ELF Range Research Articles

Some considerations of the polarization error in direction finding of atmospherics-I. Effect of the Earth's magnetic field

In order to locate the atmospheric origin, direction finding must be used. As direction finding has various types of error, the arrival direction of atmospherics is normally disturbed by these errors. In this paper, using a simple ionospheric model for nighttime, the wave polarization due to the effect of the Earth's magnetic field is calculated for both ELF and VLF bands below 10 kHz and also the behavior of the bearing error is investigated as a function of propagation distance. This paper shows that if the direction finding can be operated at a frequency in the ELF range, there would be two merits in comparison with 10 kHz direction finding.

More on field representation in the ELF range

A wave guide mode computer model is used to calculate ELF radio fields in the earth-ionosphere wave guide. Results are compared with those calculated by Galejs and by Johler and Lewis for both homogeneous and diffuse inhomogeneous ionospheres as well as with measurements of Sanguine test transmissions. Good agreement is found in all comparisons except for those with the Johler and Lewis calculations for an inhomogeneous ionosphere.

Comments on a Letter by J. Galejs, ‘On the field representations in the ELF range,’ and on the Reply by J. R. Johler and R. L. Lewis

Comments on a Letter by J. Galejs, ‘On the field representations in the ELF range,’ and on the Reply by J. R. Johler and R. L. Lewis

Reply [to “‘On the field representations in the ELF range’”

Reply [to “‘On the field representations in the ELF range’”

On the field representations in the ELF range

Spectral propagation characteristics of ELF atmospherics or slow-tail wave forms are usually determined from mode theory or a residue series representation [Jean et al., 1961; Jones, 1970; Taylor and Sao, 1970; Hughes and Theisen, 1970]. The azimuthal or distance variation of the fields is characterized by Legendre functions of complex order where special simplified forms exist near the source, in the asymptotic range, or near the antipode. The successive Schumann resonances (or circumferential resonances of the earth to ionosphere cavity, which are excited by the worldwide distribution of thunderstorm activity) can be described by Legendre polynomials of increasing integer order n [Wait, 1962; Large and Wait, 1968]. The Legendre polynomials or zonal harmonics can be also used at higher frequencies; special summation techniques are required to assure a more rapid convergence of the series [Johler and Berry, 1962], and the representation of zonal harmonics yields fields consistent with other representations [Galejs, 1969, Figure 4].

VLF-ELF radiation characteristics of a 90°-phased crossed-dipole array in a cold multicomponent magnetoplasma

Linear electromagnetic theory is used to find the VLF-ELF radiation characteristics of a quadrature-phased crossed-dipole array in a cold multicomponent magnetoplasma. Each dipole is perpendicular to the static magnetic field B0, and the current on each is assumed to have a skin-triangular distribution. Formal solutions valid throughout the VLF and ELF ranges are derived for the total radiated complex power and mutual coupling power. These solutions are used to obtain both numerical results and approximate closed-form expressions for mutual input impedance ΔZ applicable to the driving terminals of either dipole of the array. Approximate closed-form expressions for the power fluxes parallel and perpendicular to B0 are also derived. When a right-circularly phased dipole array is used as a radiating source in the VLF range, the total power radiated into the whistler mode is increased, and the power flux along the field line is enhanced by a factor of 4 compared to that from a single dipole carrying the same current. In the ELF range, the effects are similar but more complicated. The mutual input reactance due to the effects of medium anisotropy and circular phasing of the dipole array are found to be negligible. It is shown that the power flux along B0 from a right-circularly phased dipole array peaks by at least 1 order of magnitude at approximately half the electron gyrofrequency. This result suggests a possible use of the proposed array as a radiating source to trigger artificially stimulated VLF emissions.

Some new features of ELF attenuation

Computations have been made of the attenuation suffered by ELF radio waves propagating under six ionospheres having realistic variations of electron density and collisional frequency with height. These computations differ from earlier computations made by the author ( Barr, 1970b) in that allowance is made for the presence of a magnetic field. The effect of this magnetic field is to produce a minimum in the graph of ELF attenuation vs. frequency, the depth and frequency of the minimum being dependent on the ionosphere under which propagation is taking place. The depth and frequency of the attenuation minimum are also found to be strongly dependent on the geomagnetic latitude of the propagation path. The minimum is found to move to lower frequencies and gradually disappear as the latitude of the propagation path is decreased. The attenuation minimum is, however, found to be almost independent of the azimuth of the propagation path. Computations have also been made of the amplitude spectrum of atmospherics propagating under one of the ionospheres ( Deeks, 1966) and these are found to exhibit maxima in the ELF range as a result of the minima in the attenuation constant. Experimental amplitude spectra recorded by the author which exhibit spectral maxima and ‘ledges’ at low frequencies (~500 Hz) are found to be in good agreement with theoretical spectra.

ELF Propagation in an Inhomogeneous Waveguide

The laterally inhomogeneous anisotropic ionosphere is represented by a changing ionospheric surface impedance. The fields across such discontinuities can be estimated by computing the propagation characteristics on the various segments as in a homogeneous environment and by applying the resulting propagation parameters to the appropriate segments of the path. For fields observed across a day‐to‐night boundary, the resulting error is of the order of one percent. The effects of more localized ionospheric perturbations depend on their azimuthal and transverse extent. In the lower ELF range, areas with transverse dimensions of one to two thousand kilometers affect the propagation path across the perturbation to about the same extent as a propagation path tangential to the periphery of the perturbed region.

On the propagation of long waves to large distances

The mode theory is compared with a more heuristic approach where the free space power flow from a ground based source is confined by the finite space between the earth and the ionosphere. The approximate technique produces severe underestimates of the power flow in the ELF range, and it overestimates the power flow in the higher VLF range.

Excitation of the Terrestrial Wave Guide by Sources in the Lower Ionosphere

The effectiveness of a dipole source within the ionosphere is determined relative to a ground based source of the same dipole moment. The earth‐to‐ionospheric cavity is excited best if dip angles of the geomagnetic field are in excess of 15° to 20°. In the optimum orientation the axes of electric and magnetic dipoles are transverse to the geomagnetic field; axial electric dipoles are particularly ineffective. For frequencies in the VLF range the relative effectiveness of an ionospheric source is about 10% at nighttime and 1% at daytime. In the ELF range the relative effectiveness is from 20 to 100%.

Propagation of ELF and VLF Waves Below a Generally Anisotropic Ionosphere

The mode analysis of ELF and VLF waves has been generalized to allow arbitrary directions of propagation below a curved stratified ionosphere with a dipping static magnetic field. In the ELF range, the propagation parameters are changed almost linearly with the azimuthal angle ϕ by varying the direction of propagation from east to west. In the VLF range, the phase velocity exhibits its maximum value for propagation in south‐and‐north direction; and minimum values occur for propagation toward west. Also, maximum attenuation rates occur for propagation toward the west. Measured interference distances D of the two lowest waveguide modes are explained using nighttime ionosphere models that exhibit sharp density gradients in the height range from go to 85 km.

Propagation of ELF and VLF waves below an anisotropic ionosphere with a dipping static magnetic field

Fields of cylindrically curved ionosphere layers are approximated by exponential functions that consider the increase of the phase velocity and decrease of the attenuation rate with the altitude of the layers. Matrix multiplication techniques are applied to the treatment of multilayer ionosphere models. The individual ionosphere layers are thin relative to the wavelength, and the approximate field representations give in the limits of horizontal and radial static magnetic field results identical to those obtained using more accurate treatments of curvature effects. TM modes in the space between the earth and the ionosphere excite coupled TM and TE modes in the ionospheric layers, the presence of which are considered in an iterative solution of the modal equation. In the ELF range, propagation parameters computed for the east-to-west (EW) and west-to-east (WE) directions differ most for dip angles of 15-30°. In the VLF range propagation parameters may exhibit discontinuities at nighttime for the EW direction, when the fields penetrate higher into the ionosphere. The interference distance D of the two lower wave guide modes is increased for propagation in the EW direction relative to propagation in WE direction provided that the electron concentration profiles exhibit sharp density gradients at heights in the range from 80 to 85 km. The desired propagation characteristics could not be produced in the presence of a nondipping static magnetic field or using smoothly varying electron concentration profiles.