Radio frequency scattering from a heated ionospheric volume: 3, Cross section calculations

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Abstract
The proper normalization procedure for determining per‐unit‐volume properties of aspect‐sensitive scattering media from experimental measurements is discussed. This is complicated by the fact that, because of the aspect sensitivity, it is not clear a priori what the per‐pulse scattering volume actually is. In general, the correct normalization requires quantitative knowledge of the aspect sensitivity which may not be possible to determine because of fundamental limitations imposed by the spatial‐resolution capability of the measurement system on the extent to which this property of the scattering medium can actually be determined. The identical problem exists in radio‐auroral measurements. This problem is considered here, and an exact expression from which the desired per‐unit‐volume quantities of interest can be obtained from measurements is given. It is shown that proper choice of the experimental parameters leads to a simplification whereby the normalization can be carried out without knowledge of the aspect sensitivity being necessary. The results are applied to calculating from experimental data the per‐unit‐volume scattering properties of a heated ionospheric volume as a function of frequency, from which a transverse scale size for the scattering medium of 3 m is estimated. For these experiments, under maximum heating conditions, a representative value of 1% for the rms fractional electron density deviation is calculated; an upper bound is also established, showing that values as large as 4 or 5% were probably never achieved. It is shown that, for an electron density distribution axially symmetric with respect to the geomagnetic field, B, the cross section for backscatter within a plane containing B uniquely determines the cross section for bistatic scattering axially around B. Experimental results for small axial‐bistatic angles are presented showing good agreement between calculated and measured values.