Wave Normal Direction Research Articles

Wave normal directions of chorus near the equatorial source region

Wave propagation directions of post‐midnight chorus in the near‐equatorial region at L shells of 6 to 7 have been determined from OGO 5 triaxial search coil magnetometer data. Several methods were used to estimate the wave normal directions: minimum variance, imaginary part of cross‐spectral matrix, eigenvector of Hermitian cross‐spectral matrix, and fit of dispersion relations for one‐wave and two‐wave models to cross‐spectral matrix. Comparisons of the methods and results are discussed in detail. Wave propagation at all frequencies within chorus tones was found to occur most frequently along the magnetic field with median and average cone angles of 9.1° and 12.2°, respectively. All methods of analysis gave similar results. It is concluded that the wave growth is maximum for waves propagating parallel to B. Our results are consistent with emission in a narrow beam but not as a broad angular distribution. The two wave propagation model typically resulted in negligible improvements in the residual beyond that obtained by assuming that only one wave was present. In only a few cases did substantial improvement result. These cases were unusual periods when it was obvious that simultaneous rising and falling tone emissions were present and crossing. It is concluded that in most cases only one chorus wave was present. In some cases the two‐wave model gives misleading indications of waves with large energy fluxes propagating at very oblique angles near the resonance cone. This is because the wave group velocity goes to zero near the resonance cone, and if electric field data are not used, then a small amount of magnetic noise is modeled with a large wave energy flux. Some examples have been found of a lower frequency burst propagating almost exactly along the magnetic field followed by a higher frequency burst travelling at large angles to the magnetic field. These paired bursts are quasi‐periodic with a delay of about 6 s between pairs of bursts; the phenomenon is presumed to be associated with pulsating auroral patches. The physical implications are discussed.

The wave normals of magnetospheric chorus emissions observed on board GEOS 2

The wave normal directions of magnetospheric chorus emissions have been analyzed by using data from the geostationary GEOS 2 satellite which is located in the equatorial region at L = 6.6. As the result of analyses for a specific day of December 19, 1979, chorus is found to be generated in conjunction with substorms and at local times from around midnight to afternoon. Two types of chorus are observed: impulsive burstlike and rising tone. The chorus during midnight to late morning hours is impulsive, and at local times from noon to dusk we notice an increase in the occurrence of rising tone chorus. The chorus spectra have shown the importance of the characteristic frequency of fH/2 (fH is the electron gyrofrequency). We notice the impulsive chorus only in the lower band (f<fH/2; f is the emission frequency) at local times from ∼0300 to ∼0700, and then at LT = ∼0800 to ∼1600 the predominant frequency of the emissions, whether impulsive or rising tone, lies in the upper band (f>fH/2) with infrequent occurrence in the lower band, and there is obviously no correlation between the elements in both bands. However, there are several intense tones which seem to be correlated in both bands for the strong two‐banded impulsive chorus emissions observed only at LT ≃ 0800. This correlation might be related with a notch in chorus risers at f ≃ fH/2 caused by Landau damping, as previously suggested. The wave normals are determined by using only the magnetic field data. The direction finding studies have been made for impulsive and rising tone chorus, separately, which have yielded different results. The lower band is discussed first. The wave normals of the rising tones having values of df/dt as normally observed are found to take very small angles (5°–20°). Then it is found that the rising tones with increased values of df/dt have shown larger wave normal angles of 30°–45°. These relatively small wave normal angles for the lower band give further support to the loss cone instability as the generation mechanism. The impulsive chorus is found to take slightly larger wave normal angles (about 5°) than most rising tones. Further, it may be suggested that different types of chorus are associated with different wave normals. Next we are concerned with the upper band chorus, whose generation mechanism is not well agreed upon. It is shown that the impulsive chorus in the upper band is generated with its wave normal close to the oblique resonance cone. This suggests that the upper band chorus is quasi‐electrostatic, and it is furthermore confirmed by the estimated ratio, c|B|/|E| (|E| and |B| are the total electric and magnetic field intensities; c is the light velocity). The rising tones in the upper band, however, have indicated a difference such that the closeness of their wave normals to the oblique resonance cone is much less distinct. An intensive comparison is made between the direction finding results for the upper band and the theoretical mechanisms so far proposed in order to elucidate the possible generation mechanism of the upper band chorus.

Measurements of wave normal directions of magnetospheric VLF emissions observed on board satellites

AbstractThe wave normal directions of magnetospheric VLF/ELF chorus have been determined by using data from the geostationary satellite GEOS 2. They will provide useful information on the emission generation mechanism.

Characteristics of VLF emissions manifested by their cross-spectral phase information

Natural VLF emissions received by a single antenna can be characterised at each point in the emissions' frequency-time domain by a power and a phase. Emissions received at a single point by two antennae with a fixed relative orientation in space can be similarly described by the cross-spectral power and relative phase. It is shown that the cross-spectral phase contains information on the propagation characteristics of the waves which is better utilised in wave analysis than the power. In fact, the phase information allows weak signals to be identified more readily than is possible from a power spectrogram. It also allows the recognition of waves propagating with different wave normal directions. Data from the Geos-1 electric and magnetic antennae, pre-processed by the on-board correlator, are used to study the cross-spectral characteristics of VLF hiss and chorus in the Earth's magnetosphere.

Observations on the GEOS 1 satellite of whistler mode signals transmitted by the Omega Navigation System Transmitter in northern Norway

Whistler mode signals of 0.9–1.1 s duration at 10.2, 11.33, and 13.6 kHz launched by the Omega Navigation System transmitter located in northern Norway have been observed on GEOS 1. The signals were observed both inside and outside the plasmasphere in two regions of the magnetosphere, in December 1977 at 10–20° north of the equator on the morningside and in May 1978 10° south of the equator on the nightside. For a sequence of particularly strong pulses in the December period, the ‘instantaneous’ wave normal directions were calculated and found to have angles of 120–140° to the magnetic field of the earth pointing 0–40° eastward. These pulses have amplitudes of the order of 10 μV/m and refractive indices above 30. At times the amplitude envelope of the signals is unmodulated, but often the amplitude and the wave normal direction are strongly modulated on a time scale of 0.2 s. We attribute these features to ray path mixing. The signals are often prolonged up to 1 s, which is interpreted as an overlap of the primary pulse with the echo of the pulse reflected from the topside ionosphere in the southern hemisphere. While the signals do not trigger strong emissions, we do observe ∼0.1‐s long bursts at the tail of some direct pulses.

Wave normal directions and wave distribution functions for ground‐based transmitter signals observed on GEOS 1

VLF whistler mode pulses of ∼1‐s duration emitted by the omega navigation system transmitter located in Norway have been observed on‐board the GEOS 1 satellite. The wave normal directions of 7 pulses have been determined by three different methods of analysis: the cross product method, Means' method, and the maximum entropy method of determination of the wave distribution function (WDF). The first method is based on the interpretation of measurements of the three magnetic wave field components in a 300‐Hz band, including the omega frequency and the second and the third method on the interpretation of the spectral matrix elements of the three magnetic wave field components at the Omega frequency. While the cross product method and Means' method assume that the electromagnetic wave field is that of a single plane wave propagated in a fixed direction with respect to the ambient magnetic field, the WDF method assumes the wave field to be random. The three methods and their solutions are compared and discussed in terms of the statistical properties of the signals (signal to noise ratio, stationarity in time, degree of polarization, ellipticity), and in terms of sensitivity to inconsistencies in the data. Some recommendations are made concerning the best choice of method in given situations. The wave normals are found to have angles ∼130° with the earth's magnetic field direction, pointing slightly eastward of the local magnetic meridian. They exhibit a time variation with a 0.2‐ to 0.4‐s periodicity.

Electromagnetic Propagation in Homogeneous Media With Hermitian Permeability and Permittivity

The problem of electromagnetic radiation traveling in a general homogeneous, but anisotropic and gyrotropic, medium has been solved. The plane wave representation is used to convert Maxwell's equations into a general eigenproblem, which allows for tensor permeability and permittivity and for electric and magnetic gyrotropy. This formulation can be applied directly to computer evaluation of wave velocities and polarizations for a given wave-normal direction. The reflection and refraction directions and amplitudes at an interface between two different, general anisotropic and gyrotropic media are solved. It is outlined how, with the aid of a digital computer, ray tracing through a general succession of anisotropic and gyrotropic, but locally homogeneous, media can be carried out.

Effect of parallel electric fields on whistler wave propagation at low latitudes

Effect of parallel electric fields on whistler wave propagation at low latitudes is studied with the help of ray tracing computations. It is shown that in presence of such fields, whistler ray paths are defocused and their final wave normal directions at the base of the F region ionosphere in the opposite hemisphere are such that the waves would not be observed on the ground. In the absence of suitable ducts, horizontal density gradients existing in the low‐latitude ionosphere seem to play important roles in whistler propagations to ground stations.

Field and wave measurements aboard the Aureol-3 spacecraft

In the Soviet-French Arcad-3 project, 3 experiments TBF-ONCH, TRAC and ISOPROBE are carried out on board the Aureol-3 satellite to measure the AC and DC electric and magnetic fields and waves. Several modes of telemetry, real time and memory regimes are available for data transmission. TBF-ONCH is devoted to the measurement of 3 components of the DC electric field, 2 electric and 3 magnetic components of the waves. In one mode of the real time telemetry these 5 components are transmitted simultaneously in the frequency range 10 Hz-1.5 kHz in order to be able to determine the wave normal directions of natural emissions and to localize their sources. In the second mode, morphological studies of saucers, chorus, hiss and triggered emissions can be undertaken using the wide band transmission (70 Hz-16 kHz) of any one of these 5 components with the possibility of periodically changing the transmitted component every 4 seconds or keeping the same one during all the pass. TRAC makes use of the on board 3 axis flux gate magnetometer to perform a fine measurement of the magnetic effects of the currents flowing in the vicinity of the spacecraft either in the ionosphere or along the magnetic field lines, with a resolution of ∼ 12 nT and in the frequency range from DC to ∼ 20 Hz. One component of the HF electric field (0.1–10 Mhz) is measured by ISOPROBE (see companion paper). Examples of inflight measurements from the above instruments and their presentation on microfiches are shown. Some new phenomena are emphasized and briefly discussed.

One and two direction models for VLF electromagnetic waves observed on‐board Geos 1

Single propagation models are investigated for analyzing VLF electromagnetic wave fields observed in magnetosphere. They are selected according to the values of the eigenvalues of the spectral matrices of the three magnetic field components. If there is one single nonzero eigenvalue, a one‐direction model is considered, while if there are two nonzero eigenvalues, a two‐direction model is chosen. A likelihood ratio test is performed in the doubtful cases. The two models are used to analyze VLF chorus and hiss observed onboard the Geos 1 satellite. The two‐direction model is generally the most likely, suggesting that waves are simultaneously generated at all wave normal directions.

Magnetic Waves Guided by a Linearly Tapered Yig Film

A quasi-optical treatment is given for the dispersion relation and the group delay time of a magnetic wave guided by a YIG film having a weak linear taper in its thickness in the propagation direction of the guided magnetic wave. This treatment has 1) confirmed the intuitive results in which the local value of the thickness is used for the tapered film, 2) indicated the frequency regions of validity of the intuitive results, and 3) revealed interesting features of the wavenormal and ray directions inside a YIG film.

Trapping of whistler-waves through the side of ducts

It is shown that, when the whistler-mode phase refractive index is plotted along the length of geomagnetic field lines as a function of altitude, there is a minimum at an altitude of between 1400 and 2200 kms depending on magnetospheric model and wave frequency. Ray-tracing calculations are presented which show that the wave normal direction of upgoing whistler-mode waves can become field-aligned at and above the altitude of the refractive index minimum and this can lead to trapping of waves through the side of a suitably positioned duct. The mechanism is made possible by the increase of refractive index along the duct length above the altitude of the refractive index minimum. Ray paths resulting from trapping by this mechanism in both a winter night and a summer day model of the magnetospheric plasma are presented and discussed.

Rays in magneto-ionic theory-II

In a homogeneous magnetoplasma the refractive index is given by the dispersion relation, which assumes that the angle between the wave normal and the superimposed magnetic field is known. But a radio signal travels along a path known as a “ray” whose direction is in general different from the wave normal, and in many problems it is the ray direction that is known and the wave normal direction is at first unknown. In a previous paper, for a plasma in which the only effective carriers are electrons, a formula was given for finding the refractive indices when the ray direction is given. In this paper the formula is extended to allow for the presence of heavy ions. It is an equation of degree six whose solutions are associated with six different waves, although not all of them are necessarily excited by a given source. The properties of the equation are illustrated by discussion of its solutions at cut-off frequencies and resonance frequencies, and by showing its connection with resonance cones, Storey cones, and window points. A specific example of a plasma containing protons and He + ions is studied as an illustration.

Propagation directions of hydromagnetic waves in interplanetary space: Pioneer 10 and 11

The real and imaginary parts of spectral matrices of magnetic field fluctuations near 4 and 5 AU are used separately to generate estimates of hydromagnetic wave normal directions over the frequency range 10−5 to 10−2 Hz in the spacecraft frame. Both procedures suggest the predominance of the Alfvén mode over the fast and slow MHD modes among transverse magnetic field perturbations. Both procedures also show that the Alfvén mode is more common among transverse perturbations at 4 AU than at 5 AU. We develop statistical techniques for estimating uncertainties in computed wave normal directions and conclude that the real parts of the spectral matrices are more useful than the imaginary parts in specifying wave normals at times of magnetic quiet in the solar wind near 4 and 5 AU.

The analysis of 6-component measurements of a random electromagnetic wave field in a magnetoplasma -- II. The integration kernels

Summary. General expressions are derived for the kernels of the set of integral equations that relates the spectral matrix of the six components of a random electromagnetic wave field in a magnetoplasma to the wave distribution function for the field. The dependence of the kernels on wave-normal direction is examined, with particular reference to the propagation of very low-frequency waves in the whistler mode.

A universal chart for use in relating ionospheric absorption to phase path and group path

The absorption of a radio wave in the ionosphere can be approximated by A = \frac{\omega}{c}\frac{1}{2}\int\frac{Z(\mu' - \mu)}{1 + g} cos \alpha ds , where the integral is along the ray that exists when the normalized collision frequency Z = 0, \mu' and \mu are the group and phase refractive indices, respectively, and \alpha the angle between the wave normal and ray direction. Graphs are presented from which g can be obtained for any values of the ionospheric plasma parameters X and Y .

On the origin of plasmaspheric hiss: The importance of wave propagation and the plasmapause

The presence of a turbulent band of ELF hiss throughout the plasmasphere has been modeled by following unducted whistler mode waves from a restricted region of cyclotron resonant growth in the outer plasmasphere. The most unstable waves originate near the equatorial plane within a modest cone of wave normal angles aligned along the ambient magnetic field. As the waves propagate to higher latitude, their wave normal direction becomes progressively oblique, and ray paths generally migrate outward until they reach the plasmapause. A major fraction of the incident waves internally reflect at the steep plasmapause density gradient and subsequently propagate inward to populate most of the plasmasphere. Only a minor part of the wave energy is able to escape from the plasmasphere, primarily at high latitude. A detailed study of the internally trapped ray paths shows that certain waves can return to the equatorial growth region with field‐aligned propagation vectors and thus experience further amplification. This is particularly important for the maintenance of quiet time hiss when a single transit of the growth region is insufficient to amplify the background incoherent cyclotron noise to detectable levels. The model calculations demonstrate that the observed frequency spectrum and polarization of plasmaspheric hiss not only are controlled by the relative rates of cyclotron growth and Landau damping but also are strongly influenced by the wave propagation characteristics.

General formulae for absorption of radio waves in the ionosphere

The relationship between group path, phase path and absorption of radio waves is discussed and new approximations relating these quantities are presented. The new relationships include dependence on the angle between the wave normal and magnetic field directions and so, in contrast to other approximations they are not restricted to quasi-longitudinal or quasi-transverse situations. For deviative absorption it is found that the ordinary mode quasi-transverse approximation introduces errors of less than 5% except in the case of purely longitudinal propagation. For non-deviative absorption, use of the quasi-longitudinal approximation can introduce significant errors which particularly affect the determination of latitudinal variations in absorption.

Analysis of random electromagnetic wave field by a maximum entropy method

A method is developed for the analysis of measurements of n components of a random electromagnetic wave field (n ⩽6). This field observed at a fixed point in a magnetoplasma is described statistically by the distribution of wave energy with respect to the variables frequency and wave-normal direction. The frequency is supposed to be fixed. The distribution function considered as the most reasonable one maximizes the entropy and satisfies the values of the n × n elements of the spectral matrix of the n components. This solution obeys the nonnegativity constraint on the wave distribution function. Its properties are discussed in terms of stability and predictive power. Applications are proposed to simulated data and to satellite data.

Turbulent generation of electrostatic fields in the magnetosphere

Large-scale E × B turbulence can generate large potential differences across magnetic field lines in the magnetosphere. Resulting potential differences between the ionosphere and the turbulent eddies in the magnetosphere can accelerate auroral electrons. In a two-dimensional guiding center plasma, energy flows from smaller- to larger-scale sizes, so that the system tends toward a state with most energy in the longer wavelengths. Application of a numerical model demonstrates the transfer of turbulent energy from scale sizes of the order of the ion gyroradius to scale sizes where a macroscopic fluid description is valid. By taking the gyrational energy in the earthward streaming plasma sheet ions as the energy source for the turbulence it is found that some proton velocity distributions will be unstable to electrostatic flute mode instability with growth rates of the order of the ion cyclotron frequency. Large-scale turbulence is fed by nonlinear coupling of energy from the instability. Wave normal directions will be primarily perpendicular to magnetic L shells, and turbulent eddies generated by the waves may be greatly elongated in the east-west direction. The theory given here is consistent with the observed formation of multiple and irregular auroral arcs with a preference for east-west alignment.