J.A. Bennett

A model of the vertical distribution of the electron concentration in the ionosphere and its application to oblique propagation studies

An empirical model of the vertical distribution of the electron concentration of the ionosphere based on quasi-parabolic segments is presented (QPS model). The model is quite flexible and any number of ionospheric layers, valleys and ‘ledges’ can be incorporated. Nevertheless, it has been found that options of an E layer, E-F valley, F1 layer and F2 layer provide models of sufficient flexibility to give a good description of true height electron concentration profiles determined from vertical incidence ionograms. In this instance, the basic input parameters required are the same as those used by the CCIR models. The QPS models main advantage is that it can be used to obtain analytical solutions to ray parameters for propagation in spherically stratified ionospheres when the Earths magnetic field is neglected. An expression for the power of radio pulses backscattered from the Earths surface is also derived. This expression enables several effects, including those of the ionosphere, antennas and pulse length, to be readily examined. It is used, together with the QPS model, to illustrate the effects of the ionosphere and antennas on backscatter signals.

Automatic fitting of quasi-parabolic segments to ionospheric profiles with application to ground range estimation for single-station location

Abstract A method of automatically fitting a quasi-parabolic segment (QPS) model to measured profiles of electron concentration is described. The model consists of many smoothly joined quasi-parabolic segments. The base of the ionosphere is represented by a quasi-linear segment. This model has the advantage of possessing analytic solutions for ray quantities in a spherical ionosphere (neglecting the effect of the Earths magnetic field). It is also able to represent measured vertical ionospheric profiles to within a few percent in electron concentration. The usefulness of the model is illustrated by an application to the single-station location (SSL) of a distant radio transmitter from angle-of-elevation measurements. The no magnetic field results can represent the ordinary mode and approximate results for the extraordinary mode can be obtained using a frequency scaling technique.

On the relation between phase path, group path and attenuation in a cold absorbing plasma

Consideration is given to a cold absorbing plasma in which the collision frequency is zero. Expressions are developed which relate the attenuation and the group and phase refractive indices. It is found that because the expressions for the group and phase refractive indices and the imaginary part of the refractive index are closely related in form, the attenuation is related to the difference between the group and phase paths. Numerical calculations have derived approximations which significantly increase the range of known approximations of this type.

General formulae for absorption of radio waves in the ionosphere

Abstract 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.

Synthesis of oblique ionograms from vertical ionograms using quasi-parabolic segment models of the ionosphere

Abstract This paper describes a method of synthesizing oblique ionograms from vertical ionograms based on representing the ionosphere by multiple quasi-parabolic segments (QPS). The advantage of this approach is that it allows analytical solutions to be obtained for several ray parameters when the Earths magnetic field is neglected and the ionosphere is spherically stratified. The no-field results are representative of the ordinary mode. In addition, results for the extraordinary mode can be obtained by introducing a perturbation to the effective frequency and modifying the no-field results. The method is illustrated by comparing synthesized oblique ionograms with observed ionograms and with results obtained for the ordinary mode using the classical method.

Some methods of solving for the coefficients of dyadic Green's functions in isotropic stratified media

Dyadic Greens functions in multi-layered isotropic media are analysed in this paper. Three different kinds of method for obtaining the coefficients of dyadic Greens functions in multi-layered media are given, these are (a) the boundary condition method, which is well-known; (b) the recurrence matrix equation method; and (c) the ray trail method. Using these methods, several examples are considered. Some results are the same as those obtain previously. Some are obtained for the first time.

Analytic ray parameters for the quasi-cubic segment model of the ionosphere

Models of the ionosphere giving analytic ray solutions are very useful for the study of ionospheric propagation. Probably the most useful is the quasi-parabolic model which gives analytic solutions for a spherical ionosphere when the effects of the Earths magnetic field are ignored. Furthermore, its use in analytic ray tracing has been extended recently by developments in which real ionospheres are described by fitting quasi-parabolic segments (QPS) to measured vertical profiles. While numerical ray tracing is required to take account of the range of horizontal gradients that occur in the ionosphere, in some real-time applications, analytic results are still preferred because of the shorter computation time. Even though the QPS approach has greatly extended the utility of analytic ray tracing, it produces model ionospheres which are continuous in only the first derivative of the refractive index. The lack of continuity of the second derivative can lead to relatively abrupt changes in ray quantities with, for example, elevation angle. This drawback has been addressed by developing a model based on quasi-cubic segments (QCS) which also provide analytic ray solutions. In this paper the QCS model is described, and analytic solutions are derived for range, group, and phase paths. An example of an application is presented in which the QCS model was used to check the performance of a numerical ray tracing code.

The effect of large‐scale ionospheric gradients on backscatter ionograms

This paper presents the results of the synthesis of a range of backscatter ionograms using ray tracing through model ionospheres. The backscatter ionograms were obtained by the Jindalee over-the-horizon radar facility at Alice Springs in northern Australia. Sample ionograms obtained during 1990 were used, and the study concentrated on reproducing effects due to sunrise-sunset gradients and the equatorial anomaly. Backscatter ionograms were synthesized using both analytical and numerical ray tracing through ionospheric models based on FAIM (fully analytic ionospheric model). To make the synthesis realistic, signal strength was calculated taking account of ray divergence, ionospheric absorption, and antenna patterns. Analytical ray tracing produced quite realistic results when horizontal gradients were small but did not reproduce prominent features observed during sunrise-sunset or when propagation occurred through the equatorial anomaly region. Since the analytical ray tracing was restricted to a single vertical profile which could be tilted, this result shows that gradients in ionospheric electron density, rather than simple tilts, are most significant in determining propagation characteristics. Numerical ray tracing through ionospheric models based on the FAIM model reproduced dominant features of backscatter ionograms for those situations when analytical ray tracing proved inadequate. Major seasonal variations were also reproduced. Overall, the results of this initial study show that many premier features on backscatter ionograms, including the power variation of the backscattered signals, can be realistically modeled using ray tracing and ionospheric models. Further work is required before all the detailed structure of backscatter ionogram traces can be synthesized and accurately interpreted in terms of ionospheric structure.

A Ray-Tracing Technique for Determining Ray Tubes in Anisotropic Media

Ray-tracing techniques are commonly used for calculating the paths taken by electromagnetic waves in a medium that has an associated refractive index, such as the earths ionospheric plasma. Ray equations derived from Hamiltons equation are usually used to determine ray paths and ray tubes defined by tracing adjacent rays separately. There are advantages in describing ray tubes in terms of a main ray and variational rays. In this paper, equations for variational rays are derived for anisotropic inhomogeneous media such as the earths ionosphere. The ray-tracing technique is ideal for simulating ionospheric propagation experiments, and examples are given of ground illumination as a function of ground range and frequency.

Ray trajectories in an absorbing ionosphere

Abstract The present paper deals with the simulation of electromagnetic ray propagation in a cold collisional ionosphere in the presence of the Earths magnetic field. This subject has been extensively studied in the past. The novel aspect here is our attempt to assess the effect of absorption on the ray trajectories, not merely the field intensity. In addition to the theoretical interest in this problem, practical questions, such as target location by means of Over The Horizon Radar (OTHR) systems, in the presence of high losses, provide the motivation. The analytical investigation of such problems is limited by the complexity of the wave propagation field problem and the physics of the ionosphere, which combine to yield a complex dispersion relation, and the restricted capability of available computers and mathematical software packages for handling the ray tracing model. The present model is based on the familiar Appelton-Hartree, sometimes called the Appelton-Lassen, dispersion equation for the cold, collisional, magnetized ionosphere. The way that the ray tracing is performed (ray tracing being an approximation) and the model chosen by the researcher predetermines the resultant ray trajectories. Thus, in the presence of losses, certain decisions regarding the use of the Hamiltonian ray tracing model have to be made. Unlike some studies which first compute the lossless trajectories, and then add on a posteriori the attenuation along these trajectories, as a perturbation of the lossless solution, here the Hamiltonian ray tracing formalism is extended in order to include the absorption effects in the formalism a priori. For small absorption all models yield more or less the same results; therefore, in the present study high losses are considered in order to emphasize the effects. However, the present study contributes to our understanding of the basic problem of ray propagation in the presence of arbitrary losses. The extended Hamiltonian ray tracing formalism used here assumes complex space, and an additional constraint that guarantees real space and time subspace for the ray trajectories, as well as for the group velocity, whereas the propagation vector and the frequency may be complex. Other formulations for the ray equations formalism exist too. At this time it remains an open problem whether ray trajectories computed by those models will agree with the results obtained here or not. Furthermore, in the absence of sufficient direct ray trajectories empirical data, where high absorption cases are compared to lossless cases, the question as to which model better describes the physical reality must remain open. The variation of the ray paths with frequency, launching angle, collision frequency, electron density profile and other variables, are examined for Chapman type E and F layers. By using typical F layer parameters, it is found that, in certain cases, a high collision frequency affects the ray path by as much as 500 km. This result is important for sub-ionospheric propagation and for target location tracking.