Effective Length Average Height and Radius of Meteor Trails
Consider the ray geometry for a meteor burst propagation path as shown in Figure 13.7 between transmitter T and receiver R. P represents the tangent point and P' a point further along the trail such that (R1 + R'2) exceeds (R1 + R2) by half a wavelength. Thus PP' (of length L) lies within the principal Fresnel zone and the total length of the trail within this zone is 2L. Provided R1 and R2 are much greater than L, it follows that
XRi R 2
where p = angle of incidence
ยก5 = angle between the trail axis and the plane of propagation A = wavelength
In order to evaluate the scattering cross section of the trail it is usual to assume that ambipolar diffusion causes the radial density of electrons to have a Gaussian distribution and that the volume density is reduced while the line density remains constant. These assumptions lead to an equation for the volume density Nv in electrons per cubic meter as a function of radius r and time from the instant of formation t, which is
where q = electron line density per meter
D = ambipolar diffusion coefficient in m2/s r0 = initial radius of trail in meters
Both D and r0 are marked functions of height. From experimental results the following empirical formula for evaluating the average height of trails, which is a function of frequency, can be derived:
where h = average trail height (km) f = wave frequency (MHz)
The average trail height is a function of other system parameters in addition to frequency. However, equation (13.4) is a good approximation.
* This section is adapted from CCIR Rep. 251-5 (Ref. 4).
Various empirical relationships have been derived between the initial trail radius and the meteor height. An average expression is log r0 = 0.035h - 3.45 (13.5)
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