*J. Atmos. Terr. Phys., 57*, 537-556, 1995

(Received in final form 19 May 1994; accepted 27 June 1994)

Copyright © 1995, Elsevier Science Ltd

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Fig. 8. 100 Hz burst rate dependence on the magnetic field orientation [afterHo 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* [1989] 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* [1990].

This point was discussed further by *Strangeway* [1992]. 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 [afterStrangeway, 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
1/2*m**v*
=
*k**T*.
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* [1992]
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* [1989],
*Strangeway* [1992] also
investigated a beam driven instability. He assumed a
beam density of 5 cm,
parallel drift speed = parallel thermal velocity =
0.007*c*
(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.

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