The calibration is considered of an RF antenna capacitance probe carried aboard the RAE-1 spacecraft and the correction of the probe for external effects, believed to be primarily due to local positive ion sheaths and/or photoelectron sheaths surrounding the antenna. The RAE-1 spacecraft was launched in July 1968 into a 5850-km. Circular orbit of 121-degree inclination and carried several antenna and radiometer systems covering a frequency range of 0.2 to 9.2 MHz for radio astronomical studies. The RF capacitance probe measurements discussed utilized a 37-meter electric dipole antenna formed by two monopoles made of silver-coated beryllium-copper alloy tapes formed into hollow cylindrical tubes 1.3 cm in diameter

Kaiser, M. L.

Mosier, S. R.

English

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SX-693-74205
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CALIBRATION OF A CYLINDRICAL
RF CAPACITANCE PROBE
by
Stephen R. Mosier
Michael L. Kaiser
Radio Astronomy Branch
Laboratory for Extraterrestrial Physics
Goddard Space Flight Center
Greenbelt, Maryland, 20771
I
Antenna capacitance probe measurements provide a
technique of determining the local electron density in the
ionosphere and magnetosphere. Several comparisons of
capacitance probe measurements with the results of other
density measurement techniques have been made in the
laboratory and at low altitudes in the ionosphere [see,
for example, Heikkila et al., 1968; and Smith, 1972].
This report briefly considers the calibration of an RF
antenna capacitance probe carried aboard the RAE-1 space-
craft and the correction of the probe for external effects,
believed to be primarily due to local positive ion sheaths
and/or photoelectron sheaths surrounding the antenna.
The RAE-1 spacecraft was launched in July 1968 into a
5850-km. circular orbit of 121-degree inclination and carried
several antenna and radiometer systems covering a frequency
range of 0.2 to 9.2 MHz for radio astronomical studies.
The RF capacitance probe measurements discussed in this
report utilized a 37-meter electric dipole antenna formed by
two monopoles made of silver-coated beryllium-copper alloy
tapes formed into hollow cylindrical tubes 1.3 cm in dia-
meter. [For a detailed description of the RAE-1 spacecraft,
1
see Weber et al., 1971].
The capacitance probe measures the dipole antenna
capacitance in four frequency ranges centered at approxi-
mately 0.25, 0.70, 1.0, and 2.2 MHz. It finds the resonant
frequency for a tuned LC circuit consisting of the dipole
and one of four inductors available in the probe. After
accounting for uncertainties due .to oscillator stability,
the resonant frequency can be measured to 0.1 percent,
corresponding to sensitivity to capacitance changes of less
than one percent.
Considering the case where the plasma frequency is
much less than the observing frequency and the impedance
of the short dipole is predominantly a capacitive reactance,
the ratio of the antenna capacitance C in the plasma to the
free-space capacitance C can be written as [see Stone et al.,0
1966].
C 2 p 1/2
= S (cos 2 + E sin 2) , (1)C S
where e is the angle between the antenna and the static
magnetic field and, following the notation of Stix [1962]
for a collisionless plasma,
2
S = 1 - -- 22
1-Y
P= 1 - X
X = f 2/f2
p
and
Y = f /f.
g
Here f p,f , and f are the electron plasma, gyro, and ob-
serving frequencies, respectively. For magnetic field values
and orientations encountered near the equator at L values
near 2 by RAE-1, we may assume Y to be zero with resulting
errors of less than two percent. With the observing
frequency chosen so that X is much less than unity, equation
(1) reduces to
C
C 1 - X. (2)
Solving equation (2) for X yields the plasma frequency of
the medium and hence the electron density in the absence
of a positive ion sheath or a photoelectron sheath about
the antenna.
It is well-known that a body placed in a plasma will
generally acquire a potential different from that of the
plasma, due to. the fact that the thermal velocity of the
3
electrons is very much higher than that of the ions, and
also since a body in sunlight will be charged by photo-
emission. The notential of the body will then affect the
electron density in the near vicinity of the body so that
the measured density is different from that of the ambient
density in the absence of the body. Moreover, the density
as a function of radial distance from the antenna is not
known and theoretical treatment of the problem is quite
difficult.
Consider a conducting cylinder with charge Q and whose
radius R is small compared to its length. At the center
of the cylinder, the electrostatic field varies as 1/r in
the radial coordinate until, at some radial distance RT
from the cylinder, the field begins to change to a 1/r
2
radial dependence due to fringing of the field from the
ends of the cylinder. The potential of the cylinder can be
written (in rationalized MKS units) as
V Edr Q dr+ F(r) dr (3)V 21P 0 - o  e
Lo T
where F(r) is the radial field dependence beyond the
transition distance R and
4
e = 1 - 81N/f 2
is the relative dielectric constant as given by cold plasma
theory, where
N = electron concentration
and
f = operating frequency.
For the RAE-I dipole antenna and plasma c6nditions, RT is
much greater than a Debye length in the plasma and the
contribution to the potential in equation (3) beyond RT
can be neglected. The capacitance of the antenna can then
be written as
C = (4)
dr
JR er
where end effects due to fringing of the electrostatic field
have been neglected, as well as collisions and magnetic field,
and the relative dielectric constant e is assumed to be a
function only of the radial coordinate r. For free space,
E = 1 and equation (4) becomes
21
T o
5
Following a similar calculation done by Heikkila
et al., [1968], the relative change in antenna capacitance
caused by the plasma is then
RT -1f 
- (In R /R )-I
C-C R ar T 0
n-lAC o oC C
o o (In RT/R )-I
T O
which can be written as
dr
(1-6)
aC Ro re
C RT
R re
0
For the case of plasma frequency much less than ob-
serving frequency, e(r) is only slightly smaller than unity
and, using small number approximations, the above equation
can be written as
R
AC 1 dr (5)
C In R/R R r
o T o R
0
This is basically the same result obtained by Heikkila
et al., [1968] for a spherical probe geometry and, as pointed
out in that paper, the absence of an ion sheath would result
in a capacitance decrease of
6
I-e = 81N/f2,
or linearly proportional to electron density. However,
for an actual ion sheath or photoelectron sheath, S is
some unknown function of r and must remain in the integrand.
Heikkila et al. avoided the complex and difficult evaluation
of equation (5) by showing experimental results which
indicated that, for a spherical probe geometry, the net
effect of the sheath is to reduce the sensitivity of the
capacitance probe measurement by an amount which depends
only weakly upon the plasma parameters and obtained the
result of AC = (constant) N.
The results which will be presented in this report,
however, indicate that the same approximation cannot be
used for the cylindrical probe geometry and that AC is
not linearly proportional to N but rather varies as root N,
AC - (constant) N1/ 2
indicating a much more complex behavior of e in the integrand
of equation (5) than was suggested by Heikkila et al. [1968]
for a spherical probe geometry.
In order to obtain an absolute calibration of the RAE-1
capacitance probe, the electron plasma frequency was
7
determined from both the capacitance probe measurement and
from observations of the local upper-hybrid resonance
(UHR) noise bands (for a discussion of this technique, see
Mosier et al., 1973]. The difference between these two
determinations of plasma frequency is then plotted as a
function of plasma frequency. Figure 1 illustrates the
results of 48 such calculations for values of plasma
frequency between 150 kHz and 470 kHz. The upper limit
of this range was chosen so that the small-number approxi-
mations used in deriving equation (5) would result in an
error of less than ten percent. For the range of plasma
frequency in Figure 1, e varies from 0.98 to 0.74. A
positive capacitance probe error in Figure 1 indicates
that the capacitance probe determination of plasma frequency
is too high. Also shown in Figure 1 is the result of a
least-squares analytical fit to the data. Of the many
analytical curves which were attempted, only the straight
line yielded a good fit. Thus, AC varies linearly as
plasma frequency or, in terms of density,
AC = -2.88 N / 2 + 127.
8
In summary, the correction factor for the RAE-1
capacitance probe has been accurately determined from
comparison with resonance techniques, the correction
being linearly proportional to plasma frequency. Since
the antenna potential is unknown, we are unable to calculate
the function e(r) in equation (5) through the sheath region.
In principle, however, the measurement of the probe potential
would permit such a calculation since boundary conditions
could then be fit to the numerical studies performed by
several investigators. As Heikkila et al. [1968] point out,
a particularly serious feature of the capacitance probe
correction is its dependence on probe potential. It thus
appears that the capacitance probe is a more valuable
tool in regions where the probe potential is likely to be
slowly varying as in the equatorial magnetosphere. The
difference between the probe correction obtained by Heikkila
and the correction described in this report is not under-
stood but is probably due in part to the differences in
probe geometry and the resulting changes in boundary
conditions.
9
REFERENCES
Heikkila, W.J., N. Eaker, J.A. Fejer, K.R. Tipple, J. Hugill,
D.E. Schneible, and W. Calvert, "Comparison of several
probe techniques for Jonospheric electron concentration
measurements," j. Geophys. Res., 73, 3511, 1968.
Mosier, S.R., M.L. Kaiser, and L.W. Brown, "Observations
of noise bands associated with the upper hybrid
resonance by the IMP 6 radio astronomy experiment,"
J. Geophys. Res., 78, 1673, 1973.
Smith, J., "Comparison of Lanqmuir probe and rf capacitance
probe electron density measurements in low-density
plasmas," J. Appl. Phys., 43, 3031, 1972.
Stix, T.H., The Theory of Plasma Waves, McGraw-Hill, New
York, 1962.
Stone, R.G., J.K. Alexander, and R.R. Weber, "Magnetic
field effects on antenna reactance measurements at
frequencies well above the plasma frequency," Planet.
Space Sci., 14, 1227, 1966.
Weber, R.R., J.K. Alexander, and R.G. Stone, "The Radio
Astronomy Explorer Satellite, a low-frequency observatory,"
Radio Sci., 6, 1085, 1971.
/
Figure Captions
Figure 1 - Capacitance probe error as a function of plasma
frequency.
/
100 -
0
a:0 
0
w oo > o 0 0
00
0. 00
w
z
- -100
0 I I I I I
< 0 100 200 300 400 500 600
U
PLASMA FREQUENCY(kHz)
Figure 1


Calibration of a cylindrical RF capacitance probe

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