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Kirillov, V. V.; Kopeykin, V. N.

doi:10.1023/a:1023652610575

Cited by 18 publications

(11 citation statements)

References 5 publications

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“…[16] The frequency model of the matrix local ionospheric inductance for four models of the ionosphere (day and night at low and high solar activity levels) was presented by Kirillov and Kopeykin [2003]. The ionosphere model specifies profiles of electron density, effective collision frequency of electrons and ions with neutral particles, and the average mass of positive ions.…”

Section: Waveguide Modelmentioning

confidence: 99%

“…[22] We assume that the complex dielectric permeability of the ground is constant and is equal to ε g = εg + iσ/(ωω0). We also assume that at depth hg there is an ideally reflecting surface, the introduction of which allows us to avoid the appearance of a continuous part in the spectrum of normal waves [Kirillov and Kopeykin, 1989]. In addition, the ideally reflecting surface at depths 70-100 km simulates the Earth's mantle.…”

Section: Horizontally Polarized Modesmentioning

confidence: 99%

“…[5] At distances ρ exceeding a triple effective waveguide height h, only the field of one leading quasi-TEM mode is left in the electromagnetic field of a point source [Madden and Thompson, 1965;Wait, 1962]. This mode is found by numerical integration of a system of ordinary differential equations following from the Maxwell equation [Galyuk and Ivanov, 1978;Hynninen and Galyuk, 1972;Jones, 1967;Kirillov andKopeykin, 2002, 2003;Kirillov et al, 1997;Krasnushkin and Yablochkin, 1963;Madden and Thompson, 1965;Pappert and Miler, 1974] or analytically [Greifinger and Greifinger, 1978, 1979, 1986Kirillov, 1972Kirillov, , 1978Kirillov, , 1996Kirillov, , 1998Kirillov and Pronin, 1974]. Only numerical calculations yield the results corresponding to the real model of the ionosphere.…”

Section: Introductionmentioning

confidence: 99%

“…This matrix is obtained by numerical integration over the region of the ionosphere responsible for radio wave reflection. The region extends to 2 Mm in the frequency range 0.1-5 Hz [Kirillov andKopeykin, 2002, 2003]. For the plane homogeneous model of the waveguide, the two heights introduced above allow one to express the electromagnetic field of a horizontal electric dipole at the Earth's surface through the first function of the zero order and its derivatives [Kirillov and Kopeykin, 2002].…”

Section: Introductionmentioning

confidence: 99%

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Normal waves of the anisotropic Earth—ionosphere waveguide in the VLF-ULF range

Kirillov¹,

Pronin²

2007

Int. J. Geomagn. Aeron.

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The problem on determination of the electromagnetic field of a near-Earth horizontal electric dipole in the frequency range 10 −1 − 10 3 Hz at distances 10 −1 − 10 3 km in the Earth-ionosphere waveguide has been solved. The ionosphere is assumed to be horizontally stratified and anisotropic, and the Earth is assumed to be homogeneous to some depth and infinitely conducting below. The representation of the electromagnetic field as expansion in waveguide modes is given. The zero mode is regarded as anisotropic. Local modes are given in the isotropic approximation of the anisotropic ionosphere due to inclusion of an effective exponential conductivity profile. An analytical description of the field reflection for vertical and horizontal polarizations has been obtained for this model. At short distances from the source, the solution coincides with the known solution for the case of the absence of the ionosphere. The range of distances beginning from which the influence of the ionosphere on the near-Earth magnetic field manifests itself has been found.

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Section: Waveguide Modelmentioning

confidence: 99%

Section: Horizontally Polarized Modesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Normal waves of the anisotropic Earth—ionosphere waveguide in the VLF-ULF range

Kirillov¹,

Pronin²

2007

Int. J. Geomagn. Aeron.

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“…A model of a planar waveguide developed in [11] was used in [6,7], but with a homogeneous upper wall, the parameters of which took into account the appearance of a strong and extended sporadic E s layer. In [12], based on the solution of a two-dimensional telegraph equation, a model of a spherical waveguide for a source such as a horizontal magnetic dipole was developed and calculations for a vertically non-uniform ionosphere were performed, which made it possible to allow for the ionospheric Alfvén resonator (IAR) effects. The method of a two-dimensional telegraph equation was also employed in [10] to calculate the propagation of an artificial signal from ETLs at high latitudes.…”

Section: Introductionmentioning

confidence: 99%

Features of the Spectra of Ultra-Low-Frequency Magnetic Fields from Horizontal Current Sources: Models of Planar and Spherical Earth–Ionosphere Waveguides

Ermakova

Ryabov

Kotik

2021

Radiophys Quantum El

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We simulate the magnetic field components in the frequency range 0.1-30 Hz from a source such as the horizontal magnetic dipole located in the Earth-ionosphere cavity. Models of uniform spherical and planar waveguides are considered, the advantages of each model are determined, and a comparative analysis of the simulation results is performed. The results of numerical calculations lead to the conclusion about the impact of the IAR (ionospheric Alfvén resonator) and sub-IAR (resonator at altitudes of 80-300 km) on the amplitude spectra of the ultra-low-frequency (ULF) signal. It is also shown that the appearance of strong sporadic layers (with a plasma frequency exceeding 5 MHz at their maxima) along the entire propagation path of ULF fields from the source to the receiver can strongly change the amplitude spectra of artificial signals. A significant increase in the amplitude of the magnetic field at the IAR harmonic frequencies can be observed at night. The sub-IAR effect is responsible for the appearance of a dependence of the amplitude of the magnetic components, which increases with frequency. Phase shifts between the horizontal components of the ULF signal and the spectra of the polarization parameter are also analyzed. It is shown that ionospheric resonators have almost no effect on the phase characteristics of artificial signals in a uniform waveguide approximation, in contrast to the polarization of magnetic ULF fields from a vertical electric dipole. The dependences of the amplitude of the magnetic field of a signal on the distance r to the source and on the direction to the source are also analyzed. It is shown that the dependence of the decay of the magnetic field amplitude with distance can differ significantly from the 1/r 2 law. The radiation pattern is almost isotropic for k 0 r < 1, where k 0 is the wave number in free space. The lines of equal amplitude are stretched along the direction of the current source for k 0 r ≥ 1.

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On a mechanism forming a broadband maximum in the spectrum of background noise at frequencies 2–6 Hz

Ermakova

Kotik

Polyakov

et al. 2007

Radiophys Quantum El

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We study the properties of a broadband spectral maximum (BSM) of the background noise at frequencies 2-6 Hz using the data of mid-latitude observations. We find that the parameters of the maximum depend on the local ionosphere properties and that small scales (several tens of km) are absent in the field distribution at the BSM frequencies. We propose a mechanism forming the BSM, which is related to the large gradients of the refractive indices of normal ionosphericplasma waves at altitudes from 70 to 300 km. The performed simulation of BSM spectra for a plane-stratified model of anisotropic inhomogeneous ionosphere allowed us to explain the main experimentally observed BSM properties.

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Cited by 18 publications

References 5 publications

Normal waves of the anisotropic Earth—ionosphere waveguide in the VLF-ULF range

Normal waves of the anisotropic Earth—ionosphere waveguide in the VLF-ULF range

Features of the Spectra of Ultra-Low-Frequency Magnetic Fields from Horizontal Current Sources: Models of Planar and Spherical Earth–Ionosphere Waveguides

On a mechanism forming a broadband maximum in the spectrum of background noise at frequencies 2–6 Hz

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