Electron drainage current from dilute plasma through holes in high voltage dielectric probe

Grier, N. T.

Mc Kenzie, D. J., Jr.

English

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N A S A  T E C H N I C A L  
M E M O R A N D U M  
N V l - 3 2 4  
NASA TM X- 67890 
CURRENT DRAINAGE TO A HIGH VOLTAGE PROBE 
IN A DILUTE PLASMA 
by Norman T. Grier & Daniel J. McKinzie, Jr. 
Lewis Research Center 
Cleveland, Ohio 
! 
TECHNICAL PAPER proposed for presentation at 
Tenth Aerospace Science Meeting sponsored by the 
American Institute of Aeronautics and Astronautics 
Sin Diego, California, January 17-19, 1972 
https://ntrs.nasa.gov/search.jsp?R=19710023007 2020-03-23T15:14:47+00:00Z
CURRF,NT DRAINAGE TO A HIGH VOLTAGE PROBE 
IN A DILUTE PLASMA 
by Norman T. Grier & Daniel J. McKinzie, Jr. 
National Aeronautics and Space Administration 
Lewis Research Center 
Cleveland, Ohio 
ABSTRACT 
.--( 
$ 
I4 
The current drainage from a plasma through approximately 0.05 cm 
diameter holes in Kapton H polymide film, P E P  type C. ,  and quartz micro- 
sheet placed on a probe at voltages up to 2000 volts d. c .  have been determined 
both theoretically and experimentally. A Laplace field was used to numeri- 
cally predict an upper limit for the drainage current. The measured current 
was less than the theoretical current for the FEP  and quartz, and the two 
were approximately in agreement for Kapton He The measured currents were 
on the order of 5 microamperes with the theoretical currents on the order of 
10 microamperes. 
0 3  
I 
INTRODUCTION 
Solar cell a r r ays  in the kilovolt range are being proposed for power 
generation on satellites. Lf the solar cell cover glass o r  the dielectric mate- 
rial insulating the connecting tabs between solar cells develop holes or  cracks, 
a large drainage current from the ambient plasma may ensue resulting in de- 
on the order of milliamperes through 0,0254 cm diameter holes in an Epoxy 
(resin Epon 828 with curing agent Epon V-40) 2nd Kapton H polymide films 
when exposed to a plasma up to 3000 volts. A l l  of their measurements were 
made directly in the exhaust of a Kaufman ion thruster. The ion velocity 
( ~ / 8  km/sec) was, therefore, much higher than that found at orbital conditions 
in the ionosphere. This paper reports results for electron drainage current 
through known size holes in various dielectric materials. The dielectrics 
5 gradation of performance. Cole, et a1. (ref. 1) measured drainage current 
2 
were placed in a Pyrex bell attached to the side of a large vacuum tank which 
houses a Kaufman ion thruster generating an argon plasma. The specimens, 
therefore, were not located directly in the engine's exhaust beam, The 
plasma velocity was on the order of 4 km/sec, which is about half satellite 
velocity at 300 km altitude. The dielectric materials used were a quartz 
solar cell cover glass, Kapton H polymide film, and flourinated ethylene pro- 
pelene (FEP) type C. The experimental results a r e  compared with results 
calculated using a computer program developed by Parker (refs. 2, 3, 4, 
and ' 5) e 
F ac i lit y 
The tests were performed in a 45.72 cm (18 in.) diameter by 76.2 cm 
(30 in.) long Pyrex bell jar (fig. 1). The bell jar was mounted on a 61  cm 
(24 in. ) diameter port located on the side of a 3.05 meter (10 f t )  diameter 
by 4.57 meter (15 f t )  long vacuum tank. The bell jar part*s centerline was 
2.29 meters (7-1/2 f t )  from either end of the vacuum tank. The vacuum tank 
pressure was approximately 2X10F5 t o r r  for all tests. The current test speci- 
mens were mounted on one end of a 3.2 cm diameter cylindrical Pyrex sting. 
This passed through and was supported by an instrument ring attached to one 
end of the bell jar. The high voltage test location in the bell jar was approxi- 
mately 2.03 meters from the centerline of the vacuum tank and 7.6 cm (3 in.) 
off the bell jar centerline. The ammeter used to measure the drainage current 
was located between the high voltage power supply and the test specimen. A 
sketch of the complete experimental set-up is shown in figure 1. The electri- 
cal connecting lines and ammeter were shielded with the shield at a potential 
of the test specimen. In all cases the high voltage probe was biased positively 
with respect to ground. The ion engine used to generate the argon test plasma 
was mounted on the center of one end cap of the vacuum tank. 
Two cylindrical tungsten Langmuir probes and a Faraday cup were used 
to diagnose the plasma. One of the Langmuir probes (25.4 cm long by 
0.0254 cm diameter) was  located on the centerline of the tank at the axial station 
of the port to the bell jar. The other Langmuir probe (12. 4 em long by 
3 
0.0127 cm in diameter) was located in the bell jar approximately 20.32 cm 
(8 in.) front of the testing location. A 10.16 cm (4 in.) diameter Faraday 
cup was located about 25.4 cm (10 in. ) inside the vacuum tank in front of the 
bell jar port. This cup was swung out of the port entrance during tests. The 
opening for the Faraday cup faced radially into the large vacuum tank. 
Analysis 
Ions enter the bell jar from the ion engine beam as a result of scattering 
collisions. The most probable process is charge exchange collisions with 
the neutral background gas. This process produces slow ions that can enter 
the bell jar. The velocity and number density of the ions in the bell were 
estimated as follows: 
position of the bell jar, the ion number density in the ion engine exhaust 
beam is larger than that in the bell jar. The largest ion density is on the 
centerline of the beam. A potential difference exists between the engine ex- 
haust beam and the inside of the bell jar. This potential difference acclerates 
the charge exchange ions in the beam radially. Some of these enter the bell 
jar along with other scattered ions. The velocity of the ions was calculated 
from 
Velocity. - On a plane perpendicular to the axis of the tank at the axial 
v = 2 k A y / 2  (1) 
where AV is the potential difference between the centerline of the ion engine 
plasma beam and the plasma potential (assumed constant) in the bell jar 
determined from the Langmuir probes measurements, and M the mass of the 
ions. 
1 
Number density. - The plasma number density in the bell jar was found 
by two independent means. The first method uses the current measured 
with the Faraday cup. The number density was calculated from the relation 
eA v 
4 
where IF is the Faraday cup current, e the electric charge, A the area 
of the Faraday cup, and v is the velocity of the ions from equation (1) . 
electron densities expected in the bell jar and the beam, the Debye length is 
greater than the probe diameter, therefore, a thick sheath is expected about 
the Langmuir probe. According to electric probe theory (ref. 6), when there 
is a thick sheath surrounding cylindrical electric probes operating in the 
electron current saturated region and eV >> kT, the square of the current 
should vary linearly with the applied biased voltage. The number density is 
The second method used the Langmuir probe in the bell jar. For the 
related to the slope of this 
where S is the slope, A 
electronic charge. 
curve by 
(3) 
the probe area, m the electron mass, and e the 
Computed Current 
Two computer programs developed by Parker (ref. 3) were used to pre- 
dict the current drainage through the holes in the dielectrics covering probes 
which are biased at high voltages relative to the plasma. One of the programs 
calculates the field distribution surrounding a planar probe by solving 
Laplace? s equation numeri'cally. Since the Laplace equation applies where 
there is no space charge, this implies the sheath o r  the electric field extends 
to infinity. The other computer program solves Vlasorls equation numeri- 
cally for the current density when the electric field distribution is given. 
Parker (ref 3) shows that Laplace fields give the maximum values for the cur- 
rent density for a given voltage on the probe. Therefore, the Laplace field 
was  used to compute the maximum theoretical current through the holes in the 
dielectrics .,
surrounding an isolated cylinder with a planar probe embedded flush in the 
center of one of its ends. (See fig. 2, Cylindrical coordinates are chosen 
such that the center of the probe has coordinates z = 0, r = 0 with the positive 
The Laplace field program calculates the field at preselected grid points 
5 
z-space above the probe. The size of the probe radius, the cylinder radius 
and height, grid boundary, and probe voltage, are input data. A dipole law 
is assumed for the potential between the grid boundary and infinity. In the 
calculations presented herein the following dimensions were used, probe 
radius 0.0254 cm (0.020 in. in diameter), cylinder radius 1 .6  cm, cylinder 
height 3.0 cm, grid radius 50.0 cm, grid distance above cylinder (pos. z) 
100 cm, and grid distance below cylinder (neg. z) 100 cm. The total number 
grid points used were 633 with 594 points in the posi€ive z-space. 
The current computer program utilizes the same geometry as the 
Laplace field computer program. Assuming a Maxwellian gas at infinity, 
this program numerically computes the current density ratio J/Jo at the 
center of the probe for a given field distribution, probe bias voltage, gas 
temperature at infinity, and directed velocity at infinity. Jo is the current 
density for zero bias voltage on the probe. It is given by 
Jo = n (z)''~ (4) 
where n is the gas number density, T the temperature, and m the mass 
of the particles. In the tests, the kinetic energy gained by the particles from 
the probe voltage was much greater than the plasma free stream kinetic 
energy, therefore, the directed velocity was assumed zero in the calculations. 
However as a check on this assumption, a few cases  were computed with a 
directed velocity of 5 km/sec. There were no changes in the results. 
RESULTS AND DISCUSSION 
Figures 3, 4, and 5 show the results for the Kapton H film, FFP type C, 
and quartz solar cell cover glass, respectively. The following values for the 
thickness, hole diameter, number density, and AV were used for each 
specimen 
6 
Pot entia1 
difference 
1.73 
1.40 
2.25 
- - . -. 
Specimen n, 
3 ions/cm 
1 e 4X106 
1 e 7x10 6 .  
1 e 5X106 
___ ._ ---- 
Quartz solar cell cover 
Kapton H 
FEP Type C 
Thickness 
0.0305 
0.0127 
0.0127 
Hole diam, 
cm 
0.0516 
0.0508 
0.0521 
Thesg number densities were determined using equation (3) from the experi- 
mental saturation electron current of the Langmuir probe in the bell jar. These 
number densities correspond to an altitude of approximately 300 kilometers. 
The electron temperature determined from the I-V characteristics of the probe 
was approximately 3000' K (GO. 3 eV). Since the range of probe potential V 
cases, therefore, thick sheath electric probe theory applied. In determining 
the above number densities from the bell jar Langmuir probe, at least 12 values 
of the square of the current at applied bias voltages between +20 and +45 volts 
were fitted with a least square linear relation. This gave a root-mean-square 
deviation, for  all points of less than 2 percent. These number densities deter- 
mined from the Langmuir probe data were w e d  in all the theoretical calculatims. 
The values of number density listed above approximately agree with those deter- 
mined from the Faraday cup.. 
For this study, the planar probe is considered to be simulated by the hole 
in the dielectric covering a metal disc. The results are shown in figures 3, 4, 
and 5. From the results presented in these figures, the computed current 
agrees within a factor of &3 with that measured for Kapton He It is larger ay 
approximately a factor of four for that obtained with FEP, and larger by approx- 
imately a factor of ten for the quartz measured current. The magnitude being 
on the order of microamperes. A s  previously stated, the current calculated 
using a Laplace field in the space surrounding the hole yeilds an upper current 
limit for a planar probe in a plasma. Therefore, the apparent agreement between 
theory and experiment for  Kapton H is probably due to phenomena not considered 
in the theory. One phenomenon that may enhance the experimentally measured 
current is sputtering of the dielectric material. Sputtering produces a gas cloud 
near the hole. As some of the plasma electrons travel toward the hole, they 
i u s e d g a s  from 920 to +45 volts, eV was very much greater than kT in all 
7 
make ionizing collisions with the gas cloud particles creating more electrons. 
These ejected electrons along with the original electrons now travel toward 
the hole, thereby, enhancing the measured current. If sputtering is enhancing 
the measured current, the results indicate that Kapton H is sputtered the most, 
FEP  next, and quartz is sputtered the least. 
Although the magnitude of the computed current differs from the measured 
current, the variation of the current with voltage is in agreement with experi- 
mental trend. This suggests that the theory may be used to estimate the drain- 
age current at higher voltages than those presented here. However, it is 
expected that sputtering and other effects may become more severe at higher 
voltages for some materials. 
CONCLUSIONS 
Parker? s method for calculating the current through holes in dielectric 
covering probes satisfactorily predicts the trends in experimentally measured 
current in dilute plasma for voltages up to 2000 volts. A Laplace field was 
used to numerically predict an upper limit for the drainage current. For  holes 
in quartz and FEP, the theoretical current was larger than the measured current 
for all voltages presented. For  Kapton H the theoretical current and the meas- 
ured current were approximately in agreement over the full range of voltages 
presented. Since the computed current is the theoretical maximum current, 
this agreement suggests that other phenomena may be occurring near the hole 
enhancing the measured current 
WFERENCES 
1. Cole, R. K. Ogawa, H. S. 
Cell Arrays in Dilute Streaming PlasmasvT TRW-09357-6006-R000, NASA 
CR-72376, Mar.  15, 1968, TRW Systems, Redondo Beach, Calife 
and Sellen, J. M., Jr. , P90peration of Solar 
2. Parker, L. W. and Whipple, E. C., Jr., 9vTheory of Spacecraft Sheath 
Structure, Potential, and Velocity Effects on Ion Measurements by 
Traps and M a s s  Spectrometers, 9 p  Journal of Geophysical Research, 
Vol. 75, No. 25, Sept. 1, 1970, pp. 4720-4733. 
8 
3. Parker,  L. W. , "Theory of the Circular Planar (Guarding) L,angmuir 
Probe," ERL 100 - AL2, Dec, 1968, ESSA, Boulder, Colo. 
4, Parker, L. W.,  ??Theory of Electrostatic Planar and Spherical Probes, ? ?  
CR-704, 1967, NASA, Washington, D. C. 
5. Parker, L. W. and Whipple, E. C.,  Jr., "Theory of a Satellite Electro- 
static Probe," Annals of Physics, Vol. 44, No. 1, Aug. 1967, pp. 126-161. 
6. Chen, F. F., "Electric Probes, ? ?  Plasma Diagnostic Techniques, R. H. 
Huddlestone and S. L. Leonard, eds. ,  Academic Press, New York, 1965, 
pp. 113-200. 
VACUUM TANK 
rc -1 
-4 'P ................ 
................ 
t I 
10-7 
ION THRUSTER 7 
KAUFMAN 
LHNGMUIR 
PROBE1 
\ j  
i 
- 
- 0  
- 0  
- 
- 
', I L O - 2 4 V d c  -45 TO +45 V dc 
Figure 1. - Sketch of experimental facility. (Not to scale. 1 
[I 
................ ................ 
. . . . . . . . . . . . . . . .  
................ ................ 
v, = 0 
. . .  * .  * 
Figure 2. -Model for calculation: Closed cylindrical tube with a high 
potential probe embedded in one end. 
v) D-
z a 
a- 
+- e 
CT 
CT 
2 
0 
W 
m 
0 
CT Q 
0 o 8 o o o ~ o ~ 8  
'0 
0000 0 O O 
0 
0 0  
8 
THEORY -- 
0 EXPERIMENT 
r 
I 
THEORY 
0 EXPERIMENS 
_.- 
I - *  O 
I 
t- oo 
0 i 
10-7 
0 400 800 1200 1600 2000 
PROBE VOLTAGE, V, VOLTS 
Figure 5. -Probe cur ren t  as a function of probe voltage 
for 0.0516 centimeter diameter hole in quartz. 
NASA-Lewis-Com'l 


Current drainage to a high voltage probe in a dilute plasma

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