G. C. Hussey, J. A. Koehler, and G. J. Sofko

Transcription

1 Radio Science, Volume 32, Number 2, Pages , March-April 1997 Polarization of auroral backscaer 50 MHz G. C. Hussey, J. A. Koehler, and G. J. Sofko Institute of Space and Atmospheric Studies, University of Saskatchewan, Saskatoon, Canada Abstract. Auroral backscatter from the lower E region was studied using two 50 MHz bistatic, continuous wave radar links which shared a common polarimetric receiver. The polarization parameters were defined in terms of the polarization ellipse, which is described by the ellipticity angle X, orientation angle k, and polarization ratio m. Spectral analysis was applied to the intensity measurements and its corresponding polarization parameters. Observations of typical auroral spectral types 1, 2, and 3 indicated that the scattering of a linearly polarized incident wave produced an essentially linear and highly polarized scattered wave. These results imply a small scattering volume and/or a small number of discrete scatterers located close to one another, "scatterer" referring to a volume where radar waves are scattered according to weak coherent scattering theory, and also reaffirms that the scattering process is a weak coherent one. These results are typical of most observations, but not all; an otherwise typical intensity spectrum may also exhibit variable polarization parameters with an appreciable reduction in the polarization ratio and/or signals of significant ellipticity. These anomalous properties can be explained as scatter coming from a number of individual scattering volumes within the scattering region (i.e., the effective radar viewing region), which are each influencedifferently by Faraday rotation to and from the scattering region. Introduction For many years, ionospheric plasma waves have been studied through the analysis of coherent VHF radar waves scattered from these plasma waves. Many of these experiments have operated at frequencies close to 50 MHz [Fejev and Kelley, 1980; Haldoupis, 1989; Kelley, 1989]. Most coherent VHF observations of the auroral ionosphere have been Doppler spectrum and signal intensity measurements. Such measurements are directly related to the scattering plasma waves (i.e., wave phase velocities, instability mechanisms and driving terms, plasma turbulence levels, etc.) In this experiment, complete polariza- tion measurements were made of VHF scatter from 541 larization measurements would assist in further understanding E region plasma waves. For example, polarization information can be used to study the effects of propagation to and from the scattering region by measuring Faraday rotation. This is significant in determining the true echo intensity, which is often related directly to the mean scattering wave amplitude. A number of polarization experiments were performed in the early years of coherent VHF radar research [e.g., McNamara and Cuttle, 1954; Harang and Landmark, 1954; Kavadas and Glass, 1959], but only a few experiments [e.g., Sofko and Kavadas, 1971; Bgdard and Sofko, 1976] were done using a complete polarimeter. Early experiments reported the auroral lower E region ionosphere. The two main changes in polarization from the transmitted state objectives were (1) to offer a possibl explanation and observed that these changes were dependent of the observed changes in the polarization parame- upon the degree of auroral activity. Multifrequency ters, as previous experiments had observed these but experiments also indicated that the changes in ponever explained them, and (2) to determine if po- larization were less pronounced at higher radar frequencies. $ofko and Kavadas [1971] and B dard and Sofko [1976] were able to measure only the mean po- Copyright 1997 by the American Geophysical Union. larization state over the receiver bandwidth, while in Paper number 96RS this experiment, spectral polarization measurements / 97 / 96 RS were made over the receiver pass band in order to

2 542 HUSSEY ET AL.' POLARIZATION OF AURORAL BACKSCATTER provide polarization parameters of the Doppler spectrum. This spectral polarization information is important in studying and detecting multipeaked spectra. As well, this paper for the first time strongly suggests that polarization parameter changes are due to propagation effects and experiment scattering geometry. The polarization parameters describe the motion of the electric field vector of an electromagnetic wave as it passes through a fixed plane perpendicular to the direction of propagation. The general motion of the electric field vector is to trace out an ellipse; the ellipse can have special cases where it traces out a circle or a line. Using the usual x-y axis system, the polarization ellipse is described by the orientation angle b(0 ø _< p < 180ø), which describes the angle sub-tending the x axis and the major axis of the ellipse, and the elliptictry angle X (-450 _< X _< 45ø), which describes the shape and the sense of rotation of the ellipse. If X - 0ø, then the polarization ellipse collapses to a line and the wave is linearly (or plane) polarized. If X - 4'45ø, then the ellipse becomes a circle in which the electric field rotates either in a left-hand sense (+45 ø) or a right-hand sense (-45 ø) with respect to the direction of propagation, and the wave is circularly polarized. The final polarization parameter, the polarization ratio m (0 <_ m <_ 1), is a measure of the received polarized signal with respect to the total received signal. If m - 0, the signal is completely unpolarized, and if m - 1, the signal is completely polarized. All the polarization parameters are time-averaged quantities. For a complete description of polarization theory, see Born and Wolf[1964]. Experiment and Instrumentation Experiment Overview This experiment, similar to those reported by Kochlet et al. [1985], $ofko et al. [1987], and Kochlet et al. [1995], consisted of two 50 MHz bistatic continuous wave (CW) radar links where the receiver was a full polarimeter. One link consisted of a transmitter at La Crete, Alberta, and a receiver located near Saskatoon, Saskatchewan (the LS link); the other link consisted of this same receiver and a transmitter at Gillam, Manitoba (the GS link). The plasma waves detected propagate along the link bisectors and have wavelengths of Ar/2cos0, where Ar is the radar wavelength and 0 the angle from the link bisector to either the transmitted or scattered wave. The scattering region for each link is defined by the intersection of the transmitting and receiving antenna beam patterns, and this defines the effective radar viewing region (the -3 db power contour has a diameter of ~ 45 km). A surveying error resulted in a slight misalignment of the La Crete heading, but owing to the often high signal strengths of echoes it is reasonable to assume that both links observed simi- lar scattering regions (e.g., the -9 db power contours for each link overlap each other by ~ 70%). The -3 db beam width was 6.4 ø for the Gillam antenna array and 4.20 for the La Crete and Saskatoon antenna arrays. The geographic locations and antenna characteristics of the radars as well as the geographic locations of the centers of the scattering regions, at an altitude of 110 km, are shown in Table 1. The magnetic aspect angles for the LS and GS links were Table 1. Geographic Locations and Antenna Characteristics Geographic Location Antenna Heading Slant Range km Elevation Angle La Crete, Alberta, transmitter Gillam, Manitoba, transmitter Saskatoon, Saskatchewan, receiver LS link scattering region GS link scattering region N, W N, W N, ø W N, W N, W ø ø 694 (L) (G) L and G stand for La Crete and Gillam, respectively, and LS link and GS link stand for the La Crete- Saskatoon link and the Gillam - Saskatoon link, respectively. Headings are in degrees east of north. Scattering regions are at 110 km altitude.

3 HUSSEY ET AL.: POLARIZATION OF AURORAL BACKSCATTER $ and 11.5 ø, respectively (IGRF 1990 model for the year 1993). Equipment The Gillam site consisted of a 300 W transmitter fed into an 8 antenna array of horizontal Yagi antennas while the La Crete site transmitter (300 W) fed into 12 antennas. The receiving system at Saskatoon consisted of a 12 element array of polarimetric antennas, the 50 MHz polarimetric receiver, and the data collection system. The polarimetric antennas consisted of two linear Yagi antennas mounted orthogonal to one another on the same boom. The signals from each polarization channel are fed into the 50 MHz polarimetric receiver, where these RF signals are mixed down to audio frequencies, which are then fed into the data collection system. By having the transmitters at La Crete and Gillam at slightly differ- ent center frequencies, MHz and MHz, respectively, the signals from the two links were kept distinct. The receiver reference frequency was MHz, and therefore zero Doppler shift would correspond to an audio frequency of 1 khz for the LS link and 3 khz for the GS link. A positive Doppler shift corresponds to plasma wave motion toward the transmitter and receiver in the direction of the bisec- tor of the transmitter and receiver beams. The 50 MHz polarimetric receiver portion was, conceptually, two separate receivers which had common mixing frequencies. Coupling between the channels was measured to be ~ -23 db. The 50 MHz polarimetric receiver has two superheterodyne (mixing) stages; as a result, the phase of the original RF signal is conserved in the mixing process, an essential criterion for full polarimetric measurements. The audio gain and filtering stages of the data collection system amplified the audio frequency signals, filtered the signals on each polarimetric channel into i khz and 3 khz signals, and mixed the 3 khz signals down to i khz, producing four data channels; these were then digitized at approximately 5 khz, organized into data structures, and stored on tape. In addition, 10 s average spectra were calculated and stored with the digitized data. For further details about the data collection system, see Koehler et al. [1995]. Calibrations, Errors A number of calibrations Corrections, and Measured and an overall error esti- mate were performed to test the polarimetric receiver system. First, tests involving only the polarimetric instruments showed that the response of the polarimetric receiver was linear in both phase and amplitude (gain). The results showed a nominal variation of 2% in amplitude and ~3 ø in phase. Tests were also undertaken to measure the characteristics across the bandwidth of the two links. During quiet ionospheric conditions the receiver detects cosmic back- ground radiation which is uniform across the bandwidth associated with the polarimetric receiver. As a result, the amplitude bandwidth response of each channel was normalized, removing any instrumental amplitude bandwidth characteristics. Measurements of the phase response across the receiver pass band (4-400 Hz) indicated a smooth variation in phase of 5 ø for the i khz link and 2 for the 3 khz link. The amplitude response across the bandwidth of the receiver was routinely corrected. The electric field vectors of the electromagnetic waves detected at the receiving antenna array are altered from those scattered from the ionosphere because the waves detected at the receiving array are the vector sum of the direct and ground-reflected electric field vectors of the waves. The groundreflected wave is altered due to the reflection process where the electric field of the wave is reflected dif- ferently depending upon its orientation with respect to the reflecting surface. Also, the ground-reflected wave traverses a slightly longer path than the direct wave, altering its polarization state in phase with respect to the direct wave. Fortunately, at the low elevation angles (high incidence angles) of this experiment, the reflected signal phase and magnitude are not very sensitive to soil parameters, and reasonable estimates of how the reflected wave is related to the incident wave were made. The effects of the groundreflected wave on the received signal could thus be removed by removing the alteration of the groundreflected wave caused from the reflecting process, as described by the perpendicular and parallel reflection coefficients calculated from the Fresnel reflec- tion equations, and by removing the phase delay of the ground-reflected wave with respect to the direct wave. Tests of the overall accuracy of the entire polarimetric receiver system were performed using a test antenna located ~1 km in front of the receiving an- tenna array and indicated an overall accuracy of-4-5 for phase and in relative gain. Expressing the amplitude and phase measurement errors of the polarimetric receiver system in terms of the polarization ellipse parameters, the orientation angle b

4 544 HUSSEY ET AL.: POLARIZATION OF AURORAL BACKSCATTER Table 2. Accuracy Estimates of Polarimetric Parameters A x A X -- Oø (linear) [0ø[ X [25ø[(elliptical) [25ø[ < X < [35ø[(elliptical) [35ø[ < X < [45ø[(elliptical) 4-45ø (circular) 4-3 ø 4-8 ø ø 4-8 ø 4-20 ø 4-9 ø can be quite large; importance diminishes as X ' [4-45ø[ :V9 ø undefined The accuracy (worst case) of the polarimetric receiver system is expressed with respect to the polarization ellipse parameters (the orientation angle b and the ellipticity angle X). and the ellipticity angle X, an estimate of the accuracy associated with these polarimetric parameters is shown in Table 2. The error values presented are those for the worst case. For complete details about the experiment, see Hussey [1995]. Propagation and Scattering Considerations The propagation of electromagnetic waves through a magnetized plasma may be described by the linear plasma dispersion equation known as the Altar- Appleton equation [Raicliffe, 1959; Hunsucker, 1991]. Depending on the wave frequency and the plasma parameters, characteristic propagation modes are able to traverse a magnetized plasma. For the plasma properties associated with the lower E region and a wave frequency of 50 MHz, the quasi-longitudinal (QL) approximation is valid. A characteristic described by the QL approximation is that the electric field vector of a linearly polarized wave rotates as the wave traverses the plasma, an effect known as Faraday rotation. For this experiment the QL approximation (and therefore Faraday rotation) is valid for wave vectors making an angle of up to ~870 with the magnetic field; thus the QL approximation reasonably describes the propagation of a radar wave both to and from the scattering region, since the magnetic aspect angles in this experiment were ~100 (i.e., the wave vectors were ~800 with respect to the magnetic field). If the wave vectors were primarily perpendicular to the magnetic field, then the quasi-transverse (QT) approximation of magnetoionic theory becomes valid, and Faraday effects disappear. Faraday rotation is half the phase difference between the two characteristic propagation modes, the ordinary and extraordinary modes, of the QL approximation and may be expressed as [Egeland et al., 1973] -- 2ceorne2w2 B cos( ne dl _ 2c orne2w2 Bcos nedl, (1) where it is assumed that the geomagnetic field varies little along the radar wave path. The electric field vector of a linearly polarized wave rotates counter clockwise with respect to the direction of the magnetic field as the wave traverses a magnetized plasma. The terms to the left of the integral are defined as follows: e is the charge of an electron, c is the speed of light, 0 is the permittivity of free space, me is the mass of an electron, w is the angular radar wave frequency in radians per second, B is the geomagnetic field in the scattering region, and ( is the angle between the geomagnetic field and the radar wave vector. All these variables are known or can be cal- culated with B assumed to be essentially constant. The integral term f n, dl represents the integrated electron density along the radar wave path. The scattering geometry is important in determining the component of the electric field vector of the incident wave which is scattered toward the receiver, since the transmitter-to-scatterer portion of the links is almost perpendicular to the scatterer-to-receiver portion. As a result, the scattered wave is strongly affected by the orientation of the incident electric field vector (see below), which in turn is influenced by Faraday rotation. For coherent scatter, such as that from plasma waves in the ionosphere, the average scattering cross section for a distributed target may be calculated

5 HUSSEY ET AL.' POLARIZATION OF AURORAL BACKSCATTER $45 using the following assumptions: (1) the scattering of the scattered wave relative to its incident wave. volume is large with respect to the radar wavelength When c -- 0 ø and /? = 90 ø, the geometrical term but small enough to treat the scattering medium as of equation (3) is zero because the incident electric statistically uniform, (2) the radar frequency is well field lies along the direction of the scattered wave. above the plasma frequency of the ionosphere, and For c = 900 the geometrical term is always unity, (3) the scattering from the plasma waves is suffi- since the incident electric field is then perpendicular ciently weak so as not to adversely affect the scat- to the scattered wave irrespective of the value of/. tered radar wave (i.e., the Born approximation is valid) [Lovberg and Griem, 1971]. The third assump- Polarization Observations tion implies that the scattering process does not alter the polarization of the scattered wave. The average scattering cross section is given by the following pro- The results analyzed are from a geomagnetically portionality [Sheffield, 1975] disturbed period during which strong radar echoes were received by the polarimeter for a period from approximately 0200 UT to 0530 UT (LT = UT- 6) on day 342 (December 8), The Kp index for this period was 6+. Both a Canadian Auroral Network for the OPEN Program Unified Study (CANOwhere r [ x ( x/ i0)[ describes the geometrical PUS) magnetometer and riometer [Grant et al., 1992] effects of the scattering process (re is the classical and an ionosonde were located at Rabbit Lake alelectron radius, - ks/[ks[ is the unit scattered most directly under the scattering region. The magwave vector, i0 is the unit incident electric field netometer deflections were as high as ~500 nt and, describes the electron indicated currents flowing roughly to the northwest (i.e., a westward electrojet). The CANOPUS riomedensity fluctuation spectru.m for the plasma wave ter data showed no appreciable absorption during spatial Fourier component k averaged over the scat- this period. tering volume, where the angle brackets indicate the Spectral analysis was used in determining and prespatial average. senting the polarization parameters: m, X, and b, in For a linearly polarized wave the term on the right addition to the standard power spectrum analysis. side of equation (2), describing the geometrical ef- In addition to the standard intensity measurements, fects of the scattering process, may be expressed by the spectral analysis allows for the classification of evaluating the triple cross product, as the radio auroral spectral types with respect to the polarization parameters. Taking into account a reasonable balance between time and frequency reso- I g x (g x i0)[ e - 1 -sin e/ cos e ix, (3) where (see Figure 1) c is the orientation of the electric field of the incident wave and/ is the direction... scattering volume k, lies in the xz-plane Figure 1. Illustration showing the relative orientation of the incident wave vector ki and its unit electric field vector i0 and the scattered wave vector ks. lution, the spectral estimates used here were performed at a frequency resolution of 4.8 Hz, corresponding to a time resolution of ~0.2 s (1000 point fast Fourier transform). A single pair of spectral estimates for the two orthogonal polarization channels always gives a completely polarized wave. However, subsequent time averaging of the single spectrum estimates reveals the contribution of the polarized and unpolarized wave components to the total received time-averaged wave. It was found that averaging together five single spectrum estimate polarization parameters, which gave a temporal resolution of ~1 s, was very reasonable. For long-lasting stable scatter- ing events a comparison between longer time averages (~20 s) and i s time averages indicated essentially the same polarization parameters. Although E region scatterers can have lifetimes as short as a

6 546 HUSSEY ET AL.: POLARIZATION OF AURORAL BACKSCATTER few milliseconds [Hall et al., 1993], the statistically defined parameters describing the scatter do not vary substantially over much longer time periods. In an attempt to eliminate temporal effects, most of the spectra presented were from events which were unvarying for long periods (~ 5 min). Analysis and Discussion The polarization data are presented in two general formats. The "spectral time plots" show ~1 s averaged spectra plotted against time; the intensity and polarization parameters are represented by a color scale defined by the legend on the right (e.g., Plate 1). Only intensity and the polarization ratio spectra are presented, as they are the most informative in this format. The spectra are plotted with respect to Doppler frequency on the y axis and time on the x axis. The "20 s averaged spectrum plots" or "single spectrum plots" are of a single spectrum, with a time average of ~20 s, plotted with Doppler frequency on the x axis and intensity, m, X, or p plotted on the y axis (e.g., Figure 2). Each polar- ization parameter spectrum is plotted as a solid line with the intensity spectrum replotted as a dotted line. This format allows for more readily identifiable polarization parameter spectral properties. For both formats the intensity values are signal to noise ratio values plotted in decibels. Any signal to noise ratio values less than 0 db were discarded along with their respective polarization parameters. It is obvious in these spectrum plots that the polarization ratio spectrum decreases for frequencies not at or close to the peak of the intensity spectrum frequency. The polarization ratio spectrum shape roughly follows its intensity spectrum shape although, in general, the wider the intensity spectrum, the more slowly the polarization ratio spectrum decreases with respect to the intensity spectrum, while the narrower the intensity spectrum the more closely the polarization ratio spectrum follows it. The polarization ratio spectrum showed similar behavior when a test signal of very narrow bandwidth, produced by a signal generator and a power splitter, was sent through the polarimetric receiver system. It may thus be assumed that polarization measurements closer to a spectral peak will be more representative than those farther out, although this assumption is complicated when multipeaked spectra are present. Weak signals of a few decibels or less have polarization parameters of m ~ 1, X ~ 0ø, and p ~ 45 o (no exampleshown). One would expec these weak signals to be random in nature (i.e., noiselike) and therefore m ~ 0 and X and p to vary randomly. Robinson [1963], however, has shown that in the mixing process, a weak signal becomes correlated with the oscillator frequency. Because the two polarization channels of the receiver have a common oscilla- tor, this would explain the characteristics associated with weak signals. We considered a signal to be linearly polarized if the ellipticity angle was in the range X - 0ø q- 8ø (-80 < X < 80) ß This estimate was based on the accuracy of the polarimetric receiver system and any error which could be introduced by the ground reflection correction, which was based on the assumption that the scattering was coming from an altitude of 110 km. The scatter could potentially come from any altitude in the lower E region (~95 km to ~120 km), although it is more likely to be from an altitude of ~110 km JUnwin and Johnston, 1981; Wahlund et al., 1989; $ahr et al., 1991; Watermann, 1994]. Example 1: UT, Day 342, 1993 In Plate 1, spectral time plots of the intensity and polarization ratio spectra for a 5 min period starting at 0430:00 UT (day 342, 1993) on the GS link are shown. We consider this to be a typical type 1 scattering event. The signal is stable during the 5 min period, and the polarization ratio is high and uniform across the spectra. Figure 2 shows the 20.3 s time average of the intensity and polarization parameters starting at 0432:40 UT. These single spectrum plots of intensity and the polarization parameters are representative of the event presented in Plate 1. From Figure 2, the intensity spectrum is centered at a frequency of 75 Hz with a width of 24 Hz, which corre- sponds to a mean plasma wave velocity of ~310 m/s and a width of ~100 m/s. The polarization parameters are uniform around the peak of the intensity spectrum with m , X - -1ø, and p The polarization ratio is high, indicating that the Faraday dispersion was small. This in turn implies a small, well-defined scattering region and/or a small number of discrete scatterers located close to one an- other. Here scatterer refers to a volume where radar waves are scattered according to weak coherent scattering theory. The ellipticity angle value indicates that essentially a linearly polarized wave is scattered,

7 .. HUSSEY ET AL.' POLARIZATION OF AURORAL BACKSCATTER 547 intensity.. -'.-,,-..%'::.-..:.-:,:, i- -: :,..'..' '.' -. ß ß..,.-.[ OO -..., ß..Z.X-',-.... ß ', '? ' ' '.. ' ': ',. 'r " '". '.--,., r.. * -,. **t.,. ', -. ;",.. '**. ß,';'.,.,, ** '...,,,:.,.. ;.;, ß ;..., '/*'". [ -,.. :.. *..,...-,,..,..., -..., ß..... **,:.,,.,... J! ' -' c..., ,::...-..',. ], ß.q,.... ß,.. / ß.t... t,". ' - '., * & e '"*'' ' "..,.:. :-./. ;...,. :.';.., ' ,,,.,.*; ".%..., j Time (seconds) Polarisation Ratio,,,... ;',:" "' ' '.:,- ß ß... ' ',." /:'; db , , ,0 18, :200 ß. -:. *,< *h':, :'-".,' '[...?½ ', ','. V-'t,,......li....,...,,,,,......, ' ' " =' ' " '-,"' Time (seconds) ,92 0, o.67 ß :' O O.O Plate 1, Intensity and polarization ratio spectral time plots from 0430 UT to 0435 UT for day 342 on the GS link.

8 ß ß,. ß $48 HUSSEY ET AL.' POLARIZATION OF AURORAL BACKSCATTER ' ' ' i 20.3 s spectrum '~ lo o -4oo I i i i I -200 i t i J l,.,o '. i J- i o loo , 20,,,, o 2oo Figure 2. Intensity and polarization parameters for a 20.3 s averaged spectrum starting at 0432:40 UT for day 342 on the GS link. 4OO as would be expected in weak coherent scattering be- compared to type 1 (narrow spectra, therefore longer cause the incident wave was linearly polarized. lifetimes) observations over the polarimeter integra- At the same time as the type 1 event on the GS link tion time, in this case ~ 1 s. This was not observed, was observed (Figure 2), there was a typical type 2 suggesting that statistically the temporal behavior of event on the LS link (not shown). This type 2 sig- the scatterers does not vary significantly over much nal had a spectrum centered at a frequency of 33 Hz longer time periods. Although the orientation anwith a width of 56 Hz, which corresponds to a center gles of the type 1 and type 2 scattering events are velocity of ~135 m/s and a width of ~230 m/s. The similar, in general they would not be expected to be polarization characteristics of the type 2 signal were identical because the orientation angle is dependent m = 0.95, X = -2ø, and b = 108 ø. Again, the scat- on the electron density along the radar wave path tered signal is highly polarized and essentially linear. as well as the scattering geometry (note that for the It is interesting that the type 2 and type 1 events had same electron density profile for both links the oriensuch different spectra, yet such similar values of m, tation angle between the links would in general differ X and b. If lifetimes of scatterers are inferred from by ~ due to their slightly different scattering the inverse of their spectral widths [Sudan, 1983], geometries), and as these two events are on different then one may expect lower polarization ratios for radar links they traverse different paths. type 2 (broad spectra, therefore short lifetimes) as It is interesting to note that the bisector of the

9 HUSSEY ET AL.: POLARIZATION OF AURORAL BACKSCATTER $49 GS link is directed approximately along the average auroral electrojet flow direction, while the LS link bisector is directed approximately perpendicular to it. These concurrently occurring type 1 and type 2 events are in agreement with the present theories and observations which indicate that type 1 waves are produced by primary plasma wave instabilities which are excited in directions along the electrojet while type 2 waves are produced by secondary plasma waves which propagate in directions perpendicular to the electrojet [Haldoupis, 1989; Kelley, 1989]. Starting at 0410:00 UT (d y 342, 1993) and lasting for about 100 s or more, there was a typical type 3 scattering event on the LS link (not shown). The spectrum is centered t a frequency of 65 Hz with a width of 14 Hz, which corresponds to a center velocity of ~265 m/s and a width of 60 m/s. Again, the polarization parameters of the type 3 event, namely, m , X - 0 ø, and - 850, were similar to those of both the type 1 and 2 events. The polarization ellipse parameters of types 1, 2, and 3 (unfortunately, no type 4 echoes were ob- served) are essentially the same (except for the orientation angle, which depends on the integrated electron density along the radar wave path). The results indicate that the scattering of a linearly polarized incident wave produces a highly polarized and essentially linearly polarized scattered wave. Although not all of the observations had polarization ratios as high as in the examples given, these were representative of the majority (roughly 70%) of the observed echoes where, in general, m > 0.8. Example 2: UT, Day 342, 1993 In Plate 2 the intensity and polarization ratio spectral time plots are shown for a 5 minute period starting at 0345:00 UT, day 342, on the GS link. In Figure 3, the intensity and polarization parameters for a 20.3 s averaged spectrum starting at 0346:40 UT from the period presented in Plate 2 are shown. The intensity spectra would be classified as a type 1 scattering event, but the polarization parameters show neither the uniformity nor the characteristics (a very high polarization ratio and X 0 ø) shown in Plate 1 and Figure 2. At this point a few terms should be defined more clearly in the context of this paper. First, "scattering region" will refer to the region defined by the intersection to the transmitting and receiving radar beams, and "scattering volume" will refer to scattering from only a portion of the scattering region. Second, the total received signal may be thought of as being composed of multiple individual or discrete weak coherent scatterers, and these scatterers will be distributed somehow within the scattering region. In Plate 1 and Figure 2 the high and uniform polarization ratio suggests multiple well-defined scatterers with similar spatial (and temporal) characteristics all contributing to the scattered signal, thus suggesting a relatively small scattering volume. In Plate 2 and Figure 3 the intensity plots indicate that the received signal is extremely intense, even more intense than in the previous example. Therefore one may reasonably expect the received signal to show characteristics similar to those in the previous example, such as would be indicated by a polarization ratio value close to unity. Instead, the polarization ratio plot indicates an r value varying widely and randomly from 0.2 to 0.9; the ellipticity and orientation angles presented in Figure 3 exhibit similar erratic behaviors. One interpretation of these results is that the total scatter comes from many scatterers which are located in significantly different parts of the scattering region and have different spatial (and temporal) characteristics. This may be visualised as dropping a large number of shiny strips from an airplane and observing them descend randomly, glinting in the sunshine. The echo intensity might be high and, when time averaged, constant, but the polarization ratio might be low due to differential Faraday rotation over a scattering volume that is relatively large. In any case, these data show that strong scat- tering does not necessarily imply either a small or a large scattering volume. The two different polarimetric results for the type 1 echoes shown in Figures 2 and 3 indicate that without the polarization parameters these two obviously very different cases cannot be differentiated based on the intensity spectra alone. This interpretation is supported by the ear- lier observations of Sofko and Kavadas [1971], who reported "discrete"(spatially confined) radar echoes with high polarization ratios and "diffuse"(spatially extended) radar echoes with low polarization ratios. Significant Ellipticity For a significant portion of the data collection period, most signals are essentially linearly polarized. There are, however, cases in which there is significant ellipticity, such as in Figure 4, where for part of the spectrum the ellipticity angle is larger than can be accounted for by experimental error. This is an unexpected observation because the scattering pro-

10 , $$0 HUSSEY ET AL.: POLARIZATION OF AURORAL BACKSCATTER Intensity I,,,, I... J_..._,, I,,, :L I,...,... L...,...!,......,:i :.... '... ' '' 0 ':' ' -,,i"..., *,...,. 0,,",.-, - -,,,, '.; ' t. ß * ' '"' " '* '... ' ' * I ' 'd""' ' ' " '"'" * '... *'"1 ' ' *' ' '" I ' ' ' ' I ' ' ' '! ' [ ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' Time (seconds) Polarisation Ratio!... I I ' I I I I... I...!, ' ' ' l db l'* :%,".,,..,'. }:. '..',I :'1,... ;. ß I. -''"." ; : I.,,:.'... ' ß i,,:,':? r. ;.-,,, ' f:....;* ;4' ,.....':.-.',.. -: -200,<...:',.. _: ',..'.',..'_. ß ;: =.' -... :., ' - " " '... J... ' I ' I l I ' ' * ' I ' [ B : : I ' ' ' ' I ' ' ' ' I ' ' ' ' I Time (seconds) Plate 2. Intensity and polarization ratio spectral time plots from 0345 UT to 0350 UT for day 342 on the GS link O O O

11 ß ß,.,, ß. ß ß,. HUSSEY ET AL.' POLARIZATION OF AURORAL BACKSCATTER s spectrum i i i i i i,.; ". 0 i i i I i i i i i i 0.10 [ ";'.. [.., I,, ' ' ' i i i. 120 i -10 i: loo < ß I '"[,, I, [ [ I, ' ' ' ,,, I, t I i i J i , Figure 3. Intensity and polarization parameters for a 20.3 s averaged spectrum starting at 0346:40 UT for day 342 on the GS link. cess is weak and at a radar frequency of 50 MHz, differential absorption of the probing radar wave is insignificant. This is supported by the Rabbit Lake riometer measurements, which indicated no significant absorption during this period. In a number of the 20.3 s spectrum plots from day 342 it is apparent that a significant elliptical component occurs only when spectra overlap. This can be seen in the asymmetric spectrum presented in Figure 4 (compare the symmetric spectrum in Figure 2). This example was selected for its subtle indication of overlapping spectra in the intensity plot, while the ellipticity angle plot is a clear indication of overlapping spectra. Figure 4 depicts an intensity spectrum which can be interpreted to be made up of two spectra, one centered at 85 Hz and the other centered at 120 Hz. In the polarization ratio plot, there are roughly two polarization ratio values associated with the peaks; m _ 0.9 and m _ 0.7 respectively. This trend is also observed in the ellipticity angle plot (X TM 0ø and X _ -25 ø) and the orientation angle plot ( b_ 110 ø and p_ 30ø). There is a significant ellipticity associated with the 120 Hz spectrum. This apparent ellipticity can be explained by the overlapping of the two spectra. It is reasonable to assume that the two spectra are independent and originate from different volumes in the scattering region; therefore each spectrum is scattered according to weak coherent scattering processes, and as a resuit the scattered waves are linearly polarized. These linearly polarized waves, in general, will have different orientations relative to one another because they

12 $$2 HUSSEY ET AL' POLARIZATION OF AURORAL BACKSCATTER s spectrum = o 0.8 ß = 0.6 '1:: ) ( < -10 o, o, o 60 ß c o ) Figure 4. Intensity and polarization parameters for a 20.3 s averaged spectrum starting at 0425:10 UT for day 342 on the GS link. will have traversed different paths and undergone different amounts of Faraday rotation. If the spectra partially overlap (i.e., signals of the same frequency are scattered from different scattering volumes in the scattering region), the independent polarization states associated with the overlapping portions of the spectra at a given frequency will combine to give a new and likely different polarization state than either of the two from which it was created. It can thus be expected that the combination of the overlapping portions of spectra would give elliptically polarized states. For linearly polarized signals of the same frequency but different orientations, coming from two different scattering volumes in the scattering region, the spatial separation associated with the signals introduces a phase difference 6(As), where As is the mean distance between the two scattering volumes. As the distance between the scattering volumes may be any arbitrary value and the polarimeter is unable to distinguish spatial information, the received signal would in general appear as an elliptically polarized wave. Polarization Ratio Values The received signals have polarization ratio values which are, to varying degrees, less than unity, while the transmitted radar waves are completely polarized. This reduction in polarization ratio for the received signals is due to propagation and/or scattering effects. One major propagation effect is Faraday dispersion, which is the result of differential Faraday rotation. If scatter is from a single scattering

13 HUSSEY ET AL.: POLARIZATION OF AURORAL BACKSCATTER $$3 process (i.e., a single spectrum results from a unique the former case, consider two scattering volumes sepvolume of the scattering region), that scattering process will have some spatial extent associated with it; as a result, the Faraday rotation will be different for waves scattered from different portions of the scattering volume. The addition of these scattered waves of varying orientation results in a partially polarized wave. An equation was derived in order to try and explain the reduction in the polarization ratio due to Faraday dispersion. The derivation of this equation assumed independent equal amplitude linearly polarized waves uniformly distributed over an interval r/0 - A0/2 to r/0 + A0/2 and is given by arated by a fixed distance which introduces an appropriate phase difference to give a significantly elliptical wave. Also, assume that the mean orientation of the electric fields of the two scattering volumes remains constant. For each scattering volume the polarization ratio is reduced from unity by Faraday dispersion (equation(4)), and the relative mean orientation of the electric fields determines how each scattering volume contributes to the overall unpolarized component (the amount of Faraday dispersion can also be a factor). If the mean electric field orientation (linearly polarized) from the two scattering volumes is similar, then the polarization ratio will be approximately the value of the lower polarization ratio (i.e., m - sinc At/, (4) the spatial distribution of the scatter from the two volumes is similar). If the averag electric fields from where both scattering volumes are oriented 900 to one sin other (and the Faraday dispersion is distributed 450 sinc At/- or less), then the unpolarized components from both scattering volumes will contribute fully to the total unpolarized component. With this information on the origin of elliptically polarized waves, a review of some results is needed. In Figure 3 a high intensity signal which had a rel- When this equation is applied to the type 1, 2, and 3 events presented where the polarization ratios were 0.88, 0.95, and 0.97, At/ will have values of 49.5 ø, 31.5 ø, and 24.5 ø, respectively. To take into account the geometry of the experiment, it may be assumed, atively low and varying polarization ratio was preto a first approximation, that the contribution to the Faraday dispersion is equal for the incident and scattered waves. The amount of Faraday dispersion is also dependent on the ambient electron density. Any change in this parameter, however, would only be of sented. It was suggested that the low polarization ratio would indicate a large scattering volume with scatter coming from a number of individual scatterers. This interpretation, although correct, does not give any detail about the scatterers. Additional secondary importance for the relatively small scatter- information about the scatterers can be obtained ing volumes presented here. More importantly, the through the ellipticity angle. The ellipticity angle peak electron densities measured by the ionosonde, had a mean which give an indication of the ambient electron densities, were roughly the same for all of these examples. A further reduction of the polarization ratio ocvalue of ~ -200 with fluctuations of curs when spectra overlap. In these cases it has been suggested that the spectral components come from distinct scattering volumes (or plasma processes) in spectrum may be associated with an independent the scattering region; therefore the polarization ratio scattering volume (or plasma process) from which (and the other polarization parameters) is dependent linearly polarized waves are scattered. As well, each upon the relation of the scatter from these distinct individual scattering volume would have a different scattering volumes. In general, the scattering vol- Faraday rotation associated with it depending on its umes may be either stationary or moving at a constant speed with respect to one another. The latter case must be discarded, as this would mean that the measured polarization states would depend on the time average, and tests varying the time average indicated essentially the same polarization results. For ~ :520 ø. This would indicate there are two, or possibly more, overlapping spectra independently contributing to the received scattered signal. Because the polarization parameters vary a great deal, there are likely more than two overlapping spectra contributing to the received signal. Each individual radar wave path. The idea that the total scattering volume is large can be qualified by saying that the total scattering volume is made up of a large number of individual or discrete scattering volumes, where each scattering volume is associated with an individual spectrum.

14 554 HUSSEY ET AL.: POLARIZATION OF AURORAL BACKSCATTER Summary and Conclusions References In general, coherent VHF scatter of the spectral classes defined as type 1, 2, and 3 had similar polarization characteristics. For most of the observations, the scattering of a linearly polarized incident wave produced an essentially linear and highly polar- ized scattered wave. This implies a small scattering volume and/or a small number of discrete scatterers located close to one another. This also confirms that the scattering process is a weak, coherent one. These results are typical of most of the observations, but not all. An example was presented in which the intensity spectrum was that of a very intense, apparently typical, type 1 scattering event, but the polarization parameters were variable and indicated an appreciable amount of unpolarized signal (i.e., a significant reduction in the polarization ratio) and the reception of scattered waves with significant ellipticity. The appreciable unpolarized component and the significant ellipticity can be explained as scatter coming from a number of individual scattering volumes within the scattering region. There is evidence to suggest that the reduction in the polarization ratio is the result of the different scattering volumes within the scattering region each contributing an unpolarized component to the received signal. The contribution from each scattering volume is dependent upon the relative orientation of the average electric field vector from each of the scattering volumes and the amount of Faraday dispersion associated with them. For example, the two different polarimetric results for the type 1 echoes (Figures 2 and 3) indicate that without the polarization parameters these two obviously very different cases cannot be differentiated based on the intensity spectra alone. The polarization parameters thus give additional information in the interpretation of scattering from plasma processes in the auroral E region. Acknowledgments. The authors are grateful for the technical assistance of M. McKibben, B. Marshall, R. Miller, D. Danskin, R. Wilkinson, and A. Ortlepp. A special thank you as well to T. P. Eagan and R. Ostertied. We also gratefully acknowledge the daily upkeep of the receiver system by Solange Bakker. Funding for the radar experiment was provided by the Canadian Network for Space Research and by a team operating grant (G.J.S. and J.A.K.) of the National Sciences and Engineering Research Council of Canada. The authors would also like to thank the two reviewers for their helpful suggestions. B dard, N., and G. J. Sofko, Radio auroral scattering anisotropy inferred from 42 MHz polarization studies, Can. J. Phys., 5,/(24), , Born, M., and E. Wolf, Principles oj Optics, 2nd (revised) ed., Pergamon, Tarrytown, N.Y., Egeland, A., O. Holter, and A. 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15 HUSSEY ET AL.: POLARIZATION OF AURORAL BACKSCATTER 555 Sofko, G. J., and A. Kavadas, Polarization characteristics of 42-MHz auroral backscatter, J. Geophys. Res., 76(7), , Sofko, G. J., J. A. Koehler, C. Haldoupis, M. J. McKibben, and A. G. McNamara, Doppler radio observations of 3-meter irregularities in the polar cap E region, J. Geophys. Res., 92(A2), , Sudan, R. N., Unified theory of type I and type II irregularities in the equatorial electrojet, J. Geophys. Res., 88(A6), , Unwin, R. S., and P. V. Johnston, Height dependence in the power spectrum of diffuse radar aurora, J. Geophys. Res., 86(7), , Wahlund, J.-E., H. J. Opgenoorth, and P. Rothwell, Observations of thin auroral ionization layers by EISCAT in connection with pulsating aurora, J. Geophys. Res., 9 /(A12), 17,223-17,233, Watermann, J., A decade of type 3 radio aurora studies: Toward and away from the EIC interpretation, J. Geornagn. Geoelectr., J6, , G. C. Hussey, J. A. Koehler, and G. J. Sofko, Institute of Space and Atmospheric Studies (ISAS), Department of Physics and Engineering Physics, 116 Science Place, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E2, Canada. ( hussey@skisas.usask.ca; koehler@skisas.usask.ca; sofko@skisas.usask. ca) (Received April 3, 1996; revised September 25, 1996; accepted October 21, 1996.)