I. Theory of radio reflections from meteor trails: I

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Abstract
This paper deals with the evaluation of the reflection coefficient for backward scattering of an electromagnetic wave from a column of ionization having cylindrical symmetry. The application of the theory to meteors thus depends on the assumption that a meteor instantaneously forms a narrow column of ionization which subsequently diffuses radially. The theory predicts two qualitatively different categories of meteor echoes, depending on whether the electron line density, α, is greater or less than about 1012 per cm, the properties of which may be summarized as follows: If the incident electric vector is parallel to the axis of the trail (parallel scattering) it is sufficient to assume that the electrons scatter coherently and independently, each contributing an amount 4π(e 2/mc 2)2 to the backward scattering cross section. As the column expands radially, the echo amplitude decreases, the form of decay being exponential if the electron density is a Gaussian function of radius. When the incident electric vector is normal to the column (transverse scattering) the echo amplitude differs from the above in that the reflection coefficient may pass through a resonance, followed by the exponential decay. The magnitude of the resonance (measured as the ratio of the resonant reflection coefficient to that for parallel scattering) depends mainly on the diffuseness of the column (i.e. on the gradient of electron density at the radius of critical density). It has been evaluated for an electron density varying with radius as n=n 0 exp [-(r/r o) s ] and is found to range from 2.0 when s=2 (Gaussian distribution) to 10 when s=20. The echo amplitude in both cases is proportional to α, while the echo duration is independent of α. The short duration echoes which form the bulk of the experimemtal observations appear to have the above forms. In this case the column is expected to reflect similarly to a metallic cylinder. Except initially, when the parallel reflection coefficient exceeds the transverse, the reflection coefficients are equal and substantially constant. The duration is approximately proportional to α, and the peak echo amplitude is a slowly increasing function of α (˜1/4). These predictions are in agreement with the experimental data on long duration echoes. Some particular electron distributions, including a small diffuse sphered which exhibit multipole resonant scattering are discussed in Appendix II, and laboratory experiments which may be of some interest are suggested.

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