A theory of magnetospheric VLF emissions must account for the following features: (a) the triggering of monochromatic emissions by signals of sufficient strength and duration, while the background noise and weak short signals are not amplified, and (b) the occurrence of frequency changes after the emissions have reached a sufficiently large amplitude. A nonlinear mechanism exhibiting these features, with fixed and varying frequencies, is examined analytically and by computer simulation techniques. This mechanism depends on a simultaneous propagation and amplification of wave packets along geomagnetic lines to maintain the nonuniformity ratio R ∝ ▽B0/Bw in the regime |R| ≈ 0.5, corresponding to maximum amplitication. (B0 is the geomagnetic field and Bw is the wave magnetic field.) For a constant frequency, this condition yields triggering thresholds which are related to the properties of the magnetosphere. For a varying frequency ω(t), it yields the condition ∂ω/∂t ∝ ωt² for the large‐amplitude portion of the risers, where ωt ∝ Bw1/2 denotes the trapping frequency of the wave.

Cyclotron resonance is employed in a new model of the generation of narrow‐band VLF emissions from the magnetosphere. Streaming energetic resonant electrons are temporarily phase‐bunched by whistler‐mode waves, causing transverse currents to be impressed on the medium. These currents act like circularly polarized antennas, producing stimulated Doppler‐shifted radiation. The interaction takes place in an ‘emission cell’ located at or near the equatorial plane. Inclusion of feedback between the stimulated radiation and the incoming particles leads to a self‐consistent description of fields and currents in time and space. Sample calculations are made for a wave frequency of 16.5 kHz and a homogeneous interaction region of 750‐km length located on the equator at L = 3. When there is a 1‐mγ input wave and a stream density of 2.4 m−3, regular pulsations with a period of 110 msec are produced. Above a threshold stream density of 1.5 m−3, self‐sustained oscillations grow exponentially when the system is triggered by a short pulse. Following saturation, a steady state is reached in which the frequency bandwidth is zero. Predictions of the model are in good agreement with experimental observations.

The amplitude of the E‐W component Ew of the convection electric field in the nightside magnetosphere has been inferred from the observed cross‐L motions of whistler ducts within the plasmasphere. Several ducts distributed over 1–2 RE in L space and over ±15° around the longitude of the Eights, Antarctica, whistler station have been tracked simultaneously. The method appears capable of resolving fluctuations in Ew with period T ∼ 15 min and rms amplitude as low as 0.05 mv/m. For variations with T > 1 hour the method has a sensitivity of the order of 0.01 mv/m. Three case studies are presented, two of which illustrate convection activity associated with relatively isolated substorms. In these two cases Ew reversed from westward to eastward for a period following the decay of substorm bay activity. In the third case the substorm bay activity was prolonged, and Ew remained westward and at enhanced levels until local dawn. Evidence was found that, at least in a limited longitudinal sector, perturbing substorm Ew fields can penetrate deep within the plasmasphere. In two of the case studies comparisons of Ew and the interplanetary magnetic‐field θ component show evidence of a possible relation based on brief (≤ 1 hour) southward excursions but not on long preceding southward events. The growth of Ew can take the form of an initial brief (<15 min) positive surge followed by a larger surge that is simultaneous with the most active phase of the substorm. Certain of the pronounced increases in Ew were found to be coincident with activation or spreading of electrojet or auroral activity. In one instance low‐amplitude (<0.1 mv/m) presubstorm fluctuations in Ew with periods of the order of 30 min were found to correlate closely with ground‐observed midlatitude fluctuations in the magnetic H component. Calculated values of E‐field power spectral density from the tracking of two long‐lived (∼6 hours) whistler paths reveal considerable fine structure. The falloff with frequency roughly as f−2 agrees approximately with results from balloons, but the calculated spectral amplitudes appear lower than the balloon results by a factor of ∼4. The amplitudes from whistlers appear to be within the range identified by other workers as sufficient to drive radial diffusion in the radiation belts. The present research agrees with balloon measurements on the general presence of a westward field during substorms, but there is apparent disagreement on a number of details, including the post‐substorm reversal in Ew.

In this paper, numerical simulations of the scattering from time‐dependent realizations of one‐dimensional ocean surface waves are described. A new technique is used that allows efficient generation of ocean surface realizations that preserve the dominant nonlinear hydrodynamic characteristics. Thus unique scattering effects of real ocean surface waves can be explored. Until very recently, numerical simulations of rough‐surface scattering were used mainly to test and/or improve theoretical models that predict the average bistatic scatter cross section. We carry the simulations further by generating Doppler spectra from dynamically evolving surface realizations. Doppler spectra of signals scattered from the ocean surface are affected by both hydrodynamic nonlinearities and higher‐order scatter terms. The simulated Doppler spectra from nonlinear surface realizations reproduce the measured characteristics of ocean and wave‐tank data for low and high wind conditions. We also show that the results are essentially reproduced by the second‐order Kirchhoff approximation.

The evolution of small initial perturbations of the uniform equilibrium of the ‘‘classical’’ Pierce diode [J. Pierce, J. Appl. Phys. 15, 721 (1944)] is studied using particle simulations. These simulations have been performed with the new bounded-plasma code PDW1 [Wm. S. Lawson (private communication)] and cover the parameter range 0&lt;α&lt;3π, where α=ωpL/v0. In the linear regime, three stages (initial transit, adjustment, and dominant eigenmode) are distinguished; oscillation frequencies, growth/damping rates, and potential profiles of the dominant eigenmode as well as oscillation frequencies of the next-to-dominant eigenmode are recovered and shown to agree quantitatively with recent analytical results. In the linearly unstable cases, the system evolves nonlinearly to a final state which may be either a new, nonuniform dc equilibrium, or a state of large-amplitude oscillations. In particular, for α=1.5π the character of the final state is found to depend on the details of the initial conditions.

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Time-average values from particle simulations of a collisionless, single-emitter plasma device modeling single-ended Q machines or thermionic converters with a negatively biased collector are presented. These results quantitatively confirm the predictions of collisionless, kinetic plane-diode theory for spatial potential profiles that decrease monotonically. However, simulations of negative-bias potential profiles with a single internal maximum differ significantly from previous theoretical predictions which assumed electron phase space to have either (i) no trapped electrons or (ii) trapped electrons isothermal with the passing electrons. A more general class of trapped-electron model distributions is introduced from which new equilibrium potential values can be recovered that closely match the simulations. These simulations clearly demonstrate the sensitive role that trapped electrons play in shaping the potential profiles of the equilibrium (or slowly evolving) states of the simulated systems. The trapped-electron distributions in these simulations are themselves shown to be controlled critically by fluctuations whose levels are varied by the choice of particle injection scheme. These effects, although found and discussed here in the context of a particular model, are believed to be important in many bounded plasma systems where electrons can be trapped in potential wells.