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NASA - Internship Final Report 


Development of a Real Time Internal Charging Tool for 

Geosynchronous Orbit 


Nathaniel A. Posey 1 

Columbia University, New York, NY, 10027 
and 

Joseph I. Minow 2 

NASA- Marshal Space Flight Center, Huntsville, AL, 35812 


The high-energy electron fluxes encountered by satellites in geosynchronous orbit pose a 
serious threat to onboard instrumentation and other circuitry. A substantial build-up of 
charge within a satellite’s insulators can lead to electric fields in excess of the breakdown 
strength, which can result in destructive electrostatic discharges. The software tool we’ve 
developed uses data on the plasma environment taken from NOAA’s GOES-13 satellite to 
track the resulting electric field strength within a material of arbitrary depth and 
conductivity and allows us to monitor the risk of material failure in real time. The tool also 
utilizes a transport algorithm to simulate the effects of shielding on the dielectric. Data on 
the plasma environment and the resulting electric fields are logged to allow for playback at a 
variable frame rate. 


E 

0 

P 

K 

Zo 

Jr 

Jc 

o 

°dark 

kp 

dy 

dt 

X 

n 

Rex 

z 


Nomenclature 

electric field (V/m) OR particle energy (MeV) 

electric potential (V) 

charge density (C/m 3 ) 

dielectric constant 

permittivity of free space (F/m) 

radiation current density (A/m 2 ) 

conduction current density (A/m 2 ) 

conductivity (S/m) OR surface charge density (C/m 2 ) 

conductivity in the absence of radiation (S/m) 

radiation dose coefficient 

radiation dose rate (# particles-s" 1 ) 
depth (m) 

number transmission coefficient of electrons 
extrapolated range (m) 
atomic number 


I. Introduction 

S pacecraft charging and its effects on internal systems have been of great interest to the space physics community 
for the past several decades. Electrostatic Discharge (ESD) arcing as a result of charging has led to dozens of 
documented anomalies in satellite electrical subsystems, which have spurred efforts for a more detailed 
understanding of this phenomenon. Of particular interest is the process of internal charging, in which high-energy 
electrons (in the MeV range) penetrate an insulator or other dielectric material and deposit their charge and energy. 
The accumulation of charge at depth due to the high energy fluxes encountered in geosynchronous orbits can lead to 
electric fields in excess of the breakdown strength, creating a serious risk of failure within dielectric materials. 


1 Summer Intern, Natural Environments Branch, EV44, MSFC, Columbia University. 

2 AST Flight Vehicle Space Environments, Natural Environments Branch, EV44, MSFC. 


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This paper details the development of the Real Time Geosynchronous Internal Charging Tool, software which 
provides continuously updated data on the electric field intensity along a depth profile for a dielectric material across 
a wide range of conductivities. The tool receives real time input on the plasma and radiation environment from the 
National Oceanic and Atmospheric Administration’s (NOAA) Geostationary Operational Environmental Satellite 13 
(GOES-13), a weather satellite currently orbiting at a longitude of 75° west. The tool processes this data to form 
complete electron flux energy spectra. This environmental data is used as input for a modified version of the 
NUMIT (for “numerical integration”) internal charging simulation tool, an existing model which remains widely 
used within the U.S. aerospace community. To simulate the effects of shielding, the tool utilizes an empirically 
derived transport algorithm developed by Tabata and colleagues 5 . Finally, the tool automatically logs data on the 
resultant electric field conditions, which can be plotted in real time or played back at an accelerated frame rate. 

Section II details the analytical models used by the tool for the computation of the electric field within the 
dielectric, the deposition of energy from the incident electron current, and the current and energy losses due to 
shielding. Part E of Section II explains the computation of a complete electron flux energy spectrum from the 
GOES- 13 data. 

Section III explains the content and form of the tool’s output and describes its basic functionality. 

Section IV provides brief insight into the ways in which this tool might be implemented or further enhanced for 
future applications. 


II. Internal Charging Physics and Models 

A. Internal Charging Physics 

What follows is an overview of the internal charging model on which the NUMIT tool is based. For a more 
thorough derivation of this model, see Ref. 4. The interaction of injected electrons with molecules in the insulator, 
while intrinsically a microscopic phenomenon, can be reasonably modeled using bulk charging equations by 
introducing the concept of radiation-induced conductivity (RIC) 4 . This RIC value has both temporal and spatial 
dependence and is derived from the radiation dose rate throughout the material’s depth profile. From this 
macroscopic interpretation of charge transport, the electric field at any depth within the material can be succinctly 
given by the Poisson equation and the continuity of charge as follows: 

V • E = -V 2 0 = P/ 

Aa, 

— = -V • (J R +J C ) 
dt y r cj 

where E gives the electric field, ® the electric potential, p the charge density, J R the radiation (electron) current 
density, J c the conduction current density, K the dielectric constant, and e 0 the permittivity of free space. Due to the 
relatively negligible penetrating power of ions in the plasma environment, only electron currents are considered for 
the purposes of the model. From Ohm’s Law, we have that the conduction current J c will be given by 

J c =oE = \r dark + k p (£)" ] E (3) 

where a dark gives the intrinsic conductivity (in the absence of radiation) and ^ the radiation dose rate. The 

parameters k p and a depend on the energy distribution of electron trapping states in the insulating material. These 
two parameters are difficult to determine without costly experimentation, so conservative estimates are often made 
for a range of substances. 

B. NUMIT Internal Charging Model 

The NUMIT code implemented in this tool applies the macroscopic model outlined in Section II. A, which 
solves the equations in one dimension through finite difference approximation for 150 discrete spatial steps within 
the insulating material. The dose rate depth profile is computed from the electron energy flux spectra using the 
EDEPOS transport code 8 , which is based on an algorithm derived from Monte Carlo simulations. The dose rate 
computed by this subroutine is used to compute the time-dependent RIC value at each discrete depth within the 
insulating material. The charge density at each step is then modified by the surrounding differential current 
densities, which are multiplied by a constant time step of 1 second: 


( 1 ) 

( 2 ) 


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ApAx = ~(AJ c +AJ R )At (4) 

The updated charge density is then used to compute the resulting electric field using Gauss’ Law, with the charge in 
each layer treated as a uniform distribution of infinite extent in the y-z plane. 


A/= (/ r +/ c )^i)-(/ R + /c)(^) 

A/At = ApAx = a 

p 

V ■ E = — 

£ 


(5-8) 


Figure 1. NUMIT one-dimensional Charging Model 


While the depth of the material may be arbitrarily specified by the user, the NUMIT code as implemented always 
subdivides the insulator into 150 equally sized bins to ensure that computational runtime limits are not exceeded. 


C. DEPOSI Radiation Model 

The radiation current due to the electron flux was computed using the DEPOSI algorithm, a modified version of 
Tabata’s algorithm 8 which was modified to calculate fast electron currents as well as dose rates under electron 
irradiation. For a more thorough outline of the algorithm, see Ref. 8. The algorithm was derived from a simple 
model originally developed by Kobetich and Katz 2 given by 


D(x) = - 


d{E(x)rj(x)} 

dx 


(9) 


where D gives the absorbed dose per unit fluence at the depth x, E the average energy of transmitted electrons, and r\ 
the number transmission coefficient of electrons. The average energy is expressed by the following relation: 

E(x) = £ 0 exp (-a x 5 - a 2 s 1+a 3 ) (10) 


where E 0 gives the initial kinetic energy of the electrons, while the parameters ai_ 3 depend on both the incident 
energy E 0 and the atomic number of the insulator Z. Here, s represents the ratio of the depth x to the so-called 
extrapolated range R eX5 a value which is given by a semi-empirical formula 7 . The number transmission coefficient of 
electrons is given by 


T](x) = exp(—asP) ( 11 ) 

where 

« = ( 1 - 1 //" /? 02 ) 

with p a parameter also dependent on E 0 and Z. As per the original model of Kobetich and Katz, the effects of 
backscattering of incident electrons and the transport of energy by bremsstrahlung photons are neglected, but these 
effects are approximated by way of a normalization factor f given by 

/=l-/ h -/r (13) 

where f b and f r give the average fractions of incident energies backscattered from the incident surface and of the 
incident energy deposited via radiative processes at the depths corresponding to the bremsstrahlung tail, 
respectively. Thus, the final form of Eq. 9 is given by 

D(x) = (/£o/r cx ){ai + a 2 ( 1 + a 3 )s a 3 + exp (— a x 5 — a 2 s 1+a 3 — as (14) 


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For details on the empirical determination of the above parameters, please consult Ref. 8. 

D. Shielding Algorithm 

The tool utilizes a simple transport algorithm to simulate the effects of shielding on the incoming flux. This 
algorithm was taken from Ref. 1, while the treatment of analytic fits was pulled from Ref. 5. Due to the nature of the 
flux data received from the NOAA GOES- 13 satellite, all electrons are assumed to be at normal incidence to the 
surface of the shield. The formula for the extrapolated range is given as 


_ 0.2335 A w pn(l+1.78*10 _4 Z'T) 
ex ~ Z 1 - 209 L 1.78*10 -4 Z 


(0.9891— 3.01*10 _4 Z)'T ] 

1 + (1.468-1.18*10 _2 Z)7 1 - 232 / z0109 J 


(15) 


where A w gives the atomic weight, Z the atomic number, and T the ratio of the electron’s energy to its rest energy. 
The average energy of an electron transmitted through a shield of thickness d is given by Ref. 8: 


Etrans = E 0 exp(-D(b 1 + b 2 D b =>)) 

where D is given as the ratio of the shielding thickness to the extrapolated range, R e , 

d 

D ~T7 r 


(16) 

(17) 


while bi_ 3 are parameters with dependence on both the incident energy E 0 and the atomic number Z. In addition to 
depositing energy in the shielding, a mono -energetic beam of electrons will also deposit a fraction of its charge. This 
loss of current is expressed through a transmission coefficient given as 


CURR = 


l+ e (s+2)D-s 


(18) 


where s is a parameter dependent on the incident energy E 0 . For the purposes of the real time charging tool, the 
electron energy flux spectra was subdivided into 100,000 bins corresponding to mono-energetic electron beams. 
Each bin was then downshifted in energy and current density as per the algorithm above and then reorganized into 
spectra readable by the NUMIT charging model. 


E. Electron Flux Environment Model 

The primary input to the 
real time charging model is 
the electron flux spectra, the 
distribution of electron flux 
with respect to energy which 
is incident on the GOES-13’s 
detectors. Data taken by the 
GOES- 13 satellite on the 
electron flux is provided by 
NOAA in the form of five 
minute time-averaged fluxes 
(in units of # e7cm 2 -s-sr) for 
two specified energy 
thresholds: the flux of 
electrons with energies in 
excess of 0.8 MeV, and the 
flux of electrons in excess of 
2.0 MeV. 



Universal Time 


Updated 20 13 Jul 15 20:11:02 UTC 

Figure 2. Data from the GOES-13 satellite 


NGAA/SWPC Bo i 


Jul 1 6 

ilder, CO USA 


To complete the electron flux spectra for use in the charging model, we assume a power law distribution of 
electron flux density with respect to energy. The density function is given as 

f(E ) = CE k (19) 


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NASA - Internship Final Report 


where the flux of particles in excess of an energy E) is given by 

n CO 

]{E > E x ) = f(E)dE (20) 

J E i 

The two parameters C and k are determined from the simple system of equations we receive by applying this 
distribution to the observed fluxes as follows: 


]{E > 0.8 MeV ) 
]{E > 2.0 MeV) 


CE k dE 


f 

J 0.i 

r. OO 

I CE k 
J2.0 


( 21 ) 

( 22 ) 


With these two parameters, the environment model calculates the electron flux for eighteen specified energy bins 
which span from .05 MeV to 25.8 MeV. For example, the flux of particles with energies between Ej and E 2 is given 
as 

CE k dE (23) 

The flux of each of these 1 8 bins is then assigned to a mono -energetic beam whose energy is given as the weighted 
average of the bin’s energies. 


K&i <E<E 2 )=\ 

J E 


III. Output 


A. Format 

The charging model is designed to run continuously, extracting data on a five-minute loop. For each set of 
electron flux values taken from GOES- 13, the charging model outlined in part II runs through 50 complete 
iterations, each with a different value for the insulator’s dark conductivity, a dark . These values are taken at equal 
intervals on a logarithmic scale, the bounds of which are specified by the user. The results from these 50 iterations 
are displayed in a 2-dimensional color plot, where the depth is given in cm on the x-axis, the log of the conductivity 
in S/m along the y-axis, and the log of the electric field strength in V/m by the color. In the case that shielding was 
applied to the insulator, the tool provides side-by-side outputs of these color plots, with the left plot corresponding to 
the shielded insulator and the right plot giving the unshielded insulator for the purpose of comparison. 


GEO Internal Charging Model using GOES-13 e- Flux Data 
Data Extracted: 2013 07 13 0510 GMT 



0.0 0.01 0.02 0.03 0.04 0.06 0.07 0.08 0.09 0.1 

Depth (cm) 


0.0 0.01 0.02 0.03 0.04 0.06 0.07 0.08 0.09 

Depth (cm) 


(a) Shielded with 6.90E-2 g/cm 2 of A1 

Figure 3. Output from the real time charging tool. 


(b) Unshielded 


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Read from left to right at a specific y-value, the plot allows the user to view the electric field strength throughout 
the depth of the insulator of uniform conductivity. Read from top to bottom for a specific x-value, the plot shows the 
effect of varying conductivities on the electric field strength at a particular depth within an insulator under the same 
environmental conditions. The plot is color coded to roughly reflect the relative risk of breakdown within the 
dielectric, with a field strength of 10 1 - 10 4 (represented by a gradient from blue to green) corresponding to safe or 
tolerable levels, while the range from 10 5 - 10 8 (represented by a gradient from yellow to dark red) indicates a 
substantial risk of breakdown, depending of course upon the intrinsic electrical properties of the insulator. 

B. Data Playback 

While the real time charging tool outputs the color plots to the screen as they are updated by default, the tool also 
includes the option of playing back previous output at an accelerated frame rate. The tool incorporates a simple 
LINUX GUI which enables the user to specify a range of time for which data has been taken as well as the rate at 
which the data is to be displayed. The intent of course is to enable the user to study the effects of geomagnetic 
storms or other sorts of environmental events on the material in detail. 

C. Time Series 

The tool also creates twenty- four hour time plots of the maximum electric field strength measured over the entire 
depth profile for a specific conductivity. These plots allow the user to quickly scan data for a given day in order to 
identify any events of interest. 


GEO Internal Charging Model using GOES-13 e- Flux Data 
E-field time series for conductivity = 1.58e-14 S/m 



Figure 4. Time series of maximum electric field strength (V/m) vs. time (hhmm) for a conductivity of 1.58E-14 S/m 


IV. Conclusion 

This tool gives users a succinct way to visualize the charging effects of the real time plasma environment on 
satellites within geosynchronous orbit. The tool’s universality allows it to be tailored to accommodate a wide range 
of geometries and design parameters. It can be easily modified to read historical data files for the study of past 
charging events, and its output can be coupled to any number of additional tools or models designed for the study of 
internal charging phenomena, including for example routines to model the effects of electrostatic discharge within 
an insulator coupled to a spacecraft’s electrical subsystems. Such model development remains a vital part in refining 
the design of satellite and other spacecraft shielding to protect internal instrumentation and other critical systems in 
the most efficient manner possible. 


Acknowledgments 

Nathaniel Posey wishes to thank the Universities Space Research Association for its financing of the Marshall 
Space Flight Center Internship program. GOES- 13 electron data was provided courtesy of the Space Weather 
Prediction Center, Boulder, CO, National Oceanic and Atmospheric Administration (NOAA), US Dept, of 
Commerce. 


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References 

^rederickson, A. R., and Bell, J. T. “Analytic Approximation for Charge Current and Deposition by 0.1 to 100 
MeV Electrons in Thick Slabs,” IEEE Transactions on Nuclear Science , Vol. 41, June 1994, p. 1910. 

2 Kobetich, E.J. and Katz, R., “Energy Deposition by Electron Beams and 5 Rays,” Physics Review , Vol. 170, June 
1968, p.391-396. 

3 Minow, Joseph I., “Modeling Electrostatic Fields Generated by Internal Charging Materials in Space Radiation 
Environments,” NASA, Marshall Space Flight Center, Huntsville, AL, 2010 

4 Sessler, Gerhard M., Figueiredo, Mariangela T. and Ferreira, Guilherme F. Leal, “Models of Charge Transport in 
Electron-Beam Irradiated Insulators,” 11 th IEE International Symposium on Electrets, The Institute of Electrical and 
Electronics Engineers (IEEE), Melbourne, Australia, 2002, pp. 192-202. 

5 Tabata, T., and Ito, R., “An Empirical Relation for the Transmission Coefficient of Electrons under Oblique 
Incidence.” Nuclear Instruments and Methods, Vol. 136, July 1976, p. 533. 

6 Tabata, T., and Ito, R., “A Generalized Empirical Equation for the Transmission Coefficient of Electrons.” Nuclear 
Instruments and Methods , Vol. 127, August 1975, p. 429. 

7 Tabata, T., Ito, R., and Okabe, S., “Generalized Semiempirical Equations for the Extrapolated Range of Electrons.” 
Nuclear Instruments & Methods, Vol. 103, August 1972, p. 85-91. 

8 Tabata, T., Ito, R., and Tsukui, S, “Semiempirical Algorithms for Dose Evaluation in Electron-Beam Processing,” 
Radiation Physics and Chemistry, Vol. 35, 1990, pg. 821. 


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