Polarization of Impulsive Signals at Venus - Section 2
J. Geophys. Res., 96, 22, 741-22, 752, 1991
(Received: June 11, 1991; accepted: October 1, 1991)
Copyright 1991 by the American Geophysical Union.
Paper Number 91JE02506.
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As already discussed, it is often assumed that the wave electric field is polarized perpendicular to the ambient field for whistler mode waves. Before presenting specific examples, we should show under which conditions this is a reasonable assumption. Whistler mode waves propagating parallel to the ambient magnetic field are transverse electromagnetic waves, and in this case the wave field is polarized perpendicular to the ambient field. However, obliquely propagating whistler mode waves, especially those on the resonance cone, tend to be electrostatic. The wave field is polarized along the wave vector for electrostatic waves, and these waves will be polarized approximately parallel to the ambient field when the resonance cone angle is small. The degree of polarization of the wave field as a function of propagation direction and ambient plasma parameters has been taken into account explicitly by Sonwalkar et al. . We will show, however, that for most circumstances in the nightside ionosphere of Venus, whistler mode at 100 Hz will be polarized predominantly perpendicular to the ambient field.
2.1 Expected Whistler Mode Polarization
From cold-plasma theory [e.g., Boyd and Sanderson, 1969] it can be shown that the wave field polarization is given by
where Ez, is the electric field component parallel to the ambient magnetic field, Ex is the component in the plane containing the magnetic field and the wave vector, and Ey is orthogonal to the other two. The angle between the wave vector and the ambient field is given by , and is the refractive index. The variables S, D, and P are terms in the cold-plasma dielectric tensor, with
where the summation is carried over particle species, with ps being the species plasma frequency and s, being the species gyrofrequency (including the sign of the charge). In deriving (1) and (2) it is assumed that the wave fields vary as exp-i( t-k r).
Equation (1) gives the polarization in the plane perpendicular to the ambient field, while (2) gives the degree of polarization along the field. For example, the refractive index for parallel propagation is given by 2 = R or L, which on substitution into (1) gives iEx /Ey = 1 respectively, with, iEx /Ey = 1 corresponding to right-hand circular polarization.
Given the refractive index for a particular wave frequency and direction of propagation, (1) and (2) can be used to specify completely the electric field polarization. While we could use the complete cold-plasma dispersion relation to determine the refractive index, a simplified version is applicable for most parameter regimes in the Venus nightside ionosphere. First, since the lower hybrid frequency (fLHR) in a proton plasma = 0.65B Hz, where B is magnetic field magnitude in nT, fLHR would be less than 20 Hz, even if the magnetic field were as large as 30 nT. This is much less than 100 Hz, and the lower hybrid frequency would be even lower in an O+ plasma. We can consequently neglect the ions in the cold-plasma dispersion relation.
The cold-plasma dispersion relation can be further simplified using the quasi-parallel (or quasi-longitudinal) approximation provided sin2 < (2pe / 2e) cos , where pe and e are the electron plasma and gyrofrequencies (the latter does not include the sign of the electron charge). At Venus, nightside ionospheric densities are typically > 100 cm-3, while B < 30 nT. Consequently, 2pe / 2e 104, and the quasi-parallel approximation should be adequate, except for propagation near 90°. Since whistler mode waves can propagate perpendicular to the field only for f fLHR, we do not consider perpendicular propagation. Under the quasi-parallel approximation,
On substituting (3) into (1) and (2), assuming 2 1, we obtain the following:
Equations (4) and (5) depend only on the propagation direction and on the wave frequency with respect to the electron gyrofrequency, and so provided the quasi-parallel approximation is valid, these equations can be used to estimate the degree of polarization of whistler mode waves in the nightside ionosphere of Venus.
The refractive index in (3) has a resonance when = cos-1 /e = r, the resonance cone angle. Inspection of (4) shows that the wave field is always right-hand polarized for all propagation angles < r, with the polarization being circular for parallel propagation and predominantly in the x direction for propagation near the resonance cone. The dominant electric field component in the plane perpendicular to the ambient field is consequently given by Ex. With regard to the parallel electric field,(5) shows that this is largest when the wave is propagating at the resonance cone angle, and in that case, Ez / Ex = / (2e - 2)1/2. For small /e, Ez / Ex /e . At Venus the OEFD detects whistler mode waves in the 100-Hz channel. The average magnetic field at low altitudes is about 18 nT [Ho et al., 1991], and so Ez / Ex < /e 0.20 on the average. In general, then, the assumption that the wave field is perpendicularly polarized for whistler mode waves is reasonable in the nightside ionosphere of Venus.
2.2 Examples of Observed Polarization
Having demonstrated that whistler mode waves will be predominantly perpendicularly polarized in the night ionosphere of Venus, we will present specific examples of the wave polarization. Figure 1 shows OEFD wave data acquired on orbit 526 by the Pioneer Venus Orbiter. The figure shows the log10 of the wave intensity (in V2/m2/Hz) as a function of time for the four frequency channels of the OEFD. For this orbit most of the wave activity is in the 100-Hz channel, and we give examples of the wave polarization for selected intervals as indicated by the horizontal bars in Figure 2 The first two intervals were chosen since they correspond to the intervals shown by Scarf and Russell . The last interval was chosen to show an interval which contains interference signals.
Fig. 1. Time series of the wave intensity as measured by the orbiter electric field detector. Six minutes of data acquired on orbit 526 are shown. Most of the impulsive signals occur in the 100-Hz channel only. The horizontal bars mark intervals for which polarization examples are given in Figure 2.
Figure 2 shows the log10 of the wave intensity as a function of spin phase measured over a 30-s interval, corresponding to roughly 2.5 spin periods (spin period 12 s). In the plot the x axis points toward the Sun. The data are plotted on a relative scale such that the minimum wave intensity in the interval corresponds to the origin of the polar plot, with the maximum giving the unit circle. The line labeled "B" is the direction of the average magnetic field in the spin plane, with the arrow head giving the fraction of the total field lying in the spin plane. The line labeled "E" is actually the line of maximum variance through the data, which we assume corresponds to the average wave electric field direction. To the left of each plot in Figure 2, we give the minimum and maximum wave intensities, together with the maximum/minimum variance ratio and the relative orientation of the "E" and "B" directions.
Fig. 2.Three polarization plots for orbit 526. (a) and (b) Polarization of naturally occurring signals. (c) Polarization of an interference signal. Each plot is drawn using a log10 relative scale, as discussed in the text. The naturally occurring signals are polarized perpendicular to the average magnetic field.
Figures 2a and Figure 2b show polarization diagrams for the first two marked intervals in Figure 1 These plots are not identical to those shown by Scarf and Russell  since the wave data are plotted on a relative scale and we use a 30-s interval when producing the plots, as opposed to a 15-s interval as used by Scarf and Russell. We selected 30-s intervals since this length was used by Russell et al. [1988, 1989] in their occurrence rate studies, and we will use their data base in conjunction with our study. These differences notwithstanding, the data in Figures 2a and 2b support the conclusion of Scarf and Russell  that the wave electric field is polarized perpendicular to the ambient field and hence whistler mode. The conclusion that these waves are whistler mode waves was also confirmed by Sonwalkar et al. , who in addition noted that the magnetic field orientation for the interval shown in Figure 1 was such that the waves were inside the whistler mode resonance cone.
Figure 2c shows data for an interval in which the data appear to be contaminated by an interference signal. The polarization plot shows an extremely clear alignment of the electric field. If this interval were to be included in a statistical study, then the resultant distribution of polarizations would be compromised. We will discuss this interference signal in more detail later.
As a counterexample to signals that show clear whistler mode polarization, we present data from orbit 501 in Figure 3. This figure shows qualitatively different wave signatures, which are characterized by impulsive signals at all frequencies. The interval shown in Figure 3 has also been studied by Sonwalkar et al. , who noted that the magnetic field was nearly horizontal at this time, and so vertically propagating whistler mode waves would lie outside of the resonance cone.
Fig. 3. Time series of wave intensity for orbit 501. Similar in format to Figure 1. On this orbit the impulsive signals are observed in all four channels.
The polarization plots for the intervals marked in Figure 3 are given in Figure 4. The format is similar to Figure 2, with Figure 4a and Figure 4b corresponding to the broadband signals in Figure 3, while Figure 4c gives another example of an interference signal. In Figure 4a the polarization is more parallel, while Figure 4b is more perpendicular. These events are probably not whistler mode waves.
Fig. 4. Three polarization plots for orbit 501. Similar in format to Figure 2. (a) The maximum variance direction is more parallel to the magnetic field than perpendicular, while (b) the wave field is perpendicular. (c) The interference signal is greater than 45° to the magnetic field and would bias the statistics to perpendicular polarization if included in the analysis.
From the events shown in Figures 2 and 4 we see that not all events are consistent with whistler mode waves, and even those which do show perpendicular polarization are not clearly polarized. For example, it is the interference signal in Figure 1c which has the best defined polarization. Part of the reason for the relatively poor polarization data is due to the impulsive nature of the signals. The nightside signals often last for only a fraction of a spin period, unlike other plasma waves such as upstream plasma oscillations. Because the latter waves last for several spins the wave polarization can be determined quite readily [Crawford et al., 1990]. In addition to the aliasing caused by sampling a short-duration signal occurring at random spin phases, the interference phenomena may bias any statistical study of the polarization. How we address these problems will be discussed in more detail in the following section.
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