Resonance cone probe for measuring electron density, temperature, A. Piel

An Introduction to Space Instrumentation,
Edited by K. Oyama and C. Z. Cheng, 125–138.
Resonance cone probe for measuring electron density, temperature,
drift speed and beam components
A. Piel
Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität, 24098 Kiel, Germany
The diagnostics of the ionospheric plasma by in-situ measurements of the lower-oblique resonance of a
magnetized plasma is described. The electron density and temperature are derived from a nested set of resonance
cones that is excited by a small antenna and detected by a movable receiver. Asymmetries of the resonance
cones give access to electron drifts or electron beams. A detailed discussion of the hardware of resonance cone
instruments is included.
Key words: Plasma parameters, drift velocity, lower oblique resonance.
1.
Ionospheric Diagnostics with Resonance Cones ωlh , defined by Stix (1962)
The key parameters that define the state of the ionosphere
are the electron density n e and temperature Te , their altitude
profiles and their diurnal and seasonal variablity at different latitudes. In some cases, the ionospheric plasma is in
a non-equilibrium state that is caused by electric currents.
Such currents can arise from the motion of the entire population of thermal electrons and we will use the terminology
“drift” for the bulk velocity of a shifted Maxwellian electron
distribution. Otherwise, currents can be caused by groups
of suprathermal electrons that have a preferential direction
and are superimposed on a background of thermal electrons.
We will refer to such groups of electrons as “beams”. Electron drift motion and electron beams represent a source of
free energy that can lead to plasma instabilities and electron
heating. Therefore, modern ionospheric diagnostics also attempts to measure these drifts or beams.
There are various techniques for simultaneous in-situ
measurements of n e and Te , e.g. Langmuir probes (Pfaff,
1996), or dedicated instruments like the impedance probe
for n e (Oya, 1967; Steigies et al., 2000) and the temperature probe for Te (Hirao and Oyama, 1970). On the other
hand, in most cases only indirect methods are available for
detecting the current distribution, such as magnetometers.
The resonance cone (rc) method tries to fill this gap in a
single instrument that allows a simultaneous measurement
of n e , Te and the drift velocity v d , as well as the beam density and beam velocity.
The ionospheric E- and F-layers represent a weakly collisional magnetoplasma. The rc method uses the anisotropy
of this plasma, which is introduced by the magnetic field
and affects the propagation of electromagnetic waves. For
waves propagating strictly perpendicular to the magnetic
field, the ordinary wave (which has E||B) is unaffected by
the magnetic field and has a refractive index N = (1 −
2
ωpe
/ω2 )1/2 , ωpe being the electron plasma frequency. The
extraordinary wave (which has E ⊥ B) exhibits fundamental resonances (N 2 → ∞) at the lower hybrid frequency
c TERRAPUB, 2013.
Copyright 1
1
1
= 2
+
,
2
2
ωci ωce
ωlh
ωci + ωpi
(1)
2
2 1/2
and at the upper hybrid frequency ωuh = (ωpe
+ ωce
) .
Here, ωci and ωce are the ion and electron cylotron frequencies and ωpi the ion plasma frequency. Waves in the
frequency regime ωci < ω < ωce , which are propagating
along the magnetic field (k||B), are called Whistler waves.
For oblique wave propagation direction, the resonance frequency also depends on the propagation angle.
In such a magnetized plasma the radiation field of a small
antenna that is excited at an (angular) frequency ω becomes
resonantly enhanced for a characteristic propagation angle
w.r.t. the magnetic field direction. There are two frequency
regimes, where such resonances occur, the lower-hybrid
regime ωlh < ω < min(ωpe , ωce ) and the upper-hybrid
regime max(ωpe , ωce ) < ω < ωuh . For a point-like antenna,
the resonance is located on the surface of a double cone
(Fig. 1). The axis of this “resonance cone” (Fisher and
Gould, 1969) is aligned with the magnetic field direction
and its apex is located at the small transmitting antenna,
which is mounted on a boom aligned with the rocket axis.
The cone half-angle θc can easily be measured by scanning
the wave field with a small receiver antenna that is mounted
on a radial boom and rotates utilizing the payload spin. For
increasing the data rate and for matching the attitude of the
payload with respect to the magnetic field, two radial booms
of different length can be used.
In the cold-plasma approximation and neglecting ion effects, the rc angle θc is given by the formula (Fisher and
Gould, 1969)
sin2 (θc ) =
2
2
ω2 (ωpe
+ ωce
− ω2 )
2 ω2
ωpe
ce
.
(2)
The rc angle depends on the electron density n e through
the electron plasma frequency ωpe = [n e e2 /(0 m e )]1/2 , m e
being the electron mass. The electron cyclotron frequency
ωce = eB/m e is usually known from a model of the geo-
125
126
A. PIEL: RESONANCE CONE PROBE
C
B
Fig. 1. The resonance cone (rc) is excited by a small antenna which is
mounted on a vertical boom. The radiation field is scanned by rotating
a receiver antenna on a radial boom by means of the payload spin
motion. A second receiver antenna can be used to increase the data
rate. The vector B indicates the magnetic field direction and θc is the
cone half-angle.
Fig. 2. Typical experimental rc signal in the mid-latitude ionosphere at
about 120 km altitude. The two main maxima θmax represent the resonance cone. The first-order thermal interference maxima and minima
are labeled θint and θmin . The signal marked NEI is an electromagnetic
interference from an impedance probe.
magnetic field B(h) at an altitude h. Since all other parameters entering in (2) are known, the rc angle can be used to
determine the electron density. The rc method is most sensitive for ωpe < ωce but approaches a density limit at about
ωpe ≈ (2 − 3)ωce (Rohde et al., 1993). Therefore, the classical rc method can be used for ionospheric research in the
daytime E-region, the E-F valley and the lower F-region, as
well as in the nighttime F-region. The density limit encountered in the F-region can be circumvented by evaluating the
rc amplitude (Rohde et al., 1993). The rc method is also
suitable for the plasma in the magnetosphere (Koons et al.,
1974).
1.1 Thermal effects
The rc possesses an internal interference structure, first
detected in the laboratory experiments of Fisher and Gould
(1969, 1970, and 1971), which is an effect from electron
temperature (Fig. 2). The half-angle of the main maximum
θmax is now slightly shifted from the cold-plasma angle
θc . In the far field of the antenna, the shift vanishes and
the relative position of the first interference maximum with
respect to the main maximum, θ = θmax − θint , is used as
a temperature diagnostic.
Analytical expressions for this interference spacing,
which are based on the small parameter θ/θc 1, were
given by Fisher and Gould (1970, 1971), Gonfalone (1972),
Kuehl (1973) and Chasseriaux (1975), but are only useful for a large separation d of transmitter and receiver an−1
tenna, d > 200 rce , rce = (kB Te /m e )1/2 ωce
being the thermal electron Larmor radius. The applicability of these approximations was critically tested in laboratory experiments
(Burrell, 1975). The situation is different on sounding rockets, where the boom length limits the antenna distance to
d < 100 rce , typically. In this situation θ is no longer
small compared to θc . Therefore, the near field of the antenna must be calculated using kinetic theory (Singh and
Gould, 1973; Storey and Thiel, 1978; Storey et al., 1980; de
Feraudy, 1986). Peculiarities of the thermal interferences
were experimentally confirmed in laboratory experiments
by Piel and Oelerich (1984, 1985).
For the near field, it becomes more practical to consider
the angles of main maximum and first interference maximum as independent quantities. We have therefore converted the results from kinetic theory to evaluation charts
that display the rc angles θmax and θint in a plane spanned
1/2
by the density parameter p = ωpe /ωce ∝ n e and the
−1/2
temperature parameter R = d/rce ∝ Te
, as shown in
Fig. 3. Such charts were calculated for different normalized transmitter frequencies = ω/ωce . The details of the
calculation can be found in Rohde et al. (1993). The intersection of the contours for a measured pair of θmax and θint
yields a unique set of p and R.
1.2 Drift effects
From Eq. (2) it becomes evident that the rc angle increases with the transmitter frequency. A similar deformation of the rc occurs by the Doppler effect when the entire
electron population performs a B-field-aligned drift motion:
the cone is widened on the upstream side and narrowed on
the downstream side, as shown in Fig. 4(a). First attempts
to include drift effects on the rc were made by Kuehl (1974)
for the case of a field-aligned drift. This approach was extended by Michel et al. (1975) to cross field drifts, see Fig.
4(b). More refined models can be found in Singh (1977),
Storey and Thiel (1978), Fiala and Karpman (1988), Karpman and Fiala (1988). Experimental evidence for fieldaligned drifts from laboratory experiments was given by Illiano and Pottellette (1979) and Lucks and Krämer (1980).
The application of rc’s to measure field-aligned currents in
the ionosphere was discussed in Pottelette (1972), Storey
and Thiel (1984). In a simplified view, in both cases the rc
is convected with the flow. A first-order approximation to
arbitrary drift effects (Piel et al., 1992a; Rohde et al., 1993)
will be discussed in Subsection 2.4.2.
An example for the numerical calculation of the fieldaligned drift in the near field is shown in Fig. 5 (Rohde et
al., 1993). Here, and in all following theoretical rc curves,
the potential is normalized to its value in vacuum. The
widening (narrowing) of the upstream (downstream) part
of the rc is evident. Moreover, the thermal interference
spacing remains nearly unaffected by the drift. Therefore,
drift effects and thermal effects can easily be separated.
A. PIEL: RESONANCE CONE PROBE
Fig. 3. Evaluation chart for converting the measured main maximum
angle θmax (solid lines; labels inside box) and interference angle θint
1/2
(dotted lines; labels outside box) to the density parameter p ∝ n e
−1/2
and temperature parameter R ∝ Te
(from Rohde et al., 1993).
Fig. 4. A drift of the entire electron population influences the rc through
the Doppler effect. (a) Accordingly, for a drift aligned with the magnetic field the upstream part of the rc is widened and the downstream
part narrowed. (b) For a cross-field drift, the rc pattern is apparently
convected with the drift.
To first order of the small quantity vd /vth,e , in which
vth,e = (2kB Te /m e )1/2 is the electron thermal velocity, the
modification of the rc angle is symmetric about the rc angle
in a non-drifting plasma. Therefore, the n e and Te diagnostics can be performed using the arithmetic mean of the main
cone angles as the effective rc angle
eff
θmax
=
1 up
down
.
θmax + θmax
2
(3)
When small asymmetries of the interference spacing are
found, the arithmetic mean of the interference angles should
be used for temperature measurements.
1.3 Beam effects
Besides electron drifts, which are described by a shifted
Maxwellian, electric currents in a plasma are often represented by electron beams. We define a beam to be an additional electron contribution with a directed velocity greater
than the thermal velocity of the background electrons. We
further assume that, for stability reasons, the Penrose criterion (Krall and Trivelpiece, 1986) is fulfilled, i.e., there
is no minimum formed in the total distribution function between the plasma and beam electrons, which would lead to
127
Fig. 5. Calculated rc curves including thermal and drift effects. The
downstream rc (solid line) is narrower than the upstream rc (dotted
line). Note that the interference spacing θ = θmax − θint is practically
unaffected by the drift.
Fig. 6. Theoretical rc curve for vb = 2vth and different beam fractions.
Beam effects become visible in the comparison of the downstream and
upstream part of the rc. In the downstream part, the amplitude of the
main maximum and the modulation degree of the interference pattern
indicate the presence of a beam. The inset shows a sketch for a distribution function with thermal background electrons and a beam of 20%
fractional density.
growing waves. An example for such a one-dimensional
distribution function f (vz ) is sketched in the inset of Fig.
6 and consists of a background Maxwellian (fine solid line)
centered around vz = 0 and a beam at vz ≈ 2vth,e (dashed
line), whose density (beam fraction) is 20% of the background electrons.
Theory predicts that the field-aligned beam excites an
additional Čerenkov cone, which is superimposed on the
resonance cone (Singh, 1980; Thiemann and Singh, 1983).
This Čerenkov cone is caused by a resonance of the wave
speed and beam velocity and therefore only appears in the
direction of the beam. It modifies the downstream part of
the rc, whereas the upstream part of the rc remains nearly
unchanged. Figure 6 shows the calculated rc signal in the
presence of electron beams of different beam fraction. The
representation of the rc in this graph is different from the
previous graphs. Only one half of the rc is shown for each
side of the double cone. The beam direction (downstream)
corresponds to the rc angular range 0–90◦ . The waves
propagating against the beam (upstream) form the rc pattern
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A. PIEL: RESONANCE CONE PROBE
Table 1. Resonance cone instruments used on sounding rockets and satellites (S = satellite, SR = sounding rocket, MD = mother-daughter payload).
Author
Koons et al. (1974)
Folkestad and Tröim (1974)
Folkestad et al. (1976)
Gonfalone (1974)
Michel et al. (1975)
Storey and Thiel (1984)
Thiemann et al. (1988)
Rohde et al. (1993)
Rohde et al. (1995)
Thiemann et al. (1997b)
Carrier
S
MD
MD
SR
SR
SR
SR
SR
SR
SR
Latitude
pol. orbit
polar
polar
polar
polar
polar
equat.
midequat.
equat.
for 90–180◦ .
Laboratory experiments (Oelerich-Hill and Piel, 1989)
have demonstrated the capability of using the modification
by the Čerenkov cone for detecting electron beams. Figure
6 shows the result of numerical calculations for beam fractions increasing from 0.01 to 0.05. One observes that the
upstream rc remains nearly unaffected by the presence of
the beam whereas there is a significant change in the amplitude of the main maximum and in the modulation degree
of the interference pattern on the downstream side. This
asymmetry in the interference pattern can be used to detect beam effects. The shape of the rc depends on the beam
velocity and on the beam fraction. The detection limit for
electron beams was discussed by Rohde et al. (1993). For
a normalized antenna distance R ≈ 100, which is found in
the mid-latitude E-region, a beam with a density fraction of
>3% or with a beam velocity of >3.5 times the electron
thermal velocity would be detectable.
1.4 The evolution of resonance cone probes
Soon after the resonance cone was introduced in laboratory experiments (Fisher and Gould, 1969, 1971; Gonfalone, 1972), the method was adopted for studying the
ionospheric plasma and a series of specialized rc instruments was developed for applications in the polar, midlatitude and equatorial ionosphere. A summary of these instruments is compiled in Table 1. This Section is mainly focused on the technical implementation of the rc instruments
and specific design considerations. The results are primarily discussed in relation to the rc method rather than considering the ionospheric conditions that yield specific plasma
parameters.
1.4.1 The OV1-20S satellite The first implementation of an rc instrument in space was reported by Koons
et al. (1974) and, besides measuring plasma density, aimed
at detecting field-aligned currents. A pair of short electric dipole antennas was mounted on a spin-stabilized boom
system of the polar orbiting OV1-20S satellite as sketched
in Fig. 7(a). The orbit had a 106 min period, 92◦ inclination, 1948 km apogee and 75 km perigee. The antenna system consisted of a 1.12 m long boom on which the transmitting and receiving antenna were mounted at the end of a
56 cm long fiberglass tubes, which formed an angle of 90◦ .
Each dipole element was 1.27 cm long with a separation of
2.54 cm. The spin axis was approximately perpendicular to
Apogee
f
Antenna
(km)
(kHz)
distance (m)
75–1948
192
260
(121)
159
464/451
323
359
324
433/425
300
1100–9000
800–5000
700
700
100–1500
600
606
600
507
0.79
80–850
94–1600
0.80
0.74
0.93
1.0
0.96/1.07
1.0
1.0
the geomagnetic field. The spacecraft spin (6.5 rpm) was
used to scan the resonance cone pattern. The method resembles the approach in laboratory experiments, where a
receiver antenna is rotated about the transmitter antenna at
a fixed distance. While in the laboratory the magnetic field
direction is well known, rc measurements in space need a
magnetometer for reconstructing the magnetic attitude of
the payload and the spin phase angle.
The transmitter frequency was chosen at 300 kHz, which
is below the electron cyclotron frequency that varies between 600 and 1200 kHz during the orbit. A high excitation
voltage of 30 Vpp was used. The received signal was sampled 22 times per second resulting in an angular resolution
of the antenna radiation pattern of about 1.8◦ .
The basic rc phenomenon could be verified by this instrument under actual ionospheric conditions but the resonance main maxima turned out to be much broader than
those observed in corresponding investigations in the laboratory (Fisher and Gould, 1971). No interference structure
could be detected in these data sets. The authors conjectured that the high exciter level led to a substantial increase
of the sheath region about the transmitter antenna, which
may be responsible for the observed broadening. The authors also report that the rc possesses no significant asymmetry, which would have been expected from field-aligned
drifts of the plasma electrons.
1.4.2 Mother-Daughter rocket flights A different
approach for studying rc phenomena was chosen by
Folkestad and Tröim (1974) and Folkestad et al. (1976).
There, two sounding rockets with a separable daughter payload were used to study the ionosphere at auroral latitudes.
The observational geometry is sketched in Fig. 7(b) The
daughter payload was fully equipped with power supplies
and telemetry arrangements. Because the line connecting
the transmitter on the mother payload and the receiver on
the daughter payload formed a fixed angle of (45 ± 3)◦
with respect to the geomagnetic field direction, the rc phenomenon could only be detected by sweeping the transmitter frequency. The sweep range covered the range 1.1 to
9 MHz in Folkestad and Tröim (1974) and 0.8 to 5 MHz in
Folkestad et al. (1976). This compares to a typical electron
cyclotron frequency of f ce = 1.3 MHz at (135–250) km altitude.
The transmitting antenna was an electric dipole of 5 m
A. PIEL: RESONANCE CONE PROBE
129
Fig. 7. Cartoons of the various antenna systems for rc studies. (a) The spin-stabilized boom system of the OV1-20S satellite (T=transmitter, R=receiver,
B=geomagnetic field line), (b) the Mother-Daughter experiments, (c) a fixed-frequency rc with scanning by the rocket spin, (d) the MF probe used in
the PORCUPINE project.
length and the receiving antenna consisted of two discs of
40 cm2 area, which were fed into high-impedance amplifiers and were mounted at the ends of hinged booms of
40 cm length. The transmitter dipole was fed with an rf
voltage of 30 V amplitude at the lowest frequency to 5 V at
the highest frequency. The received signal was processed
by an array of eight channels with bandpass characteristic.
The sharp spikes observed in the first experiment by
Folkestad and Tröim (1974), which occur in the frequency
range of 1.8 to 3.2 MHz, could be identified as upper-hybrid
resonance cones. In the second experiment by Folkestad
et al. (1976), also the conventional lower-hybrid rc was
detected for frequencies below the electron cyclotron frequency. For this purpose the lower limit of the frequency
scan was reduced to 0.8 MHz.
The high transmitter voltage level in these experiments
leads to a number of non-linear effects. Folkestad and
Tröim (1974) report that several harmonics of the transmitter frequency appeared in the channels with higher center
frequencies. A detailed discussion of nonlinear effects can
be found in Folkestad et al. (1976). A general disadvantage of swept-frequency rc instruments is the wide receiver
bandwidth, which picks up natural wave noise and any kind
of spurious signals from other instruments. A discussion of
the various spectral components of natural origin can also
be found in Folkestad et al. (1976).
1.4.3 Scanning by the rocket spin A fixed frequency
rc instrument that uses the rocket spin for scanning the wave
field was used by Gonfalone (1974) for studying the polar
ionosphere from Kiruna, Sweden. The antenna geometry
is shown in Fig. 7(c). One aim of this experiment was to
detect the thermal fine structure of the rc. The transmitting
antenna was a small cylinder of 1.5 cm diameter and 1 cm
length that was mounted on a telescopic boom along the
spin axis. The receiving antenna was also a small cylinder,
but of 0.5 cm diameter and 1 cm length mounted on a lateral
arm. The line connecting the antennas formed an angle of
38◦ with the spin axis. The spin-scanning of the rc could
be applied here because the spin axis formed a large angle
with respect to the geomagnetic field direction.
The transmitting antenna can be considered as an electric
monopole that is fed by rf voltages of stepwise increased
amplitude. The rocket body forms the common “ground”
reference which is shared by the transmitting and receiving monopole. This arrangement differed from the dipoledipole scheme used on the OV1-20S satellite. The amplitude of a sine wave at f = 700 kHz was changed every 2.3 s, taking the values: 0, 0.7, 2.5, and 4.9 Vpp . The
sheath size around the transmitting antenna was reduced by
a positive dc bias of the order of 100 mV with respect to
the rocket body. The received signal was bandpass filtered
with two tuned circuits. The receiver input was protected
by a high-frequency filter tuned to the telemetry frequency
of 240 MHz. A wide dynamic range was achieved by using
a logarithmic amplifier after rectifying the received signal.
The major result of this experiment was the simultaneous
recording of the main rc and its thermal interference structure, from which the electron density and temperature could
be derived.
The same scanning geometry was used in the experiment
performed by Michel et al. (1975), which was launched
from Hayes island, Russia, within the IPOCAMP 1 campaign. The transmitter frequency (700 kHz), antenna distance (74 cm) and orientation angle (42◦ ) were similar to the
experiment of Gonfalone (1974). Unfortunately, the transmitter voltage and bias were not documented in Michel et
al. (1975). The recorded rc signals show the main maximum but the intersection with the interference cone is incomplete due to an unfavourable rocket attitude. The interference pattern shows two minima but the interference max-
130
A. PIEL: RESONANCE CONE PROBE
ima have apparently merged into a single maximum. Nevertheless, by evaluating the main maxima and interference
minima electron density and temperature profiles could be
derived from the rc data using a chart similar to that shown
in Fig. 3.
1.4.4 The medium frequency probe for the PORCUPINE project Within the PORCUPINE project three
Aries rockets were launched from Kiruna, Sweden. A
“medium frequency” (MF) probe was installed to study
field-aligned plasma drifts (Storey and Thiel, 1984; Thiel
et al., 1984). Because the rockets were launched nearly
vertically with the rocket axis being aligned with the geomagnetic field, the MF probe used a complex set of antennas as shown in Fig. 7(d). Four spherical monopole antennas of 3 cm diameter were mounted on radial telescopic
booms which held the antennas at 2 m and 1.5 m distance
from the payload axis, respectively. The boom separation
was 0.79 m. The rocket body served as common ground. It
was pointed out by Storey (2000) that in this case the sheath
impedance of the rocket body becomes a common circuit
element of the transmitter and receiver circuit. Because the
rocket axis coincided with the magnetic field, the attitude of
the wave propagation direction remained fixed during a spin
period. This alleviates the analysis of drift effects in the rc
data. The fixed attitude, however, requires a frequency scan
of the rc, as in the Mother-Daughter experiments.
The MF probe consisted of a transmitter and a receiver
that were connected to a pair of neighboring antennas
through a switching logic. A measurement of drift effects
requires the simultaneous measurement of the rc in forward
and reversed wave propagation direction, as indicated by
the double-tipped arrows in Fig. 7(d). For this purpose, the
frequency sweep was realized in terms of 256 individual
steps that cover the range from 0.1 to 1.5 MHz. Between
each frequency step and the next, the wave propagation direction was interchanged. A complete sweep took 137 ms.
Between each frequency sweep and the next, the sensor arrangement was changed, using the sensor units 1–2, 2–3,
3–4, and again 2–3 in a sequence, as indicated in Fig. 7(d).
While the MF probe was able to detect rc asymmetries
that were expected from field-aligned electron drifts, Storey
and Thiel (1984) concluded that the high apparent velocities
cast doubt on their authenticity. It was suggested that the
MF probe was perturbed by the payload body. Further,
the sensitivity of the method needed to be increased by one
order of magnitude to detect the expected drift velocities.
1.4.5 Resonance cone instrument for the equatorial
ionosphere The method to excite the rc with an electric
monopole antenna on top of the rocket payload and to scan
the wave field by a monopole sensor on a radial boom with
the aid of the rocket spin was also used in the equatorial
ionosphere (Thiemann et al., 1987, 1988). The transmitting
antenna sphere of 10 mm diameter was operated at a frequency of 600 kHz and a voltage of 3 Vpp . The receiver sensor had 22 mm diameter and was mounted on a radial boom
of 1 m length. The Rohini RH560-30 rocket was launched
on 4-May-1987, 10:10h IST, from Sriharicota Range, India.
The rc signals showed clear main maxima and interference
maxima, which allowed a quantitative analysis of the electron density and temperature profiles.
A second flight was performed on 19-April-1993 at
11:20h IST with a refined rc instrument based on the experience with the COREX rc instrument (Rohde et al., 1995).
The quasi-simultaneous measurements of rc’s for forward
and reversed wave propagation direction was used to detect
electron drift effects. Results will be discussed in Subsection 2.4.2.
1.5 The COREX project
The COREX project (Piel et al., 1988b, 1989, 1991)
aimed at studying a winter-time temperature anomaly in
the mid-latitude ionosphere over Japan that was conjectured
to be caused by non-thermal electrons (Oyama and Hirao,
1979; Oyama et al., 1983). For this purpose, an rc instrument was designed that could simultaneously measure
electron density, electron temperature, electron drifts and
electron beams. The instrument was flown on the K-9M-81
rocket from Kagoshima Space Center (31.15N, 131.05E) on
Jan 25, 1988, 11:00 JST. Since the instrument used in this
campaign essentially marks the final stage of evolution of
rc instruments, it will serve as example for the design considerations and typical results of the COREX campaign will
be presented below.
2.
The COREX Instrument
The basic design of the COREX rc instrument comprised
a fixed-frequency transmitter and a set of three electric
monopole antennas that were mounted on a central telescopic boom and two radial arms of different lengths (Fig.
8). The transmitter frequency was designed to be at f =
600 kHz ≈ f ce /2 to obtain an optimum sensitivity of the rc
angle on plasma density. The actual transmitter frequency
was 606 kHz at a transmitter level of 0.72 Vpp . The radiation field was scanned using the rocket spin. The rocket attitude could be reconstructed from magnetometer data. The
payload also comprised an impedance probe (NEI) and a
temperature sensor (TEL), which could be used for comparison with the rc data. For detecting electron drifts and
Fig. 8. The antenna geometry and switching scheme for the COREX rc
instrument.
A. PIEL: RESONANCE CONE PROBE
131
Fig. 9. The antenna design for the COREX project. (a) Two hinged booms and a central telescopic boom in stowed and deployed position. The lines of
sight form angles of 29◦ and 38◦ w.r.t. to the payload axis. The nose cone is indicated by the dashed line. (b) Photograph of the stowed antennas.
Fig. 10. Block diagram of the COREX rc instrument.
Fig. 11. The front end of the transmitter / receiver circuit in the COREX
rc instrument.
made of a pair of hollow brass hemispheres that contained
electron beams the COREX instrument performed a set of part of the first preamplifier stage and the switching logic.
interlaced measurements by rapidly interchanging the role The surface was polished and coated with a thin gold layer.
of transmitter and receiver within a pair of sensors (Fig. 8). The sensors were attached to the boom by a conical shaft
made of polyimide, as can be seen in Fig. 9(b).
2.1 Mechanical aspects
The reconstruction of the true wave propagation angle θ
The antenna aspect angle α had to be chosen in such
with
respect to the magnetic field is performed using the
a way that it matched the expected magnetic attitude an◦
formula
gle σ ≈ 35 during the flight. Under ideal conditions,
the measured rc pattern should then cover the entire range
cos θ = sin σ sin α cos ϕ + cos σ cos α ,
(4)
0 < θ < 2α. Due to coning of the rocket, however, σ may
change during the flight and the smallest wave propagation in which ϕ is the spin phase angle. It should be mentioned
angle becomes |σ − α|, which may lead to a merging of the that small errors in determining the spin-phase angle had
interference maxima. For minimizing such unfavourable been reported earlier (Michel et al., 1975) and were atconditions, the COREX instrument was equipped with two tributed to induced currents in the payload hull. A simbooms of different length that resulted in aspect angles of ilar zero-point correction was made for the COREX-data
α1 = 28.7◦ and α2 = 37.7◦ . The antenna distance was (Rohde et al., 1993). These ambiguities can be minimized
0.96 m and 1.07 m respectively. This distance was inten- by placing the magnetometer at the end of a boom, as in the
tionally chosen larger than the 70–80 cm distance in earlier DEOS campaign (Thiemann et al., 1997a, b).
instruments (Gonfalone, 1974; Michel et al., 1975; Storey 2.2 Electronics design
The block diagram of the COREX rc instrument is shown
and Thiel, 1984) in order to find more pronounced rc interference structures, which are known to become sharper in Fig. 10. The sinusoidal signal of f = 606 kHz frequency
towards the far field. The details of the boom system are is fed to one of the three sensors via a switching matrix
which also selects the receiving sensor. The received signal
shown in Fig. 9.
The spherical sensors of 22 mm outer diameter were is bandpass filtered, amplified and rectified. The resulting
132
A. PIEL: RESONANCE CONE PROBE
Fig. 12. The data arrangement within the telemetry frame. The strobe pulse STROBE1 is used for advancing the mode switch to the next position.
DC voltage is A/D converted with 12 bit resolution and
transferred as two bytes to the digital telemetry input. Two
additional bits are used to encode the mode of the antenna
switch. The antenna mode is advanced by the data strobe
signal from the telemetry.
The sensor spheres contain the front end of the transmitter and receiver circuit (Fig. 11). The transmitter signal is
connected to the sensor sphere via the FET-switch T1 and
a blocking capacitor of 1 µF. The sensor can be biased by
a current source formed by the bias voltage (+15 V) and
a 10 M series resistor. In receiving mode, the transmitter is decoupled from the sensor by a switch in the electronics box. In addition, T1 is switched off to a highimpedance state to eliminate the capacitive load by the
feeder cable. Then, the received signal appears at the gate
of T2 with practically 1 M input impedance. T2 and T3
form a preamplifier with about 20 dB gain and a low output impedance. The amplified signal is connected to the
receiver box by a 50 cable. For minimizing the size of
the pre-amplifier, SMD components were used for the capacitors and resistors. As suitable SMD FETs were not yet
available in 1987, conventional components had to be used.
T1 and T2 are a dual n-channel J-FET (TD5912) with a low
input capacitance (<5 pF) in a TO-71 package and T3 is a
bipolar pnp transistor BFX48 in a TO-18 package. Because
of the negative feedback, the effective input capacitance of
the receiver was 1–2 pF.
The interplay between the rc instrument and the telemetry scheme can be retrieved from Fig. 12. The bit rate of
the telemetry system was 102.4 kBit/s with 200 frames per
second. Each frame of 5 ms duration is subdivided into 64
words of 8 bit length. These words have the octal numbers W00–W77. The COREX rc instrument was allotted
8 × 2 words per frame, which are marked W00/W01 to
W70/W71. The rc data comprise 12 bits, which are stored
in two subsequent words, as shown in the top row. The remaining half-byte is used two transmit the actual mode by
the bits A0/A1.
The data is read from the rc instrument by means of two
strobe signals. The signal STROBE1 was also used to advance the mode switch every 625 µs to the next position
after the data from the previous cycle was processed. This
leaves roughly 500 µs for the analog processing to settle
and for performing the A/D-conversion. A set of four interlaced rc data is completed every 2.5 ms, thus giving a net
data rate of 400 s−1 . For a spin rate of about 1.8 s−1 , we
could obtain about 220 data sets per revolution. This corresponds to an angular resolution of about 1.6◦ . The electronics box of the COREX rc instrument had dimensions
of 180 mm length, 105 mm width and 105 mm height. The
mass was 1550 g and the power consumption 2.9 W.
2.3 Strength and weakness of the resonance cone
method
The rc method has the advantage that the measurement
of electron density and temperature is only determined by
the plasma medium between the transmitting and receiving
antenna. In this way, it is a non-invasive technique and is
also insensitive to surface contamination of the sensors. The
same information on electron density and temperature can
in principle be derived from Langmuir probe characteristics
when special precautions are taken to minimize surface contamination of Langmuir probes (Oyama, 1976; Amatucci et
al., 2001), which would lead to overestimating the electron
temperature or need a dedicated correction algorithm (Piel
et al., 2001; Hirt et al., 2001). With the COREX instrument, a mature state of the rc method on sounding rockets
had been reached. A slightly modified descendant of this instrument was later flown on three sounding rockets within
the DEOS campaign (Thiemann et al., 1997a, b).
2.4 Typical results
The detailed results from the COREX campaign can be
found in Rohde et al. (1993). The rc booms were deployed
after 51.7 s at an altitude of 75.8 km. An apogee of 359 km
was reached at 366 s flight time. The geomagnetic aspect
angle σ varied between 35◦ and 55◦ , which was larger than
expected. Therefore, the rc instrument could not cover the
interference peaks for some time, which caused a few data
gaps for temperature evaluation.
2.4.1 Density and temperature profiles During one
spin period of the rocket, we obtain four readings of the resup
onance cone maximum angle from one sensor pair, |θL |,
up
down
down
|θL |, |θR | and |θR |. There is a similar set of four readings for the interference maximum angle. All these four
angles are sensitive to plasma density, electron temperature
and electron drift. In a real plasma situation, one has to
manage all these effects simultaneously. As will become
evident from Table 2, the influence of the drift cancels in
the average of all four angles, because of symmetry. Hence,
the averaged maximum angles and interference maximum
angles can be used to deduce electron density and tempera-
A. PIEL: RESONANCE CONE PROBE
Fig. 13. (a) Electron density profile and (b) electron temperature profile at
E-region altitudes. The full lines give the comparison with independent
instruments.
ture with the aid of the universal diagram in Fig. 3.
In the E-region, main maxima and interference maxima
are clearly visible, as shown in Fig. 2. Even second-order
interferences appear. From the average cone angles density
profiles are compiled for the upleg and downleg of the trajectory. Figure 13 shows the comparison of the rc data with
the impedance probe and temperature probe. In this altitude
regime, a good agreement is found between the rc technique
and conventional techniques.
In the F-region, the situation for the rc method is different. At high plasma density, the rc angle θmax becomes
insensitive to electron density. This can be seen in Fig. 14.
The maximum angle approaches a limiting angle, which is
marked by the dotted line.The conventional rc technique by
reading the angular position of the main maximum, therefore, faces a density maximum, which prevents a density
measurement for p > 3.
This limitation can be circumvented by noting that the rc
amplitude continuously decreases with plasma density, as
shown by the dashed line in Fig. 14. The evaluation of rc
amplitudes does not yield absolute density values but needs
a calibration in a regime, where the main cone angle is still
sensitive. Such a calibration was performed in the COREX
campaign at E-region altitudes and allowed an extension of
the density measurements into the F-region. The extrapolation is based on the assumption that the impedance of the
sheath around the sensors is small compared to the plasma
impedance between transmitter and receiver.
The resulting density profile is shown in Fig. 15(a) in
comparison with the data from the impedance probe. The
profiles show a satisfying absolute agreement. An electron
density maximum is found at about 260 km altitude.
The evaluation of the interference structures for electron
temperature measurements was hampered by rocket coning,
which caused an unfavourable attitude of the rocket axis in
two parts of the F-region (Rohde et al., 1993). In Fig. 15(c)
the attitude angle σ is plotted. When σ > 45◦ , the minimum detectable angle became 7.3◦ < θ < 17.3◦ , which
led to a merging of the interference maxima. Therefore, for
evaluating the electron temperature, evaluation charts had
133
Fig. 14. The rc angle θc (full line) approaches a density limit, indicated
by the dotted line. The amplitude of the rc maxima (dashed line) can be
used to circumvent the density limit.
been calculated that involved the positions of the main maximum and the first interference minimum. This procedure
gives the temperature values displayed in Fig. 15(b). In the
regime σ < 45◦ the measured electron temperatures show
a good agreement with data from the temperature sensor.
For larger rocket attitudes, the resulting electron temperatures became unreliable or even data gaps appeared, when
the interference minima disappeared.
2.4.2 Drift effects The peculiarity of the rc method
is its sensitivity to electron drift effects. In order to gain
a deeper understanding of the relationship between resonance cone shifts and the underlying drift, we have to analyse the wave propagation geometry in more detail. In Fig.
16 the COREX antenna system is shown for the case that
the rc is excited by antenna I and the wave field is scanned
by antenna II, which intersects the rc at positions L and R
that correspond to the left and right maxima in the rc plots.
These reference points correspond to the non-drifting case
and the drift effects are treated as linear perturbations to this
geometry. Since the rc represents the energy flow from the
transmitter to receiver, the group velocity vector v g points
from transmitter to receiver and is tangential to the rc. It
is the peculiarity of a magnetoplasma that group velocity
and wave vector k become perpendicular at resonance (Stix,
1962) and lie in a plane that contains the magnetic field direction. Since the rc shift is effected by the Doppler effect ω = k · v d , the rc is only sensitive to the projection
of the drift velocity v d on the k-direction. Fortunately, we
have two different wave vectors for the L and R intersections, which have the same z -component but opposite y components. This allows us to reconstruct two components
of the drift velocity vector.
When we describe the Doppler effect in a coordinate
system (x , y , z ) that is aligned with the magnetic field
direction (see Fig. 16), the frequency shift is given by k ·
v d = k z vz + k⊥ v⊥ cos(β). Here, β is the angle between
v ⊥ and k ⊥ . Noting that k⊥ ≈ −k z cot(θmax ), we obtain an
analytical expression for the modification of the main cone
134
A. PIEL: RESONANCE CONE PROBE
Fig. 15. (a) Electron density profile in the F-region compared with impedance probe (NEI) results. (b) Electron temperature profile compared with
temperature probe (TEL). For an unfavourable rocket attitude, σ > 45◦ the interference maxima tend to merge and lead to unreliable temperature
values and even data gaps, when the minima disappear. (c) Attitude angle σ with respect to the magnetic field direction.
Fig. 17. The field-aligned and cross-field component of the drift velocity
measured during the COREX flight. Each data point is an average over
3 s.
Fig. 16. Resonance cone with L and R intersection points by the receiving
antenna. The rc half-angle is θmax Here, σ is the magnetic attitude of the
rocket and φ the spin phase angle. The group velocity vg is aligned with
which determines the doppler effect,
the rc, whereas the wavevector k,
is perpendicular to the rc.
angle at the L and R intersection points
θL,R
∂θmax
=
k z (vz − cot θmax v⊥ cos β) .
∂
Table 2. Drift-related shifts of the rc maxima for reversed wave propagation direction.
Left maximum (L)
Right maximum (R)
Forward
θmax − θL + θB
θmax − θR − θB
Reversed
θmax + θL + θB
θmax + θR − θB
(5)
The proper value of k z has to be taken at the inflection point
of the dispersion curve (Rohde et al., 1993). This expression turned out to be sufficiently accurate for R > 150. For
smaller distances, we have used the full kinetic model to
determine the proper coefficient for the field-aligned drift,
which was then used in Eq. (5) for the case of arbitrary drift
direction.
The influence of the electron drift on the four maxima of
the rc pattern is summarized in Table 2. Here, θmax is the rc
angle in a non-drifting plasma, θL and θR are the shift
of the left and right maximum due to the drift and θB is
an uncertainty of the zero point of the horizontal magnetic
field.
For a purely field-aligned electron drift we have θL =
−θR , which results in the simple up-down asymmetry described in Fig. 4(a). For an arbitrary drift geometry, we
find θL = −θR and can reconstruct the field-aligned
and cross-field component of the electron drift velocity, as
shown in Fig. 17. It turned out that the cross-field component was much larger than the field-aligned component.
In this way, the finding of the COREX flight was that the
rc does not possess the symmetry expected for field-aligned
drifts (Piel et al., 1992a, b). Moreover, the magnitude
of the electron drift, vd ≈ 30–35 km s−1 , corresponding
to ≈6% of the electron thermal velocity, is unexpectedly
high. Wind velocities in the mid-latitude thermosphere are
A. PIEL: RESONANCE CONE PROBE
135
Fig. 18. (a) The measured rc patterns in the mid-latitude COREX campaign. RC modes 4 (full line) and 3 (dotted line) show a shift of the rc in azimuthal
direction. (b) Geometry of an electron E×B drift resulting from the potential difference between payload body and ambient plasma.
Fig. 19. (a) The measured rc patterns in the equatorial SPICE-3 campaign. A polar plot of the RC in forward (full line) and reversed mode (dotted line)
shows a shift of the rc perpendicular to the magnetic field direction. (b) The geometry of the electron E×B drift has changed according to the nearly
horizontal magnetic field direction.
typically below 1 km s−1 . Unusually high cross-field drifts
of up to 8.8 km s−1 were also reported by Storey and Thiel
(1984). This value was much larger than the one derived
from electric field measurements of v⊥ ≈ 0.5 km s−1 .
Assuming that, for the COREX data, the cross-field drift
were an extended phenomenon in the ambient ionospheric
plasma, we would obtain a cross-field current density of
j⊥ ≈ 5 mA m−2 , which is much beyond the Sq-current
density of 5–10 µA m−2 . Such large currents should have
also been visible in the magnetometer data. Therefore, we
had concluded that the electron drift is a phenomenon that
is restricted to the immediate rocket environment.
Besides the magnitude of the observed drift, also the
topology of the rc shifts hints at a local effect. The main
maxima in one antenna mode show a characteristic shift in
angular direction with respect to the maxima in the corresponding mode for reversed wave propagation direction, as
can be seen in Fig. 18(a) (Rohde et al., 1993). Applying
the fundamental idea that the rc is convected with the flow,
this pattern was attributed to a circulation of the electrons
around the rocket, as sketched in Fig. 18(b).
The origin of this electron circulation was attributed to
an E×B drift that arises from an electrostatic field in the
vicinity of the payload body. It is known from Langmuir
probe characteristics taken on the same flight that the pay-
load floats at a potential of f ≈ −2 V with respect to the
ambient plasma. The observed angular shift of the rc pattern can be converted to an effective electric field, which
is typically 0.1 V m−1 in the E-region and 0.4 V m−1 in the
F-region.
Similar electron circulation effects on the rc pattern were
also observed in the equatorial ionosphere (Rohde et al.,
1995). There, the nearly horizontal magnetic field yields an
approximately perpendicular orientation of the rocket axis
with respect to the magnetic field, which allows a measurement of both halves of the double cone. This geometry
would also lead to a circulation pattern that convects the
rc in cross-field direction. Such a topology of the rc becomes evident from polar plots of the rc amplitude signal
shown in Fig. 19(a). Notice how all four maxima in the
dashed contour are convected across the magnetic field direction. The geometry of the E×B-flow for a large attitude
angle σ ≈ 82◦ is sketched in Fig. 19(b) and would lead to a
mainly cross-field convection of the rc pattern.
The electron drift also affects the rc amplitudes, as can be
seen in the calculated rc pattern in Fig. 5. The upstream rc
maxima are higher than those downstream. This effect on
the amplitudes is also found in the COREX results in Fig.
18, where in the solid curve the left maximum is higher than
the right and—for reverted wave propagation direction—
136
A. PIEL: RESONANCE CONE PROBE
3.
Fig. 20. Correlation between rc shifts and amplitude modification in the
COREX data.
the right becomes larger than the left maximum. This gives
a further hint that the observed rc modification can be attributed to drift effects. The same reversal of the amplitude
asymmetry is also found in the SPICE-3 data as can be seen
most clearly on the the right-hand part of the polar plot in
Fig. 19(a). It was shown by Rohde et al. (1993) that this
pattern is not accidental but a systematic effect, by plotting
the angular shifts θ vs. the amplitude variation A, which
resulted in a very high correlation as shown in Fig. 20.
It was, however, not possible to derive the drift velocities from the amplitude effects. This is mainly due to the
fact that the rc instrument had an unknown signal background from clock noise and electromagnetic interference
from other instruments. This background could not be measured during the flight because there was no “transmitter
off” mode available. Therefore, the reference amplitude A
in Fig. 20 uses only an estimate for such a background. In
future instruments, a careful calibration of the received signal could make amplitude effects accessible as an independent check of drift effects.
In summary, the drift effects in the COREX campaign
were not of geophysical origin, but could be attributed to
electron E×B motion in the immediate rocket environment.
A more detailed discussion of the magnitude of the electric
field derived from the cross-field drift data in comparison
with theoretical predictions can be found in Rohde et al.
(1993).
The typical asymmetries in the interference pattern of the
rc that are caused by electron beams could not be found in
the COREX data. The detection limit of the COREX instrument was discussed in Rohde et al. (1993). For assumed
beam velocities of 2vth,e and 3vth,e , the observed fluctuations in the modulation of the downstream interference pattern remained below the detection limit. The absence of
beam effects agrees with the observation of the other instruments that there was no temperature anomaly present during
the K-9M-81 flight, which would have been expected in the
presence of anomalous plasma heating by beams.
Improvements and Alternatives
The measurement of electron density and temperature by
using rc angles proved to be reliable at E-region altitudes. In
the F-region, density measurements require the analysis of
rc amplitudes. Temperature measurements in the F-region
require a proper resolution of the interference structure. The
general layout of a future rc instrument could start from the
COREX design, which represented the “state of the art” at
its time.
Comparing the rc technique with other established methods for electron density measurements, it turned out that
impedance probes and Langmuir probes can give much
higher spatial resolution than the rc method. Moreover, the
determination of absolute electron densities and irregularities by impedance and Langmuir probes proved to be highly
accurate, see e.g. Steigies et al. (2001), Hirt et al. (2001).
These competing techniques do not require a complex boom
system but rely on a single sensor, only. On the other hand,
the impedance probe with its typical frequency sweep from
0.5 to > 10 MHz may be in conflict with other instruments,
whereas an rc probe with a coherent signal at ≈600 kHz
may be tolerable.
When the focus lies on electron density and temperature measurements, a general improvement for the accurate
measurement of rc angles could be achieved by larger antenna separations of ≈2–3 m. Then, the thermal interference spacing θ would diminish (Fisher and Gould, 1971;
Kuehl, 1974) and the interference maxima could be resolved even at F-region altitude. A further significant improvement could also be a achieved by a narrow rocket coning angle that provides an optimized matching of the magnetic attitude σ with the antenna orientation angle α.
An important result from the COREX and SPICE-3 experiments was the observation that the immediate rocket
environment is affected by local electron drifts. For separating geophysical electron drifts from local effects even
longer boom systems should be considered, similar to those
used for electric field measurements. Progress in this field
will depend on a deeper understanding of the shielding of
the rocket by the ambient magnetoplasma.
Doubtlessly, the electronics of the rc instrument could be
improved by the advancement in electronics, in particular
through the availability of SMD components that allow an
even larger part of the preamp and switch electronics being
integrated into the sensor spheres. The signal-to-noise ratio
of the receiver section would benefit from integrating the
first bandpass filter into the sensor. For an unambiguous
information about the interference from other instruments,
the rc transmitter should be switched off at regular intervals.
The angular resolution of the rc instrument will benefit from
today’s higher telemetry rate that lie in the Mbit/s range,
compared to the 100 kbit/s in 1988. The angular resolution
of the COREX instrument was limited by the fact that it
consumed 25% of the available total telemetry capacity.
The use of modern electronic components could also lead to
a substantial reduction in size and weight of the electronics
box.
The detection of subthermal electron drifts and electric currents by in-situ techniques is still a challenging
task. Large-scale plasma motion is nowadays detected with
A. PIEL: RESONANCE CONE PROBE
ground-based techniques like Doppler-radar measurements,
which e.g., have revealed many details of the equatorial
ionosphere. Plasma motion is also investigated indirectly
by electric field measurements aboard satellites and rockets,
which yield the driving force for the drifts. Therefore, for
a direct verification of electron drifts future improved rc instruments may help clarifying the distribution, homogeneity and variability of these electron currents. Moreover, the
case of non-Maxwellian distribution functions, which affect
the propagation of lower-hybrid waves in such a characteristic way, will be a suitable target for rc measurements.
In conclusion, further improved rc instruments are
promising candidates for the study of subthermal electron
drifts or low-energy electron beams and will give supporting information about electron density and temperature.
Acknowledgments. The author is indebted to the late Heinz Thiemann, whose expertise and leadership as co-investigator or principal investigator have made the COREX and DEOS projects a
success. These investigations were funded by BMFT/DARA and
DLR, which is gratefully acknowledged.
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A. Piel (e-mail: [email protected])