RADIO SCIENCE, VOL. 45, RS4013, doi:10.1029/2009RS004266, 2010
Direct measurement of the radiation resistance of a dipole
antenna in the whistler/lower hybrid wave regime
Patrick Pribyl,1 Walter Gekelman,2 and Alex Gigliotti1
Received 31 August 2009; revised 8 January 2010; accepted 31 March 2010; published 27 August 2010.
[1] An electrically short dipole antenna radiating high‐frequency waves is instrumented in
such a way as to directly measure its radiation impedance when immersed in a laboratory
plasma. By measuring both current and voltage at the radiating end, transmission line
effects are largely eliminated, and extremely accurate results can be obtained. Initial results
are presented for wave frequencies ranging from lower‐hybrid to whistler, for density
varying from 2 × 1018 m−3 down to 2 × 1015 m−3. The initial experiments are performed
for w/wce 1. At the highest density, the impedance is approximately real, varying
from 400 W at 30 MHz down to 100 W at 180 MHz, while at the lowest density, the
impedance is almost entirely capacitive, at roughly 1.6 pF.
Citation: Pribyl, P., W. Gekelman, and A. Gigliotti (2010), Direct measurement of the radiation resistance of a dipole
antenna in the whistler/lower hybrid wave regime, Radio Sci., 45, RS4013, doi:10.1029/2009RS004266.
1. Introduction
[2] In a free‐space broadcasting arrangement, such as a
ham radio or a commercial broadcast station, a high‐
frequency antenna is located at the end of a transmission
line. The antenna and the transmission line connection
are carefully constructed so as to present a real impedance, matched to the transmission line impedance. Thus,
there is little or no reflected wave energy back into the
transmission line, and the bulk of the energy is broadcast
as radio waves. In contrast, when an antenna is located in
a plasma, it does not radiate into free space but is surrounded by a dielectric medium with tensor components
to the dielectric. In addition, the load is generally not
constant, and the impedance of the antenna system cannot be matched to its feeder line. In particular, in the
laboratory case, the transmitting antenna is located at the
end of a probe shaft and is immersed in the plasma; a
feeder transmission line is threaded through the shaft,
connecting to a driver at the outside and the antenna at
the plasma end; the plasma is anisotropic and linearly
dispersive. There have been numerous attempts to
directly measure the antenna impedance in both space
plasma and laboratory plasma settings. Many of the
1
Basic Plasma Science Facility, Los Angeles, California, USA.
Department of Physics and Astronomy, University of
California, Los Angeles, California, USA.
measurements rely on a circuit model of the antenna and
transmission line feed even if a network analyzer is used.
The model itself can be a large source of error. In this
work we have constructed a specialized dipole in which
the current and voltage is measured at the probe tips
eliminating the necessity for modeling.
[3] Whistler waves [Helliwell, 2006] have long been
observed in space [Kintner et al., 1995; Parks, 2003] and
were in fact first observed in the early days of telephony
[Preece, 1894; Fuchs, 1958]. They were a puzzle until
they were explained as a wave in the plasma surrounding
the earth, triggered by high‐altitude lightning [Shawhan,
1979; Sonwalker and Inan, 1989]. They have since been
observed in the magnetospheres of other planets [Gurnett
et al., 1979; Xin et al., 2006a, 2006b] and may be excited
in the solar corona [Le Quéau and Roux, 1986]. The first
laboratory observation of whistlers was by Gallet et al.
[1960]. Subsequent to this, highly detailed laboratory
observations of whistlers were made by Stenzel [1976a]
and Sugai et al. [1978]. Whistlers near the earth have
relatively low frequencies (f ∼ 1 kHz) and are audible
after detection by a suitable receiver. In space around the
earth, the plasma density and magnetic field are low (n =
103 cm−3; B < 10−6 T). The dispersion of the waves is
complicated, and the group and phase velocities are, in
general, not in the same direction. However, for cold
plasma, the frequency is related to the wavelength by
2
Copyright 2010 by the American Geophysical Union.
0048‐6604/10/2009RS004266
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"
#12
!2pe
c
¼
1
!ð! !ce cos Þ
f
ð1Þ
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where wpe, wce are the electron plasma and cyclotron
frequencies, respectively, and is the propagation
direction with respect to the local magnetic field. For
parallel propagation equation and w wce and w wpe,
equation (1) reduces to
sffiffiffiffiffiffi
B
p 5:6
;
nf
ð2Þ
where n is the plasma density in units of 1012 cm−3, B is
in units of gauss, f in units of MHz, and the wavelength
in units of centimeter. For the above mentioned conditions in space above the equator at L = 3 the parallel
wavelength is about 30 km at 10 kHz. However, the same
physics is readily accessible in laboratory plasmas: much
shorter wavelengths can be achieved by scaling to higher
plasma densities, magnetic field, and higher‐frequency
waves. The upper frequency limit that whistler waves
exist is the electron cyclotron frequency (fce = 2.8 ×
106 B Hz, if B is given in gauss).
[4] There has been a great deal of theoretical work on
the impedance of antennas in magnetoplasmas. For
example the impedance of a short dipole antenna
(antenna length shorter than the wavelength of radiated
wave) in a magnetoplasma was worked out analytically
by Balmain [1964] in 1964, and this formula is still used.
This and other works assumed an RF current profile
along the dipole, generally triangular with no current on
the tips. [Wang and Bell, 1972a] derived an analytic
expression for the impedance in a cold, collisionless
plasma and then a finite temperature plasma [Wang and
Bell, 1972b]. Chevalier et al. [2008] have calculated
the impedance of a dipole probe, in the lower hybrid, and
whistler regime with no restriction on the current profile
across the antenna for magnetospheric conditions. They
conclude that for a plasma frequency up to twenty times
what is generally found at L = 2 the cold plasma theory of
Wang and Bell works well. The radiation pattern of
dipole probe in a magnetoplasma was measured by
Stenzel [1976b], but the antenna impedance was not
evaluated. Recent experiments done at National Research
Laboratory (NRL) measured the impedance of spherical
antennas [Blackwell et al., 2005] as well as dipoles
[Blackwell et al., 2007]. The experiments were done at
low densities (n < 1015 m−3) and low magnetic fields (4 ≤
B ≤ 50 G). The experiments were done at frequencies
close to the plasma frequency, and data in the whistler
wave regime were not emphasized; however, experiment
seemed to agree well with theory. Another NRL experiment in the whistler regime [Amatucci et al., 2005] used
a loop antenna to launch the waves. In the NRL whistler
regime experiment, the data trend follows theory, but
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there are frequency regimes where there is an order on
magnitude difference.
2. Experimental Setup, Radiated Whistler
Wave Pattern
[5] These experiments were performed in the Large
Plasma Device at UCLA [Gekelman et al., 1991]. The
plasma is 18 m long and 60 cm in diameter with axial
magnetic fields of up to 2.5 kG. The plasma is formed
with a DC discharge between a barium oxide‐coated
cathode on one end and an anode located 50 cm from the
cathode. Plasmas are typically generated from inert gases
(He, Ne, Ar, and Xn). The machine has over seventy gate
valves through which probes and antennas may be
inserted into the plasma. Vacuum interlocks with cryopumps and small turbomolecular pumps are used to
pump down the probes and antennas before they are
inserted into the machine. Computer‐activated probe
drives controlled by a custom data acquisition system
move the probes in lines or planes orthogonal to the
background magnetic field. The plasma is driven by an
electrical arc discharge at one end of the machine for
(typically) 15 ms and is pulsed at 1 Hz. Once the drive
stops, the plasma density decays exponentially by a
factor of 10 every 50 to 100 ms. The plasma profile is
approximately flat over its diameter of 60 cm during this
period, with nonuniformities in density being a few
percent or less.
[6] As an initial test, we verified the launch of a
whistler wave from the antenna. This measurement was
performed 4 ms after the Helium discharge was terminated. At this time the plasma density had dropped to 5.0 ×
1017 m−3, the electrons were cold (Te ≈ 0.5 eV), and the
plasma very quiescent. The background magnetic field
was B0z = 0.6 kG. The corresponding plasma frequency
is 2.0 GHz, the electron cyclotron frequency is 1.7 GHz
and the lower hybrid frequency about 30 MHz. For this
test, whistler waves were launched using a tone burst at
170 MHz, well below wce/2, and the parallel wavelength
for zero degree propagation is 14 cm. The launching
antenna length is about 5 cm tip‐to‐tip, or about 0.03 of
the free‐space wavelength; this is excited with tone burst
having peak voltage between 0.05 and 0.2 V. The
receiving probe is an antenna with each of three
orthogonal one‐turn loops having a diameter of 1 cm. A
schematic diagram of the experimental setup is shown in
Figure 1, and Figure 2 shows the whistler wave radiation
pattern on two planes (25 × 25 cm) located 1 and 2 m
from the dipole radiator. The waves were detected using
a three‐axis orthogonal magnetic loop detector, each loop
i
1 cm in diameter, sensitive to @B
@t (i = x, y, z). The radiating
dipole had its tips perpendicular to the machine axis. The
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Figure 1. A schematic view of the experiment. The Large Plasma Device plasma is produced by a
DC discharge at one end of the chamber and streams down the axial field. The vacuum chamber has
more than 400 diagnostic ports. The launching dipole is inserted in one of them about 3 m from the
plasma source, and measurements of the radiated wave pattern for this experiment (see Figure 2) are
taken “downstream” of the launcher, in this case, at planes located at 1 and 2 m from the antenna.
antenna voltage and detected magnetic field was digitized
with a sampling rate of 5 GHz.
3. Antenna Impedance
[7] There are at least three schemes for measuring (or
inferring) the impedance of an antenna, and in particular
the antenna as it is immersed in the plasma. In the most
common, as discussed in many textbooks [Maxwell,
1990; Van Valkenburg, 1993], forward and reflected
powers are measured at some point in the system.
Assuming only a single transmission line is present in the
signal path and knowing its exact characteristics as a
function of frequency, the antenna impedance can be
inferred as follows:
Z ðd Þ ¼ Z0
1 þ Gð d Þ
;
1 Gð d Þ
ð3Þ
Here Z0 is the transmission line impedance and G(d) is a
generalized reflection coefficient, G(d) ≡ GRe−2gd, where
Figure 2. The measured magnetic field vectors of whistler waves at two axial distances from the
dipole launch antenna. The planes are both transverse to the background (B0Z = 600 G) magnetic
field. Each plane is 25 cm on a side, and data were acquired at spatial locations 0.6 cm apart. The
wave frequency is 170 MHz.
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Figure 3. Schematic diagram of the dipole launch antenna that measured the current to the legs of
the dipole. The antenna current is measured with the two 50 W surface mount resistors.
GR is the reflection coefficient at the antenna end of the
transmission line (ZL is the load impedance).
GR Z L Z0
:
Z L þ Z0
ð4Þ
Note that in the general case (which is necessary to
reproduce the observed behavior, as discussed below),
both conductor and dielectric losses in the transmission
line must be taken into account. Thus:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
R þ j!L
1
Z0 ¼
; with pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
G þ j!C
ðR þ j!LÞðG þ j!C Þ
ð5Þ
The quantities R, L, G, and C, are the value per unit
length of the series resistance, series inductance, shunt
conductance (=1/shunt resistance) and shunt capacitance
that characterize the transmission line [Jordan, 1968].
Measurement of the load impedance requires determination of 4 unknowns for the transmission line in question. In fact, the situation is worse because R and G can
be weak functions of frequency in the regime of interest.
Obviously, when there are two transmission lines in
series with the load, determination of these parameters is
complicated not only by the fact that there are twice as
many characteristic quantities to be accounted for (R, L,
G, C) but also by the reflections at the junction between
the lines.
4. Measurement of Probe Impedance: First
Antenna Design
[8] The first dipole probe used to launch and measure
the radiation resistance is shown schematically in Figure 3.
The transmission line feeding the dipole is composed
of the outer conductors of two semirigid coaxial cables,
insulated from each other. In a cup at the outside end of
the probe, these cables are each wrapped once through a
small ferrite toroid, then the outer conductors are
connected to ground. The RF source is connected to
another winding on the toroid in a balun configuration,
i.e., in such a way that a balanced emf is generated on
the transmission line in the shaft, launching the propagating mode that is eventually radiated/reflected by the
antenna. At the plasma end, a 50 W resistor is connected
in series with each arm of the dipole antenna, and the
coax inner conductors are connected to these resistors to
monitor the current through them. The 50 W impedance
of the coax is in parallel with the resistor if it is appropriately terminated, so when the coax finally penetrates
the vacuum boundary at the outside end of the probe,
the voltage on the center conductor referred to ground is
Iant × 25 W for each leg (with the associated phase
delay). The probe, except for the dipole arms, is housed
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Figure 4. Equivalent circuit of transmission line. The balun in the end cap was a small ferrite
toroid.
inside a shaft which has two components. One is a 1.4 m
long 3/8″ diameter stainless steel tube, while the second is
a 5 mm diameter ceramic extension supporting the last
25 cm of transmission line as it penetrates the plasma.
Thus, there may be two or more sections of different
impedance transmission lines in series. For simplicity,
these were modeled as a single coax, which may have led
to some errors described below.
[9] This first measurement of the antenna impedance
was performed with the idea that measuring the instantaneous current at the antenna end would be advantageous and would help avoid some of the pitfalls in
estimating the large number of unknowns. However,
determination of the impedance requires both voltage and
current measurements and, consequently, the voltage
needed to be computed from the transmission line
equations. Measurements of a set of known resistive
loads over a range of 0 to 5100 W, together with 5 and
10 nF capacitors, were used to back out the transmission
line characteristics. The resistors were attached to the
antenna leads by twisting their leads onto the antenna
conductors. The equivalent circuit is shown in Figure 4.
[10] When computing Zend, the best fits to the known
impedances included 20 nH of inductance in series with
it, together with a stray capacitance of about 2 pF. Note
that a total of 50 W of resistance also needed to be taken
into account, representing the two current‐sense impedances, so thehload as
i measured was Zload = [Zknown +
1
50 + jwLend] k j!Cstray , where the operator Z1 k Z2 is
intended to mean that the two impedances are in parallel.
Inferred characteristics of the transmission line are shown
in Table 1.
[11] The above transmission line model performed
quite well when used to predict the measured response as
a function of frequency for various loads. Even so, this
model proved to be inadequate for measurement of the
plasma‐loaded impedance. As an example, Figure 5a
shows the computed versus measured amplitude response
when a 5 pF capacitor is attached to the antenna leads.
Despite the excellent agreement between the measurement and the predictions around the frequencies of
interest (170 MHz in this case) with the various defined
load impedances, the open circuit measurement diverges
sharply from the prediction.
5. Measurement of Probe Impedance:
Second Antenna Design
[12] The uncertainties in the transmission line approach
led to the design of a second antenna in which both the
current and voltage at the dipole tips were measured. The
reconfigured antenna is shown in Figure 6. In this version, the transmission line conductors are actually a pair
of semirigid coaxial cables with shields soldered
together. The conductors are then insulated with Teflon
before they are threaded into the shaft.
[13] The transformer coupling for the driver was also
simplified for this antenna. Rather than coupling through
a ferrite core, which led to a large leakage inductance in
the first antenna version, an air core coupling arrangement was constructed by simply threading a loop into the
shaft in proximity with the conductors making up the
transmission line. This arrangement is illustrated in
Figure 7a. The loop is composed of one turn of coax with
the shield split at the far end to allow flux to escape. The
RF driver is connected to one end of this loop, with the
other terminated by 50 W. The actual drive signal that
couples to the transmission line is made approximately
Table 1. Inferred Transmission Line Characteristicsa
Transmission line characteristics
Capacitance per length C0
Inductance per length L0
Impedance Z0
Lumped elements
Stray capacitance at antenna Cstray
Stray inductance in series with
known impedance Lstray
Series inductance at driver Lseries
Series resistance at driver Rseries
Transmission lines losses
Conduction losses R
Insulator losses G
58.3
390
81.7
pF/m
nH/m
W
1.75
20
pF
nH
2900
200
nH
W
2.5
0.0027
W/m
mhos/m
a
A series of known resistances and capacitances were measured and
used to fit these numbers.
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Figure 5. Predicted and measured ratio j IVmeasured
j close to launch frequency. The measured current
applied
is taken from the current monitoring resistors at the probe tips and the applied voltage is measured
at the outside end of the probe shaft. Despite excellent agreement with a series of known impedances, for example, (a) 5.6 pF, (b) the open circuit result is poorly predicted. This transmission
line technique was abandoned for the more accurate measurement described in the text.
Figure 6. Antenna in which the current and voltage are both measured at the probe tips. Resistors
marked a, identical in function to those in Figure 3, are used to measure the antenna current; for
example, Ileft = Va25lef t . The voltage is divided by 25 W because resistor a (50 W) is in parallel with the
coaxial cable terminated by 50 W. Resistors b and c are used to measure the voltage between the tips
V
and in a voltage divider configuration wherein V1 = tip2 left . The differential voltage and current
signals that exit the vacuum boundary are connected to balun transformers to perform the subV
Vtip right
. The outer conductors of the paired coax cables
traction, with the result that Zmeas = tipIleft
left Iright
comprise the transmission line, with an emf being applied as shown in Figure 7.
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Figure 7. (a) A transformer consisting of a one turn coaxial loop, 30 cm long, is placed inside the
shaft in such a way that it couples flux to the transmission line. The outer conductor is removed to
allow flux from the drive loop to couple to the transmission line. The ferrite core minimizes the
common mode voltage and allows for balanced drive of the differential transmission line. A
50 W resistor terminates the flux loop coax. Note that the shield of both legs of the primary are
connected together, and to ground, at the driver end. (b) Schematic detail of coupling scheme.
Figure 8. (a) Real and (b) imaginary parts of the dipole impedance at a magnetic field of 1000 G.
f
f
As the plasma decays the ratio of fpece changes from 4.54 ≤ fpece ≤ 0.454. The dipole antenna is aligned
with the magnetic field in this case.
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Figure 9. (a) Real and (b) imaginary parts of the dipole impedance at a magnetic field of 1000 G.
These traces are sections of the contour plots shown in Figure 8, taken at 0, 75, and 150 ms.
Corresponding plasma densities are 2 × 1018 m−3, 3 × 1016 m−3, and 3 × 1015 m−3. The oscillation in
Figure 9a for the lowest density case is almost certainly an artifact of the measurement, as we expect
this impedance to approach zero. In Figure 9b, the dashed line shows the impedance of a 1.6 pF
capacitor for comparison.
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differential by using a ferrite toroid to create a large
impedance to common‐mode signals, as shown (i.e., to
create a balun). Figure 7b is a simple circuit diagram
illustrating this coupling.
[14] The currents I1 and I2 form a differential signal
proportional to the antenna current. This was made single
ended using a commercial balun connected outside the
vacuum. The same is true for voltages V1 and V2. The
final current and voltage signals went to a network analyzer (HP E5100A), which recorded their ratio as a
function of time. The driver frequency was set within the
network analyzer and was constant for a given plasma
discharge and changed from shot to shot. For a given
value of the magnetic field, the drive frequency was
varied in steps of 5 MHz from 25 to 180 MHz. The ratio
of the plasma frequency to the cyclotron frequency was
varied by changing the background magnetic field. The
antenna tips were field aligned. A measurement of the
real and imaginary parts of the impedance is shown in
Figures 8 and 9. The discharge is terminated at t = 10 ms,
and during the plasma afterglow, the density decreases
from n = 2 × 1018 m−3 (during the discharge) to approxif
mately 2 × 1015 m−3 changing the ratio of fpece . The real part
of the impedance at late times is largest at close to 25 MHz
which corresponds to the lower hybrid resonance.
fLH ¼
1
1
þ
fpi2 þ fci2 fce fci
!1=2
fpi 1 þ
fpe2
fce2
!1=2
: ð6Þ
The approximation is true if fpi fci, which is true in this
case. Here fpi is the ion plasma frequency. The lower
hybrid frequency at 100 ms after the main discharge is
approximately 18 MHz; lower hybrid waves occur above
the lower hybrid frequency. Debye length in these experiments is quite short, varying from about 10 to 70 mm as
the density decays and is small compared to every
dimension including the radius of arms of the launching
antenna. Computationally, with the small amplitude of the
launched wave, we expect to be in the quasilinear regime.
The Gendrin angle = cos‐1 2w/wce varies from approximately 89° at the lowest frequency to about 83°. As the
density decreases, the plasma becomes more like a
vacuum and the antenna load becomes more capacitive.
This is reflected in reactive part of Z which is negative
and larger at low frequencies. The small periodic oscillations versus frequency at late times most likely are an
artifact due to a slight mistermination of the coax. During
the discharge and at high frequencies, the real part and
reactive parts of the antenna impedance is very low
(several Ohms) indicating the antenna is well coupled to
the plasma and is a good radiator. Near the lower hybrid
frequency, the opposite is true; this makes dipoles poor
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sources for lower hybrid waves. In fact, specialized
antennas have to be constructed to effectively radiate them
[Stenzel and Gekelman, 1975; Bernabei et al., 1975;
Bellan and Porkolab, 1975]. Data were acquired with the
dipole aligned with the background magnetic filed as well
as perpendicular to it, and in both cases, the impedance
was similar; the behavior is also similar at B = 400 G.
6. Conclusions
[15] A novel dipole antenna was constructed which
allows its radiation impedance to be measured as a
function of frequency in the whistler wave regime. The
design allows one to circumvent the complications of
calculating the transmission line properties of the antenna
and modeling the plasma dielectric. Measurements show
the antenna impedance is high close to the lower hybrid
frequency, but it is an effective radiator at higher frequencies and densities. In an upcoming publication, these
results will be compared to a theoretical calculation by
Chevalier et al. [2008] in this parameter regime.
[16] Acknowledgments. We acknowledge support by the ONR
under the MURI grant N000140710789. This work was done on the
Large Plasma Device at UCLA. The device is part of the Basic Plasma
Science Facility funded by the Department of Energy and the National
Science Foundation. We would also like to thank Marvin Drandell,
Zoltan Lucky, and Mio Nakamoto for their expert technical assistance.
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University of California, Los Angeles, CA 90095, USA.
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