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VALIDATION OF NASCAP-2K SPACECRAFT-ENVIRONMENT 
INTERACTIONS CALCULATIONS 


V.A. Davis 

Science Applications International Corporation 
10260 Campus Point Dr., M.S. A1 
San Diego, CA, 92121 
Phone: 858-826-1608 
Fax: 858-826-1652 
E-mail: victoria.a.davis@saic.com 


M.J. Mandell 
B.M. Gardner 

I. G Mikellides 

Science Applications International Corporation 

L.F. Neergaard 

Jacobs Sverdrup Technology 

D.L. Cooke 

Air Force Research Laboratory /VSBS 

J. Minor 

NASA Marshall Space Flight Center 

Abstract 


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. 


Introduction 


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>/^,) 


max(l,C((|),E)) 

l+V^/e/ 2 


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 — . 

y 2nm 

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. 


Nascap-2k Parker-Murphy 



Figure 3. Electron current collected by a 100 V sphere from a 0.2 eV plasma. Densities are in 


in 


Table 1. 90% worst case environment for geosynchronous orbits as defined in Reference 24. 



Temperature 

(keV) 

Density (cm 3 ) 

Ions 

29.5 

0.236 

Electrons 

12.0 

1.12 


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 
(MeV) electrons. 

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. 


Code 

Number 

of 

surfaces 

Time to 
build 
model 
(min) 

Time to set 
up 

calculation 

(min) 

Time for charging 
calculation to complete on 
800 MHz PC (min) 

NASCAP/GEO 

296 

30 

5 

0.8 

SEE 

Handbook 

166 

15 

2 

2 

Nascap-2k 

623 

30 

3 

12 


Table 3. Results of NASCAP/GEO, Nascap-2k, and SEE Handbook calculations, given in kV. 



Chassi 

s 

Kapton 

OSR 

Solar Cells 

Teflon 

Non- 

conducting 

paint 

Absolute potentials (kV) 

NASCAP/GE 

O 

-10.0 

-8.2 to -13.1 

-8.23 to - 
10.7 

-5.2 to -7.68 

-7.5 to - 
12.7 

-8.3 to -10.3 

SEE 

Handbook 

-8.6 

none in model 

-7.3 to -9.6 

-3.6 to —5.7 

-6.8 to 

1 1.3 

-7.5 to -8.9 

Nascap-2k 

-12.0 

-11.5 to -14.4 

-10.0 to - 
13.7 

-7.2 to -10.8 

-7.9 to - 
14.0 

-10.0 to -12.2 

Differential potentials (kV) 

NASCAP/GE 

O 


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 

SEE 

Handbook 


none in model 

1.3 to -1.0 

5 to 2.9 

1.8 to -2.7 

1.1 to -0.3 

Nascap-2k 


0.5 to -2.4 

2 to -1.7 

4.8 to 1.2 

4.1 to -2 

2 to -0.2 





Surface Potentials 



-4500. 

-5000. 

-5500. 

-6000. 

-6500. 

-7000. 

-7500. 


-6500. _ 
-9000. L_ 


-1.E+04 

-1.05E+04 


-1.1E+04 

-1.15E+04 


-1.2E+04 
-1.25E+04 
-1.3E+04 
-1.35E+04 
-1.4E+04 
12/14/1 17:02:11 


Figure 5. Results of spacecraft charging 
calculation using NASCAP/GEO. 



12000 

11000 

10000 

-9000 

-8000 

-7000 

-6000 

-5000 

-4000 

-3000 


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. 


Time (s) 

0 200 400 600 800 1000 



Figure 8. Comparison of chassis potential 
versus charging time as computed by 
NASCAP/GEO, SEE Handbook, and 

Nascap-2k. 


Table 4. Comparison of equilibrum 
solutions (kV). 



Chassi 

s 

Max Differential 


Positiv 

e 

Negative 

NASCAP/G 

EO 

-20.3 

10.8 

-2.5 

SEE 

Handbook 

-17.8 

10.4 

-0.14 

Nascap-2k 

-19.5 

7.8 

-3.6 

Nascap-2k 

with 

Handbook 

object 

-19.2 

9.4 

-0.06 


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 
environment. 



Figure 10. Nascap-2k potential contours 
with one sphere at +46 kV with respect 
to spacecraft ground and spacecraft 
ground at -6 kV. 



Contour Levels 
-1000 
-100 
-10 
-1 
1 

10 

100 

1000 

10000 


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 
Geophysical Union. 




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. 


Sphere 

Bias 

(kV) 

Chassis 

floating 

potential 

(kV) 

Sphere and 
bushing current 
(mA) 


LEO 

N2k 

LEO 

N2k 

46 

-8.3 

-5.9 

45.2 

40.6 

24 

-5.3 

-3.9 

26.9 

21.6 

12 

-3.3 

-2.6 

13.4 

10.9 

1 

-0.6 

-0.58 

1.4 

0.61 



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 
results do. 

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 


nexp 


V 0 max J 


+ <gauss E exp 


r 

E gauss - E 'j 

2^ 

V 

V ^ J 

J 


+ <p~~E- 


3 power 


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. 



Density 

3 x 10 9 m 3 

Low energy plasma 

Temperature 

0.2 eY 


Hydrogen fraction 

9% 

High energy electrons 



Maxwellian component 

Density 

2.49 x 10 s m 3 

Temperature 

3200 eV 

Gaussian component 

Coefficient 

1.5 x 10 4 

Energy 

3.5 x 10 4 eV 


Width 

1.8 x 10 4 eY 

Power law component 

Coefficient 

2x 10 10 

Minimum energy 

50 eV 

Maximum energy 

1.6 x 10 6 


Exponent 

1.05 





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 
Nascap-2k. 



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. 


Conclusions 


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, 
jody.minor@nasa.gov or David Cooke david.cooke@hanscom.af.mil (Air Force users). 



Figure 19. Resulting surface potentials 
for case with all Teflon and self- 
consistent charge density computed by 

Nascap-2k. 



Figure 20. Resulting surface potentials 
for case with all Teflon and self- 
consistent charge density computed by 

Nascap-2k. 



Time (s) 


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. 







-3500 



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. 


Ackowlegements 


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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