing down approximation [Wilson et al. 1991, 2005], in which atomic processes are described by the 

stopping power Sj(E) for each ion type j (vanishes for neutrons, j = n), the transport equation is given as 

4

1 ( ) ( ) ( , , ) ( , ', , ') ( , ', ') ' ' j jj jk k E

j k

SE E E E E E d dE

A E p s f s f

é ù ¶ ¥ ê ú  - + = ¶ ë û

åò ò W W WW W W  x x , (1)

and is solved subject to a boundary condition over the enclosure of the solution domain. In equation (1), σj(E) and 

σjk(E,E ',Ω,Ω') are the media macroscopic cross sections. The double differential cross section, σjk(E,E ',Ω,Ω'), 

represents all those processes by which type k particles moving in direction Ω' with energy E ' produce a type j

particle in direction Ω with energy E (including decay processes). A first approach to a computational procedure for 

solving equation (1) was to limit the interaction products to the forward direction (straight-ahead approximation) as 

( , ', , ') ( , ') ( ') s sd jk E E W W = jk E E W-W , (2)

and is mainly an expression of approximate momentum conservation. Unlike the straight-ahead approximation that 

reduces equation (1) to a Volterra equation to be solved along a ray connected to the boundary, the first correction 

follows from a separation of the interaction into forward and isotropic components as 

, ,

1 ( , ', , ') ( , ') ( , ', , ') 4 jk E E jk iso EE EE jk for s ss p W W = + W W , (3)

wherein the fluence is separated as 

, , (, , ) (, , ) (, , ) j j E EE for j iso ff f x xx W WW = + . (4) 

The forward fluence, , (, , ) fj for x W E , is defined to satisfy 

,

, , 4

1 ( ) ( ) (, , )

( , ', , ') ( , ', ') ' '

j j jfor

j

jk for k for E k

SE E E

A E

E E E d dE p

s f

s f ¥

é ù ¶ ê ú - +

¶ ë û

= åò ò

W W 

WW W W

x

x

, (5)
3 

and is solved using the straight-ahead approximation meeting the prescribed boundary conditions. The forward 

component generates an interior isotropic source of neutrons, j = n, given by 

,0 , 0 , 0 4 (, , , ) ( , ', , ) ( , , ') ' n iso nk iso k for E k

E E E E dE p x s f ¥x x W W = åò ò WW W , (6)

that is the driving source generating the isotropic neutron perturbation field according to 

, , 4

, 0

[ ( )] ( , , ) ( , ', , ') ( , ', ') ' '

(,,,

n n iso nk k iso E k

n iso

E E EE E d dE

z E

p s f s f

x

¥

 + =

+ é ù ë û

åò ò WW W  W W W

W W

x x

x)

. (7)

Whereas the forward field in equation (5) is solved for a given direction W0 in the straight-ahead approximation, the 

field generated by the isotropic source in equation (7) is solved using the bi-directional approximation [Clowdsley et 

al. 2000, 2001] along an arbitrary ray W see Fig. 1) This solution of the Boltzmann equation is implemented in 

3DHZETRN and has been shown to produce reasonable results for the isotropic neutron sources by comparison with 

various Monte Carlo simulations [Wilson et al. 2015a,b]. 

Fig. 1. Geometric relations of quantities useful in solving equation (1). The symbol 

n is a unit normal vector. 

Geometry/Material Selection 

Since space radiation protection is the design of the material arrangement about a sensitive volume, how 

the geometry and materials are chosen to provide adequate protection is at issue [Wilson et al. 2004]. Many 

materials are chosen according to other functional requirements/properties. For example, structural aluminum has 

been chosen in the past for construction of spacecraft pressure vessels, micrometeoroid bumper, and support 

structures. More recent technologies are switching to polymer-composites to capitalize on their strength to weight 

ratios and improved radiation protection properties. Foodstuffs and water have always been part of the inherent 

shielding [Wilson 2000] and encapsulated polyethylene has been used for shield augmentation because of its 

improved shielding quality and low launch costs [Shavers et al. 2003]. 

Spherical Geometries 

 In this section, the geometry of interest is an aluminum spherical shell with a thickness of 7.41 cm (20 

g/cm2

) surrounding an inner 30 cm diameter (30 g/cm2) ICRU [1993] tissue sphere (astronaut proxy) separated by a 

1 m void as shown in Fig. 2. The external radiation environment, taken here as the Webber [1966] representation of 

the 1956 solar particle event, is assumed to be anti-parallel with the z-axis, uniform in the x-y plane, positioned 

above the geometry and directed down along 0. The fluence, dose, and dose equivalent will be computed using 

3DHZETRN at the top and bottom of the tissue sphere; these values will be used as a baseline for comparison 

against related geometric representations derived with approximations used in the past. 
4 

Fig. 2. A 30 cm diameter ICRU sphere within a 7.41 cm thick aluminum shell with a 1 m void (referred to as "orig. 

geom." in subsequent figures and tables). 

The first geometric simplification to be considered represents the materials in linear dimensions (cm) as 

they occur within the geometry, but the void region is eliminated, as shown in Fig. 3. Fluences obtained in the 

spherical geometry with and without the voids are shown in Fig. 4. It is clear that removal of the void results in a 

perturbation of mainly the neutron field up to ~200 MeV but also in the charged particle fields below ~10 MeV. 

Fig. 3. A 30 cm diameter ICRU sphere within a 7.41 cm thick aluminum shell (referred to as "void removed" in 

subsequent figures and tables). 

Fig. 4. The effects on the particle fields at the top and bottom of the sphere induced by removing the void in Fig. 2. 
5 

In sector analysis, it is customary to use dimensions of g/cm2

, thereby eliminating all void regions with 

nearly 0 g/cm2

 of material [Robins 1965, Raymes 1965] and introducing further geometric distortion, as shown in 

Fig. 5. 

Fig 5. A 30 g/cm2 diameter ICRU sphere within a 20 g/cm2 thick aluminum shell in g/cm2 scale (referred to as 

"g/cm2

 geom." in subsequent figures and tables). 

Even more extreme assumptions have been used in the past by replacing various materials with an 

equivalent amount of aluminum by scaling according to the primary incident protons and their atomic interactions in 

the specific materials as discussed above [Walker et al. 2011]. In the example considered presently, the tissue sphere 

is replaced by an equivalent aluminum sphere, where the aluminum sphere radius is computed as 

,

,

,

(50)

(50)

p Al

eq Al tissue

p tissue

R

x x

R = . (8)

In equation (8), xtissue = 15 g/cm2

 is the original tissue thickness, Rp,Al(50) = 2.92 g/cm2 is the range of a 50 MeV 

proton in aluminum, Rp,tissue(50) = 2.22 g/cm2

 is the range of a 50 MeV proton in tissue, and xeq,Al = 19.73 g/cm2 is 

the equivalent aluminum thickness. The equivalent aluminum approximate geometry is shown in Fig. 6. 

Fig. 6. A 30 g/cm2

 diameter ICRU sphere made of equivalent aluminum within a 20 g/cm2 thick aluminum shell 

(referred to as "eq. Al geom." in subsequent figures and tables). 
6 

The three approximate geometries of Figs. 3, 5, and 6 are analyzed using the 3DHZETRN code and 

compared with results derived from the original geometry (Fig. 2) with resultant fluence shown in Fig. 7. To better 

emphasize the differences in neutron fluence, the results are given as ratios in Fig. 8, where the results for the 

approximate geometries are divided by the result for the original geometry. As expected, a large error occurs in 

replacing the tissue by equivalent aluminum. This approximation is based on the assumption that atomic processes 

reasonably scale from one material to another and ignores the fact that nuclear interactions (cross sections) are 

strongly material dependent and do not scale in this way. Atomic interactions are largely dependent on the electron 

density within the material with only somewhat small binding corrections [Krumbein et al. 1962]. As a result, the 

atomic processes depend only on the nuclear charge in distinction to nuclear processes that depend on not only the 

nuclear charge but strongly dependent on the nuclear mass. 

Fig. 7. 3DHZETRN results of fluence vs. kinetic energy for detectors at the top and bottom of an ICRU tissue sphere 

within an aluminum shell for the configuration depicted in Figs. 2, 3, 5, and 6. 

Fig. 8. Neutron fluence ratios for the approximate geometries (Figs. 3, 5, and 6) relative to solutions of the original 

geometry (Fig. 2). 
7 

Figs. 7 and 8 show that the various geometric approximations can induce large differences in the neutron 

fluence. However, the impact on dose and dose equivalent values, as seen in Table 1, is not as severe. Table 2 gives 

the relative differences between the original and approximate geometry results previously given in Table 1. The 

relative differences are on the order of ten percent or less and may be significant depending on the approximation 

used. Clearly, use of the native geometry is the reliable method for evaluation. 

Table 1. Dose and dose equivalent at top and bottom of tissue sphere contained within an aluminum shell 

represented with various levels of approximation. 

Geometry Dose (cGy) Dose equivalent (cSv) 

Top Bottom Top Bottom 

orig. geom. 6.99 0.51 10.87 1.06 

void removed 7.06 0.50 11.92 0.95 

g/cm2

 geom. 7.04 0.51 11.50 1.03 

eq. Al geom. 7.04 0.46 11.86 1.14 

Table 2. Relative differences (%) between values in Table 1 for geometry with void region compared to values for 

various levels of approximation. 

Geometry Dose (%) Dose equivalent (%) 

Top Bottom Top Bottom 

void removed 0.93 -1.81 9.50 -8.52 

g/cm2 geom. 0.55 -0.68 5.34 -3.10 

eq. Al geom. 0.70 -9.97 9.19 8.33 

Complex Geometries 

In this example, a more complex geometry is considered. It consists of a 30 cm diameter tissue equivalent 

sphere [ICRU 1993] shielded by a 2.47 cm (5 g/cm2

) thick truncated cylindrical aluminum shell (diameter 75 cm, 

length 175 cm) with 4.94 cm (10 g/cm2

) thick end caps as shown in Fig. 9. In addition to the ICRU sphere at the 

center of the aluminum cylindrical shell, an interior aluminum box with dimensions 1254040 g/cm2

 (yellow box 

in upper portion of Fig. 9) and a second aluminum box with dimensions 6060100 g/cm2

 (red box in lower portion 

of Fig. 9) are also included. As in the previous section, the external radiation environment is taken here as the 

Webber [1966] representation of the 1956 solar particle event and assumed to be oriented anti-parallel with the zaxis, uniform in the x-y plane, positioned above the geometry and directed down along 0. The fluence, dose, and 

dose equivalent are computed at the top and bottom detector locations using 3DHZETRN as in the previous section.

This geometry and boundary condition configuration has been extensively studied using Monte Carlo (MC) 

simulation to allow testing of the 3DHZETRN computational procedures in a realistic combinatorial geometry.

Fig. 9. Complex geometry used in the current study: ICRU tissue sphere shielded by an aluminum cylindrical shell 

with internal components (referred to as "orig. geom." in subsequent figures and tables). 
8 

The resultant fluences are given in Fig. 10 for the shield arrangement with the voids included as shown in 

Fig. 9, after removing the voids (collapsed), expressing the collapsed geometry in g/cm2

, and replacing the tissue 

sphere by an equivalent aluminum sphere. Only minor differences are seen in the light ion fluences at the lowest 

energies, but large differences in the neutron fluence are observed up to 100 MeV, especially when the tissue sphere 

is replaced by an equivalent aluminum sphere. The ratio of the neutron fluence results computed in the approximate 

geometry to the results computed in the original geometry arrangement is shown in Fig. 11. The neutron fluence 

below 100 MeV is overestimated by a factor of 2 as a result of simply removing the void, but does not appear to 

depend heavily on switching between cm and g/cm2

 length scales. There is little variation in fluence at the bottom of 

the sphere for the approximate geometries in terms of cm and g/cm2

 relative to the original geometry. In an isotropic 

environment (as expected in a real solar particle event) the results at top and bottom become averaged. It is seen that 

even under isotropic conditions, the traditional equivalent aluminum approximation is not a good substitute for the 

actual geometry. 

Fig. 10. Fluence spectra in complex geometry for detectors at the top and bottom of the geometry configuration 

depicted in Fig. 9 and related approximate geometries. 

Fig. 11. Neutron fluence ratios in complex geometry for the approximate geometries relative to solutions of the 

original geometry. 
9 

Although there are large differences in the neutron fluence for all three approximate geometries compared 

to the original geometry, the impact on dose and dose equivalent values, as seen in Table 3, is modest. Relative 

differences between values in Table 3 for the original geometry with void region compared to values for various 

approximate geometries are provided in Table 4. Only the results computed in equivalent aluminum approximate 

geometry exhibit significant differences (see Table 4 at bottom detector) for this mono-directional case. For 

isotropic incidence, the errors in the three approximate geometries are expected to behave like the average of the top 

and the bottom.

In the past, various approximations were used to make the problem of estimating dosimetric quantities 

practical within the limitations of knowledge of physical parameters and computational procedures. With 

improvements in knowledge, procedures, and computational speed over the last four decades, there is no need to 

make such approximations. Results presented herein suggest there is no need to correct past results from a geometric 

point of view, although issues related to knowledge of the response of instruments and conversion to dosimetric 

quantities remain. With modern computational procedures, the main development remains to improve knowledge of 

physical interaction parameters, continued improvement of computational procedures and improved understanding 

of the driving physical parameters as related to biological response [Wilson 2000]. 

Table 3. Dose and dose equivalent in complex geometry at top and bottom of tissue sphere contained within an 

aluminum shell represented with various levels of approximation. 

Geometry Dose (cGy) Dose equivalent (cSv) 

Top Bottom Top Bottom 

orig. geom. 42.78 1.04 65.89 1.90 

void removed 42.88 1.04 66.94 1.84 

g/cm2

 geom. 42.85 1.04 66.57 1.84 

eq. Al geom. 42.81 0.94 66.77 1.94 

Table 4. Relative differences (%) between values in Table 3 for geometry with void region compared to values for 

various approximate geometries. 

Geometry Dose (%) Dose equivalent (%) 

Top Bottom Top Bottom 

void removed 0.23 -0.64 1.60 -3.08 

g/cm2 geom. 0.15 -0.69 1.04 -3.33 

eq. Al geom. 0.07 -10.34 1.33 2.06 

Conclusions 

Methods examined in this work and used in the past for radiation analysis of spacecraft included sector 

analysis in which voids between components are eliminated within the sector, or replaced by areal density (g/cm2

), 

or in other instances replaced all areal density of each material by equivalent areal density of aluminum. Each 

approximation results in distortions in the geometry and was shown to affect computational results where 3D effects 

are of importance (especially for neutrons with large diffusion coefficients). Even the most benign approximation of 

removing voids has a significant effect on the neutron fluence below 100 MeV of up to a factor of four depending on 

the geometry. Even so, the effect on dose and dose equivalent is a more modest error of up to 10 percent depending 

on geometric detail. The effect of further changing from linear scale (cm) to areal density (g/cm2

) scale are similarly 

distorted transport results. Still more inaccurate is the replacement of materials by equivalent aluminum (areal 

density), which includes not just geometric distortions but also affects atomic and especially nuclear properties. 

Acknowledgements 

This work was supported by the Human Research Program under the Human Exploration and Operations 

Mission Directorate of NASA and by NASA Grant number NNX09AR20A. 
10 

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HZETRN; Radiation

3DHZETRN: Inhomogeneous Geometry Issues 

Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.

 

20

NASA

651549.02.07.10

Historical methods for assessing radiation exposure inside complicated geometries for space applications were limited by computational constraints and lack of knowledge 

associated with nuclear processes occurring over a broad range of particles and energies. Various methods were developed and utilized to simplify geometric representations 

and enable coupling with simplified but efficient particle transport codes. Recent transport code development efforts, leading to 3DHZETRN, now enable such approximate 

methods to be carefully assessed to determine if past exposure analyses and validation efforts based on those approximate methods need to be revisited. In this work, 

historical methods of representing inhomogeneous spacecraft geometry for radiation protection analysis are first reviewed. Two inhomogeneous geometry cases, previously 

studied with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric approximation. Fluence, dose, and dose equivalent values are computed in 

all cases and compared. It is found that although these historical geometry approximations can induce large errors in neutron fluences up to 100 MeV, errors on dose and 

dose equivalent are modest (<10%) for the cases studied here.