Power series solution of the F2-layer diffusion equation

Abstract

If the equatorial electron density profile in the region is known, the equilibrium electron density everywhere else can in theory be computed. A method is given for carrying out this process for regions within 30° of latitude of the dip equator for an exponential atmosphere of constant scale height and for symmetry about the dip equator. This is achieved by simplifying the diffusion equation for an isothermal atmosphere, then expanding in a power series, convergent at great height and whose coefficients are functions of latitude. The method is applied to a study of the distributions of electron density expected from an equatorial profile with a single maximum, similar to a Chapman profile. Attention is confined to the case of no production and loss, with an upward electrodynamic drift at right angles to the magnetic field lines and uniform at the dip equator. The results are of interest in connexion with the electron density at great height in the F2-layer, and illuminate the nature of the diffusion equation. The electrodynamic drift causes the latitudinal peaks in electron density at constant height to move in towards the dip equator, and a concentration of ionization at low heights closer to the dip equator. It is suggested by analogy with a straight field line model that in fact the electron density becomes infinite at infinitely low heights in this region of concentration, corresponding to a distribution of sources there. Thus an equilibrium layer, in absence of production and loss must be supported from below.