Whistler inversion by spectral expansion

Abstract

A method has been developed for the inversion of the integral equation connecting whistler propagation times with the distribution of electrons along the propagation path. The path is taken to be a geomagnetic dipole field line, but the method assumes no model for the field aligned distribution of electrons. The calculation is based on the Backus-Gilbert technique ( gilbert, 1971; parker, 1977) and represents the electron density distribution as a sum of orthogonal functions, the coefficients of which are computed from the time delays measured on the whistler trace at a series of frequencies. The application of this method to synthetic and observed whistlers has demonstrated the feasibility of obtaining magnetosphere electron densities. At the same time it is found that some of the approximations of conventional whistler analysis (omission of ionic effects and a term of +1 from the phase refractive index) are inadequate and lead to certain difficulties in the inversion of higher latitude ( L ≥3) measured whistlers.