Theory of the initial radius of meteor trains

Abstract

During the thermalization process a meteor train expands very rapidly to an initial distribution, the extent of which one would expect, on general grounds, to scale as the inverse of the atmospheric density. Experimental determinations of the 'initial radius' r { , however, show a much weaker dependence with height than this implies. In a re-examination of the initial radius problem we have followed earlier workers in modelling the initial expansion by assuming the meteoric particles (ions or atoms) and atmospheric atoms to be elastic spheres. We have obtained an analytic result for r i? exact within the framework of the model, as the rms value of the radial positions of the particles. However, this value is sufficient to calculate the radar echo amphtude only if the profile is known to be Gaussian. To obtain more detailed results, therefore, we have simulated the expansion process in a computer calculation of the motion of 10 000 particles. The exact result for the rms value is important in enabling us to check the accuracy of this simulation. The calculation shows that the initial distribution is not Gaussian but has a core, with effective line density of the order of one-tenth of the total initial line density, and radius of the order of 0.4^, immersed in a more diffuse distribution. Experimental determinations of the initial radius have been based upon the assumption of a Gaussian initial distribution but, more generally, the experiments provide values of ratios of Fourier components of the ionization profile, and when the simulation is compared with experiment on this basis satisfactory agreement is obtained. As the time development of the train from its initial distribution is usually treated by assuming a Gaussian profile we have added a discussion of the diffusion process applicable to general initial distributions.