Theory of the modulation imposed on an obliquely incident radio wave reflected in a disturbed region of the lower ionosphere

A powerful disturbing wave enters the lower ionosphere and causes a periodic modulation of the electron collision frequency. A simple model is adopted for this disturbed region. The modulation transferred to an obliquely incident wanted wave that is reflected in or near it is investigated. The reflexion coefficient of the wanted wave is found by applying the phase integral method. The complex reflexion height of the wanted wave is a function of time in the modulation cycle. Results are discussed first for an isotropic ionosphere and are then extended to include the effect of the Earth’s magnetic field, and the calculation uses the Booker quartic equation. It is shown that the phase integral method is admirably suited to solve this kind of problem. Some examples are given to illustrate that the greatest amount of modulation is transferred when the wanted wave is reflected near the most disturbed part of the ionosphere. The relation of this to some observed effects near sunrise is discussed.

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The effect of a time varying collision frequency on a radio wave obliquely incident on the lower ionosphere

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1976.0037 ◽

1976 ◽

Vol 348 (1653) ◽

pp. 245-263 ◽

Cited By ~ 4

Keyword(s):

Radio Wave ◽

Collision Frequency ◽

Modulation Frequency ◽

Average Power ◽

Lower Ionosphere ◽

Angle Of Incidence ◽

Disturbed Region ◽

Quartic Equation ◽

Obliquely Incident ◽

Cross Modulation

The phenomenon of ionospheric cross-modulation occurs when a ‘wanted’ radio wave passes through a region of the ionospheric plasma where a powerful modulated ‘disturbing’ radio wave is strongly absorbed. Many previous studies have assumed that the wanted wave is vertically incident and, in some cases, that the ionosphere is isotropic. The theory is studied here for an obliquely incident wanted wave propagating through an anisotropic ionosphere. The Booker quartic equation is used to find the modulation transferred to the wanted wave, and how it depends on height, angle of incidence, azimuth and radio frequency. It is assumed that the disturbing wave has a sinusoidal amplitude modulation so that the collision frequency in the disturbed region varies periodically with the modulation frequency. The physical processes that occur in various situations are reviewed. It is found that many of the results from the simpler theories still apply, but some new effects are found. For example, there can be a marked difference in the modulation transferred to two ordinary (or two extraordinary) wanted waves with the same angle of incidence, one travelling obliquely upwards, and the other downwards through the disturbed region. It is found that an increase in the average power of the disturbing wave does not necessarily imply a corresponding increase in the modulation transferred to the wanted wave. The radio engineer who requires an accurate assessment of cross-modulation as a possible source of interference in communications could apply some methods of this paper with the aid of modern computers.

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Variation with electron velocity powers of electron collision frequency and energy transport coefficients in weakly ionised plasmas: Earth's lower ionosphere†

International Journal of Electronics ◽

10.1080/00207217208938380 ◽

1972 ◽

Vol 33 (4) ◽

pp. 447-456

Author(s):

V. N. SHARMA

Keyword(s):

Energy Transport ◽

Collision Frequency ◽

Transport Coefficients ◽

Lower Ionosphere ◽

Electron Velocity ◽

Electron Collision ◽

Electron Collision Frequency

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Reflexion levels and coupling regions in a horizontally stratified ionosphere

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1959.0014 ◽

1959 ◽

Vol 252 (1004) ◽

pp. 53-68 ◽

Cited By ~ 18

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.

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Effects of temperature and electron collision frequency on the elastic electron–ion collisions in a collisional plasma

Journal of Plasma Physics ◽

10.1017/s0022377813000056 ◽

2013 ◽

Vol 79 (5) ◽

pp. 553-558 ◽

Cited By ~ 2

Author(s):

YOUNG-DAE JUNG ◽

WOO-PYO HONG

Keyword(s):

Phase Shift ◽

Temperature Effect ◽

Cross Section ◽

Collision Frequency ◽

Electron Collision ◽

Elastic Electron ◽

Dynamic Temperature ◽

Electron Collision Frequency ◽

Dynamic Screening ◽

Ion Collision

AbstractThe effects of dynamic temperature and electron–electron collisions on the elastic electron–ion collision are investigated in a collisional plasma. The second-order eikonal analysis and the velocity-dependent screening length are employed to derive the eikonal phase shift and eikonal cross section as functions of collision energy, electron collision frequency, Debye length, impact parameter, and thermal energy. It is interesting to find out that the electron–electron collision effect would be vanished; however, the dynamic temperature effect is included in the first-order approximation. We have found that the dynamic temperature effect strongly enhances the eikonal phase shift as well as the eikonal cross section for electron–ion collision since the dynamic screening increases the effective shielding distance. In addition, the detailed characteristic behavior of the dynamic screening function is also discussed.

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