Field line integration and localized modes in the equatorial spread F

The field line integrated Rayleigh‐Taylor and localized mode models of the equatorial spread F (ESF) are unified by a variational principle. Those modes which can be analyzed by taking local approximations in two dimensions are considered. It is shown that the field line integrated Rayleigh‐Taylor model can be interpreted as a one‐term Rayleigh‐Ritz approximation to the localized mode model of Basu and Coppi [1983]. In making this observation, the field line integration technique is generalized, so as to include the effects of the perturbation electric field parallel to the Earth's magnetic field. As additional terms are included into the Ritz sum, the growth rate found for ESF increases. At the smaller perpendicular wavelengths, localization of the electrostatic potential along the field line reduces the effects of E region loading.