High-frequency electrostatic microinstabilities in magnetospheric plasmas are considered in detail. Rather special plasma parameters are found to be required to match the theoretical wave spectrum with satellite observations in the magnetosphere. In particular it is necessary to have a cold and a warm species of electrons such that (1) the warm component has an anomalous velocity distribution function that is nonmonotonic in v. and is the source of free energy driving the instabilities, (2) the density ratio of the cold component to the hot component is greater than about 10 -•', and (3) the temperature ratio of the two components for cases of high particle density is no less than 0.1. These requirements and the corresponding instability criteria are satisfied only in the trapping region (4 _< L _< 10); this is also the region in which the waves are most frequently observed. The range of unstable wavelengths and an estimate of the diffusion coefficient are also obtained. The waves are found to induce strong diffusion in velocity space for low-energy electrons (<•1 key) during periods of moderate wave amplitude (<•10 my/m). Electrons with energies of up to 100 key can be strongly diffused when the wave amplitude is large (•100 my/m). Geophysical implications are discussed; predicted results compare favorably with available observations pertaining to electrostatic waves, the particle distribution function, particle acceleration, and pitch angle diffusion in the magnetosphere. With reference to their influence on the dynamics of laboratory plasmas, such as particle acceleration and diffusion, electrostatic waves usually are more important than electromagnetic waves. However, because of electronic technology difficulties, electrostatic waves were not unambiguously observed in the magnetosphere until recently [Kennel et al., 1970; Scarf et al., 1971]. Consequently, theoretical studies of magnetospheric electrostatic waves in conjunction with dependable experimental observations are very scarce. This paper provides an extensive linear stability analysis of electrostatic half-harmonic waves (•o/9• • n + •/• where n = 1, 2, 3, ". ) observed on Ogo 5. We study the fundamental cause, wave vector, and frequency range of the waves. Various plasma models are considered to obtain unambiguous theoretical predictions. All the calculated results are shown to compare favorably with the relevant known data. In the following paragraph satellite observations of electrostatic waves by 0go 5 [Kennel et ed., 1970; Scarf et al., 1971] are summarized for later reference. The observed wave spectrum is narrow, and the frequency (o is found to be above the local electron gyrofrequency 9e. (Activity below 9e has also been observed [Coroniti et ed., 1971], but we will not discuss that regime in this paper because there are few data available for these less frequently observed modes.) The waves occurring most frequently are the second halfharmonic modes, i.e., 1.25 < (o/9e < 1.75, and the frequency has no apparent preference within this range. ...
Instability analysis shows that the wave observations at frequencies slightly above one half of the electron gyrofrequency (Coroniti et al., 1971) in the trapping region (4 ≲ L ≲ 10) were likely to be caused by two species of electrons with comparable densities: a cold species and a warm species that has a small temperature anisotropy (2.0 ≲ T⊥w/T∥w ≲ 2.5). The scarcity of detection of these waves relative to that of the second‐half harmonic waves near one and a half of the electron gyrofrequency can be interpreted as evidence that the distribution function of the warm electrons is more often nonmonotonic in υ⊥ than temperature anisotropic in the trapping region.
The triggering and saturation mechanisms of the electrostatic waves having frequencies near 1½ times the electron gyrofrequency in the magnetosphere are studied. Also studied is the corresponding evolution of the electron distribution function caused by the wave‐particle interaction. The linear instabilities supporting these waves are found to require a cold species of electrons having density between 0.1 cm−3 and 1 cm−3 and a warm species whose distribution function has a relatively weak positive slope in the velocity space perpendicular to the background magnetic field. The corresponding unstable wavelengths are short and thus result in much smaller diffusion coefficients than those derived previously. Such instabilities when triggered by an enhanced injection of ionospheric cold electrons into the warm plasma clouds can support wave amplitudes that grow to nonlinear saturation levels much greater than 10 mV/m and as large as a few hundred millivolts per meter. The majority of the observed wave activity (1–10 mV/m) can be explained as marginal instabilities maintained by a convection‐induced slow increase of the cold electrons in the plasma clouds. The evolution of the waves and plasma is described in a simple physical model for different plasma parameters.
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