A METHOD FOR INTERPRETING THE DISPERSION CURVES OF WHISTLERS

Abstract

This paper considers how the dispersion curves of whistlers may be interpreted to provide information on the distribution of electron density with height in the outer atmosphere.The simpler inverse problem, that of computing the dispersion curve for a given distribution, is considered first. On the assumption of longitudinal propagation in a dipole magnetic field, the dispersion curve is derived in the form of an equation relating the product [Formula: see text] to the frequency f. The equation can be represented by a power series in f, which is useful for estimating departures from the elementary [Formula: see text] relationship at frequencies where these departures are small. The coefficient of fⁿ in this series is termed the ‘dispersion constant of order n’.The main problem is now treated, regarding the above equation as an integral equation determining the distribution of electron density along the path. This integral equation is solved in series, making use of the same power series in. The dispersion constant of order n is shown to be proportional to the nth moment of the distribution, suitably expressed and weighted. From the values of the moments it is possible to deduce both the initial geomagnetic latitude of the path and the distribution of electron density along it. When the observed dispersion curve is incomplete, so that only the dispersion constants of lower order can be measured, the method yields an approximation to the distribution.