J. Atmos. Terr. Phys., 57, 537-556, 1995
(Received in final form 19 May 1994; accepted 27 June 1994)
Copyright © 1995, Elsevier Science Ltd
3. Lightning or Whistler-Mode Instability
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Fig. 1. Sketch of the solar wind interaction with the ionosphere of Venus [after Crawford et al., 1993]. The nightside ionosphere of Venus has considerable structure. Regions known as "holes", containing enhanced radial magnetic field and reduced plasma density, are often observed. These holes appear to act as ducts for upgoing whistler-mode waves.
The most striking of the structures observed within the nightside ionosphere of Venus are "ionospheric holes". These are regions of reduced ionospheric plasma density and enhanced magnetic field. The field within holes is often close to radial, and as we shall discuss later, these regions of near-radial field act as ducts for whistler-mode waves. One other interesting feature of holes is that they are mainly a solar maximum phenomenon. Holes do not appear to have been detected during the entry phase of the Pioneer Venus Orbiter, which occurred during solar intermediate conditions [Theis and Brace, 1993]. This implies that holes are generated through day to night transport of plasma and magnetic field, since this transport is reduced for lower levels of solar activity.
At low altitudes within the nightside ionosphere of Venus two basic types of VLF/ELF signal are detected. Figure 2 shows an example of the first type of signal, which occurs only in the 100 Hz channel of the OEFD. Because of weight, power, and telemetry constraints, the OEFD has only four channels at 100 Hz, 730 Hz, 5.4 kHz and 30 kHz, with each channel having a bandwidth of ±15% of the center frequency [Scarf et al., 1980b]. The top four panels of Figure 2 show the wave intensity, while the bottom four show the magnetic field data cast into radial-east-north coordinates. In this coordinate system the radial component is vertically out, and the east component is horizontal and parallel to the Venus orbital plane. East is defined as positive in the direction opposite to the planetary rotation, since Venus rotates in a retrograde sense. North completes the triad. It can be seen that throughout most of the interval shown the radial component of magnetic field dominates, and 100 Hz bursts are detected throughout this interval of strong radial field. Since these bursts only occur at 100 Hz, they would have been counted as possible lightning generated whistlers in studies such as Scarf and Russell .
Fig. 2. Example of plasma wave and magnetic field data for orbit 526. These data are typical of the 100 Hz waves that have been attributed to lightning generated whistler-mode waves. The upper panels show the wave intensity in the four channels measured by the OEFD. The bottom four panels show the magnetic field data cast into radial-east-north coordinates.
The second type of signal often observed at low altitudes is shown in Figure 3. These "wide-band" bursts have also been cited as possibly due to lightning [Singh and Russell, 1986; Russell, 1991]. However these bursts are clearly not whistler-mode waves, and because of this, Scarf et al. [1980a] cautioned against using signals at higher frequencies as being possible lightning signals. Unlike the 100 Hz only bursts, Figure 3 shows that the wide-band bursts are detected in regions of mainly horizontal field [Ho et al., 1992]. In discussing the wide-band signals, it should be noted that while the earlier study of Singh and Russell  suffered from contamination due to the inclusion of spikes caused by telemetry errors [Taylor and Cloutier, 1988; Russell and Singh, 1989], subsequent studies [e.g., Ho et al. 1991, 1992] specifically excluded possible telemetry errors.
Fig. 3. Example of wideband bursts observed on orbit 501. Similar in format to Figure 2.
Sonwalkar and Carpenter  have argued that the wide-band bursts are non-propagating modes and therefore generated locally within the plasma. Hence, they do not consider wide-band bursts as being lightning generated. While this is almost certainly true for many of the higher altitude bursts (altitudes greater than ~ 1000 km), this need not be the case for the lower altitude bursts. At the Earth, for example, anomalous VLF bursts which arrived prior to the whistler-mode wave packet have been detected in the ionosphere above lightning [Kelley et al. 1985]. Boeck et al.  have reported observations of lightning induced brightening of the airglow, while Burke et al.  have reported the detection of keV electrons and large electric field transients above a hurricane. These various observations all suggest that at the Earth, at least, lightning may couple to the ionosphere. The coupling mechanisms are not well understood, but it seems probable that "capacitive coupling" through the displacement current my drive conduction currents within the ionosphere [Hale and Baginski, 1987]. In light of these observations, it is possible that the "wide-band" bursts detected at low altitudes in the Venus ionosphere could be due to direct coupling between lightning and the ionosphere.
To further emphasize the altitudinal dependence of the bursts detected at Venus we present maps of the fractional occurrence of bursts in the 100 Hz channel only (Figure 4) and in the 5.4 kHz channel (Figure 5). In these two figures we have binned the data for the first 22 seasons of nightside periapsis passes of the Pioneer Venus Orbiter. We have employed a technique similar to that described by Russell et al.  and Russell , where the data are separated into 30 s intervals, and each interval is classified as being active or quiet at each frequency. The fractional occurrence rate of 100 Hz only burst activity is plotted as a function of position in Figure 4, where position is expressed in units of Venus radii (R, and 1 R = 6052 km). The 100 Hz only signals tend to occur most frequently at low altitudes, and extend to highest altitudes near the anti-subsolar point. In generating Figure 4 we have excluded all intervals for which additional signals occur at higher frequencies. For this reason we have classified the events as 100 Hz whistler events.
Fig. 4. Fractional occurrence for 100 Hz only bursts. Data from the first 22 seasons of nightside periapsis passes have been binned as a function of radial distance and solar zenith angle. The x-axis is along the Venus-Sun line, and the Sun lies to the left of the figure. The vertical axis gives the distance perpendicular to the Venus-Sun line, = (y + z). The data have been binned using 0.05 R by 3° bins, and then smoothed and interpolated to generate the plot.
Fig. 5. Fractional occurrence rate for 5.4 kHz bursts. Similar in format to Figure 4. Three different 5.4 kHz signals are observed, as indicated by the labels "A", "B" and "C".
Figure 5, on the other hand, shows the presence of several distinct plasma wave populations as measured at 5.4 kHz. First, at lowest altitude we see several peaks in the occurrence rate, labeled "A". These correspond with the "wide-band" bursts discussed above. Second, at high altitudes and high solar zenith angles (i.e. < 0.7 R and x < -1.2 R), there is a peak in the occurrence rate, labeled "B". Unlike the low altitude wide-band bursts, there are no additional signals at higher or lower frequencies when these waves occur at 5.4 kHz, and they are plasma oscillations in very low density regions of the Venus tail [Ho et al., 1993]. Lastly, additional wave bursts occur near the edge of the optical shadow (i.e. > 0.7 R), labeled "C". These waves are often correlated with waves at lower frequencies (730 Hz and 100 Hz), and may correspond to ion acoustic waves generated in the low density wake region of the planet. It is clear from Figure 5 that the properties of the VLF bursts at high altitudes cannot be used to infer the source of VLF bursts at low altitude.
There have been several studies on the morphology of the low altitude bursts (see Russell ), and we will describe only the more recent results. In their recent studies Ho et al. [1991, 1992] developed a method for determining the burst rate of the VLF waves observed at low altitudes, as opposed to the occurrence rate as shown in Figures 4 and 5. The burst rate studies are useful for comparison with the lightning rate at the Earth, for example, but suffer from possible over- or under-sampling, depending on the data rate. The occurrence rates cannot be easily compared with other rates, but do not suffer from dependence on the telemetry rate. With these points in mind, Figure 6 shows the burst rate as a function of local time for all four channels of the OEFD. As with other studies, the higher frequency bursts tend to peak in the dusk local time sector, while the 100 Hz bursts occur throughout the nightside.
Fig. 6. VLF/ELF Burst rate as a function of local time for the low altitude bursts detected in the first three seasons of nightside periapsis passes [after Ho et al., 1991].
Strangeway [1991a] and Sonwalkar et al.  point out that if the 100 Hz waves are lightning generated whistler-mode waves, then they will be refracted vertically on entering the ionosphere from below. This is because the refractive index in the ionosphere is typically around 1000. Whistler-mode waves can only propagate within a cone about the ambient field, known as the resonance cone. The resonance cone angle is given by cos = f/f, where f is the wave frequency (100 Hz), and f, is the electron gyro-frequency (= 28B Hz, where B is the magnetic field strength in nT). If the magnetic field makes an angle with respect to the vertical, then the resonance cone test requires < . Alternatively, the resonance cone test requires that the vertical component of the magnetic field B > f/28 = 3.6 nT for 100 Hz.
As an example of the importance of the resonance cone test, Figure 7, from Ho et al. , shows the burst rate as a function of altitude. For the 100 Hz waves each sample has been tested to determine if vertical whistler-mode propagation is allowed, and the rate for the 100 Hz waves inside the resonance cone is plotted separately from the 100 Hz waves outside the resonance cone. It is clear from the figure that the waves observed at low altitudes separate into two types of signal. The rate for 100 Hz waves inside the resonance cone decreases slowly with increasing altitude. The higher frequency waves and the 100 Hz waves outside the resonance cone all decrease rapidly with increasing altitude, and further all decrease at roughly the same rate with a scale height of about 20 km.
Fig. 7. VLF/ELF burst rate as a function of altitude [after Ho et al., 1992].
Figure 7 implies a common source for the 100 Hz waves outside the resonance cone and the high frequency bursts. The rate is generally highest at low altitude, while Figure 6 shows that the wide-band bursts are observed mainly in the post-dusk local time sector. We do not expect the ionosphere to display a strong asymmetry as a function of local time. However, the neutral atmosphere does, because of super-rotation. Thus, an atmospheric source for the non-whistler-mode signals is probable, and lightning coupling directly to the ionosphere is a reasonable explanation for the wide-band signals. As will become clear in discussing the 100 Hz whistler-mode signals in subsequent sections, the dominant controlling factor for the whistler-mode waves is the degree of accessibility for these signals. The whistler-mode waves are observed wherever a propagation window is present, while the non-whistler signals are more closely related to the underlying source. Thus the wideband data are used to determine lightning rates and Ho et al.  found planet-wide rates comparable to terrestrial lightning.
The resonance cone test is very powerful. It only applies for waves that are assumed to have propagated from below the ionosphere. That the 100 Hz waves separate into two distinct classes by applying this test is strongly supportive of the lightning hypothesis, since any in situ instability does not require vertical propagation. Strangeway [1991b] also used the resonance cone test to investigate the polarization of the 100 Hz waves. He found that the waves which satisfied the resonance cone test were polarized perpendicular to the ambient field, as expected for whistler-mode waves. Sonwalkar et al.  applied the resonance cone test to several burst intervals, and they found that 6/7 of the intervals which contained wave activity at 100 Hz only were consistent with whistler-mode propagation from below the ionosphere.
3. Lightning or Whistler-Mode Instability
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