The Ray Theory of Doppler Frequency Shifts

Bennett, J. A.

doi:10.1071/ph680259

Cited by 31 publications

(20 citation statements)

References 16 publications

(16 reference statements)

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“…The other mechanism is associated with phase path variations of a ray between a source and a receiver due to fluctuations of the refractive index along the propagation path. As was shown by Bennett [1968], in this case we have where P is the length of the phase path and l is a ray coordinate along the propagation trajectory L .…”

Section: Discussionmentioning

confidence: 99%

“…Let us consider the details of the Doppler frequency variations in the EIS signal. There are two possible mechanisms of Doppler frequency shifts f D [ Bennett , 1968]. One of these is physical motion of the signal source (or scattering inhomogeneities in our case), which yields [ Rytov et al , 1978] Here is the velocity vector of the scattering inhomogeneities and s = r − i is the scattering vector, with r and i being wave vectors of the reflected (scattered) and incident waves.…”

Section: Discussionmentioning

confidence: 99%

“…[33] Let us consider the details of the Doppler frequency variations in the EIS signal. There are two possible mechanisms of Doppler frequency shifts f D [Bennett, 1968]. One of these is physical motion of the signal source (or scattering inhomogeneities in our case), which yields [Rytov et al, 1978]…”

Section: Rs3010mentioning

confidence: 99%

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Self‐scattering of a powerful HF radio wave on stimulated ionospheric turbulence

et al. 2009

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An analysis is presented of high‐frequency (HF) signals from the European Incoherent Scatter HF ionospheric modification transmitter received during 26–30 October 2002 at three sites, two in Europe and one in Antarctica. Two components with different characteristics (“mirror‐reflected” and “scattered”) were observed in the signal spectra. The mirror‐reflected component can be associated with radiation through the side lobes of the transmitting antenna thus bypassing the modified volume on its way to the receiving sites. In contrast, the scattered component was radiated through the main antenna beam and then scattered by pump‐induced ionospheric irregularities above the heater. As a result, variations in the scattered component signal intensity and Doppler frequency shifts (DFS) recorded at the greatly separated sites showed a high level of correlation. It is shown that the Doppler frequency variations can be associated with variations in the plasma density and/or physical motion velocities of stimulated inhomogeneities within the volume common to all propagation paths. Analysis of Doppler frequency shifts at greatly separated sites would allow identifying the mechanism responsible for the self‐scattering effect. In the case of DFSs due to motion of the pump‐induced scatterers it would be also possible to reconstruct the full velocity vector of the inhomogeneities.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Self‐scattering of a powerful HF radio wave on stimulated ionospheric turbulence

et al. 2009

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“…(At a corner q' in particular is discontinuous.) To deal with a ray having a finite number of corners it may be divided at the corners into a number of curves with continuously turning tangents, and then the results summed [Bennett, 1968] To simplify further discussion of (23) we introduce some more notation. We put…”

Section: The First Variation Of Pmentioning

confidence: 99%

On the Application of Variation Techniques to the Ray Theory of Radio Propagation

Bennett¹

1969

Radio Science

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The first variation of the phase path is developed from the point of view of Hamilton, and the result is applied to the calculation of Doppler frequency shift and group path. The second variation δm δnP of the phase path P is considered in the general case when the medium depends on both m and n. By generalizing identities arising in the usual investigation of extrema and by obtaining equations that must be satisfied because the arcs concerned are rays, a number of alternative expressions are found. These involve contributions due to the end‐points of the ray, due to the m,n dependence of the medium along a fixed ray, and due to the m,n dependence of the actual ray path. The application of the results to differential Doppler and Faraday fading measurements is briefly discussed. As an illustration a problem involving approximately straight rays in a plane, horizontally stratified medium is discussed and approximate expressions are found for P and dP/dt.

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“…In more recent times this same approach has been used in the investigation of a number of questions involving radio propagation in the ionosphere [e.g., Appleton, 1928;Kelso, 1960Kelso, , 1961Brandstatter, 1963;Ross, 1965;Kirnura and Nishina, 1967;Bennett, 1968Bennett, , 1969Bennett, , 1971aBennett, , 1971b. General investigations of the associated variations have been made by Kelso [1960Kelso [ , 1961 and Bennett [1969].…”

Section: Introductionmentioning

confidence: 99%

Variations of the ray path and phase path: A Hamiltonian formulation

Bennett¹

1973

Radio Science

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Using a formulation based on Hamilton's ray equations, the variations of the path of a ray, and of the corresponding phase path, due to changes in the ray end points or the medium properties, are investigated. General expressions are obtained which represent lhe variations in terms of the solution of systems of ordinary differential equations. These may be integrated along the unvaried rays in order to evaluate the variations. The results, which may be applied to the analysis of a number of propagation problems, represent a simplification for anisotropic media and are also particularly well adapted to numerical applications. RAY AND PHASE PATH: HAMILTONIAN FORMULATION 743

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The Ray Theory of Doppler Frequency Shifts

Cited by 31 publications

References 16 publications

Self‐scattering of a powerful HF radio wave on stimulated ionospheric turbulence

Self‐scattering of a powerful HF radio wave on stimulated ionospheric turbulence

On the Application of Variation Techniques to the Ray Theory of Radio Propagation

Variations of the ray path and phase path: A Hamiltonian formulation

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