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Linear and nonlinear propagating characteristics of right-hand polarized, slow electromagnetic, magnetoplasma waves (whistlers) are discussed in terms of stability and dispersion. An analysis of the stability of whistlers propagating at an angle to the static magnetic field is presented. A new mechanism is derived for the onset of stimulated emissions, and modulational instability for nonlinear whistlers are discussed.
Very low frequency (VLF) electromagnetic wave phenomenon called the magnetospherically reflected (MR) whistler was investigated. VLF (0.3 to 12.5 kHz) data obtained from the Orbiting Geophysical Observatories 1 and 3 from October 1964 to December 1966 were used. MR whistlers are produced by the dispersive propagation of energy from atmospheric lightning through the magnetosphere to the satellite along ray paths which undergo one or more reflections due to the presence of ions. The gross features of MR whistler frequency-time spectrograms are explained in terms of propagation through a magnetosphere composed of thermal ions and electrons and having small density gradients across L-shells. Irregularities observed in MR spectra were interpreted in terms of propagation through field-aligned density structures. Trough and enhancement density structures were found to produce unique and easily recognizable signatures in MR spectra. Sharp cross-field density dropoff produces extra traces in MR spectrograms.
Inspection of broadband VLF records from OGO-4 shows that some whistlers exhibit a banded structure in which one or more bands of frequencies are missing from the whistler's spectrum. The phenomenon is commonly observed by satellites on midlatitude field lines at all local times and at various longitudes around the world. The dispersion of banded whistlers (BW) is of several tens of sec to the 1/2 power, indicating that they originated in the opposite hemisphere and are propagating downward at the satellite. BW are generally spread in time (tenths of seconds) rather than sharply defined and tend to occur at random. The frequency spacing of the bands may be either uniform or irregular, and may vary radically between successive events. Several possible explanations for BW are considered. In particular, an analysis of the interaction of plane electromagnetic waves traveling in an anisotropic plasma with a field aligned slab of enhanced ionization is presented with promising results.
Derivation of the modulational instability characteristics of whistlers in cold and hot plasmas. The cold-plasma analysis considers both ion motion and relativistic effects; the unstable band, with a growth rate proportional to (B/B sub zero)squared, is contiguous to Omega sub e/4 and, depending on the plasma density, lies above or below that frequency (Omega sub e is the electron cyclotron frequency of the static magnetic field; B and B sub zero are the whistler and static magnetic fields). In hot plasmas, stability occurs between Omega sub e/4 and Omega prime (less than Omega sub e), with Omega prime depending mainly on the mean energy and anisotropy of the energetic electron population; the complementary unstable band has a growth rate proportional to (B/B sub zero) to the 1/2 power. The relevance of the instability to whistlers in the magnetosphere is discussed.
We use OGO 5 measurements made within the plasmapause on May 15, 1969, to investigate the possible association between changes in lightning whistler dispersion characteristics and local density fluctuations. It is shown that groups of whistlers with relatively constant dispersions tended to be detected in regions where the local ion concentration was significantly enhanced. It is assumed that these local density fluctuations represent characteristics of large-scale field-aligned variations. The results are then compared with ray refraction estimates appropriate for low-frequency whistler mode propagation (wave components with frequencies comparable to the local lower hybrid frequency) in a nonuniform medium.
Whistler mode waves that propagate through the magnetosphere exchange energy with energetic electrons by wave-particle interaction mechanisms. Using linear theory, a detailed investigation is presented of the resulting amplitude variations of the wave as it propagates. Arbitrary wave frequency and direction of propagation are considered. A general class of electron distributions that are nonseparable in particle energy and pitch-angle is proposed. It is found that the proposed distribution model is consistent with available whistler and particle observations. This model yields insignificant amplitude variation over a large frequency band, a feature commonly observed in whistler data. This feature implies a certain equilibrium between waves and particles in the magnetosphere over a wide spread of particle energy, and is relevant to plasma injection experiments and to monitoring the distribution of energetic electrons in the magnetosphere.
A theory is developed for the generation of Alfven waves by the mixing of whistler waves. Calculations are carried out for interaction in the magnetosphere where the whistlers fall in the VLF frequency range and the Alfven wave falls in the ULF(1-5 Hz) range. Typical amplitudes of 2-5 milligammas for the Alfven wave are calculated, and it is shown that these values might be increased by one order of magnitude through suitable variation of the experimental parameters. The study thereby develops a possible explanation for naturally occurring Pc 1 micropulsations and demonstrates the feasibility of artificial generation of such micropulsations by ground-launched whistlers.
Observations of whistler-mode waves associated with beams of electrons injected into the ionosphere are reported. The measurements are from the plasma-wave experiments carried on the Electron Echo 2 sounding rocket launched on September 24, 1972. Over 2000 electron injections were made with durations of 8 ms and 64 ms and pitch angles from 0 to 180 deg. The electric field receivers carried on the ejected nose cone observed strong whistler waves in the range from less than 100 kHz up to the electron cyclotron frequency of 1400 kHz. The whistler characteristics fall into four distinct types depending on pitch angle and gun energy. Both frequency and amplitude showed strong dependence on time from the start of the pulse and pitch angle. Cases of enhancement at the leading edge of a gun pulse, growth during a pulse, and echoes after the end of a pulse were all observed.
The feasibility of generating whistlers by means of an array of helical electron and proton beams is investigated. It is found that quasi-static beam-plasma instabilities will play a vital role in limiting the effective coherent length of the beam. The total radiated power for the whistlers is consequently decreased by 2 orders of magnitude below previously predicted levels (Dowden, 1973). A proton beam is shown to be somewhat less efficient than an electron beam for generating whistlers.
Results are presented for simultaneous observations of whistlers at two Alaskan stations (L roughly 4) during one occasion lasting 24 hr, another lasting 10 hr, and a third lasting 6 hr. Of the three periods of simultaneous observations studied, two showed patterns of equatorial electron density which were stationary in L-LMT space and which were unchanging for at least 1.5 hr of UT. The third showed a marked change, the nature of which being accounted for by east-west gradients corotating with the stations. All three periods exhibited persistent stationary patterns of whistler duct tracks, each thin in the cross-L direction and extensive in the east-west direction. It would appear that either the ducts are stable shells or there is a succession of ducts arrayed along the contours and possibly corotating with the earth along the stationary tracks. Multistation direction finding on the whistler exit points may elucidate the relevant interpretations.
The paper examines some of the consequences of relativistic electrons in stably trapped equilibrium with parallel propagating whistlers in the inner magnetosphere of Jupiter. Approximate scaling laws for the stably trapped electron flux and equilibrium wave intensity are derived, and the equatorial growth rate for whistlers is determined. It is shown that fluxes are near the stably trapped limit, which suggests that whistler intensities may be high enough to cause significant diffusion of electrons, accounting for the observed reduction of phase space densities.
The predicted instability of obliquely propagating whistler waves in a plasma penetrated by an electron beam is verified in a laboratory experiment. The observations support the model for the generation of auroral hiss and compare favorably with ground and satellite observations of VLF hiss. In contrast to the conventional small-diameter laboratory beam-plasma systems the device used is large compared to the characteristic whistler wavelength. Unstable whistlers can therefore, propagate and grow oblique to the beam over many wavelengths before encountering the plasma boundaries.
During the Voyager 1 encounter with Jupiter a number of discrete signals were identified in the wideband plasma wave data with characteristics similar to whistlers generated by lightning. In this paper we show that the calculated whistler-mode travel times from Jupiter to the spacecraft are in good agreement with the measured dispersion characteristics, thereby confirming that the signals are caused by lightning on Jupiter and substantiating the Voyager 1 photographic evidence for lightning on Jupiter. A quantitative estimate of the north-south thickness of the Io plasma torus is also obtained from the measured whistler dispersion.
The presence of whistler mode waves in, and upstream from, the bow shock has been well established by observation. Theoretical descriptions of the mode under solar wind conditions have been relatively meagre, however, and it may not be generally appreciated how readily whistler waves generated in the shock could occupy most of the region ahead of the shock most of the time. Graphic descriptions of phase and group velocities and group velocity directions for typical solar wind parameters are presented by using the cold plasma approximation over all appropriate frequencies and directions with respect to the IMF. The relations of whistler phase and group velocities to observations of a quasi-perpendicular shock crossing by ISEE are illustrated.
A theory explaining Jupiter's banded whistler emission, in particular low-frequency hiss and chorus, is proposed. It is shown that superthermal electrons described by a kappa distribution function cause whistler instability below one-third of the electron gyrofrequency, whereas a two temperature Maxwellian leads to a band of unstable growing modes just below one-half of the electron gyrofrequency. A superposition of both yields almost exactly the structure of whistler mode hiss and chorus detected by the Voyager 1 and 2 plasma wave instrument.
The evolution of whistler mode turbulence and particle participation in a cold plasma release are studied experimentally as part of the Active Magnetospheric Particle Tracers Explorer (AMPTE) program. The investigation used a simple time dependent cold plasma density model, and an atypical ambient radiation belt was assumed. It is shown that a cold lithium injection in the AMPTE parameter range can give rise to whistler mode turbulence with significant gain to the wave amplitude in a single pass through a flux tube. Whistler mode growth results in the pitch angle diffusion of energetic electrons, which are in turn precipitated. The rate of power input into the ionosphere from these precipitating electrons is roughly estimated at 2 ergs per sq cm/s. It is found that this value of the precipitated power is large enough to continue producing a visible aurora until the injected plasma in the flux tube is lost or destroyed by magnetospheric convection or other processes.
In this study, the propagation and growth of whistler mode waves generated by electron beams within earth's bow shock is investigated using a planar model for the bow shock and a model electron distribution function. Within the shock, the model electron distribution function possesses a field-aligned T greater than T beam that is directed toward the magnetosheath. Waves with frequencies between about 1 and 100 Hz with a wide range of wave normal angles are generated by the beam via Landau and anomalous cyclotron resonances. However, because the growth rate is small and because the wave packets traverse the shock quickly, these waves do not attain large amplitudes. Waves with frequencies between about 30 and 150 Hz with a wide range of wave normal angles are generated by the beam via the normal cyclotron resonance. The ray paths for most of these waves are directed toward the solar wind although some wave packets, due to plasma convection travel transverse to the shock normal. These wave packets grow to large amplitudes because they spend a long time in the growth region. The results suggest that whistler mode noise within the shock should increase in amplitude with increasing upstream theta sub Bn. The study provides an explanation for the origin of much of the whistler mode turbulence observed at the bow shock.
In this study, properties of small-amplitude parallel and oblique whistler-mode waves are investigated for a wide range of plasma parameters by numerically solving the full electromagnetic Vlasov-dispersion equation. To investigate the cold-plasma and electrostatic approximations for the whistler mode, the results are compared with results obtained using these descriptions. For large wavelengths, the cold-plasma description is often accurate, while for short wavelengths and sufficiently oblique propagation, the electrostatic description is often accurate. The study demonstrates that in a Vlasov plasma the whistler mode near resonance has a group velocity more nearly parallel to the magnetic field than that predicted by cold-plasma theory.