Theory of the reflexion of low-frequency radio waves obliquely incident on the ionosphere

1974 ◽  
Vol 336 (1607) ◽  
pp. 525-542 ◽  
Keyword(s):  
Low Frequency ◽  
Extraordinary Wave ◽  
Meridian Plane ◽  
Radio Waves ◽  
Quartic Equation ◽  
Obliquely Incident ◽  
Full Wave ◽  
Magnetic Meridian ◽  
Electron Gyrofrequency ◽  
Wave Normal

The properties of the two principal reflexions for radio waves obliquely incident on a horizontally stratified ionosphere in and near the magnetic meridian plane, for frequencies less than the electron gyrofrequency, are investigated using 'full wave’ numerical methods. When the wave normal of the incident wave is close to either of two directions, which are in the magnetic meridian plane, at particular angles θ b and θ e to the vertical, then for propagation from south to north (northern hemisphere), the polarizations of the two reflexions are found to take anomalous values. This behaviour is related to the properties of the Booker quartic equation. An extraordinary wave incident at an angle near θ e in the N–S direction generates some of the upgoing ‘whistler’ mode, an d this process is also investigated.

Theory of wave polarization of radio waves in magnetospheric cavities

1987 ◽  
Vol 412 (1842) ◽  
pp. 25-44 ◽  
Keyword(s):  
Magnetic Field ◽  
Low Frequency ◽  
Extraordinary Wave ◽  
Wave Polarization ◽  
Radio Waves ◽  
Full Wave ◽  
Magnetic Field Change ◽  
Planetary Magnetic Field ◽  
Wave Normal ◽  
The Magnetic Field

When interpreting observations of radio waves of low frequency in magnetospheric cavities, it is often assumed that the electron concentra­tion is small enough for the ray paths to be treated as straight, but great enough to ensure that a wave that starts as a pure ordinary (or extraordinary) wave has a wave polarization close to that of an ordinary (or extraordinary) wave at each point of the path. This polarization changes because the magnitude and direction of the planetary magnetic field change along the path. But the change of the magnetic field also introduces coupling between the ordinary and extraordinary waves. If the electron concentration is small or zero, this coupling may be cumulative so that it restricts or prevents the change of polarization. A full-wave integration of the governing differential equations is used to study this problem. It is similar to the problem of limiting polarization for a radio wave emerging from the ionosphere into free space. It is concluded that the polarization of an initially ordinary (or extraordinary) wave remains close to that of a locally produced ordinary (or extra­ordinary) wave with the same wave-normal direction, provided that the plasma frequency exceeds a minimum value. This value depends on the direction of the path. Some typical examples are given.

scholarly journals A review of unusual VLF bursty-patches observed in Northern Finland for Earth, Planets and Space

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Claudia Martinez-Calderon ◽  
Jyrki K. Manninen ◽  
Jemina T. Manninen ◽  
Tauno Turunen
Keyword(s):  
Low Frequency ◽  
Spectral Features ◽  
Radio Waves ◽  
Very Low Frequency ◽  
Ground Station ◽  
New Type ◽  
The Moment ◽  
Electron Gyrofrequency ◽  
Different Characteristics ◽  
Large Frequency

AbstractUsing numerical filtering techniques allowing us to reduce noise from sferics, we are able to clearly study a new type of differently structured very low frequency (VLF) radio waves above f = 4 kHz at the ground station of Kannuslehto in northern Finland (KAN, MLAT = 64.4°N, L = 5.5). These emissions are intriguing, since they are detected at frequencies above half the electron gyrofrequency in the equatorial plane (fce) for the L-shell of Kannuslehto (fce ~ 5–6 kHz). They are commonly observed at Kannuslehto, but have also been infrequently reported at other stations, sometimes under different names. Their possible common origin and manner of propagation is still under investigation. This paper unifies the nomenclature by regrouping all these waves detected at frequencies higher than the local equatorial 0.5 fce at the L-shell of observation under the name of VLF bursty-patches. While these waves have different spectral features, they appeared mostly composed of hiss bursts with durations of a few seconds to several minutes. They also show periodic features with varying periodicity and shape. They are sometimes characterized by single bursts covering very large frequency ranges of several kHz. We also give a review of the different characteristics of VLF bursty-patches observed at Kannuslehto, which at the moment, is the station with the highest observation rate. We present recent observations between 2019 and 2021.

Reflexion levels and coupling regions in a horizontally stratified ionosphere

1959 ◽  
Vol 252 (1004) ◽  
pp. 53-68 ◽  
Keyword(s):  
Collision Frequency ◽  
Plasma Frequency ◽  
Wave Theory ◽  
Electron Collision ◽  
Ray Theory ◽  
Radio Waves ◽  
Quartic Equation ◽  
Full Wave ◽  
Electron Collision Frequency ◽  
Full Solution

The propagation of radio waves through a horizontally stratified and slowly varying ionosphere is governed, in the case of oblique incidence, by a quartic equation (Booker 1938). Ray theory breaks down when two roots of this quartic are equal, for then coupling occurs between the characteristic waves, and full wave theory must be used. This paper is concerned with determining the conditions under which the two roots are equal; it is not concerned with the full wave theory. Values of the plasma frequency, and electron collision frequency, which lead to equal roots, are determined, and are exhibited in a set of curves. A full solution of the ‘Booker’ quartic is also given for a case of special interest. It is pointed out that the electric wave-field is unlikely to become very large in a slowly varying ionosphere, so that, if the ionosphere were irregular, scattering cannot be unduly enhanced by a plasma resonance.

scholarly journals Subpacket structure in strong VLF chorus rising tones: characteristics and consequences for relativistic electron acceleration

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
John C. Foster ◽  
Philip J. Erickson ◽  
Yoshiharu Omura
Keyword(s):  
Low Frequency ◽  
Phase Variation ◽  
Electron Acceleration ◽  
Continuous Phase ◽  
Equatorial Wave ◽  
Generation Region ◽  
Electron Gyrofrequency ◽  
Wave Normal ◽  
Relativistic Electron Acceleration

AbstractVan Allen Probes in situ observations are used to examine detailed subpacket structure observed in strong VLF (very low frequency) rising-tone chorus elements observed at the time of a rapid MeV electron energization in the inner magnetosphere. Analysis of the frequency gap between lower and upper chorus-band waves identifies fceEQ, the electron gyrofrequency in the equatorial wave generation region. Initial subpackets in these strong chorus rising-tone elements begin at a frequency near 1/4 fceEQ and exhibit smooth gradual frequency increase across their > 10 ms temporal duration. A second much stronger subpacket is seen at frequencies around the local value of 1/4 fce with small wave normal angle (< 10°) and steeply rising df/dt. Smooth frequency and phase variation across and between the initial subpackets support continuous phase trapping of resonant electrons and increased potential for MeV electron acceleration. The total energy gain for individual seed electrons with energies between 100 keV and 3 MeV ranges between 2 and 15%, in their nonlinear interaction with a single chorus element.

scholarly journals Subpacket Structure in Strong VLF Chorus Rising Tones: Characteristics and Consequences for Radiation Belt Acceleration

2021 ◽  
Author(s):  
John C. Foster ◽  
Philip J. Erickson ◽  
Yoshiharu Omura
Keyword(s):  
Low Frequency ◽  
Phase Variation ◽  
Continuous Phase ◽  
Inner Magnetosphere ◽  
Equatorial Wave ◽  
Generation Region ◽  
Electron Gyrofrequency ◽  
Wave Normal ◽  
Local Value

Abstract Van Allen Probes in situ observations are used to examine detailed subpacket structure observed in strong VLF (very low frequency) rising tone chorus elements observed at the time of a rapid MeV electron energization in the inner magnetosphere. Analysis of the frequency gap between lower and upper chorus-band waves identifies fceEQ, the electron gyrofrequency in the equatorial wave generation region. Initial subpackets in these strong chorus rising-tone elements begin at a frequency near 1/4 fceEQ, exhibit smooth gradual frequency increase across their > 10 ms temporal duration. A second much stronger subpacket is seen at frequencies around the local value of 1/4 fce with small wave normal angle (< 10 deg) and steeply rising df/dt. Smooth frequency and phase variation across and between the initial subpackets supports continuous phase trapping of resonant electrons and increased potential for MeV electron acceleration. The total energy gain for seed electrons with energies between 100 keV and 3 MeV ranges between 2 % and 15 %, in their nonlinear interaction with a single chorus element.

A Discussion on the early days of ionospheric research and the theory of electric and magnetic waves in the ionosphere and magnetosphere - Phase integral methods for studying the effect of the ionosphere on radio propagation

1975 ◽  
Vol 280 (1293) ◽  
pp. 111-130 ◽  
Keyword(s):  
Integral Method ◽  
Propagation Constant ◽  
Extraordinary Wave ◽  
Radio Propagation ◽  
Radio Waves ◽  
Exact Methods ◽  
Quartic Equation ◽  
Integral Methods ◽  
Phase Integral ◽  
Physical Principles

The phase integral method is a form of ray theory, extended to use complex values of the space coordinates. Its application to radio propagation studies was pioneered by T. L. Eckersley who showed how to use it for calculating (a) the reflexion coefficient of the ionosphere, (b) the propagation constant for radio waves guided by the Earth’s surface and by the ionosphere or troposphere, and (c) the coefficient for coupling of an ordinary and an extraordinary wave in the ionosphere. The method involves the evaluation of integrals along suitably chosen contours in complex space. It is approximate but often capable of high accuracy and often quicker to use than more exact methods. Its justification is based on the physical principles of analytic continuation and of uniform approximation. For reflexion and coupling problems in a horizontally stratified ionosphere, the contours used for the phase integrals are determined by those real or complex heights called ‘reflexion’ or ‘coupling’ points, where two roots of the Booker quartic equation are equal. The study of the behaviour of the governing equations near these points shows when failure of the phase integral method may be expected.

Theory of the reflexion in the ionosphere of radio waves with frequencies near the electron gyrofrequency

1975 ◽  
Vol 343 (1632) ◽  
pp. 133-153 ◽  
Keyword(s):  
Extraordinary Wave ◽  
Radio Waves ◽  
Electron Gyrofrequency

A study is made of the reflecting properties of the ionosphere for radio waves with frequencies near the electron gyrofrequency. The reflexion and absorption of the extraordinary wave is of particular interest. Extraordinary waves from two different reflexion levels can be present and, in some conditions, can interfere. Standard magnetoionic theory is compared with the modified formulae of Sen & Wyller.

Radio and Electrical Measurements on Glacial Streams

1987 ◽  
Vol 33 (114) ◽  
pp. 239-242
Author(s):  
M. E. R. Walford
Keyword(s):  
Electrical Conductivity ◽  
Water Channel ◽  
Water System ◽  
Low Frequency ◽  
Water Channels ◽  
Radiative Loss ◽  
Radio Waves ◽  
Electrical Measurements ◽  
Water Conductivity ◽  
Glacier Surface

AbstractWe discuss the suggestion that small underwater transmitters might be used to illuminate the interior of major englacial water channels with radio waves. Once launched, the radio waves would naturally tend to be guided along the channels until attenuated by absorption and by radiative loss. Receivers placed within the channels or at the glacier surface could be used to detect the signals. They would provide valuable information about the connectivity of the water system. The electrical conductivity of the water is of crucial importance. A surface stream on Storglaciären, in Sweden, was found, using a low-frequency technique, to have a conductivity of approximately 4 × 10−4 S m−1. Although this is several hundred times higher than the conductivity of the surrounding glacier ice, the contrast is not sufficient to permit us simply to use electrical conductivity measurements to establish the connectivity of englacial water channels. However, the water conductivity is sufficiently small that, under favourable circumstances, radio signals should be detectable after travelling as much as a few hundred metres along an englacial water channel. In a preliminary field experiment, we demonstrated semi quantitatively that radio waves do indeed propagate as expected, at least in surface streams. We conclude that under-water radio transmitters could be of real practical value in the study of the englacial water system, provided that sufficiently robust devices can be constructed. In a subglacial channel, however, we expect the radio range would be much smaller, the environment much harsher, and the technique of less practical value.

scholarly journals Investigation of ionosphere response to geomagnetic storms over the propagation paths of very low frequency radio waves

2020 ◽  
Author(s):  
Victor U. J. Nwankwo ◽  
Jean-Pierre Raulin ◽  
Dra. Emilia Correia ◽  
William F. Denig ◽  
Olanike Akinola ◽  
...  
Keyword(s):  
Geomagnetic Storms ◽  
Low Frequency ◽  
Radio Waves ◽  
Very Low Frequency ◽  
Propagation Paths
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