J. Atmos. Terr. Phys., 57, 537-556, 1995
(Received in final form 19 May 1994; accepted 27 June 1994)
Copyright © 1995, Elsevier Science Ltd
Plasma wave data from the Pioneer Venus Orbiter provide the largest body of data cited as evidence for lightning on Venus. These data are also the most controversial, mainly because of the ambiguity in mode identification due to limited spectral information. We review some of the more recent studies of the plasma wave data at Venus, and we demonstrate that the characteristics of the 100 Hz waves are consistent with whistler-mode waves propagating vertically from below the ionosphere. We further show that in situ instabilities are too weak to generate whistler-mode waves, mainly because the thermal pressure is comparable to the magnetic field pressure in the ionosphere of Venus. The lower hybrid drift instability has also been suggested as an alternative source for the 100 Hz waves. However, the wave properties are more consistent with whistler-mode propagation; the lower hybrid drift instability requires very short gradient scale lengths to overcome damping due to collisions. We also note that an apparent association between Langmuir probe anomalies and 100 Hz waves is much lower than previously reported, once we apply a consistent intensity threshold for identifying wave bursts. The lightning hypothesis remains the most probable explanation of the plasma waves detected at low altitudes in the nightside ionosphere of Venus.
Whether or not lightning occurs on Venus has been an issue of considerable debate over many years. Much of that debate has centered on the observation of plasma wave bursts in the ELF/VLF range, as measured by the Pioneer Venus Orbiter Electric field Detector (OEFD) in the nightside ionosphere of Venus. Russell  recently reviewed the evidence for lightning on Venus, and he describes the results of many of the earlier studies of the OEFD data. In particular, he notes that the plasma wave data are more consistent with a lightning source within the Venus cloud layer, rather than active volcanism as originally suggested by Scarf and Russell . Thus the interpretation of the plasma wave data has more to say about the atmosphere of Venus, rather than issues concerning active volcanism.
Lightning within the cloud deck of Venus has important implications for the dynamics and chemistry of the Venus atmosphere. In their search for an optical signature for lightning Borucki et al.  pointed out that, based on our knowledge of terrestrial lightning, the meteorological conditions in the atmosphere of Venus may not be appropriate for the generation of lightning. Sulfuric acid, which is the main constituent in the clouds at Venus, has nearly the same dielectric constant as water, but it is not clear that sufficiently large particles are formed to allow charge separation. Thus, if lightning does occur on Venus, we may need to re-evaluate the mechanisms responsible for charge separation within clouds. With regard to the importance of atmospheric lightning, Borucki et al.  noted that lightning of sufficiently high rate can cause the formation of pre-biological molecules. Russell  also noted that a high lightning rate may be an issue for the safety of space probes, in addition to possible modifications of the atmospheric chemistry. The plasma wave data obtained by the Pioneer Venus Orbiter are the most extensive, and these data are hence suitable in determining lightning rates at Venus. It is therefore important to determine the likelihood that the wave bursts do correspond to lightning.
In support of the lightning interpretation of the VLF/ELF bursts, Russell  pointed out that there is other evidence for lightning on Venus. Optical measurements from the Venera 9 spacecraft [Krasnopol'sky, 1983], and the observation of impulsive electromagnetic signals by the Venera landers [Ksanfomality et al., 1983] both provide evidence for lightning within the Venus atmosphere. More recently, radio observations during the flyby of Venus by the Galileo spacecraft have also been interpreted as evidence for lightning [Gurnett et al., 1991]. The Galileo observations are probably the least controversial, since the data were acquired several planetary radii from Venus, in the solar wind. It is highly unlikely that plasma instabilities can generate impulsive signals around 1 MHz in the solar wind.
On the other hand, there have also been negative results in the search for lightning at Venus, most notably in searches for optical signatures. Data from the VEGA balloons did not show any evidence for lightning. Borucki et al. , using data from the star sensor on board the Pioneer Venus spacecraft, did not find any optical flashes whose rate exceeded the false alarm rate. However, both these searches tended to concentrate over the dawn local time sector, while it appears that lightning is mainly a dusk related phenomenon.
Irrespective of the other evidence for lightning, there is still the issue of whether or not the plasma waves observed in the nightside ionosphere are due to lightning. In testing the lightning hypothesis we are investigating the plasma wave properties of a weakly magnetized and weakly collisional plasma which is quite different from the terrestrial ionosphere. In particular, as we will emphasize throughout this review, the energy density of the thermal plasma can be comparable to the magnetic field energy density. This has important implications for both wave propagation and also possible plasma instabilities.
Our approach in this review is to compare and contrast the expected plasma wave signatures from the lightning hypothesis with the various plasma instabilities proposed as alternatives. We hope to demonstrate the strengths and weaknesses of the different hypotheses. It is not out intention to prove, nor do we expect to find, that all plasma waves observed in the nightside ionosphere of Venus are due to atmospheric lightning. Rather, our purpose is to assemble sufficient evidence to determine the most probable source for the majority of the plasma waves observed at Venus. Given the nature of the plasma wave data, this assessment must be based on statistics, rather than case studies. The question then becomes, given the various statistical properties of the waves, which hypothesis best explains the bulk (but not necessarily all) of the data?
The structure of this review is as follows. In the next section we discuss the morphology of the wave bursts. We demonstrate why the ELF (100 Hz) waves are probably whistler-mode waves, and further that they entered the ionosphere from below, consistent with a lightning source. In the third section we discuss the likelihood that plasma instabilities can generate whistler-mode waves at low altitudes. Because of the relatively high electron thermal pressure, we show that whistler-mode waves tend to be damped, rather than driven unstable. In the fourth and fifth section we discuss the most recent alternative explanation for the 100 Hz waves, that they are associated with density fluctuations corresponding with short wavelength lower hybrid resonance waves driven unstable through a gradient drift instability. However, this instability requires very steep density gradients to produce a large enough drift to overcome the damping due to collisions. In the final section we will summarize the discussion presented in this review.
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.
Fig. 8. 100 Hz burst rate dependence on the magnetic field orientation [after Ho et al., 1992]. The upper plot shows the time spent as a function of (the angle between the magnetic field and the radius vector) and (the angle between the magnetic field and the spacecraft velocity vector). Note that, for 0°, 90°. The lower plot shows the burst rate, which peaks at 0°. At higher there is no dependence on .
In this section we will concentrate on whistler-mode instabilities. Maeda and Grebowsky  argued that the signature of VLF saucers, which occur at low altitudes in the Earth's auroral zone ionosphere, would be similar to the bursts detected at Venus by the OEFD, if the same instrument were to be flown at the Earth. However, this argument neglects a fundamental difference between the terrestrial and Venusian ionosphere. At the Earth, there is a strong internal magnetic field that ensures that the plasma is low ( = , the ratio of thermal to magnetic energy density, where is the permeability of free space, n is the plasma number density, k is the Boltzmann constant, T is the plasma temperature, and B is the ambient magnetic field strength). At Venus, on the other hand, the magnetic field is relatively weak and the plasma can have a high , as noted by Strangeway .
This point was discussed further by Strangeway . For the sake of discussion, we will assume that the electron density in an ionospheric hole 3 10 cm, and the magnetic field 30 nT. For these values the electron plasma frequency - gyro-frequency ratio (/) 500. This ratio will be higher outside of holes since the magnetic field is weaker and the density is higher. Whistler-mode dispersion curves for this ratio are shown in Figure 9. The figure shows that the highest parallel phase speed is 300 kms, corresponding to an electron energy of 0.26 eV. Thus we expect whistler-mode waves to be damped by thermal electrons in the nightside ionosphere of Venus, and this damping will suppress any whistler-mode instability.
Fig. 9. Whistler-mode dispersion curves for different propagation angles [after Strangeway, 1992]. Wave frequencies are normalized to the electron gyro-frequency, while the parallel wave vector is normalized to the inverse of t he plasma skin depth. The shaded regions show where thermal electron Landau and gyro-damping are expected to occur.
To demonstrate this point more clearly, in Figure 10 we plot the damping rate of 100 Hz waves as a function of the normalized electron thermal velocity (v/c)(/), where v is the thermal velocity of the electrons. We have used the convention that 1/2mv = kT. The normalized thermal velocity = , where is the electron beta. In calculating we have used 2-s averages of the electron density and temperature measured by the Langmuir probe onboard the Pioneer Venus Orbiter, and the magnetic field. The data were acquired from orbits 484 - 560, and we have restricted the altitude range to < 300 km. The convective damping rate has been calculated for parallel propagating waves at 100 Hz. We find that for = 1, the damping decrement is 5 dB/km. Thus the wave intensity will have decreased by ten orders of magnitude after propagating some 20 km in the nightside ionosphere. Clearly whistler-mode waves cannot propagate any great distance in the high regions of the nightside ionosphere. Thus ionospheric holes, which are low , are where whistler-mode waves are more likely to be found. The magnetic fields within holes also have a large vertical component, allowing vertical propagation of whistler-mode waves from below the ionosphere. That 100 Hz wave bursts are found within ionospheric holes is entirely consistent with the lightning hypothesis. Strangeway  further showed that the 100 Hz wave intensity was largest in regions where the thermal electron damping was lowest.
Fig. 10. The convective damping rate of 100 Hz whistler-mode waves as a function of the normalized electron thermal velocity (= ). The observed magnetic field strength, electron density and temperature are used to calculate the damping rate for parallel propagating whistler-mode waves at 100 Hz, assuming an isotropic plasma. The thick line passing through the data gives the median as a function of the damping rate, binned every half decade. A damping rate of 8.686 dB/km corresponds with 1 e-folding of the wave amplitude/km.
As a last comment on the work of Maeda and Grebowsky , Strangeway  also investigated a beam driven instability. He assumed a beam density of 5 cm, parallel drift speed = parallel thermal velocity = 0.007c (12.5 eV), and a temperature anisotropy T/T = 2. This beam represented precipitating solar wind electrons that had gained access to the nightside ionosphere of Venus. He found growth rates less than 0.1 dB/km, requiring growth paths of at least 1000 km for a gain of 100 dB. It is hence very difficult for whistler-mode waves to grow to appreciable intensities within the nightside ionosphere, especially at low altitudes.
Grebowsky et al.  did compare their rate of coincidence with that expected from the burst rate studies of Ho et al. . However the burst rate studies used a fixed threshold of 2 10 V/m/Hz, while Grebowsky et al. counted signals as low as a factor of 2 above background as being bursts. For reference, the background of the 100 Hz channel is variable, but typically is around 10 V/m/Hz. Thus it is difficult to compare the coincidence rate as reported by Grebowsky et al.  with that expected for random coincidence. Furthermore, Grebowsky et al. did not compare the coincidence rate for anomalous scans with the rate found for normal scans, again making a comparison with random coincidence difficult.
Here, we will take a statistical approach to determine if the apparent association of Langmuir probe anomalies is more than simply random coincidence. We have used the Langmuir probe anomaly data (J. M. Grebowsky, personal communication, 1992) for the first three nightside periapsis seasons as a basis for this determination. As a first step we use the burst counting method of Ho et al.  to calculate the probability that one or more bursts exceeding the 2 10 V/m/Hz threshold will occur in any 2-s interval. We have chosen this length of interval since the Langmuir probe anomaly timing is given to the nearest second. Using that probability we can then compare the coincidence rate for bursts and Langmuir probe anomalies with that expected through random coincidence.
The first row of Table 1 shows the results of this calculation for all the data acquired within 0.9 R of the Venus-Sun line, and altitudes < 300 km in the nightside ionosphere. The table shows that 20% of the Langmuir probe anomalies have one or more 100 Hz bursts occurring within a 2-s interval including the Langmuir probe sweep. Since the probability that one or more bursts will occur in any 2-s interval is 7%, the observed degree of coincidence lies in the upper 0.1% of the tail of the Binomial distribution for 150 samples with a 7% event probability, under the assumption of independent events. Another way of assessing the significance of the observed degree of coincidence is to note that for a binomial distribution with event probability of 7%, the mean number of events is 10 for 150 samples, while the variance is also 10. The standard deviation is therefore 3, and the observed number of coincident events is at least 6 standard deviations away from the mean. Thus the 20% coincidence is statistically significant, but it is much less than that reported by Grebowsky et al. .
Table 1. Comparison of burst probability and the coincidence rate for Langmuir probe (OETP) anomalies. The binomial probability gives the probability that the number of coincident events > m, for N Langmuir probe anomalies (corresponding to a one-tail test).
In previous sections, we have emphasized that the 100 Hz waves correspond with vertically propagating whistler-mode waves. In computing the burst probability, however, we have assumed that the bursts occur independently of the underlying ionospheric conditions. In the lower two rows of Table 1 we have tested each interval for whether or not vertical whistler-mode propagation is allowed. The table shows that the probability of a burst occurring in an interval in which vertical propagation is allowed is 9%, somewhat higher than for all intervals, while the degree of coincidence has dropped slightly, 18%. Thus, the coincidence rate lies in the upper 1% of the Binomial distribution for 90 samples with 9% event probability. This again suggests that the coincidence is not random, but is much less than one would expect for a direct causal relation between Langmuir probe anomalies and 100 Hz bursts. For completeness, Table 1 also includes the "non-whistler" intervals.
One interesting feature in the table is that regardless of the selection criteria, the coincidence rate is roughly constant. This suggests that the coincidence occurs because of some underlying property of the ionosphere that is common to both signatures. In the previous section we have shown that low is required for whistler-mode propagation. Huba  suggested that the Langmuir probe anomalies may be signatures of the lower hybrid drift instability, and he has shown that low also applies to the lower hybrid drift instability. However, in Table 1 we have included all intervals, irrespective of . This will reduce the predicted probability for 100 Hz bursts. In Table 2 we show the burst probability for those intervals for which < 1. In order to determine we need to know the electron density and temperature. We have used Langmuir probe data from the Unified Abstract Data System (UADS) for this purpose. We have interpolated the data to the 2-s resolution used earlier. UADS data are not available for all the intervals, and we have included the probabilities for all intervals for which we have UADS data, and those intervals for which < 1.
Table 2. Comparison of burst probability and the coincidence rate for Langmuir probe (OETP) anomalies, using those intervals for which Langmuir probe UADS data are available.
Table 2 shows that the coincidence rate is similar to Table 1 for all the intervals, although the probability of random coincidence is higher, because of the smaller sample. The bottom row of Table 2 shows that the burst probability is quite high, 13%, for < 1, while the coincidence rate is 19%. For the number of samples, this rate lies in the upper 13% of the Binomial distribution. This is a "one-tailed" test, while it is usual to use a "two-tailed" test when testing against random coincidence. For this purpose one can roughly double the percentage, and there is a less than 75% probability that the observed coincidence is not random. When testing for a non-random association of events it is usual to require at least a 95% probability before the null hypothesis of random coincidence is rejected [e.g., Pollard, 1977].
Given the relatively low likelihood of non-random coincidence, and the generally low degree of correlation (< 20%), we conclude that the Langmuir probe anomalies do not explain the 100 Hz bursts. Rather, both 100 Hz bursts and Langmuir probe anomalies tend to occur in regions of low .
The lower hybrid drift instability is generated by the relative drift between electrons and ions caused by a density gradient. The magnitude of the particle drift is determined by the gradient perpendicular to the ambient magnetic field; a parallel gradient does not cause a drift. The drift is perpendicular to both the magnetic field and the gradient, and the waves propagate in the direction of the drift. For a particular species the density gradient drift is given by
where v is the thermal velocity of the species, L is the scale length of the density gradient and is the species gyro-frequency. For a magnetic field gradient the drift is given by
where L is the scale length for the change in magnetic field magnitude.
If the plasma is in pressure balance then it can be shown that
where the subscript e and i denote electrons and ions respectively. If the ion and electron temperatures are equal then L = -L. Thus, as increases, the magnetic field gradient drift becomes comparable to the pressure gradient drift, but is in the opposite direction, and the instability is quenched for > 1. Low is therefore a necessary condition for both the lower hybrid drift instability and whistler-mode propagation in the nightside ionosphere of Venus.
However, unlike the whistler-mode, low is not the only requirement for the lower hybrid instability. As noted above, the lower hybrid resonance frequency is only a few Hz, and the electron collision frequency can be large enough to damp the instability, especially for high densities and weak magnetic fields. The electron collision frequency v = 2.91 10nT s, where is the Coulomb logarithm 15, the density is expressed in cm and the temperature is in eV [Huba and Grebowsky, 1993]. For a density of 10 cm and a temperature of 0.1 eV, v = 15 s, while the lower hybrid resonance frequency () 30 rads when B = 30 nT. Thus, the collision frequency can be comparable with the wave frequency.
Another condition that applies to the 100 Hz waves, but not to the density fluctuations, is the requirement that the wavelength be 100 m, so that the wave can be Doppler-shifted to 100 Hz through spacecraft motion. Huba and Grebowsky  found maximum growth occurred for k 2, although the actual value depended on the choice of the plasma parameters, and the gradient scale length. As noted above, this implies an electron Larmor radius 35 m, which for T = 0.1 eV requires a magnetic field strength of 30 nT. If the field strength is smaller than this, then the k required for Doppler-shift to 100 Hz becomes too large, and the waves tend to be damped.
Thus, the lower hybrid drift instability requires low , low collision frequencies, and small electron Larmor radii to generate short wavelength waves that can be Doppler-shifted to 100 Hz. In Figure 11 we show where the burst intervals used in determining the burst rates discussed above occur as a function of electron density and magnetic field strength. In order to explore whether or not these bursts correspond to lower hybrid drift waves, we have plotted several reference curves. Above, we discussed the various parameters relevant to the lower hybrid instability assuming an electron temperature of 0.1 eV. However, the temperature is not constant, and we find that T = 0.188 (n/2.45 10) for the burst intervals, using a least squares regression, where T is in eV, and n is in cm. The correlation coefficient is 0.686, with 1234 points. This regression line allows us to specify the temperature for a given density, and so determine the following reference curves as a function of density and magnetic field strength: = 1, v/ = 0.25, and k = 3. As an approximate rule of thumb, we expect the lower hybrid drift instability to generate Doppler-shifted 100 Hz waves in regions for smaller values of these parameters.
Fig. 11. Scatter plot of burst occurrence as a function of electron density and magnetic field strength. Various limiting curves are also shown. The lower hybrid drift instability is most likely to occur for low , low v/, and low k. The whistler-mode requires low only. At any particular density, lower values of , v/, and k lie above the limiting curves shown.
Figure 11 indicates that there are large regions of the B-n parameter space where bursts occur, but the approximate conditions for lower hybrid instability are not satisfied. However, most of the bursts occur in the region where < 1, as we expect for the whistler-mode. A word of caution is in order when interpreting Figure 11. The various limiting curves are indicative of the likely region of lower hybrid drift instability, but we have not performed an instability analysis. Huba and Grebowsky  present instability limits in a similar format. They find that for sufficiently high drift speeds, corresponding to short gradient scales, the collision frequency and constraint can be relaxed for high densities, while the Larmor radius restriction is less important for low densities. The maximum drift speed used is twice the ion thermal velocity, i.e., v 2 kms. From (1) v/v = /2L, implying that L 0.25. The ion Larmor radius is 10 km for B 30 nT, and the high drifts invoked by Huba and Grebowsky  correspond to gradients scale lengths 2.5 km. This is an extremely short scale length; with this scale length, the density changes by two orders of magnitude in 12 km which, for a spacecraft velocity of 10 kms, would correspond to a two order of magnitude change in density in just over 1 s. Another possible restriction of the applicability of the lower hybrid drift instability at Venus is the extremely narrow propagation angle because the plasma composition is mainly O. Huba and Grebowsky  note that electron Landau damping will become important for angles ~ 0.33° away from perpendicular propagation.
In summary, it is possible that the lower hybrid drift instability can operate in the Venus nightside ionosphere. However, the gradients required are extremely steep, and electron Landau damping is likely to be important. In addition, we noted earlier that the association between Langmuir probe anomalies and 100 Hz bursts is low, about 20%. Thus, the lower hybrid drift instability may explain the anomalies reported by Grebowsky , but it only explains a small fraction of the 100 Hz bursts observed at Venus. The 100 Hz waves are more likely to be whistler-mode waves.
Fig. 12. Diagram illustrating the hypothesis that lightning is a source for plasma waves in the nightside ionosphere of Venus.
On escaping from the atmosphere whistler-mode waves will be refracted vertically, assuming a horizontally stratified medium, and we can determine if the waves are within the whistler-mode resonance cone solely from the orientation of the magnetic field with respect to the vertical. The resonance cone test, which applies only for a wave source below the ionosphere of Venus, clearly shows that many of the 100 Hz wave bursts are whistler-mode waves propagating from below the ionosphere. Vertical refraction explains why the burst rate of 100 Hz waves is a maximum for vertical magnetic fields. The burst rate for 100 Hz waves inside the resonance decreases much more slowly with increasing altitude, in contrast to the non-whistler-mode high frequency bursts and the 100 Hz bursts outside the resonance cone. The waves within the resonance cone are polarized perpendicular to the ambient field.
One alternative explanation for the 100 Hz waves is that they are whistler-mode waves generated in situ by a plasma wave instability. However, because of the weak magnetic field in the nightside ionosphere of Venus, the electron beta () can be large. Thus we expect 100 Hz waves to be detected in "ionospheric holes", where the plasma density is low, and the ambient field is large, with a large vertical component. The damping due to thermal electrons will be lowest in such a region. However, even in holes, there is sufficient damping to quench any instability due to precipitating electrons that may have come from the solar wind.
More recently, the lower hybrid drift instability has been postulated as an alternative explanation of the 100 Hz waves. As with the whistler-mode, the lower hybrid waves are expected to occur in regions of low . However, the lower hybrid drift instability requires small electron Larmor radii, and hence large fields, since the wavelength of the waves must be 100 m to be Doppler-shifted to 100 Hz through spacecraft motion. Additionally, the required gradient scale length must be very short, 2.5 km, so that the resultant gradient drift velocity is large enough to overcome the damping due to collisions in high density regions. The ion Larmor radius is typically 5 km.
The lower hybrid instability may better explain the Langmuir probe anomalies investigated by Grebowsky et al. . Grebowsky et al. reported a high degree of coincidence between 100 Hz wave bursts and Langmuir probe anomalies, but they did not use a consistent identification criterion for the wave bursts. We find a much lower degree of coincidence ( 20%). This level of coincidence appears to be because both the wave bursts and Langmuir probe anomalies are mainly detected in regions of low , rather than being due to a common source.
The major question remaining for the 100 Hz waves concerns how much of the energy generated by lightning gains access to the ionosphere. Huba and Rowland  have determined the attenuation due to collisions as the waves enter the atmosphere. They found that for peak densities of 10 cm, approximately 0.1% of the incident wave energy could be transmitted through the ionospheric density peak, provided the vertical magnetic field was 30 nT. The attenuation scale depends quite strongly on the ambient magnetic field strength and plasma density. Strangeway et al.  compared the observations at very low altitudes ( 130 km) obtained during the Pioneer Venus Orbiter entry phase with predictions for the attenuation scale. The observed attenuation scale lengths were 1 km, consistent with lightning generated whistler-mode waves propagating through a moderately dense plasma with a vertical field < 10 nT. However, possible spacecraft interactions with the neutral atmosphere cannot be completely discounted as a source for the waves at very low altitudes.
The wide-band bursts detected at low altitudes may also be due to lightning, and may be evidence for direct coupling of lightning into the ionosphere of Venus. However, this interpretation is somewhat speculative, and additional study of coupling mechanisms and alternative sources is warranted. Some insight into the nature of the broadband waves may be obtained through comparison with the recent GEOTAIL results [Matsumoto et al., 1994]. The GEOTAIL data indicate that broadband signals observed in the geomagnetic tail consist of short wave packets, which have a broad frequency signature when sampled as a function of frequency. Doppler-shift may cause additional broadening of the signal. By analogy with these signals, the broadband bursts detected at Venus may correspond to short duration wave packets, as expected from an impulsive source such as lightning.
In conclusion, the preponderance of the evidence points towards atmospheric lightning as the dominant source of plasma waves at low altitudes within the nightside Venus ionosphere. Some may reject this explanation, citing an as yet unknown plasma instability as an alternative. However, in the absence of any viable alternative, and given the consistency of the observations with the lightning hypothesis, the plasma wave data acquired by the Pioneer Venus Orbiter provide strong evidence for the existence of lightning in the atmosphere of Venus.
Acknowledgments-I wish to thank C. T. Russell and C. M. Ho for many useful discussions on lightning and the plasma wave observations at Venus. I also wish to thank J. M. Grebowsky and J. D. Huba for many fruitful exchanges. The late F. L. Scarf was the original Principal Investigator for the Orbiter Electric Field Detector. His efforts were the motivation behind much of the work presented in this paper. This work was supported by NASA grant NAG2-485.
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