VALIDATION OF NASCAP-2K SPACECRAFT-ENVIRONMENT
Science Applications International Corporation
10260 Campus Point Dr., M.S. A1
San Diego, CA, 92121
I. G Mikellides
Science Applications International Corporation
Jacobs Sverdrup Technology
Air Force Research Laboratory /VSBS
NASA Marshall Space Flight Center
The recently released Nascap-2k, version 2.0, three-dimensional computer code models
interactions between spacecraft surfaces and low-earth-orbit, geosynchronous, auroral, and
interplanetary plasma environments. It replaces the earlier three-dimensional spacecraft
interactions codes NASCAP/GEO, NASCAP/LEO, POLAR, and DynaPAC. Nascap-2k has
improved numeric techniques, a modem user interface, and a simple, interactive satellite surface
definition module (Object ToolKit).
We establish the accuracy of Nascap-2k both by comparing computed currents and potentials
with analytic results and by comparing Nascap-2k results with published calculations using the
earlier codes. Nascap-2k predicts Langmuir-Blodgett or Parker-Murphy current collection for a
nearly spherical (100 surfaces) satellite in a short Debye length plasma depending on the absence
or presence of a magnetic field. A low fidelity (in geometry and time) Nascap-2k
geosynchronous charging calculation gives the same results as the corresponding low fidelity
NASCAP/GEO calculation. A high fidelity calculation (using the Nascap-2k improved geometry
and time stepping capabilities) gives higher potentials, which are more consistent with typical
observations. Nascap-2k predicts the same current as a function of applied potential as was
observed and calculated by NASCAP/LEO for the SPEAR I rocket with a bipolar sheath. A
Nascap-2k DMSP charging calculation gives results similar to those obtained using POLAR and
consistent with observation.
The three-dimensional spacecraft plasma environment interactions computer code Nascap-
2k 1 ’ 2 ’ 3 ’ 4 version 2.0 has recently been released. Nascap-2k computes a wide variety of plasma
phenomena. These include spacecraft charging in geosynchronous, interplanetary, auroral, and
low-earth-orbit plasmas, volume potentials, particle trajectories, and resulting variations in
plasma density. The user interface is designed so that the non-expert user can do common
problems and the expert can tackle questions that have not been previously contemplated.
Nascap-2k takes advantage of improvements in computer technology, advances in understanding
of the phenomena, and enhanced charging algorithms to improve upon the earlier three-
dimensional computer codes. (NASCAP/GEO, 5 ' 6 ’ 7 ’ 8 NASCAP/LEO, 9, 10, n> 12, 13 POLAR, 14 and
DynaPAC 15, 16, 17 ). While each code works well for the range of problems for which it was
designed, by today’s standards, these codes are complicated to use and require expertise to use
properly. In addition NASCAP/GEO and POLAR are limited with respect to geometry. Nascap-
2k builds on our experience with these codes and is designed to address their limitations. It
incorporates all of the DynaPAC computational modules.
Previous papers have described Nascap-2k, x ’ 2 ’ 3 ’ 4 its algorithms, and the new numeric
techniques used. This paper focuses on comparison of Nascap-2k results with analytic solutions
and with the results of NASCAP/GEO, NASCAP/LEO, and POLAR calculations.
Current Collection by a Sphere
We first validate that Nascap-2k reproduces analytic results for current collection by a sphere
in a dense plasma. Nascap-2k incorporates the algorithms developed for NASCAP/LEO to
model charge density and current collection in plasmas with Debye lengths short with respect to
the mesh size of the calculational grid. 11, 14, 18, 19
Nascap-2k provides a number of charge density models to use when solving Poisson’s
equation to obtain volume potentials. These include both analytic functions of the potential (and
local electric field) and various combinations of tracked particle densities and analytic functions
(such as the sum of a tracked ion density and a barometric function for electrons). In a dense
plasma, when the spacecraft velocity and Earth’s magnetic field have minimal effect on the
charge density within the sheath, the non-linear analytic formula developed for NASCAP/LEO 11,
18 is generally appropriate. This analytic function of the potential smoothly interpolates between
linear Debye screening at low potentials and the charge density of a single accelerated and
converging species at high potentials.
p/e 0 =-(<j>/^,)
C (<|>, E) = min (( R sh /r f , 3 .545 |(t>/0 nl f' 2 )
(R sh /r) 2 =2.29|Ek nl /0 nl | I ' 262 |e nl /C 5 ° 9
>V= max(/.| )cbyc / g, D 2 )
0 nl =0(^,g/^ ebye ) 2/3
where the symbols refer to the local potential, § , the local electric field, E, the plasma
temperature, 0, the debye length, k t | c b y e, the local mesh spacing, D, and the local reduction in
plasma density due to wake effects (neutral model), g.
Generally the charge density is multiplied by a convergence factor, C, which is a function of
the local potential and electric field. This factor accounts for the increase in charge density as
charged particles from a large area are attracted to a small region. The function was developed to
fit the results of Langmuir and Blodgett 20 for current collection by a sphere.
Current is computed by tracking macroparticles from a sheath edge. The sheath is the region
from which the repelled species is excluded. Because the sheath absorbs the attracted species, the
density of the attracted particles at the sheath edge is one-half the ambient plasma density. By
quasi-neutrality, the density of the repelled species is the same, giving a sheath edge potential of
4> s =±01n(n/n o ) = ±01n(O.5).
The charge stabilization algorithm, 14 ’ 19 which makes solution of Poisson’s equation possible
in these dense plasmas, limits the potential drop in a single volume element. In the lowest
potential regions of the computational space, this leads to computed potentials dropping off more
slowly than the real potentials. This would lead to an error in the physical location of the sheath
edge. To account for this, the calculation places the sheath edge at a potential that depends on the
mesh size of the grid within which the sheath falls.
The current density through the sheath is the one-sided plasma thermal current, J = en I — .
Langmuir and Blodgett 20 analytically solved for the current collected by a biased sphere.
Figure 1 shows the current collected by a sphere as a 0.1 m radius function of density as
computed using Langmuir and Blodgett’s results and by Nascap-2k. Figure 2 shows the current
collected as a function of potential. Nascap-2k reproduces the Langmuir-Blodgett results.
In the presence of a significant magnetic field, the collected current is reduced. Parker and
Murphy 21 developed an upper limit on the amount of current that can be collected in the limit of
zero temperature and cylindrical symmetry. They accounted for the difficulty of attracting
current into the sheath across magnetic field lines. Nascap-2k includes the magnetic field in
1.E+07 1.E+08 1.E+09 1.E+10 1.E+11 1.E+12
Density (m' 3 )
Figure 1. Electron current collected by a
100 V sphere from a 0.2 eV plasma, for
no magnetic field.
Figure 2. Electron current collected by a
sphere from a 1011 m-3, 0.2 eV plasma.
Figure 3. Electron current collected by a 100 V sphere from a 0.2 eV plasma. Densities are in
Table 1. 90% worst case environment for geosynchronous orbits as defined in Reference 24.
Density (cm 3 )
current calculations in two ways. First, the magnetic field is included in the computation of
macroparticle trajectories. With high magnetic fields, some of the particle trajectories that start at
the sheath edge leave the sheath and cross the problem boundaries and other particles circle within
the sheath and are never collected. Physically, these trapped particles provide an increased charge
density that shrinks the sheath, thus reducing the current. However, this effect is not included in the
analytic non-linear charge density model. The second way the magnetic field enters Nascap-2k
calculations is when the Larmor radius exceeds the mesh size of the outer most grid by a factor of
two, Nascap-2k reduces the sheath current by the cosine of the angle between the magnetic and
electric fields. This accounts for the reduction of current to the sheath across magnetic field lines.
Figure 3 compares the current collected by a 0.1 m radius sphere as a function of magnetic
field for a range of densities. Figure 2 shows the current collected as a function of sphere
potential for a 0.4 Gauss magnetic field. The 10 12 m 3 calculations were done with a small grid
and Nascap-2k computed the sheath current in the same manner as in the absence of a magnetic
field. In all the other calculations, the cross field sheath current was reduced. The Nascap-2k
calculations are in agreement with the Parker-Murphy limits.
Charging in a Geosynchronous Plasma 22
To validate Nascap-2k for geosynchronous charging calculations, we compare potentials
computed using Nascap-2k with those computed with the industry standard NASCAP/GEO. To
further illustrate the differences, we also compare the results with those obtained using the SEE
Interactive Spacecraft Charging Handbook. 4, 23 The SEE Handbook is an interactive spacecraft
charging code for the non-expert. It computes spacecraft surface charging for geosynchronous
and auroral zone spacecraft along with internal charging due to the deposition of high-energy
Avery simple spacecraft geometry, illustrated in Figure , was created to facilitate the
comparison. The orientation of the solar arrays is appropriate to a spacecraft at 6 am local time.
The proportions of the spacecraft were chosen to fit neatly in the NASCAP/GEO grid structure.
The proportions of actual spacecraft almost always must be distorted in order to fit within the
17 x 17 x 33 grid. The SEE Handbook and Nascap-2k do not have this constraint.
The calculations use the environment recommended in Reference 24 (see Table 1) for initial
modeling during the spacecraft design process. The spacecraft charges for 15 minutes, which is
longer than any spacecraft would be exposed to such a severe environment.
The sun is taken to be incident on the spacecraft from the (0.92, 0.39, -0.02) direction. This
is appropriate to a spacecraft in geosynchronous orbit at 0 longitude at 6 am GMT on January 1,
2000, consistent with the geometry model.
An important part of defining any spacecraft charging calculation is the determination of the
appropriate values to use for the material properties for each surface. NASCAP/GEO, the SEE
Handbook, and Nascap-2k all use the same fourteen material properties and incorporate them
into the calculation in the same way. The focus here is in understanding variations between the
results given by these codes. Therefore, the specific values are not important as long as they are
consistent. We use the Nascap-2k provided default values for all the materials except the non-
conducting paint on the antenna. For these surfaces, the values for Npaint 5 provided as a default
material of NASCAP/GEO are used.
NASCAP/GEO calculations are done within a nested grid structure, with the innermost main
grid 17 x 17 x 33 units in size. With the exception of booms that can extend beyond the
] Teflon blankets [most of body] I I Non-conducting paint [top antenna]
] OSR [1/3] of side I I Graphite [antennas]
| Kapton [booms and solar array back]
Figure 4. Illustrative spacecraft used for comparison of Nascap-2k , NASCAP/GEO, and
SEE Interactive Spacecraft Charging Handbook.
main grid, the complete object must fit within this main grid. The object is made up of cubes,
plates, wedges, tetrahedrons, and what is left of a cube after a tetrahedron is cut off of it. Booms
(long cylindrical projections of arbitrary radius) can also be used. Booms must extend along the
X, Y, or Z direction. Figure shows potentials on the best fidelity model that can be made. The
Optical Solar Reflector (OSR) area is one-half rather than two-thirds of the spacecraft side and a
cube represents the omni antenna. Actual spacecraft require even more distortion in order to fit
them within the grid.
The SEE Handbook sets the location of each of the components. The user has no control over
the distance between the various components or the zoning. This was done in order to insure
stability and reasonable calculation speed in the tool, which is intended for general
investigations. The orientation of the solar arrays is set by the longitude, date, and time.
Nascap-2k has a flexible geometric modeling capability. The user can control the size, shape,
and gridding of each component. The omni antenna is represented by an octagonal cylinder and
the side antennas are concave dishes.
The calculations were set up for 99 timesteps for a time period of 1000 seconds. The
timesteps were chosen in the way most natural for each code. The NASCAP/GEO calculation
uses geometrically growing timesteps starting with 1 second, with subsequent timesteps of 1.045
times the previous timestep. The SEE Handbook uses geometrically-distributed timesteps that
the user cannot control. For the Nascap-2k calculation, we used the default geometrically
distributed timesteps with a minimum of 0.1 seconds and a maximum of 60 seconds.
Table 2 compares the time required for an expert user to build a model and set up a
calculation. This does not include the time needed to determine the most reasonable parameters
for a specific problem. The determination of the appropriate material properties, geometry,
environment, and calculation parameters for an actual analysis is typically days to weeks. It takes
approximately as long to build a Nascap-2k model as to build a NASCAP/GEO model. However,
the model created has the actual geometry and the resolution required. Sometimes it is necessary
to build two NASCAP/GEO models at different resolutions in order to resolve questions.
The results of these sample calculations are summarized in Table 3. The potentials at 1000
seconds are shown in Figure 5 through Figure 7. The three codes give consistent results. The
least negative surfaces are the ends of the solar arrays. The shaded Teflon surfaces are the most
negative. All the surfaces that are more negative than the chassis are shaded insulators. In the
center of the sun-facing side of the spacecraft body, the Teflon is slightly positive with respect to
the chassis. This is most pronouced in the highest resolution Nascap-2k model. The sunlit
insulators on the body are near the chassis potential or positive with respect to the chassis.
With the exception of the solar arrays, the surface potentials computed by the three codes are
within approximately 35% of each other. The differences are primarily driven by the difference in
the chassis potential. At the ends of the solar arrays, where the conductivity of the coverglass and
barrier formation dominate the relative potentials, the differential potentials predicted by all three
codes are within 4%. At the inner edges of the solar arrays, where the geometry is complex, the
differentials vary by almost a factor of two between the minimum and the maximum.
There are two main contributions to differences between the solutions obtained using these
three codes: resolution of the geometry and time fidelity.
In order to obtain a stable solution, the variation of the potential within a single timestep is
limited. The algorithms for this limiting are complex and different for each of these codes. The
SEE Handbook uses a strong limiting algorithm in order to ensure that the results are stable for a
wide variety of problems. In NASCAP/GEO the limiting is partially under user control and
moderate limiting (the default) was used for this calculation. Nascap-2k uses much less
stabilization as the user is assumed to understand the code well enough to make the appropriate
adjustments in the number and distribution of the timesteps in order to obtain a stable solution. As
can be seen in Figure 8, the charging in Nascap-2k is faster than in either of the other two codes.
Table 2. Comparison of ease of use.
Time to set
Time for charging
calculation to complete on
800 MHz PC (min)
Table 3. Results of NASCAP/GEO, Nascap-2k, and SEE Handbook calculations, given in kV.
Absolute potentials (kV)
-8.2 to -13.1
-8.23 to -
-5.2 to -7.68
-7.5 to -
-8.3 to -10.3
none in model
-7.3 to -9.6
-3.6 to —5.7
-7.5 to -8.9
-11.5 to -14.4
-10.0 to -
-7.2 to -10.8
-7.9 to -
-10.0 to -12.2
Differential potentials (kV)
1.8 to -3.1
1.77 to -0.7
4.8 to 2.3
2.5 to -2.7
1.7 to -0.3
none in model
1.3 to -1.0
5 to 2.9
1.8 to -2.7
1.1 to -0.3
0.5 to -2.4
2 to -1.7
4.8 to 1.2
4.1 to -2
2 to -0.2
Figure 5. Results of spacecraft charging
calculation using NASCAP/GEO.
Figure 6. Results of spacecraft charging
calculation using SEE Handbook.
Figure 7. Results of spacecraft charging calculation using Nascap-2k.
The importance of geometric resolution can be illustrated by a comparison of the equilibrum
solution given by the three codes as shown in Table 4. In order to further understand the differences
due to geometry, a Nascap-2k object very similar to the SEE Handbook object was built and
Nascap-2k used to compute potentials on it. The maximum negative differential in the
NASCAP/GEO and Nascap-2k calculations are on the Kapton booms supporting the solar arrays.
The SEE Handbook model and the simplified Nascap-2k model do not have these booms and the
maximum negative differential potential is smaller than in the other cases. The chassis potentials
computed by all three codes are within 13% of each other. The maximum positive differential
potential is on the ends of the solar arrays. After 15 minutes of charging, all three codes give 5 kV
differential. At equilibrum, the results are within 30% of each other. Most of this difference appears
to be due to the differences in the geometric resolution, as the Nascap-2k calculation with the
simplified model gives a differential closer to the SEE Handbook than the full geometry model. In
all cases the maximum positive differential is about half of the chassis potential.
Nascap-2k improves our ability to model spacecraft surface charging, including improved
geometric resolution and time fidelity. The surface charging calculated by Nascap-2k using low
geometric and time fidelity is similar to the charging calculated by NASCAP/GEO.
0 200 400 600 800 1000
Figure 8. Comparison of chassis potential
versus charging time as computed by
NASCAP/GEO, SEE Handbook, and
Table 4. Comparison of equilibrum
Potentials and Currents in Dense Plasmas
A common issue on low-earth-orbit spacecraft is the prediction and control of interactions
between a spacecraft with high-voltage components (ranging from a few volts to kilovolts) and the
ionospheric environment. Since electron guns were first placed on rockets, the voltage on the main
body necessary to collect ionospheric electrons and complete the circuit has been the subject of
numerous theoretical and experimental studies. A large-scale effort to address such issues was the
Space Power Experiments Aboard Rockets (SPEAR) series of experiments. SPEAR-I 10 was
designed to measure whether or not the Earth’s magnetic field impedes electron collection,
SPEAR-II to test pulsed high-voltage components, and SPEAR-III 17 to test proposed spacecraft
grounding mechanisms. An analysis of the bipolar sheath using NASCAP/LEO (and POLAR) was
published 10 . We compare key published results with results computed using Nascap-2k.
The PATRAN object originally used for the NASCAP/LEO calculations and used here for a
Nascap-2k calculation is shown in Figure 9. It consists of gold-plated spheres mounted on
cylindrical nickel booms. The nickel booms are bushings constructed with grading rings that are
connected by resistors. The graded boom created a uniform potential gradient from the positively
biased sphere to payload ground. The booms are connected to a cylindrical support boom
covered with plastic. This boom is in turn connected to the main (aluminum) rocket body.
Nascap-2k requires a finer resolution computational grid around the spheres than that used in
the earlier NASCAP/LEO calculations. Five nested grids, with an outer grid resolution of 1.1 m
and an inner grid resolution of 0.06875 m, were used in the Nascap-2k calculations.
The calculations use a density of 5 x 10 10 m 3 , a temperature of 0.1 eV, and Oxygen ions. The
0.4 Gauss magnetic field is normal to the plane determined by the spheres and the axis of the
body. Nascap-2k provides a selection of space charge density models. As this is a steady-state
calculation in a short Debye length motionless plasma, the non-linear analytic space charge
density model, including convergence, is used.
The Nascap-2k and NASCAP/LEO potential calculations give similar results. Figure 10 and
Figure 1 1 show space potential contours as computed by the two codes for the same applied
potentials. The shapes and locations of the contour levels are the same. Figure 12 and Figure 13
show sample electron trajectories as computed by the two codes. The differences in the
trajectories are due to the differences in the potential solution (different grid structure and
interpolation functions) and the initial position of the trajectory.
Figure 9. PATRAN model of SPEAR I used
for the study of current collection in a
bipolar sheath in a low-earth-orbit
Figure 10. Nascap-2k potential contours
with one sphere at +46 kV with respect
to spacecraft ground and spacecraft
ground at -6 kV.
Figure 11. NASCAP/LEO potential
contours for one sphere at +46 kV with
respect to spacecraft ground and
spacecraft ground at -6 kV.10
Reproduced by permission of American
Figure 12. Sample electron trajectory in
potential contours shown in Figure 10.
Figure 13. Sample electron trajectory in
potential contours shown in
Figure 11 . 10 Reproduced by permission of
American Geophysical Union.
Table 5. Calculated Chassis Floating
Potential and Current as computed by
NASCAP/LEO and Nascap-2k.
Figure 14. The white dots show the electron sheath edge with 46 kV bias and -8.3 kV
chassis potential as computed by Nascap-2k.
Reference 10 compares NASCAP/LEO calculations with flight measurements of the spacecraft
ground floating potential and the current collected by the biased sphere as a function of the bias
value. The high energy cutoff in the ion flux spectra of the energetic particle detectors gives the
floating potential. The width of the peak limited the accuracy of the floating potential measurement
to within only an order of magnitude. The NASCAP/LEO results are near the center of the range.
The NASCAP/LEO and Nascap-2k calculated floating potentials and sphere and bushing
currents are given in Table . The Nascap-2k floating potentials are slightly less as the electron
currents computed by Nascap-2k are about one-third those computed by NASCAP/LEO for the
same potentials. This is a result of the reduction in sheath current due to the magnetic field, a
phenomenon that is not accounted for in NASCAP/LEO. Figure 14 shows the location of the
electron sheath. The magnetic field limits the plasma thermal current entering the sheath from the
top, significantly reducing the electron current.
The measured collected electron current as a function of applied bias can be fit by a line
I(mA) = 0.880 V(kV). The NASCAP/LEO results can be fit by a line I(mA) = 0.985 V(kV). The
Nascap-2k results can be fit by a line I(mA) = 0.886 V(kV). The Nascap-2k currents as a function of
floating potential agree with the flight measurements even better than the earlier NASCAP/LEO
Auroral Spacecraft Charging
To validate Nascap-2k for auroral charging, a comparison of results obtained using
Nascap-2k with those obtained using POLAR for the Defense Meteorological Satellite Program
spacecraft (DMSP) was done. 25 The DMSP spacecraft definition used for the calculations
described in Reference 25 was used for the Nascap-2k calculations.
Charging in eclipse from an initial potential of-10 V was computed for a period of 6 s with 45
timesteps varying from 0.0125 s to 0.2 s. In all cases, the charging currents were computed using
an analytic model for the electrons and tracked ions. The charge density can be computed either
analytically or self-consistently with the ion trajectories. In the first case, the ion currents are
computed by tracking macroparticles from the sheath and in the second case by tracking
macroparticles from the boundary of the computational space. The environment is described by a
low energy plasma and high energy auroral electrons. The low energy plasma is a Maxwellian. The
high energy electrons are described by a three component Fontheim 26 distribution.
Flux Font (E) =
2rc0max m e 0 max
V 0 max J
+ <gauss E exp
E gauss - E 'j
V ^ J
The plasma environment parameters used are shown in Table 6. The spacecraft is moving at
6565 m/s in the -X direction.
Calculations can be done for two different charge density models: the analytic charge density
model used in the SPEAR I calculation, and the self-consistent with ion trajectories model. We used
the second charge density model as it is more appropriate for moving spacecraft. Ions are tracked
from the problem boundaries and their spacecharge deposited on grid nodes at each step. Each ion is
tracked until it reaches the spacecraft or leaves the grid. After the tracking step, the charge density is
computed from the resulting ion density and a barometric description of the electrons.
Table 6. Parameters used to describe auroral environment.
3 x 10 9 m 3
Low energy plasma
High energy electrons
2.49 x 10 s m 3
1.5 x 10 4
3.5 x 10 4 eV
1.8 x 10 4 eY
Power law component
2x 10 10
1.6 x 10 6
Figure 15. Resulting surface potentials for
case with self-consistent charge density
computed by Nascap-2k.
Figure 16. Resulting space potentials for case
with self-consistent charge density
computed by Nascap-2k.
— - 587, sunshade wake
Figure 17. Time history of charging with self-
consistent charge density computed by
The results of the calculations are given in Figure 15 through Figure 17. With these choices
for parameters, the resulting chassis potential is -845 V and surface potentials vary between
-710 and -1025 V. The well-shadowed surfaces are the most negative. The chassis rapidly
charges to the -500 V level and continues to charge at about 60 V per second. With more
timesteps, the results might be slightly different.
These results can be compared with Figure 5 of Reference 25, shown here as Figure 18. The
Nascap-2k results do not have the, presumably spurious, hump at 0.2 sec, show more charging, and
are continuing to charge. The charging of the surfaces with respect to each other is not the same, but
as the selected surfaces are probably different, no firm conclusions can be drawn.
Another set of calculations in the same paper was also repeated. The thickness of Teflon was
set to 2.8 x 10 3 and all the Kapton was changed to Teflon. The results are shown in Figure 19
through Figure 21. These results can be compared with Figure 22 through Figure 24 obtained
from POLAR. Again, the results using the two codes are similar in character. The shaded
surfaces are the most negative and the ram-wake difference is small. Using POLAR, the wake
side charges more than the ram side. Using Nascap-2k, the ram side charges slightly more than
the wake side. The incident ions are focused onto the wake side of the spacecraft. The Nascap-2k
and POLAR auroral charging results have the same character.
Nascap-2k is already proving valuable with its improved geometric modeling and surface
electric field accuracy. It can be used to do the highest accuracy three-dimensional spacecraft-
plasma interaction calculations with a single, straight-forward user interface. Calculations of
interactions of a sphere with a surrounding plasma using Nascap-2k are consistent with analytic
solutions. Nascap-2k reproduces or improves upon results from NASCAP/GEO, NASCAP/LEO,
and POLAR for a selection of typical interactions calculations. Nascap-2k includes the limitation
of collected current due the magnetic field in low-earth-orbit problems and provides much
improved geometric and time fidelity in tenuous charging calculations.
Nascap-2k can be obtained from NASA’s SEE Program. Contact Jody Minor,
email@example.com or David Cooke firstname.lastname@example.org (Air Force users).
Figure 19. Resulting surface potentials
for case with all Teflon and self-
consistent charge density computed by
Figure 20. Resulting surface potentials
for case with all Teflon and self-
consistent charge density computed by
Figure 21. Time history of charging with
all Teflon and self-consistent charge
density computed by Nascap-2k.
Figure 22. Resulting surface potentials
using POLAR for Teflon only case
from Reference 25.
II. a . Ill i jS -l.OEltS ! : : 1.3 -3. Ill lira -2.5H3S
Figure 23. Resulting surface potentials
using POLAR for Teflon only case
from Reference 25.
Figure 24. Time history of surface
potentials using POLAR for Teflon
only case from Reference 25.
Nascap-2k is jointly funded by the Air Force Research Laboratory and NASA’s Space
Environments and Effects (SEE) Program. This paper was written under contract with the Air
Force Research Laboratory.
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Sciences Meeting & Exhibit, 39th, Reno, NV, Jan. 2001.
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AIAA Paper AIAA 99-0379, 1999.
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4. Y. A. Davis, L. F. Neergaard, M.J. Mandell, I. Katz, B.M. Gardner, J. M. Hilton, J. Minor,
Spacecraft Charging Calculations: Nascap-2k and SEE Interactive Spacecraft Charging
Handbook, AIAA Paper, AIAA 2002-0626, 2000.
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CR 191044, 1993.
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dimensional charging analyzer program for complex spacecraft, IEEE Trans. Nucl. Sci.,
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NASCAP/LEO, AIAA Paper AIAA-90-0725, 1 990.
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