Resonance cone probe for measuring electron density ... · Resonance cone probe for measuring electron density, temperature, drift speed and beam components A. Piel Institut f¨ur

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 fur Experimentelle und Angewandte Physik, Christian-Albrechts-Universitat, 24098 Kiel, Germany

The diagnostics of the ionospheric plasma by in-situ measurements of the lower-oblique resonance of amagnetized plasma is described. The electron density and temperature are derived from a nested set of resonancecones that is excited by a small antenna and detected by a movable receiver. Asymmetries of the resonancecones give access to electron drifts or electron beams. A detailed discussion of the hardware of resonance coneinstruments is included.Key words: Plasma parameters, drift velocity, lower oblique resonance.

1. Ionospheric Diagnostics with Resonance ConesThe key parameters that define the state of the ionosphere

are the electron density ne and temperature Te, their altitudeprofiles and their diurnal and seasonal variablity at differ-ent latitudes. In some cases, the ionospheric plasma is ina non-equilibrium state that is caused by electric currents.Such currents can arise from the motion of the entire popu-lation of thermal electrons and we will use the terminology“drift” for the bulk velocity of a shifted Maxwellian electrondistribution. Otherwise, currents can be caused by groupsof suprathermal electrons that have a preferential directionand are superimposed on a background of thermal electrons.We will refer to such groups of electrons as “beams”. Elec-tron drift motion and electron beams represent a source offree energy that can lead to plasma instabilities and electronheating. Therefore, modern ionospheric diagnostics also at-tempts to measure these drifts or beams.

There are various techniques for simultaneous in-situmeasurements of ne and Te, e.g. Langmuir probes (Pfaff,1996), or dedicated instruments like the impedance probefor ne (Oya, 1967; Steigies et al., 2000) and the tempera-ture probe for Te (Hirao and Oyama, 1970). On the otherhand, in most cases only indirect methods are available fordetecting the current distribution, such as magnetometers.The resonance cone (rc) method tries to fill this gap in asingle instrument that allows a simultaneous measurementof ne, Te and the drift velocity vd, as well as the beam den-sity and beam velocity.

The ionospheric E- and F-layers represent a weakly col-lisional magnetoplasma. The rc method uses the anisotropyof this plasma, which is introduced by the magnetic fieldand affects the propagation of electromagnetic waves. Forwaves propagating strictly perpendicular to the magneticfield, the ordinary wave (which has E ||B) is unaffected bythe magnetic field and has a refractive index N = (1 −ω2

pe/ω2)1/2, ωpe being the electron plasma frequency. The

extraordinary wave (which has E ⊥ B) exhibits fundamen-tal resonances (N 2 → ∞) at the lower hybrid frequency

Copyright c© TERRAPUB, 2013.

ωlh, defined by Stix (1962)

1

ω2lh

= 1

ω2ci + ω2

pi

+ 1

ωciωce, (1)

and at the upper hybrid frequency ωuh = (ω2pe + ω2

ce)1/2.

Here, ωci and ωce are the ion and electron cylotron fre-quencies and ωpi the ion plasma frequency. Waves in thefrequency regime ωci < ω < ωce, which are propagatingalong the magnetic field (k||B), are called Whistler waves.For oblique wave propagation direction, the resonance fre-quency also depends on the propagation angle.

In such a magnetized plasma the radiation field of a smallantenna that is excited at an (angular) frequency ω becomesresonantly enhanced for a characteristic propagation anglew.r.t. the magnetic field direction. There are two frequencyregimes, where such resonances occur, the lower-hybridregime ωlh < ω < min(ωpe, ωce) and the upper-hybridregime 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 andGould, 1969) is aligned with the magnetic field directionand 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 scanningthe wave field with a small receiver antenna that is mountedon a radial boom and rotates utilizing the payload spin. Forincreasing the data rate and for matching the attitude of thepayload with respect to the magnetic field, two radial boomsof different length can be used.

In the cold-plasma approximation and neglecting ion ef-fects, the rc angle θc is given by the formula (Fisher andGould, 1969)

sin2(θc) = ω2(ω2pe + ω2

ce − ω2)

ω2pe ω2

ce

. (2)

The rc angle depends on the electron density ne throughthe electron plasma frequency ωpe = [nee2/(ε0me)]1/2, me

being the electron mass. The electron cyclotron frequencyωce = eB/me 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 ismounted on a vertical boom. The radiation field is scanned by rotatinga receiver antenna on a radial boom by means of the payload spinmotion. A second receiver antenna can be used to increase the datarate. The vector B indicates the magnetic field direction and θc is thecone half-angle.

magnetic field B(h) at an altitude h. Since all other param-eters entering in (2) are known, the rc angle can be used todetermine the electron density. The rc method is most sen-sitive for ωpe < ωce but approaches a density limit at aboutωpe ≈ (2 − 3)ωce (Rohde et al., 1993). Therefore, the clas-sical rc method can be used for ionospheric research in thedaytime E-region, the E-F valley and the lower F-region, aswell as in the nighttime F-region. The density limit encoun-tered in the F-region can be circumvented by evaluating therc amplitude (Rohde et al., 1993). The rc method is alsosuitable for the plasma in the magnetosphere (Koons et al.,1974).1.1 Thermal effects

The rc possesses an internal interference structure, firstdetected in the laboratory experiments of Fisher and Gould(1969, 1970, and 1971), which is an effect from electrontemperature (Fig. 2). The half-angle of the main maximumθmax is now slightly shifted from the cold-plasma angleθc. In the far field of the antenna, the shift vanishes andthe relative position of the first interference maximum withrespect to the main maximum, �θ = θmax − θint, is used asa temperature diagnostic.

Analytical expressions for this interference spacing,which are based on the small parameter �θ/θc � 1, weregiven by Fisher and Gould (1970, 1971), Gonfalone (1972),Kuehl (1973) and Chasseriaux (1975), but are only use-ful for a large separation d of transmitter and receiver an-tenna, d > 200 rce, rce = (kBTe/me)

1/2ω−1ce being the ther-

mal electron Larmor radius. The applicability of these ap-proximations was critically tested in laboratory experiments(Burrell, 1975). The situation is different on sounding rock-ets, where the boom length limits the antenna distance tod < 100 rce, typically. In this situation �θ is no longersmall compared to θc. Therefore, the near field of the an-tenna must be calculated using kinetic theory (Singh andGould, 1973; Storey and Thiel, 1978; Storey et al., 1980; deFeraudy, 1986). Peculiarities of the thermal interferenceswere experimentally confirmed in laboratory experimentsby Piel and Oelerich (1984, 1985).

For the near field, it becomes more practical to consider

Fig. 2. Typical experimental rc signal in the mid-latitude ionosphere atabout 120 km altitude. The two main maxima θmax represent the reso-nance cone. The first-order thermal interference maxima and minimaare labeled θint and θmin. The signal marked NEI is an electromagneticinterference from an impedance probe.

the angles of main maximum and first interference max-imum as independent quantities. We have therefore con-verted the results from kinetic theory to evaluation chartsthat display the rc angles θmax and θint in a plane spannedby the density parameter �p = ωpe/ωce ∝ n1/2

e and thetemperature parameter R = d/rce ∝ T −1/2

e , as shown inFig. 3. Such charts were calculated for different normal-ized transmitter frequencies � = ω/ωce. The details of thecalculation can be found in Rohde et al. (1993). The inter-section 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 in-creases with the transmitter frequency. A similar deforma-tion of the rc occurs by the Doppler effect when the entireelectron population performs a B-field-aligned drift motion:the cone is widened on the upstream side and narrowed onthe downstream side, as shown in Fig. 4(a). First attemptsto include drift effects on the rc were made by Kuehl (1974)for the case of a field-aligned drift. This approach was ex-tended 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), Karp-man and Fiala (1988). Experimental evidence for field-aligned drifts from laboratory experiments was given by Il-liano and Pottellette (1979) and Lucks and Kramer (1980).The application of rc’s to measure field-aligned currents inthe ionosphere was discussed in Pottelette (1972), Storeyand Thiel (1984). In a simplified view, in both cases the rcis convected with the flow. A first-order approximation toarbitrary 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 field-aligned drift in the near field is shown in Fig. 5 (Rohde etal., 1993). Here, and in all following theoretical rc curves,the potential is normalized to its value in vacuum. Thewidening (narrowing) of the upstream (downstream) partof the rc is evident. Moreover, the thermal interferencespacing remains nearly unaffected by the drift. Therefore,drift effects and thermal effects can easily be separated.

A. PIEL: RESONANCE CONE PROBE 127

Fig. 3. Evaluation chart for converting the measured main maximumangle θmax (solid lines; labels inside box) and interference angle θint

(dotted lines; labels outside box) to the density parameter �p ∝ n1/2e

and temperature parameter R ∝ T −1/2e (from Rohde et al., 1993).

Fig. 4. A drift of the entire electron population influences the rc throughthe Doppler effect. (a) Accordingly, for a drift aligned with the mag-netic field the upstream part of the rc is widened and the downstreampart narrowed. (b) For a cross-field drift, the rc pattern is apparentlyconvected with the drift.

To first order of the small quantity vd/vth,e, in whichvth,e = (2kBTe/me)

1/2 is the electron thermal velocity, themodification of the rc angle is symmetric about the rc anglein a non-drifting plasma. Therefore, the ne and Te diagnos-tics can be performed using the arithmetic mean of the maincone angles as the effective rc angle

θ effmax = 1

2

(θup

max + θdownmax

). (3)

When small asymmetries of the interference spacing arefound, the arithmetic mean of the interference angles shouldbe used for temperature measurements.1.3 Beam effects

Besides electron drifts, which are described by a shiftedMaxwellian, electric currents in a plasma are often repre-sented by electron beams. We define a beam to be an addi-tional electron contribution with a directed velocity greaterthan the thermal velocity of the background electrons. Wefurther assume that, for stability reasons, the Penrose cri-terion (Krall and Trivelpiece, 1986) is fulfilled, i.e., thereis no minimum formed in the total distribution function be-tween the plasma and beam electrons, which would lead to

Fig. 5. Calculated rc curves including thermal and drift effects. Thedownstream rc (solid line) is narrower than the upstream rc (dottedline). Note that the interference spacing �θ = θmax − θint is practicallyunaffected 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 andupstream part of the rc. In the downstream part, the amplitude of themain maximum and the modulation degree of the interference patternindicate the presence of a beam. The inset shows a sketch for a distri-bution function with thermal background electrons and a beam of 20%fractional density.

growing waves. An example for such a one-dimensionaldistribution 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 (dashedline), whose density (beam fraction) is 20% of the back-ground electrons.

Theory predicts that the field-aligned beam excites anadditional Cerenkov cone, which is superimposed on theresonance cone (Singh, 1980; Thiemann and Singh, 1983).This Cerenkov cone is caused by a resonance of the wavespeed and beam velocity and therefore only appears in thedirection of the beam. It modifies the downstream part ofthe rc, whereas the upstream part of the rc remains nearlyunchanged. Figure 6 shows the calculated rc signal in thepresence of electron beams of different beam fraction. Therepresentation of the rc in this graph is different from theprevious graphs. Only one half of the rc is shown for eachside of the double cone. The beam direction (downstream)corresponds to the rc angular range 0–90◦. The wavespropagating against the beam (upstream) form the rc pattern


Table 1. Resonance cone instruments used on sounding rockets and satellites (S = satellite, SR = sounding rocket, MD = mother-daughter payload).

Author Carrier LatitudeApogee f Antenna

(km) (kHz) distance (m)

Koons et al. (1974) S pol. orbit 75–1948 300 0.79

Folkestad and Troim (1974) MD polar 192 1100–9000 80–850

Folkestad et al. (1976) MD polar 260 800–5000 94–1600

Gonfalone (1974) SR polar (121) 700 0.80

Michel et al. (1975) SR polar 159 700 0.74

Storey and Thiel (1984) SR polar 464/451 100–1500 0.93

Thiemann et al. (1988) SR equat. 323 600 1.0

Rohde et al. (1993) SR mid- 359 606 0.96/1.07

Rohde et al. (1995) SR equat. 324 600 1.0

Thiemann et al. (1997b) SR equat. 433/425 507 1.0

for 90–180◦.Laboratory experiments (Oelerich-Hill and Piel, 1989)

have demonstrated the capability of using the modificationby the Cerenkov cone for detecting electron beams. Figure6 shows the result of numerical calculations for beam frac-tions increasing from 0.01 to 0.05. One observes that theupstream rc remains nearly unaffected by the presence ofthe beam whereas there is a significant change in the am-plitude of the main maximum and in the modulation degreeof the interference pattern on the downstream side. Thisasymmetry in the interference pattern can be used to de-tect beam effects. The shape of the rc depends on the beamvelocity and on the beam fraction. The detection limit forelectron beams was discussed by Rohde et al. (1993). Fora normalized antenna distance R ≈ 100, which is found inthe mid-latitude E-region, a beam with a density fraction of>3% or with a beam velocity of >3.5 times the electronthermal velocity would be detectable.1.4 The evolution of resonance cone probes

Soon after the resonance cone was introduced in labo-ratory experiments (Fisher and Gould, 1969, 1971; Gon-falone, 1972), the method was adopted for studying theionospheric plasma and a series of specialized rc instru-ments was developed for applications in the polar, mid-latitude and equatorial ionosphere. A summary of these in-struments is compiled in Table 1. This Section is mainly fo-cused on the technical implementation of the rc instrumentsand specific design considerations. The results are primar-ily discussed in relation to the rc method rather than consid-ering the ionospheric conditions that yield specific plasmaparameters.

1.4.1 The OV1-20S satellite The first implementa-tion of an rc instrument in space was reported by Koonset al. (1974) and, besides measuring plasma density, aimedat detecting field-aligned currents. A pair of short elec-tric dipole antennas was mounted on a spin-stabilized boomsystem of the polar orbiting OV1-20S satellite as sketchedin Fig. 7(a). The orbit had a 106 min period, 92◦ inclina-tion, 1948 km apogee and 75 km perigee. The antenna sys-tem consisted of a 1.12 m long boom on which the trans-mitting and receiving antenna were mounted at the end of a56 cm long fiberglass tubes, which formed an angle of 90◦.Each dipole element was 1.27 cm long with a separation of2.54 cm. The spin axis was approximately perpendicular to

the geomagnetic field. The spacecraft spin (6.5 rpm) wasused to scan the resonance cone pattern. The method re-sembles the approach in laboratory experiments, where areceiver antenna is rotated about the transmitter antenna ata fixed distance. While in the laboratory the magnetic fielddirection is well known, rc measurements in space need amagnetometer for reconstructing the magnetic attitude ofthe payload and the spin phase angle.

The transmitter frequency was chosen at 300 kHz, whichis below the electron cyclotron frequency that varies be-tween 600 and 1200 kHz during the orbit. A high excitationvoltage of 30 Vpp was used. The received signal was sam-pled 22 times per second resulting in an angular resolutionof the antenna radiation pattern of about 1.8◦.

The basic rc phenomenon could be verified by this in-strument under actual ionospheric conditions but the res-onance main maxima turned out to be much broader thanthose observed in corresponding investigations in the labo-ratory (Fisher and Gould, 1971). No interference structurecould be detected in these data sets. The authors conjec-tured that the high exciter level led to a substantial increaseof the sheath region about the transmitter antenna, whichmay be responsible for the observed broadening. The au-thors also report that the rc possesses no significant asym-metry, which would have been expected from field-aligneddrifts of the plasma electrons.

1.4.2 Mother-Daughter rocket flights A differentapproach for studying rc phenomena was chosen byFolkestad and Troim (1974) and Folkestad et al. (1976).There, two sounding rockets with a separable daughter pay-load were used to study the ionosphere at auroral latitudes.The observational geometry is sketched in Fig. 7(b) Thedaughter payload was fully equipped with power suppliesand telemetry arrangements. Because the line connectingthe transmitter on the mother payload and the receiver onthe daughter payload formed a fixed angle of (45 ± 3)◦

with respect to the geomagnetic field direction, the rc phe-nomenon could only be detected by sweeping the transmit-ter frequency. The sweep range covered the range 1.1 to9 MHz in Folkestad and Troim (1974) and 0.8 to 5 MHz inFolkestad et al. (1976). This compares to a typical electroncyclotron frequency of fce = 1.3 MHz at (135–250) km al-titude.

The transmitting antenna was an electric dipole of 5 m


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 inthe PORCUPINE project.

length and the receiving antenna consisted of two discs of40 cm2 area, which were fed into high-impedance ampli-fiers and were mounted at the ends of hinged booms of40 cm length. The transmitter dipole was fed with an rfvoltage of 30 V amplitude at the lowest frequency to 5 V atthe highest frequency. The received signal was processedby an array of eight channels with bandpass characteristic.

The sharp spikes observed in the first experiment byFolkestad and Troim (1974), which occur in the frequencyrange of 1.8 to 3.2 MHz, could be identified as upper-hybridresonance cones. In the second experiment by Folkestadet al. (1976), also the conventional lower-hybrid rc wasdetected for frequencies below the electron cyclotron fre-quency. For this purpose the lower limit of the frequencyscan was reduced to 0.8 MHz.

The high transmitter voltage level in these experimentsleads to a number of non-linear effects. Folkestad andTroim (1974) report that several harmonics of the transmit-ter frequency appeared in the channels with higher centerfrequencies. A detailed discussion of nonlinear effects canbe found in Folkestad et al. (1976). A general disadvan-tage of swept-frequency rc instruments is the wide receiverbandwidth, which picks up natural wave noise and any kindof spurious signals from other instruments. A discussion ofthe various spectral components of natural origin can alsobe found in Folkestad et al. (1976).

1.4.3 Scanning by the rocket spin A fixed frequencyrc instrument that uses the rocket spin for scanning the wavefield was used by Gonfalone (1974) for studying the polarionosphere from Kiruna, Sweden. The antenna geometryis shown in Fig. 7(c). One aim of this experiment was todetect the thermal fine structure of the rc. The transmittingantenna was a small cylinder of 1.5 cm diameter and 1 cmlength that was mounted on a telescopic boom along thespin axis. The receiving antenna was also a small cylinder,

but of 0.5 cm diameter and 1 cm length mounted on a lateralarm. The line connecting the antennas formed an angle of38◦ with the spin axis. The spin-scanning of the rc couldbe applied here because the spin axis formed a large anglewith respect to the geomagnetic field direction.

The transmitting antenna can be considered as an electricmonopole that is fed by rf voltages of stepwise increasedamplitude. The rocket body forms the common “ground”reference which is shared by the transmitting and receiv-ing monopole. This arrangement differed from the dipole-dipole scheme used on the OV1-20S satellite. The am-plitude of a sine wave at f = 700 kHz was changed ev-ery 2.3 s, taking the values: 0, 0.7, 2.5, and 4.9 Vpp. Thesheath size around the transmitting antenna was reduced bya positive dc bias of the order of 100 mV with respect tothe rocket body. The received signal was bandpass filteredwith two tuned circuits. The receiver input was protectedby a high-frequency filter tuned to the telemetry frequencyof 240 MHz. A wide dynamic range was achieved by usinga logarithmic amplifier after rectifying the received signal.The major result of this experiment was the simultaneousrecording of the main rc and its thermal interference struc-ture, from which the electron density and temperature couldbe derived.

The same scanning geometry was used in the experimentperformed by Michel et al. (1975), which was launchedfrom Hayes island, Russia, within the IPOCAMP 1 cam-paign. The transmitter frequency (700 kHz), antenna dis-tance (74 cm) and orientation angle (42◦) were similar to theexperiment of Gonfalone (1974). Unfortunately, the trans-mitter voltage and bias were not documented in Michel etal. (1975). The recorded rc signals show the main maxi-mum but the intersection with the interference cone is in-complete due to an unfavourable rocket attitude. The inter-ference pattern shows two minima but the interference max-


ima have apparently merged into a single maximum. Nev-ertheless, by evaluating the main maxima and interferenceminima electron density and temperature profiles could bederived from the rc data using a chart similar to that shownin Fig. 3.

1.4.4 The medium frequency probe for the POR-CUPINE project Within the PORCUPINE project threeAries rockets were launched from Kiruna, Sweden. A“medium frequency” (MF) probe was installed to studyfield-aligned plasma drifts (Storey and Thiel, 1984; Thielet al., 1984). Because the rockets were launched nearlyvertically with the rocket axis being aligned with the ge-omagnetic field, the MF probe used a complex set of an-tennas as shown in Fig. 7(d). Four spherical monopole an-tennas of 3 cm diameter were mounted on radial telescopicbooms which held the antennas at 2 m and 1.5 m distancefrom the payload axis, respectively. The boom separationwas 0.79 m. The rocket body served as common ground. Itwas pointed out by Storey (2000) that in this case the sheathimpedance of the rocket body becomes a common circuitelement of the transmitter and receiver circuit. Because therocket axis coincided with the magnetic field, the attitude ofthe wave propagation direction remained fixed during a spinperiod. This alleviates the analysis of drift effects in the rcdata. The fixed attitude, however, requires a frequency scanof the rc, as in the Mother-Daughter experiments.

The MF probe consisted of a transmitter and a receiverthat were connected to a pair of neighboring antennasthrough a switching logic. A measurement of drift effectsrequires the simultaneous measurement of the rc in forwardand reversed wave propagation direction, as indicated bythe double-tipped arrows in Fig. 7(d). For this purpose, thefrequency sweep was realized in terms of 256 individualsteps that cover the range from 0.1 to 1.5 MHz. Betweeneach frequency step and the next, the wave propagation di-rection was interchanged. A complete sweep took 137 ms.Between each frequency sweep and the next, the sensor ar-rangement 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 asymmetriesthat were expected from field-aligned electron drifts, Storeyand Thiel (1984) concluded that the high apparent velocitiescast doubt on their authenticity. It was suggested that theMF probe was perturbed by the payload body. Further,the sensitivity of the method needed to be increased by oneorder of magnitude to detect the expected drift velocities.

1.4.5 Resonance cone instrument for the equatorialionosphere The method to excite the rc with an electricmonopole antenna on top of the rocket payload and to scanthe wave field by a monopole sensor on a radial boom withthe aid of the rocket spin was also used in the equatorialionosphere (Thiemann et al., 1987, 1988). The transmittingantenna sphere of 10 mm diameter was operated at a fre-quency of 600 kHz and a voltage of 3 Vpp. The receiver sen-sor had 22 mm diameter and was mounted on a radial boomof 1 m length. The Rohini RH560-30 rocket was launchedon 4-May-1987, 10:10h IST, from Sriharicota Range, India.The rc signals showed clear main maxima and interferencemaxima, which allowed a quantitative analysis of the elec-tron density and temperature profiles.

A second flight was performed on 19-April-1993 at11:20h IST with a refined rc instrument based on the expe-rience with the COREX rc instrument (Rohde et al., 1995).The quasi-simultaneous measurements of rc’s for forwardand reversed wave propagation direction was used to detectelectron drift effects. Results will be discussed in Subsec-tion 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 inthe mid-latitude ionosphere over Japan that was conjecturedto be caused by non-thermal electrons (Oyama and Hirao,1979; Oyama et al., 1983). For this purpose, an rc in-strument was designed that could simultaneously measureelectron density, electron temperature, electron drifts andelectron beams. The instrument was flown on the K-9M-81rocket from Kagoshima Space Center (31.15N, 131.05E) onJan 25, 1988, 11:00 JST. Since the instrument used in thiscampaign essentially marks the final stage of evolution ofrc instruments, it will serve as example for the design con-siderations and typical results of the COREX campaign willbe presented below.

2. The COREX InstrumentThe basic design of the COREX rc instrument comprised

a fixed-frequency transmitter and a set of three electricmonopole antennas that were mounted on a central tele-scopic boom and two radial arms of different lengths (Fig.8). The transmitter frequency was designed to be at f =600 kHz ≈ fce/2 to obtain an optimum sensitivity of the rcangle on plasma density. The actual transmitter frequencywas 606 kHz at a transmitter level of 0.72 Vpp. The radia-tion field was scanned using the rocket spin. The rocket at-titude could be reconstructed from magnetometer data. Thepayload also comprised an impedance probe (NEI) and atemperature sensor (TEL), which could be used for com-parison with the rc data. For detecting electron drifts and

Fig. 8. The antenna geometry and switching scheme for the COREX rcinstrument.


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 ofsight 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.

electron beams the COREX instrument performed a set ofinterlaced measurements by rapidly interchanging the roleof transmitter and receiver within a pair of sensors (Fig. 8).2.1 Mechanical aspects

The antenna aspect angle α had to be chosen in sucha way that it matched the expected magnetic attitude an-gle σ ≈ 35◦ during the flight. Under ideal conditions,the measured rc pattern should then cover the entire range0 < θ < 2α. Due to coning of the rocket, however, σ maychange during the flight and the smallest wave propagationangle becomes |σ − α|, which may lead to a merging of theinterference maxima. For minimizing such unfavourableconditions, the COREX instrument was equipped with twobooms of different length that resulted in aspect angles ofα1 = 28.7◦ and α2 = 37.7◦. The antenna distance was0.96 m and 1.07 m respectively. This distance was inten-tionally chosen larger than the 70–80 cm distance in earlierinstruments (Gonfalone, 1974; Michel et al., 1975; Storeyand Thiel, 1984) in order to find more pronounced rc in-terference structures, which are known to become sharpertowards the far field. The details of the boom system areshown in Fig. 9.

The spherical sensors of 22 mm outer diameter were

Fig. 11. The front end of the transmitter / receiver circuit in the COREXrc instrument.

made of a pair of hollow brass hemispheres that containedpart of the first preamplifier stage and the switching logic.The surface was polished and coated with a thin gold layer.The sensors were attached to the boom by a conical shaftmade of polyimide, as can be seen in Fig. 9(b).

The reconstruction of the true wave propagation angle θ

with respect to the magnetic field is performed using theformula

cos θ = sin σ sin α cos ϕ + cos σ cos α , (4)

in which ϕ is the spin phase angle. It should be mentionedthat small errors in determining the spin-phase angle hadbeen reported earlier (Michel et al., 1975) and were at-tributed to induced currents in the payload hull. A sim-ilar zero-point correction was made for the COREX-data(Rohde et al., 1993). These ambiguities can be minimizedby placing the magnetometer at the end of a boom, as in theDEOS campaign (Thiemann et al., 1997a, b).2.2 Electronics design

The block diagram of the COREX rc instrument is shownin Fig. 10. The sinusoidal signal of f = 606 kHz frequencyis fed to one of the three sensors via a switching matrixwhich also selects the receiving sensor. The received signalis bandpass filtered, amplified and rectified. The resulting


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 andtransferred as two bytes to the digital telemetry input. Twoadditional bits are used to encode the mode of the antennaswitch. The antenna mode is advanced by the data strobesignal from the telemetry.

The sensor spheres contain the front end of the transmit-ter and receiver circuit (Fig. 11). The transmitter signal isconnected to the sensor sphere via the FET-switch T1 anda blocking capacitor of 1 µF. The sensor can be biased bya current source formed by the bias voltage (+15 V) anda 10 M� series resistor. In receiving mode, the transmit-ter is decoupled from the sensor by a switch in the elec-tronics box. In addition, T1 is switched off to a high-impedance state to eliminate the capacitive load by thefeeder cable. Then, the received signal appears at the gateof T2 with practically 1 M� input impedance. T2 and T3form a preamplifier with about 20 dB gain and a low out-put impedance. The amplified signal is connected to thereceiver box by a 50 � cable. For minimizing the size ofthe pre-amplifier, SMD components were used for the ca-pacitors and resistors. As suitable SMD FETs were not yetavailable in 1987, conventional components had to be used.T1 and T2 are a dual n-channel J-FET (TD5912) with a lowinput capacitance (<5 pF) in a TO-71 package and T3 is abipolar pnp transistor BFX48 in a TO-18 package. Becauseof the negative feedback, the effective input capacitance ofthe receiver was 1–2 pF.

The interplay between the rc instrument and the teleme-try scheme can be retrieved from Fig. 12. The bit rate ofthe telemetry system was 102.4 kBit/s with 200 frames persecond. Each frame of 5 ms duration is subdivided into 64words of 8 bit length. These words have the octal num-bers W00–W77. The COREX rc instrument was allotted8 × 2 words per frame, which are marked W00/W01 toW70/W71. The rc data comprise 12 bits, which are storedin two subsequent words, as shown in the top row. The re-maining half-byte is used two transmit the actual mode bythe bits A0/A1.

The data is read from the rc instrument by means of twostrobe signals. The signal STROBE1 was also used to ad-vance the mode switch every 625 µs to the next positionafter the data from the previous cycle was processed. Thisleaves roughly 500 µs for the analog processing to settleand for performing the A/D-conversion. A set of four in-terlaced 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, wecould obtain about 220 data sets per revolution. This cor-responds to an angular resolution of about 1.6◦. The elec-tronics box of the COREX rc instrument had dimensionsof 180 mm length, 105 mm width and 105 mm height. Themass was 1550 g and the power consumption 2.9 W.2.3 Strength and weakness of the resonance cone

methodThe rc method has the advantage that the measurement

of electron density and temperature is only determined bythe plasma medium between the transmitting and receivingantenna. In this way, it is a non-invasive technique and isalso insensitive to surface contamination of the sensors. Thesame information on electron density and temperature canin principle be derived from Langmuir probe characteristicswhen special precautions are taken to minimize surface con-tamination of Langmuir probes (Oyama, 1976; Amatucci etal., 2001), which would lead to overestimating the electrontemperature or need a dedicated correction algorithm (Pielet al., 2001; Hirt et al., 2001). With the COREX instru-ment, a mature state of the rc method on sounding rocketshad been reached. A slightly modified descendant of this in-strument was later flown on three sounding rockets withinthe DEOS campaign (Thiemann et al., 1997a, b).2.4 Typical results

The detailed results from the COREX campaign can befound in Rohde et al. (1993). The rc booms were deployedafter 51.7 s at an altitude of 75.8 km. An apogee of 359 kmwas reached at 366 s flight time. The geomagnetic aspectangle σ varied between 35◦ and 55◦, which was larger thanexpected. Therefore, the rc instrument could not cover theinterference peaks for some time, which caused a few datagaps for temperature evaluation.

2.4.1 Density and temperature profiles During onespin period of the rocket, we obtain four readings of the res-onance cone maximum angle from one sensor pair, |θup

L |,|θdown

L |, |θupR | and |θdown

R |. There is a similar set of four read-ings for the interference maximum angle. All these fourangles are sensitive to plasma density, electron temperatureand electron drift. In a real plasma situation, one has tomanage all these effects simultaneously. As will becomeevident from Table 2, the influence of the drift cancels inthe average of all four angles, because of symmetry. Hence,the averaged maximum angles and interference maximumangles can be used to deduce electron density and tempera-


Fig. 13. (a) Electron density profile and (b) electron temperature profile atE-region altitudes. The full lines give the comparison with independentinstruments.

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-orderinterferences appear. From the average cone angles densityprofiles are compiled for the upleg and downleg of the tra-jectory. Figure 13 shows the comparison of the rc data withthe impedance probe and temperature probe. In this altituderegime, a good agreement is found between the rc techniqueand conventional techniques.

In the F-region, the situation for the rc method is dif-ferent. At high plasma density, the rc angle θmax becomesinsensitive to electron density. This can be seen in Fig. 14.The maximum angle approaches a limiting angle, which ismarked by the dotted line.The conventional rc technique byreading the angular position of the main maximum, there-fore, faces a density maximum, which prevents a densitymeasurement for �p > 3.

This limitation can be circumvented by noting that the rcamplitude continuously decreases with plasma density, asshown by the dashed line in Fig. 14. The evaluation of rcamplitudes does not yield absolute density values but needsa calibration in a regime, where the main cone angle is stillsensitive. Such a calibration was performed in the COREXcampaign at E-region altitudes and allowed an extension ofthe density measurements into the F-region. The extrapo-lation is based on the assumption that the impedance of thesheath around the sensors is small compared to the plasmaimpedance between transmitter and receiver.

The resulting density profile is shown in Fig. 15(a) incomparison with the data from the impedance probe. Theprofiles show a satisfying absolute agreement. An electrondensity maximum is found at about 260 km altitude.

The evaluation of the interference structures for electrontemperature measurements was hampered by rocket coning,which caused an unfavourable attitude of the rocket axis intwo parts of the F-region (Rohde et al., 1993). In Fig. 15(c)the attitude angle σ is plotted. When σ > 45◦, the min-imum detectable angle became 7.3◦ < θ < 17.3◦, whichled to a merging of the interference maxima. Therefore, forevaluating the electron temperature, evaluation charts had

Fig. 14. The rc angle θc (full line) approaches a density limit, indicatedby the dotted line. The amplitude of the rc maxima (dashed line) can beused to circumvent the density limit.

been calculated that involved the positions of the main max-imum and the first interference minimum. This proceduregives the temperature values displayed in Fig. 15(b). In theregime σ < 45◦ the measured electron temperatures showa good agreement with data from the temperature sensor.For larger rocket attitudes, the resulting electron tempera-tures became unreliable or even data gaps appeared, whenthe interference minima disappeared.

2.4.2 Drift effects The peculiarity of the rc methodis its sensitivity to electron drift effects. In order to gaina deeper understanding of the relationship between reso-nance cone shifts and the underlying drift, we have to anal-yse the wave propagation geometry in more detail. In Fig.16 the COREX antenna system is shown for the case thatthe rc is excited by antenna I and the wave field is scannedby antenna II, which intersects the rc at positions L and Rthat correspond to the left and right maxima in the rc plots.These reference points correspond to the non-drifting caseand the drift effects are treated as linear perturbations to thisgeometry. Since the rc represents the energy flow from thetransmitter to receiver, the group velocity vector vg pointsfrom transmitter to receiver and is tangential to the rc. Itis the peculiarity of a magnetoplasma that group velocityand wave vector k become perpendicular at resonance (Stix,1962) and lie in a plane that contains the magnetic field di-rection. Since the rc shift is effected by the Doppler ef-fect �ω = k · vd, the rc is only sensitive to the projectionof the drift velocity vd on the k-direction. Fortunately, wehave two different wave vectors for the L and R intersec-tions, which have the same z′-component but opposite y′-components. This allows us to reconstruct two componentsof the drift velocity vector.

When we describe the Doppler effect in a coordinatesystem (x ′, y′, z′) that is aligned with the magnetic fielddirection (see Fig. 16), the frequency shift is given by k ·vd = kz′vz′ + k⊥v⊥ cos(β). Here, β is the angle betweenv⊥ and k⊥. Noting that k⊥ ≈ −kz′ cot(θmax), we obtain ananalytical expression for the modification of the main cone


Fig. 15. (a) Electron density profile in the F-region compared with impedance probe (NEI) results. (b) Electron temperature profile compared withtemperature probe (TEL). For an unfavourable rocket attitude, σ > 45◦ the interference maxima tend to merge and lead to unreliable temperaturevalues and even data gaps, when the minima disappear. (c) Attitude angle σ with respect to the magnetic field direction.

Fig. 16. Resonance cone with L and R intersection points by the receivingantenna. The rc half-angle is θmax Here, σ is the magnetic attitude of therocket and φ the spin phase angle. The group velocity vg is aligned withthe rc, whereas the wavevector k, which determines the doppler effect,is perpendicular to the rc.

angle at the L and R intersection points

�θL,R = ∂θmax

∂�kz′(vz′ − cot θmaxv⊥ cos β) . (5)

The proper value of kz has to be taken at the inflection pointof the dispersion curve (Rohde et al., 1993). This expres-sion turned out to be sufficiently accurate for R > 150. Forsmaller distances, we have used the full kinetic model todetermine the proper coefficient for the field-aligned drift,which was then used in Eq. (5) for the case of arbitrary driftdirection.

The influence of the electron drift on the four maxima ofthe rc pattern is summarized in Table 2. Here, θmax is the rcangle in a non-drifting plasma, �θL and �θR are the shiftof the left and right maximum due to the drift and �θB isan uncertainty of the zero point of the horizontal magneticfield.

Fig. 17. The field-aligned and cross-field component of the drift velocitymeasured during the COREX flight. Each data point is an average over3 s.

Table 2. Drift-related shifts of the rc maxima for reversed wave propaga-tion direction.

Left maximum (L) Right maximum (R)

Forward θmax − �θL + �θB θmax − �θR − �θB

Reversed θmax + �θL + �θB θmax + �θR − �θB

For a purely field-aligned electron drift we have �θL =−�θR, which results in the simple up-down asymmetry de-scribed in Fig. 4(a). For an arbitrary drift geometry, wefind �θL = −�θR and can reconstruct the field-alignedand cross-field component of the electron drift velocity, asshown in Fig. 17. It turned out that the cross-field compo-nent was much larger than the field-aligned component.

In this way, the finding of the COREX flight was that therc does not possess the symmetry expected for field-aligneddrifts (Piel et al., 1992a, b). Moreover, the magnitudeof the electron drift, vd ≈ 30–35 km s−1, correspondingto ≈6% of the electron thermal velocity, is unexpectedlyhigh. Wind velocities in the mid-latitude thermosphere are


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 azimuthaldirection. (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 nearlyhorizontal magnetic field direction.

typically below 1 km s−1. Unusually high cross-field driftsof up to 8.8 km s−1 were also reported by Storey and Thiel(1984). This value was much larger than the one derivedfrom electric field measurements of v⊥ ≈ 0.5 km s−1.

Assuming that, for the COREX data, the cross-field driftwere an extended phenomenon in the ambient ionosphericplasma, we would obtain a cross-field current density ofj⊥ ≈ 5 mA m−2, which is much beyond the Sq-currentdensity of 5–10 µA m−2. Such large currents should havealso been visible in the magnetometer data. Therefore, wehad concluded that the electron drift is a phenomenon thatis restricted to the immediate rocket environment.

Besides the magnitude of the observed drift, also thetopology of the rc shifts hints at a local effect. The mainmaxima in one antenna mode show a characteristic shift inangular direction with respect to the maxima in the corre-sponding mode for reversed wave propagation direction, ascan be seen in Fig. 18(a) (Rohde et al., 1993). Applyingthe fundamental idea that the rc is convected with the flow,this pattern was attributed to a circulation of the electronsaround the rocket, as sketched in Fig. 18(b).

The origin of this electron circulation was attributed toan E×B drift that arises from an electrostatic field in thevicinity of the payload body. It is known from Langmuirprobe characteristics taken on the same flight that the pay-

load floats at a potential of �f ≈ −2 V with respect to theambient plasma. The observed angular shift of the rc pat-tern can be converted to an effective electric field, whichis typically 0.1 V m−1 in the E-region and 0.4 V m−1 in theF-region.

Similar electron circulation effects on the rc pattern werealso observed in the equatorial ionosphere (Rohde et al.,1995). There, the nearly horizontal magnetic field yields anapproximately perpendicular orientation of the rocket axiswith respect to the magnetic field, which allows a measure-ment of both halves of the double cone. This geometrywould also lead to a circulation pattern that convects therc in cross-field direction. Such a topology of the rc be-comes evident from polar plots of the rc amplitude signalshown in Fig. 19(a). Notice how all four maxima in thedashed contour are convected across the magnetic field di-rection. The geometry of the E×B-flow for a large attitudeangle σ ≈ 82◦ is sketched in Fig. 19(b) and would lead to amainly cross-field convection of the rc pattern.

The electron drift also affects the rc amplitudes, as can beseen in the calculated rc pattern in Fig. 5. The upstream rcmaxima are higher than those downstream. This effect onthe amplitudes is also found in the COREX results in Fig.18, where in the solid curve the left maximum is higher thanthe right and—for reverted wave propagation direction—


Fig. 20. Correlation between rc shifts and amplitude modification in theCOREX data.

the right becomes larger than the left maximum. This givesa further hint that the observed rc modification can be at-tributed to drift effects. The same reversal of the amplitudeasymmetry is also found in the SPICE-3 data as can be seenmost clearly on the the right-hand part of the polar plot inFig. 19(a). It was shown by Rohde et al. (1993) that thispattern is not accidental but a systematic effect, by plottingthe angular shifts �θ vs. the amplitude variation �A, whichresulted in a very high correlation as shown in Fig. 20.

It was, however, not possible to derive the drift veloci-ties from the amplitude effects. This is mainly due to thefact that the rc instrument had an unknown signal back-ground from clock noise and electromagnetic interferencefrom other instruments. This background could not be mea-sured during the flight because there was no “transmitteroff” mode available. Therefore, the reference amplitude Ain Fig. 20 uses only an estimate for such a background. Infuture instruments, a careful calibration of the received sig-nal could make amplitude effects accessible as an indepen-dent check of drift effects.

In summary, the drift effects in the COREX campaignwere not of geophysical origin, but could be attributed toelectron E×B motion in the immediate rocket environment.A more detailed discussion of the magnitude of the electricfield derived from the cross-field drift data in comparisonwith theoretical predictions can be found in Rohde et al.(1993).

The typical asymmetries in the interference pattern of therc that are caused by electron beams could not be found inthe COREX data. The detection limit of the COREX instru-ment was discussed in Rohde et al. (1993). For assumedbeam velocities of 2vth,e and 3vth,e, the observed fluctua-tions in the modulation of the downstream interference pat-tern remained below the detection limit. The absence ofbeam effects agrees with the observation of the other instru-ments that there was no temperature anomaly present duringthe K-9M-81 flight, which would have been expected in thepresence of anomalous plasma heating by beams.

3. Improvements and AlternativesThe measurement of electron density and temperature by

using rc angles proved to be reliable at E-region altitudes. Inthe F-region, density measurements require the analysis ofrc amplitudes. Temperature measurements in the F-regionrequire a proper resolution of the interference structure. Thegeneral layout of a future rc instrument could start from theCOREX design, which represented the “state of the art” atits time.

Comparing the rc technique with other established meth-ods for electron density measurements, it turned out thatimpedance probes and Langmuir probes can give muchhigher spatial resolution than the rc method. Moreover, thedetermination of absolute electron densities and irregulari-ties by impedance and Langmuir probes proved to be highlyaccurate, see e.g. Steigies et al. (2001), Hirt et al. (2001).These competing techniques do not require a complex boomsystem but rely on a single sensor, only. On the other hand,the impedance probe with its typical frequency sweep from0.5 to > 10 MHz may be in conflict with other instruments,whereas an rc probe with a coherent signal at ≈600 kHzmay be tolerable.

When the focus lies on electron density and tempera-ture measurements, a general improvement for the accuratemeasurement of rc angles could be achieved by larger an-tenna separations of ≈2–3 m. Then, the thermal interfer-ence spacing �θ would diminish (Fisher and Gould, 1971;Kuehl, 1974) and the interference maxima could be re-solved even at F-region altitude. A further significant im-provement could also be a achieved by a narrow rocket con-ing angle that provides an optimized matching of the mag-netic attitude σ with the antenna orientation angle α.

An important result from the COREX and SPICE-3 ex-periments was the observation that the immediate rocketenvironment is affected by local electron drifts. For sep-arating geophysical electron drifts from local effects evenlonger boom systems should be considered, similar to thoseused for electric field measurements. Progress in this fieldwill depend on a deeper understanding of the shielding ofthe rocket by the ambient magnetoplasma.

Doubtlessly, the electronics of the rc instrument could beimproved by the advancement in electronics, in particularthrough the availability of SMD components that allow aneven larger part of the preamp and switch electronics beingintegrated into the sensor spheres. The signal-to-noise ratioof the receiver section would benefit from integrating thefirst bandpass filter into the sensor. For an unambiguousinformation 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 fromtoday’s higher telemetry rate that lie in the Mbit/s range,compared to the 100 kbit/s in 1988. The angular resolutionof the COREX instrument was limited by the fact that itconsumed 25% of the available total telemetry capacity.The use of modern electronic components could also lead toa substantial reduction in size and weight of the electronicsbox.

The detection of subthermal electron drifts and elec-tric currents by in-situ techniques is still a challengingtask. Large-scale plasma motion is nowadays detected with


ground-based techniques like Doppler-radar measurements,which e.g., have revealed many details of the equatorialionosphere. Plasma motion is also investigated indirectlyby electric field measurements aboard satellites and rockets,which yield the driving force for the drifts. Therefore, fora direct verification of electron drifts future improved rc in-struments may help clarifying the distribution, homogene-ity and variability of these electron currents. Moreover, thecase of non-Maxwellian distribution functions, which affectthe propagation of lower-hybrid waves in such a character-istic way, will be a suitable target for rc measurements.

In conclusion, further improved rc instruments arepromising candidates for the study of subthermal electrondrifts or low-energy electron beams and will give support-ing information about electron density and temperature.

Acknowledgments. The author is indebted to the late Heinz Thie-mann, whose expertise and leadership as co-investigator or prin-cipal investigator have made the COREX and DEOS projects asuccess. These investigations were funded by BMFT/DARA andDLR, which is gratefully acknowledged.

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Thiemann, H., S. P. Gupta, G. Mayer, and A. Piel (1997a) DEOS: Dynam-ics of the Equatorial Ionosphere Over SHAR joint Indo-German rocketcampaign, 13th ESA Symposium on European Rocket and Balloon Pro-grammes and Related Research, Eur. Space Agency Spec. Publ. 397,349–354.

Thiemann, H., W. Noack, P. Brauer, and F. Primdahl (1997b) DEOS: Dy-namics of the Equatorial Ionosphere Over SHAR: Instruments: Reso-nance cone and DC vector magnetometer experiment, 13th ESA Sym-posium on European Rocket and Balloon Programmes and Related Re-search, Eur. Space Agency Spec. Publ. 397, 355–360.

A. Piel (e-mail: [email protected])

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Resonance cone probe for measuring electron density ... · Resonance cone probe for measuring electron density, temperature, drift speed and beam components A. Piel Institut f¨ur