Abstract
Ray paths are computed for waves refracted by meteor trails having a Gaussian radial distribution of ionization density. From the spreading of initially parallel rays as they pass through the trail, a measure of reflected signal intensity vs. scattering angle is obtained; the results are presented in polar scattering diagrams, valid in the limit of large trail size. Equivalence theorems are derived relating both intensity and scattering angle for rays incident upon the trail at an arbitrary angle to the intensity and scattering angle for rays incident in the plane normal to the trail. Curves are presented showing the dependence of echo duration on forward-scatter-angle with trail orientation as parameter; it is found that the sec 2 φ law developed for under-dense trails applies to over-dense trails only if the plane of propagation contains the trail axis. If not, the effective secant exponent may be as small as 0·3. The theory is compared with McKinley and McNamara's duration measurements. It is found that although the general agreement is satisfactory, the details of their experimental results depend on the way that winds change the trail orientation. The ray theory is also compared with Keitel's wave theory solution. Unfortunately, he could not get wave solutions for dense trails of age greater than 0·357 per cent of the minimum echo duration. Even so, the ray solutions agree with Keitel's results for scatter angles up to 155°, thus including all angles available to ground-based stations.
Published Version
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