NASA/TP–2010–216133

Spacecraft Solar Particle Event (SPE) Shielding:

Shielding Effectiveness as a Function of

SPE Model as Determined with the FLUKA

Radiation Transport Code

 

Steve Koontz1

William Atwell2

Brandon Reddell1

Kristina Rojdev1,3

1

NASA Johnson Space Center, Houston

2

The Boeing Company, Boeing Research & Technology, Houston

3

PhD Student, University of Southern California, Los Angeles

Johnson Space Center, Houston

September 2010

National Aeronautics and

Space Administration

Johnson Space Center

Houston, TX 77058
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NASA/TP–2010–216133

Spacecraft Solar Particle Event (SPE) Shielding:

Shielding Effectiveness as a Function of

SPE Model as Determined with the FLUKA

Radiation Transport Code

 

Steve Koontz1

William Atwell2

Brandon Reddell1

Kristina Rojdev1,3

1

NASA Johnson Space Center, Houston

2

The Boeing Company, Boeing Research & Technology, Houston

3

PhD Student, University of Southern California, Los Angeles

Johnson Space Center, Houston

September 2010

National Aeronautics and

Space Administration

Johnson Space Center

Houston, TX 77058
Available from:

NASA Center for AeroSpace Information National Technical Information Service

7115 Standard Drive 5285 Port Royal Road

Hanover, MD 21076-1320 Springfield, VA 22161

Phone: 301-621-0390 or 703-605-6000

Fax: 301-621-0134

This report is also available in electronic form at http://ston.jsc.nasa.gov/collections/TRS/
iii

Contents

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

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

2 Calculating Spacecraft Ionizing Dose and Single-event Rates with FLUKA .......................................... 2

2.1 Number of proton reaction upsets = [event proton fluence > 50 MeV] × σ(proton > 50 MeV)............... 3

3. Solar Particle Event Spectra ..................................................................................................................... 4

4. Results and Discussion – Ionizing Dose and Star Density ....................................................................... 7

5. Results and Discussion – Single-event Environment Rates ..................................................................... 18

6. Summary and Conclusions....................................................................................................................... 19

7. References................................................................................................................................................ 20

Appendix .................................................................................................................................................. 22
iv

Figures

1 The concentric spherical shell spacecraft structured used in FLUKA simulations .................................. 3

2 A comparison of the Band and Exponential SPE spectra (differential and integral forms) for 

the July 2000 SPE .................................................................................................................................... 5

3 A comparison of the Band and Exponential SPE spectra (differential and integral forms) for the 

November 2001 SPE................................................................................................................................ 6

4 A comparison of the Band and Exponential SPE spectra (differential and integral forms) 

for the November 1997 SPE..................................................................................................................... 6

5 A comparison of the Band and Exponential SPE spectra (differential and integral forms) for

the October 2003 SPE .............................................................................................................................. 7

6 Dose, in cGy (y axis, range 10-3 to 105

), to the silicon detector shells as a function of 

shielding mass in g/cm2 aluminum (x axis, range 0.1 to 1 000) for each of the four particle 

events considered in this paper................................................................................................................. 9

7 Dose, in cGy (y axis, range 10-3 to 105

), to the silicon detector shells as a function of 

shielding mass in g/cm2 polyethylene (x axis, range 0.1 to 100) for each of the four particle 

events considered in this paper................................................................................................................. 10

8 Dose, in cGy (y axis, range 10-3 to 105

), to the silicon detector shells as a function of 

shielding mass in g/cm2 carbon (x axis, range 0.1 to 103

) for each of the four particle events

considered in this paper............................................................................................................................ 11

9 Dose, in cGy (y axis, range 10-3 to 105

), to the silicon detector shells as a function of 

shielding mass in g/cm2 titanium (x axis, range 0.1 to 1 000) for each of the four particle events

considered in this paper............................................................................................................................ 12

10 Proton star density, in number per cc (y axis, range 0.1 to 105

), to the silicon detector shells 

as a function of shielding mass in g/cm2 aluminum (x axis, range 0.1 to 103

) for each of the four 

particle events considered in this paper.................................................................................................... 14

11 Proton star density, in number per cc (y axis, range 0.1 to 105

), to the silicon detector shells 

as a function of shielding mass in g/cm2 polyethylene (x axis, range 0.1 to 100) for each of the 

four particle events considered in this paper ............................................................................................ 15

12 Proton star density, in number per cc (y axis, range 0.1 to 105

), to the silicon detector shells 

as a function of shielding mass in g/cm2 carbon (x axis, range 0.1 to 100) for each of the 

four particle events considered in this paper ............................................................................................ 16

13 Proton star density, in number per cc (y axis, range 0.1 to 105

), to the silicon detector shells as

a function of shielding mass in g/cm2 titanium (x axis, range 0.1 to 1 000) for each of the four

particle events considered in this paper.................................................................................................... 17

14 Proton, neutron, and pion star density, in number per cc (y axis, range 10 to 108

), to the silicon 

detector shells as a function of aluminum or polyethylene shielding mass in g/cm2

................................ 18

App-1 In 1a and 1b above, HZETRN two-dimensional calculations of dose as a function of depth 

are compared for the Band and Exponential forms of the event spectra; in 1c and 1d above, threedimensional FLUKA and two-dimensional HZETRN calculations of dose vs. depth are compared....... 22

Tables

1 Shielding mass or thickness exterior to each silicon detector shell.......................................................... 3

2 Solar particle event parameters ................................................................................................................ 4

3 A comparison of observed in-flight SPE SEU counts with estimates of SPE SEU counts 

calculated with FLUKA radiation transport code..................................................................................... 19
v

Acronyms

AU astronomical unit

DRAM dynamic random access memory

DSP digital signal processor

EMU extravehicular mobility unit

ESP energetic solar particle event

EVA extravehicular activity

FLUKA FLUktuierende KAskade

GLE ground-level event

GEO geosynchronous Earth orbit

ICRU International Commission on Radiation Units

LET linear energy transfer

SEE single-event environment

SEU single-event upset

SPE solar particle event

SRAM standard random access memory

SSR solid-state recorder

TID total ionizing dose
vi
1

Abstract

In the following paper, we report the results of modeling and simulation studies in which the radiation transport 

code FLUKA (FLUktuierende KAskade) is used to determine the changes in total ionizing dose (TID) and singleevent effect (SEE) environments behind aluminum, polyethylene, carbon, and titanium shielding masses when the 

assumed form (ie, Band or Exponential) of the solar particle event (SPE) kinetic energy spectra is changed.

FLUKA simulations have fully three spatial dimensions with an isotropic particle flux incident on a concentric 

spherical shell shielding mass and detector structure. The effects are reported of both energetic primary protons

penetrating the shield mass and secondary particle showers caused by energetic primary protons colliding with 

shielding mass nuclei. SPE heavy ion spectra are not addressed. Our results, in agreement with previous studies,

show that use of the Exponential form of the event spectra can seriously underestimate spacecraft SPE TID and 

single-event environments in some, but not all, shielding mass cases.

1. Introduction

The design and verification of any spacecraft, piloted or unpiloted, required to function in a solar particle event 

(SPE) environment must begin with the selection of a reasonable worst-case SPE design and verification environment1

, a task complicated by the extreme variability of SPEs2. Another difficulty is posed by the fact that event

kinetic energy spectra are measured by spacecraft instruments over a limited range of particle kinetic energies, and 

the full spectrum is only obtained by modeling and extrapolation3-6

. Radiation transport and modeling studies have 

shown that the single-event and total ionizing dose (TID) environments behind spacecraft shielding mass depend 

strongly on the assumed form (ie, Band or Exponential) of the SPE kinetic energy spectra3–6

.

In this paper, we report the results of modeling and simulation studies in which the radiation transport code 

FLUKA (FLUktuierende KAskade) is used to determine the changes in both the TID and SEE environments behind

various thicknesses of aluminum, polyethylene, carbon, and titanium, shielding when the assumed form (ie, Band 

or Exponential) of the SPE kinetic energy spectra is changed4-6

. FLUKA is a fully integrated and extensively verified

Monte Carlo simulation package for the interaction and transport of high-energy particles and nuclei in matter7-9

.

The SPE spectra investigated are taken from four specific SPEs that produced ground-level events (GLEs) during 

solar cycle 23 (1997–2008)6

. GLEs are produced by highly energetic solar particle events (ESP), ie, those that contain significant fluences of 700 MeV to 10 GeV protons. High-energy protons interact with Earth’s atmosphere via 

nuclear reaction to produce secondary particles, some of which are neutrons that can be detected at the Earth’s surface

by the global neutron monitor network10,11. GLEs are one part of the overall SPE resulting from a particular solar

flare or coronal mass ejection event on the Sun. The ESP part of the particle event, detected by spacecraft, is often 

associated with the arrival of a “shock front” at Earth6 some hours after the arrival of the GLE.

Highly energetic SPEs are implicated in increased rates of spacecraft anomalies and spacecraft failures12–14

. The 

specific SPEs used in this analysis are those of: 1) November 6, 1997 – GLE only; 2) July 14-15, 2000 – GLE from 

the 14th plus ESP from the 15th; 3) November 4-6, 2001 – GLE and ESP from the 4th; and 4) October 28-29, 2003 –

GLE and ESP from the 28th plus GLE from the 29th. The corresponding Band and Exponential spectra used in this 

paper are like those previously reported4-6

.

The effects are reported of both energetic primary protons penetrating spacecraft shielding mass and secondary

particle showers caused by energetic primary protons colliding with shielding mass nuclei. The SPE spectra impinging on a particular spacecraft will depend on spacecraft location and trajectory14. SPE spectra inside planetary

magnetospheres are not the same as those observed in interplanetary space. The SPE spectra used in the modeling 

and simulation study reported here are interplanetary free-space spectra; the results are applicable only at or beyond 

geosynchronous Earth orbit (GEO) and only at distances on the order of 1 astronomical unit (AU) from the sun. SPE

heavy ion spectra and their effects on spacecraft ionizing dose and single-event rates are not directly addressed in 

this paper15.
2

2. Calculating Spacecraft Ionizing Dose and Single-event 

Rates with FLUKA

FLUKA is a fully integrated Monte Carlo simulation package for the interaction and transport of high-energy

particles in matter, including explicit physics-based hadron-nucleus and nucleus-nucleus collisions, with fully 

developed and complete secondary particle shower production7-9

. The code is widely and successfully used in

particle physics, high-energy experimental physics and engineering, shielding, detector and telescope design, cosmicray studies, radiation dosimetry, medical physics, and radiobiology because its precision and accuracy has been 

exhaustively validated16-18.

The highest priority in the design and development of FLUKA has always been the implementation and improvement of sound and modern physical models. Microscopic models are adopted whenever possible, with consistency ensured among all reaction steps and/or reaction types. Conservation laws are enforced at each step, and 

results are checked against experimental data at the single-interaction level. As a result, final predictions are obtained

with a minimal set of free parameters for all energy/target/projectile combinations. Therefore, results in complex cases,

as well as properties and scaling laws, arise naturally from the underlying physical models. Predictivity is provided 

where no experimental data are directly available, and correlations within interactions and among shower components are preserved.

FLUKA simulations were conducted on a generic concentric spherical shell “spacecraft” geometry with thin layers 

(100 microns) of silicon “scoring” detectors between layers of aluminum (or other) shielding masses. The concentric 

spherical shell geometry is shown in figure 1. FLUKA randomly samples the natural particle kinetic energy spectra 

appropriate to the specific flight environment to specify particle identity and particle kinetic energy. The selected 

particles are randomly directed into the spherical shell structure from the outside so as to simulate an isotropic 

(ICRU [International Commission on Radiation Units] definition) particle flux incident on the “spacecraft.”

Each silicon scoring detector shell has a well-defined shielding mass distribution function that is calculated looking

outward from the scoring detector shell. The millions of randomly directed particles FLUKA sends into the target 

sphere during execution of the program accurately sample that shielding mass distribution function. The minimum 

shielding mass, measured along the spherical target radius and exterior to each silicon detector shell, is shown in 

Table 1 along with the distance in centimeters from each detector shell to the exterior surface of the concentric 

spherical target “spacecraft.” The interior of the sphere is treated as a perfect particle absorber.

FLUKA reports results based on the isotropic flux to an entire detector shell, not on results based on a limited area 

of the shell. For each particle fired into the “spacecraft,” FLUKA calculates the following through the thickness of 

the target structure: 1) energy loss (linear energy transfer [LET]) of primary particles, 2) nuclear reactions and reaction products (secondary particle showers), and 3) energy loss and further nuclear reactions of secondary particles.

The FLUKA “SCORE” output tables19 report total energy deposition, a number proportional to TID, by all primary 

and secondary particles in each silicon detector shell as well as the number of inelastic nuclear interactions (nuclear 

reactions or “stars”*

) produced by > 50 MeV protons, neutrons, and pions. Hadrons < 50 MeV are not scored as stars 

but do contribute to TID. Because FLUKA is a Monte Carlo code, results will vary from run to run as the random

number seed is changed. It follows that only the average of two or more FLUKA runs should be compared with the 

results of deterministic codes like HZETRN20. The general characteristics of HZETRN were communicated to 

author 2in a conversation with Dr Martha S. Clowdsley, NASA Langley Research Center in 2007.

Spacecraft proton SEE rates for each particle event are estimated from the total > 50 MeV proton fluence for 

each silicon detector shell. The contribution to the single-event rate from proton nuclear reactions for each silicon 

detector shell is estimated by multiplying the >50 MeV proton event fluence for each silicon shell by the saturated 

proton cross section for the component of interest as determined by ground-based heavy ion testing combined with 

the Petersen-Barak method21. The total > 50 MeV proton fluence for each detector shell is calculated from the 

 *

A star is a nuclear reaction event in a solid target material caused by the collision of an energetic hadron (proton, neutron, or 

pion) with a target material nucleus.
3

detector shell proton star density and the inelastic collision length of protons22. Finally, SPE proton-induced single 

event upsets are estimated using the equation below.

Number of proton reaction upsets = [event proton fluence > 50 MeV] × σ(proton > 50 MeV)

SEE rate calculations (estimates) were made for three different spacecraft, flying at GEO or beyond, for which SPE

SEE rates have been measured in-flight. The three spacecraft/electronic component combinations are: 1) Cassini23

SSR [solid-state recorder] DRAM [dynamic random access memory], 2) SOHO24 SSR DRAM, and, 3) Thuraya25

DSP [digital signal processor] SRAM [static random access memory]. Cassini was exposed to the November 6, 1997

SPE shortly after launch. SOHO was exposed to both the November 6, 1997 and the July 14-15, 2000 SPEs. Thuraya

was exposed to both the November 4-6, 2001 and the October 28-29, 2003 events. All three spacecraft were located

at approximately 1 AU from the sun and are either in geosynchronous orbit or beyond but still very close to 1 AU 

Figure 1. The concentric spherical shell spacecraft structure used in FLUKA simulations.

Table 1. Shielding mass or thickness exterior to each silicon detector shell

Concentric 

Sphere Shield 

Thickness 

(g/cm2)

SiDet1 SiDet1 SiDet1 SiDet1 SiDet1 SiDet1 SiDet1 SiDet1

Polyethylene 0.036 0.175 0.380 1.854 3.677 7.316 18.213 36.719

Carbon 0.074 0.357 0.775 3.783 7.504 14.93 37.169 74.963

Aluminum 0.100 0.482 1.046 5.107 10.131 20.155 50.178 101.164

Titanium 0.167 0.803 1.743 8.512 16.885 33.592 83.603 168.607

Shield 

Geometric 

Thickness 

(cm)

0.056 0.300 0.593 2.926 5.778 11.519 28.704 57.852
4

from the sun. All three spacecraft reported significant increases in single-event upset (SEU) rates during the SPEs

and much lower background rates, caused by galactic cosmic rays, before and after the events.

SPE proton-induced SEU rate calculations are very sensitive to assumptions concerning the spacecraft shielding 

mass. Unfortunately, detailed shielding mass distribution functions are not available for the subject spacecraft. So, 

shielding mass is estimated as follows: The minimum shielding mass estimate provided in Refs. 23-25 is configured

as a hollow sphere, and the SEE-sensitive devices are placed on the inner wall of the sphere. The median shielding

mass for each device is then found by multiplying the minimum shielding mass by 1.56 to obtain the median shielding

mass at that location. The interior of the sphere, containing the rest of the spacecraft mass, is treated as opaque to the 

vast majority of the event protons so that only protons entering the device through the spherical shell exterior to the 

device are effective in causing upsets. The estimated median shielding mass for each spacecraft/electronic component combinations is as follows: 1) Cassini SSR DRAM, 7 g/cm2

; 2) SOHO SSR DRAM, 2 g/cm2; and 3) Thuraya

DSP SRAM, 2 g/cm2

. Spacecraft shielding mass is assumed to be aluminum.

The proton star density from the FLUKA simulations corresponding to the median shielding mass is then used to 

calculate the >50 MeV proton event fluence. One half of the event proton fluence so calculated is used to calculate 

the estimated event SEU rate. One half of the event fluence is the appropriate fluence to use in the assumed spacecraft geometry because particle flux is incident from 4π steradians on the entire surface of the concentric sphere 

structure used in the FLUKA simulations and FLUKA reports results for entire spherical regions, eg, detector

shells. In contrast, the particle flux to any single point on an opaque sphere is incident from only 2π steradians.

The spacecraft components listed above are not subject to SEE effects resulting from direct ionization by the 

energetic protons passing through the components because the maximum proton LET [linear energy transfer] is 

well below the device LET threshold in all cases. Instead, SEE effects result from both the nuclear reactions between

primary and secondary energetic protons (and other hadrons) and the silicon nuclei in the electronic devices that 

produce high-LET secondary particles internal to the devices.

SPEs also contain a not insignificant heavy ion (eg, carbon, oxygen, and iron) content that can cause SEE events in

microelectronic devices by direct ionization15, although the magnitude of the contribution varies from spacecraft to 

spacecraft and event to event25,26. The expected contribution of heavy ions to the event SEU observations for the 

spacecraft considered here are examined below in the results and discussion section of this paper.

3. Solar Particle Event Spectra

For the SPEs considered in this paper, the full event was taken into account; ie, the summation of the semiempirical exponential spectra observed by satellite (ESP) and the enhanced GLE, when available and that may 

have occurred on the same day or the day before or after. The GLE is a higher-energy part of the spectrum (> 700 MeV)

associated with the SPEs that are detected by high-latitude neutron-monitoring stations. These neutrons are a result 

of the secondary particle shower created when the high-energy protons interact with the Earth’s atmosphere6,10,11. 

The spectra used in this paper were derived using the parameters shown in Table 2.

Table 2. Solar particle event parameters

Event Start Date Event 

Type

J0(#/cm2) γ1 γ2 R0(MV)

Nov. 6, 1997 GLE 8.15E+8 0.284 5.38 116

July 14, 2000 GLE 2.94E+9 0.506 7.46 123

July 15, 2000 ESP 6.01E+7 3.235 7.85 226

Nov. 4, 2001 GLE 2.14E+9 0.242 6.67 93

Nov. 4, 2001 ESP 4.78E+8 2.363 11.2 129

Oct. 28, 2003 GLE 8.44E+9 0.0086 6.48 89

Oct. 28, 2003 ESP 1.12E+8 2.812 8.92 171

Oct. 29, 2003 GLE 7.62E+7 2.004 6.86 206
5

The Band integral spectra for the GLEs were computed using the above parameters and the following expressions6

:

( ) ( ) 1

0 2 1 0

0

exp , . −  

>= − ≤ −      

R J R J R R for R

R

γ

γ γ

( ) ( ) ( ) ( ) ( ) 2 2 1

0 1 2 2 1 0 2 1 0 exp , . −   −

>= −   − ≥ −      

J R J R R R for R γ γ γ

γ γ γ γ γ γ

As mentioned above, for each event the integral spectra from all associated GLEs and ESPs were summed to get

a total integral spectrum for that event. The total differential spectrum was created by differentiating the integral 

spectra with respect to particle kinetic energy.

For the Exponential spectra, only the J0 parameter is used from Table 2. The expression to derive the Exponential 

spectra is as follows:

( ) 0

0

exp .

 

>= −     

R J R J

R

The total Exponential spectrum for each event was created in a similar manner to the Band total integral spectrum.

However, for this spectrum, the total differential spectrum was created from a code that maintains the Exponential 

functional form in rigidity based on the total integral (> 30 MeV) and (>100 MeV) values. Because the exponential 

fluence drops off rapidly, only energies up to 1 000 MeV were considered in this paper. Contributions to dose and 

SEE are negligible at these higher energies.

The integral form of the Band and Exponential SPE kinetic energy spectra are compared in figures 2 through 5 for 

each of the four SPEs considered in this paper.

Figure 2. A comparison of the band and exponential SPE spectra 

(differential and integral forms) for the July 2000 SPE. X axis = particle 

kinetic energy in MeV; Y axis = protons /cm2 for integral spectra and 

protons/(cm2 MeV) for differential spectra

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

10 100 1000 10000

Band - Integral

Band - Diff.

EXP - Integral

EXP - Diff.

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

10 100 1000 10000

Figure 2. A comparison of the Band and Exponential SPE spectra

(differential and integral forms) for the July 2000 SPE. X axis = particle

kinetic energy in MeV; Y axis = protons/cm2 for integral spectra and

protons/(cm2 MeV) for differential spectra.
6

Figure 3. A comparison of the band and exponential SPE spectra 

(differential and integral forms) for the November 2001 SPE. X axis = 

particle kinetic energy in MeV; Y axis = protons /cm2 for integral spectra 

and protons/(cm2 MeV) for differential spectra

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

10 100 1000 10000

Band - Integral

Band - Diff.

EXP - Integral

EXP - Diff.

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

10 100 1000 100

Figure 3. A comparison of the Band and Exponential SPE spectra

(differential and integral forms) for the November 2001 SPE. X axis =

particle kinetic energy in MeV; Y axis = protons/cm2 for integral spectra

and protons/(cm2 MeV) for differential spectra.

Figure 4. A comparison of the Band and Exponential SPE spectra

(differential and integral forms) for the November 1997 SPE. X axis =

particle kinetic energy in MeV; Y axis = protons/cm2 for integral spectra

and protons/(cm2 MeV) for differential spectra.
7

4. Results and Discussion – Ionizing Dose and Star Density

The results of FLUKA calculations of SPE TID, expressed in cGy, as a function of shielding mass, expressed 

in g/cm2

, are shown in figures 6 through 9 as is the ratio (Band dose)/(Exponential dose). Note that in all the figures, the curve connecting the calculated data points is merely a guide for the eye, not a fitting function. For TID, 

the statistical run-to-run variation is on the order of 10% of the indicated value or less, so error bars are not plotted. 

Results are plotted on log-log axes, and data ranges for the x and y axes are indicated in the figure captions. With the 

exception of the November 1997 event, the TID produced by the Band spectra exceeded that produced by Exponential

spectra only at the lowest and highest shielding masses. In the middle shielding mass range, the Band TID and

Exponential TID are very nearly the same. Band TID is significantly greater than Exponential TID only at high

shielding mass in the November 1997 event. For all particle event shielding mass combinations, Band TID and 

Exponential TID are very nearly equal in the shielding mass range of 1 to 10 g/cm2

.

The comparison of Band and Exponential TID as a function of shielding mass (shown in figs. 6-9) is reminiscent

of the comparison of the Band and Exponential spectra shown in figures 2 through 5. The Band and Exponential 

spectra are very nearly identical between 30 and 200 MeV, while diverging only below 30 and above 200 MeV.

The relationship between proton kinetic energy and range in solids suggests that the low-energy protons are the most 

important contributors to dose at low shielding mass while the highest-energy protons are the most important contributors to dose at the highest shielding mass. Protons between and 200 MeV are the most important contributors to dose 

in the middle shielding mass range.

With the exception of the November 1997 event and for all shielding materials studied, the shielding mass needed

to reduce the event ionizing dose to 1 cGy or less is always greater than 10 but less than 50 g/cm2

. The usual atomic

number dependence of shielding effectiveness is observed. For example, in the July 2000 event Band plots the shielding

mass, measured along the sphere radius needed to reduce the event ionizing dose to 1 cGy or less in the concentric

sphere configuration, is 30 g/cm2 polyethylene, 37 g/cm2 carbon, 40 g/cm2 aluminum, and 43 g/cm2 titanium. Using 

the Exponential July 2000 event spectrum, the shielding mass needed to reduce the event ionizing dose to 1 cGy or 

less is 22 g/cm2 polyethylene, 25 g/cm2 carbon, 29 g/cm2 aluminum, and 32 g/cm2 titanium. Use of the Band spectra

Figure 5. A comparison of the band and exponential SPE spectra 

(differential and integral forms) for the October 2003 SPE. X axis = particle 

kinetic energy in MeV; Y axis = protons /cm2 for integral spectra and 

protons/(cm2 MeV) for differential spectra

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

10 100 1000 10000

Band - Integral

Band - Diff.

EXP - Integral

EXP - Diff.

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

10 100 1000 1

Figure 5. A comparison of the Band and Exponential SPE spectra

(differential and integral forms) for the October 2003 SPE. X axis =

particle kinetic energy in MeV; Y axis = protons/cm2 for integral spectra

and protons/(cm2 MeV) for differential spectra.
8

for design and verification will lead to a heavier spacecraft, but this additional weight may be necessary to assure 

meeting some event TID requirements. The weight impact can be minimized by selecting materials and spacecraft

configurations with optimum radiation shielding performance.

The choice of Band or Exponential event spectra can significantly affect spacecraft mass for allowable doses of 

1 cGy or less. However, as shown in figures 6 through 9, for allowable doses between 10 and 100 cGy the difference 

between Band and Exponential TID is negligible. If either the Exponential or Band spectra are selected in combination with an allowable event TID between 10 and 100 cGy, the spacecraft should meet allowable dose design 

requirements during flight operations.

Event TIDs between 10 and 100 cGy correspond to shielding masses between 1 and 10 g/cm2

, so there is no significant difference in the TID produced by the Band or Exponential event spectra over the subject shielding mass 

range. For spacecraft having shielding mass between 1 and 10 g/cm2

, the choice of Exponential or Band event 

spectra for design and verification is of no special importance in all cases studied.

The choice of Band or Exponential spectra can be important at shielding mass values below 1 g/cm2 where the event

TID can exceed 104 cGy and the Band TID can be an order of magnitude greater than the Exponential TID. With the 

exception of the November 1997 event, Band TID is between two and 10 times Exponential TID in all cases studied 

over the subject shielding mass range. Selection of the Exponential spectra for design and verification can lead to

unacceptable hardware degradation during SPEs and may even impact crew health if extravehicular mobility units 

(EMUs; aka spacesuits) do not provide adequate protection to limit dose during emergency extravehicular activity

(EVA; aka spacewalk) termination following an SPE event warning.

The general features of the dose depth curves shown in figures 6 through 9 are also visible in two-dimensional 

deterministic simulations executed with the HZETRN [a galactic cosmic ray transport code developed at NASA 

Langley Research Center] on slab targets. As shown in the Appendix, the features of the dose depth curve in figures 

6 through 9 are not the result of unexpected three-dimensional geometric effects.
9

Figure 6. Dose, in cGy (y axis, range 10-3 to 105), to the silicon detector shells as a function of shielding mass 

in g/cm2 aluminum (x axis, range 0.1 to 1 000) for each of the four particle events considered in this paper. Event 

dose resulting from Band () and Exponential () event spectra is plotted as is the ratio [Band dose]/[Exponential 

dose] ().
10

Figure 7. Dose, in cGy (y axis, range 10-3 to 105), to the silicon detector shells as a function of shielding mass in g/cm2

polyethylene (x axis, range 0.1 to 100) for each of the four particle events considered in this paper. Event dose resulting 

from Band () and Exponential () event spectra is plotted as is the ratio [Band dose]/[Exponential dose] ().
11

July 2000 - Dose Comparison

Band vs Exp - Carbon

0.01 1 100

1 10− 3 ×

0.01

0.1

1

10

100

1 103 ×

1 104 ×

1 105 ×

Dosej00bndCj

Dosej00expCj

Dosej00bndCj

Dosej00expCj

Cshldj

November 2001 - Dose Comparison

Band vs Exp - Carbon

0.01 1 100

1 10− 3 ×

0.01

0.1

1

10

100

1 103 ×

1 104 ×

1 105 ×

Dosen01bndCj

Dosen01expCj

Dosen01bndCj

Dosen01expCj

Cshldj

November1997 - Dose Comparison 

Band vs Exp - Carbon

0.01 1 100

1 10− 3 ×

0.01

0.1

1

10

100

1 103 ×

1 104 ×

1 105 ×

Dosen97bndCj

Dosen97expCj

Dosen97bndCj

Dosen97expCj

Cshldj

October 2003 - Dose Comparison

Band vs Exp - Carbon

0.01 1 100

1 10− 3 ×

0.01

0.1

1

10

100

1 103 ×

1 104 ×

1 105 ×

Doseo03bndCj

Doseo03expCj

Doseo03bndCj

Doseo03expCj

Cshldj

Figure 8. Dose, in cGy (y axis, range 10-3 to 105), to the silicon detector shells as a function of shielding 

mass in g/cm2 carbon (x axis, range 0.1 to 103) for each of the four particle events considered in this 

paper. Event dose resulting from Band () and Exponential () event spectra is plotted as is the 

ratio [Band dose]/[Exponential dose] ().
12

The production of stars, occurring at particle kinetic energy greater than 50 MeV for protons, neutrons, and pions, 

was dominated by protons for all shielding material SPE combinations studied. The results of FLUKA calculations 

of proton star density in the silicon detector shells, expressed as stars per cc, are shown in figures 10 through 13 as 

a function of shielding mass, expressed in g/cm2 measured along the sphere radius..

For proton star production, the 

statistical run-to-run variation is on the order of 10% of the indicated value or less for shielding masses less than

20 g/cm2

, so error bars are not plotted. Results are plotted on log-log axes, and the data ranges for the x and y axes

are indicated in the figure captions

Figure 9. Dose, in cGy (y axis, range 10-3 to 105), to the silicon detector shells as a function of shielding mass in g/cm2

titanium (x axis, range 0.1 to 1 000) for each of the four particle events considered in this paper. Event dose resulting from 

Band () and Exponential () event spectra is plotted as is the ratio [Band dose]/[Exponential dose] ().
13

The Band and Exponential spectra are essentially the same for proton kinetic energies between 30 and 200 MeV, 

and the comparison of Band and Exponential star densities reflect this fact. The Band and Exponential proton star 

density plots, which are essentially the same at low shielding mass, only diverge for a shielding mass greater than 

10 g/cm2

. The ratio (Band star density)/(Exponential star density) is close to 1 below 10 g/cm2, and can increase to 

between 2 and 10 at greater shielding mass values. Band and Exponential proton star densities are the same at lower 

shielding masses because protons having < 50 MeV kinetic energy do not contribute to the star score, yet can be an 

improtant part of the primary SPE spectrum.

The shielding materials studied exhibit a different order of effectiveness from those observed for ionizing dose. 

Using the July 2000 SPE Band spectra as an example again, the shielding mass needed to reduce the proton star 

density to 105 stars/cm3 is 30 g/cm2 polyethylene, 32 g/cm2 carbon, 30 g/cm2 aluminum, and 50 g/cm2 titanium.

Using the July 2000 SPE Exponential SPE band spectra, the shielding mass needed to reduce the proton star density 

to 105 stars/cm3 is 23 g/cm2 polyethylene, 24 g/cm2 carbon, 22 g/cm2 aluminum, and 32 g/cm2 titanium.

If maintaining the proton star density (for proton kinetic energies > 50 MeV) during an SPE is a design and 

verification objective, the selection of the Band or Exponential design environments can lead to substantial differences in spacecraft weight. Picking the Exponential environment may lead to a failure to meet requirements during 

flight operations.

Neutron and pion star densities, as expected for the relatively small number of particles produced, displayed 

considerable run-to-run statistical variability; so the results are accurate only to the nearest order of magnitude. 

Unlike proton stars or ionizing dose, the neutron and pion star density showed little variation with shielding mass. 

Neutron star densities were between 105 and 106 stars /cm3 for higher fluence events and between 104 and 105 stars/cm3

for the lower-fluence November 1997 event.

Proton, neutron, and pion star density is shown as a function of aluminum and polyethylene shielding mass for 

the November 2001 SPE (Band and Exponential spectra) in figure 14. Figure 14 is representative of all SPE event 

spectra shielding mass combinations. The most immediately obvious difference between the Band and Exponential 

spectra plots in figure 14 is the essential absence of pion stars in the Exponential case, a not unexpected result given 

the kinetic energy threshold for pion production. The single pion point in the polyethylene exponential spectra is most

probably a statistical fluke (ie, low probability event). The Exponential spectra pion star density was zero for all 

other shielding mass event combinations.

Despite the relatively large statistical uncertainty on the neutron and pion data, some general trends are apparent. 

First, the neutron and pion star yields are not significantly higher for the Band than for the Exponential spectra.

Second, the number of neutron and pion stars increases to a shallow maximum at or around 10 g/cm2 before decreasing again at greater shielding mass values. Third and finally, as compared to proton stars, neutron and pion star density

shows relatively weak dependence on shielding mass, generally varying by less than an order of magnitude across 

the entire shielding mass range. At the highest shielding mass values, the neutron star density can be larger than 

the proton star density.

Star density for > 50 MeV hadronic particles is of interest because it can be used to calculate the corresponding 

particle flux and fluence at different shielding depths using the particle inelastic interaction collision length22. Star 

density is also directly related to the SEU rate caused by hadronic interactions in or near electronic device sensitive 

volumes. Proton-driven single-event rates for various spacecraft are predicted using this approach in the next section 

of this paper for comparison with observed in-flight rates.
14

Figure 10. Proton star density, in number per cc (y axis, range 0.1 to 105), to the silicon detector shells as a function 

of shielding mass in g/cm2 aluminum (x axis, range 0.1 to 103) for each of the four particle events considered in this 

paper. Event star density resulting from Band () and Exponential () event spectra is plotted as is the ratio 

[Band star density]/[Exponential star density] ().
15

Figure 11. Proton star density, in number per cc (y axis, range 0.1 to 105), to the silicon detector shells as a function 

of shielding mass in g/cm2 polyethylene (x axis, range 0.1 to 100) for each of the four particle events considered in this 

paper. Event star density resulting from Band () and Exponential () event spectra is plotted as is the ratio [Band 

star density]/[Exponential star density] ().
16

July 2000 - Proton Star Density

Comparison - Band vs Exp - Carbon

0.01 1 100

0.1

1

10

100

1 103 ×

1 104 ×

1 105 ×

1 106 ×

1 107 ×

1 108 ×

Pstrj00bndCj

Pstrj00expCj

Pstrj00bndCj

Pstrj00expCj

Cshldj

November 2001 - Proton Star Density

Comparison - Band vs Exp - Carbon

0.01 1 100

0.1

1

10

100

1 103 ×

1 104 ×

1 105 ×

1 106 ×

1 107 ×

1 108 ×

Pstrn01bndCj

Pstrn01expCj

Pstrn01bndCj

Pstrn01expCj

Cshldj

November1997 - Proton Star Density

Comparison - Band vs Exp - Carbon

0.01 1 100

0.1

1

10

100

1 103 ×

1 104 ×

1 105 ×

1 106 ×

1 107 ×

1 108 ×

Pstrn97bndCj

Pstrn97expCj

Pstrn97bndCj

Pstrn97expCj

Cshldj

October 2003 - Proton Star Density

Comparison - Band vs Exp - Carbon

0.01 1 100

0.1

1

10

100

1 103 ×

1 104 ×

1 105 ×

1 106 ×

1 107 ×

1 108 ×

Pstro03bndCj

Pstro03expCj

Pstro03bndCj

Pstro03expCj

Cshldj

Figure 12. Proton star density, in number per cc (y axis, range 0.1 to 105), to the silicon detector shells as 

a function of shielding mass in g/cm2 carbon (x axis, range 0.1 to 100) for each of the four particle events 

considered in this paper. Event star density resulting from Band () and Exponential () event spectra is 

plotted as is the ratio [Band star density]/[Exponential star density] ().
17

Figure 13. Proton star density, in number per cc (y axis, range 0.1 to 105), to the silicon detector shells as a function 

of shielding mass in g/cm2 titanium (x axis, range 0.1 to 1 000) for each of the four particle events considered in this 

paper. Event star density resulting from Band () and Exponential () event spectra is plotted as is the ratio [Band 

star density]/[Exponential star density] ().
18

5. Results and Discussion – Single-event Environment Rates

Calculated (estimated) and observed SPE SEU rates are compared in Table 3, along with the ratio (estimated 

rate)/(observed rate) for the three spacecraft/system and device combinations modeled here. The ratio (calculated

rate)/(observed rate) ranges from 0.32 to 2.5, showing that the calculated and observed rates are within a factor of 3

of each other in all cases – a remarkably good agreement given the uncertainties in system device shielding mass and

the use of a constant proton upset cross section estimated with the Petersen-Barak method21. Agreement between

estimated and observed upset rates to within a “factor of a few” is generally viewed as acceptable for engineering

design and verification purposes27 and is better than the order-of-magnitude agreement often seen in the published 

literature28-30.

Figure 14. Proton, neutron, and pion star density, in number per cc (y axis, range 10 to 108), to the silicon 

detector shells as a function of aluminum or polyethylene shielding mass in g/cm2. November 2001 SPE Band 

and Exponential event spectra. Proton star density (X), neutron star density (+), and pion star density ().
19

The magnitude of the heavy ion contribution to solar particle SEU rates is highly variable25,26. The SPE heavy ions, 

helium through iron, are of low kinetic energy compared to galactic cosmic rays of the same atomic number and can 

be easily removed by relatively thin shielding. In some cases, heavy ions have contributed as much as 45% of the

observed SPE SEU rates while in others no heavy ion contributions are detectable26. Hansen et al25 have shown that, 

for Thuraya, the observed upset rate is a complex function not only of proton and heavy ion flux but also of particle 

kinetic energy spectra and device shielding environment. Based on published literature on the subject25-30, it seems 

unlikely the heavy ion content of the SPEs modeled here could increase the calculated rates by more than a factor 

of 1.5 so that heavy ion effects do not affect our conclusion; ie, that the reasonable agreement between in-flight 

SPE SEU rates and rates estimated using the FLUKA-based approach reported here provides at least partial 

validation of the subject FLUKA modeling approach.

Table 3. A comparison of observed in-flight SPE SEU counts with estimates of SPE

SEU counts calculated with FLUKA radiation transport code

Spacecraft/System 

and Device

Nov. 1997 SPE

Upsets/bit

July 2000 SPE

Upsets/bit

Nov. 2001 SPE

Upsets/bit

Oct. 2003 SPE

Upsets/bit

Cassini/Solid State 

Recorder DRAM

1) Observed upsets

2) Estimated upsets

3) Estimated Observed

1) 4.4×10-7

2) 1.4×10-7

3) 0.32

NA NA NA

SOHO/Solid State 

Recorder DRAM

1) Observed upsets

2) Estimated upsets

3) Estimated/Observed

1) 4.4×10-6

2) 2.110-6

3) 0.48

1) 4.7×10-5

2) 2.1×10-5

3) 0.4

NA NA

Thuraya/DSP DRAM

1) Observed upsets

2) Estimated upsets

3) Estimated/Observed

NA NA 1) 2.0×10-6

2) 2.8×10-6

3) 1.4

1) 1.5×10-6

2) 3.8×10-6

3) 2.5

6. Summary and Conclusions

The FLUKA radiation transport code has been successfully used to determine changes in the TID and SEE environments behind aluminum, polyethylene, carbon, and titanium shielding masses when the assumed form (Band

or Exponential) of the SPE kinetic energy spectra is changed. For all particle event and shielding mass combinations, 

the following are found to be true: The differences in the TID environment and the SEE environment between the 

two SPE spectral forms are most pronounced when the shielding mass is greater than 10 g/cm2 or less than 1 g/cm2

. 

Band and Exponential spectra produce nearly identical results between 1 and 10 g/cm2

. Direct comparison of SPE 

spectral forms revels that the Band form has higher particle flunece than the Exponential form at both low and high 

kinetic energies, while the two forms are nearly identical at intermediate kinetic energies. It is likely that TID and

SEE are dominated by low-energy protons at low ( < 1g/cm2

) shielding mass values and high-energy protons at high 

(> 10 g/cm2

) shielding mass values while intermediate mass protons dominate dose between 1 and 10 g/cm2. Similar 

results were obtained using the HZETRN deterministic transport code in a simple two-dimensional slab geometry, as 

shown in the Appendix.

The usual atomic number dependence of shielding mass effectiveness was observed. For example, using the July 

2000 event Band spectrum, the shielding mass, measured along the sphere radius, needed to reduce the event

ionizing dose to 1 cGy or less in the concentric sphere configuration is 30 g/cm2 polyethylene, 37 g/cm2 carbon, 

40 g/cm2 aluminum, and 43 g/cm2 titanium. Using the Exponential July 2000 event spectrum, the shielding mass 

needed to reduce the event ionizing dose to 1 cGy or less is 22 g/cm2 polyethylene, 25 g/cm2 carbon, 29 g/cm2 

aluminum, and 32 g/cm2 titanium.

For particle kinetic energies >50 MeV, proton star density displayed a very different dose depth distribution than 

did neutron and pion star density. Proton star density decreased rapidly with increasing shielding mass and was often 

overtaken by neutron star density between 10 and 100 g/cm2

. Pion and neutron star density was nearly constant as
20

shielding mass increased, typically exhibiting a shallow maximum near 10 g/cm2

. In nearly all cases, the Exponential

spectral form produced no pion stars at all – a result expected from the energetic threshold for pion production and 

the very small number of primary protons above that kinetic energy in the Exponential spectra. The Band and Exponential spectral forms produced comparable secondary neutron yields and plots of star density vs. shielding mass.

Calculation of the >50 MeV proton event fluence at various shielding mass values using the corresponding proton

star density and the proton inelastic interaction length allowed estimation of SPE SEU counts for three spacecraft 

that are in reasonable agreement with the observed in-flight SPE SEU counts, thus at least partially confirming the 

validity of the FLUKA-based modeling process.

7. References

1

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the radiation environment design specifications for NASA's Constellation Program. Paper presented at: American 

Geophysical Union, Fall Meeting 2007; December 10, 2007; San Francisco, Calif. Available at:

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2

Reames DV. Solar energetic particle variations. Adv Space Res. 2004;34:381–390.

. Accessed August 31, 2010.

3

Burrell MO, Wright JJ, Watts JW. A Preliminary Report on Energetic Space Radiation and Dose Rate Analysis.

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solar cosmic ray events. In: Solar Proton Manual. Washington, D.C.: NASA Headquarters; 1963. NASA-TRR-169. 

c)Webber WR. An Evaluation of the Radiation Hazard Due to Solar-Particle Events. Seattle, Wash: AeroSpace 

Division, the Boeing Company; 1963. Boeing Report D2-90469.

4

Tylka AJ, Dietrich WF. Proton spectra in ground-level enhanced (GLE) solar particle events. Paper presented at: 

Committee on Space Research (COSPAR); July 2008; Montreal, Canada. Paper D23-0003-08.

5

Atwell W, Tylka A, Dietrich W, Badavi FF. Radiation exposure estimates for extremely large solar proton events.

Paper presented at: Committee on Space Research (COSPAR); July 2008; Montreal, Canada. Paper F25-0027-08.

6

Atwell W, Tylka A, Dietrich W. Radiation exposures form several ground level enhancements during the 23rd Solar 

cycle. Paper presented at: AIAA SPACE 2009 Conference; September 14-17, 2009; Pasadena, Calif. Paper AIAA2009-6597.

7

Battistoni G, Muraro S, Sala PR, et al. The FLUKA code: description and benchmarking, In: Albrow M, Raja R, 

eds. Proceedings of the Hadronic Shower Simulation Workshop 2006 Fermilab. September 6-8, 2006., Am Inst Phys

Conf Proc. 2007;896;31-49.

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Ferrari A, Sala PR, Fasso A, Ranft J. FLUKA: a multi-particle transport code. Available at: 

http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-r-773.pdf. Accessed September 1, 2010.

9

The official FLUKA site. Available at: http://www.fluka.org/fluka.php. Accessed September 1, 2010.

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11University of Delaware Bartol Research Institute Neutron Monitor Program. Available at: 

http://neutronm.bartol.udel.edu/. Accessed September 1, 2010.

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Trans Plasma Sci. 2000;28(6);2007-2016.
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13Dyer CS, Hunter K, Clucas S, Campbell A. Observation of the solar particle events of October and November 

2003 from CREDO and MPTB. IEEE Trans Nucl. Sci. 2004:51(6)3388–3393.

14Bedingfield KL, Leach RD, and Alexander MB, eds. Spacecraft System Failures and Anomalies Attributed to the 

Natural Space Environment. Huntsville, Ala: NASA Marshall Space Flight Center; 1993. NASA Reference 

Publication 1390.

15Tylka AJ, Dietrich WF, Boberg PR, Smith EC, Adams JH Jr. Single event upsets caused by solar energetic heavy 

ions. IEEE Trans Nucl Sci. 1996:43(6):2758-2766.

16Parodi K, Paganetti H, Cascio E, et al. PET/CT imaging for treatment verification after proton therapy: a study

with plastic phantoms and metallic implants. Med Phys. 2007:34:419-435.

17Autischer M, Beck P, Kindl P, Latocha M, Rollet S. Calibration and background measurements with a tissue 

equivalent proportional counter. Radiat Prot Dosim. 2007:125(1-4):429-432. Available at: 

http://rpd.oxfordjournals.org/content/125/1-4/429.full. Accessed September 1, 2010.

18Beck P, Wind M, Rollet S, et al. Microdosimetric GEANT4 and FLUKA Monte Carlo simulations and measurements of heavy ion irradiation of silicon and tissue. IEEE Trans Nucl Sci. 2006:53:3701-3706.

19FLUKA Online Manual. Available at: http://www.fluka.org/fluka.php?id=man_onl. Accessed September 1, 2010.

20Wilson JW, Cucinotta FA, Shinn JL, Simonsen LC. Overview of HZETRN and BRNTRN space radiation 

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21Barak J, Reed, RA, LaBel, KA. On the figure of merit model for SEU rate calculations. IEEE Trans Nucl Sci.

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satellite. IEEE Trans Nucl Sci. 2002;49(3);1345-1350.

25Hansen DL, Jobe K, Whittington J, Shoga M, Sunderland DA. Correlation of Prediction to on-orbit SEU 

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22

Appendix

Figures App-1a and -1b, below, show the results of two-dimensional (slab target) HZETRN dose depth calculations for the band and exponential forms of the July 14, 2000 SPE over the shielding mass range 1 to 100 g/cm2

. As 

was observed for the FLUKA three-dimensional (spherical shell target) calculations, the Band and Exponential spectra 

produce nearly the same dose over the 1 to 10 g/cm2 shielding mass range while the Band dose exceeds the

Exponential dose over the 10 to 100 g/cm2 shielding mass range.

Figures App-1c and -1d compare the three-dimensional FLUKA and two-dimensional HZETRN dose-depth results for the July 14, 2000 Band spectra. As expected, the two-dimensional HZETRN and three-dimensional FLUKA

results are similar at low shielding mass and diverge at higher shielding mass where the three-dimensional effects of 

the shielding mass distribution function become more important.

Figure App-1. In 1a and 1b above, HZETRN two-dimensional calculations of dose as a function of depth are 

compared for the Band and Exponential forms of the event spectra; in 1c and 1d above, three-dimensional FLUKA 

and two-dimensional HZETRN calculations of dose vs. depth are compared.
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Spacecraft Solar Particle Event (SPE) Shielding: Shielding Effectiveness as a Function of 

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13. ABSTRACT (Maximum 200 words)

In this paper, we report the results of modeling and simulation studies in which the radiation transport code FLUKA (FLUktuierende 

KAskade) is used to determine the changes in total ionizing dose (TID) and single-event effect (SEE) environments behind aluminum, 

polyethylene, carbon, and titanium shielding masses when the assumed form (ie, Band or Exponential) of the solar particle event 

(SPE) kinetic energy spectra is changed. FLUKA simulations have fully three spatial dimensions with an isotropic particle flux 

incident on a concentric spherical shell shielding mass and detector structure. The effects are reported of both energetic primary 

protons penetrating the shield mass and secondary particle showers caused by energetic primary protons colliding with shielding mass 

nuclei. SPE heavy ion spectra are not addressed. Our results, in agreement with previous studies, show that use of the Exponential 

form of the event spectra can seriously underestimate spacecraft SPE TID and single-event environments in some, but not all, 

shielding mass cases.

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