The effect of X-ray radiation from a solar flare on the frequencies of Schumann resonances

In this paper, a theoretical model of the effect of X-ray radiation from a solar flare on the Earth's ionosphere and on the Schumann resonance frequencies in the Earth-ionosphere waveguide has been constructed. A flat transient flux of X-ray photons incident on the Earth is considered. By making the assumption that the absorption coefficient of photon energy depends on their energy and air density, the air ionization rate under the action of X-ray radiation is found as a function of altitude. Changes in the number densities of electrons and ions are described by a set of differential equations, which take into account the rate of production and recombination of particles, as well as the attachment of electrons to neutral molecules. The altitude profiles of all reaction constants, as well as the mobility of electrons and ions, are approximated using tabular data. The solution of these equations is used to calculate changes in ionospheric conductivity caused by X-rays from a solar flare. A case study of X6.9-class solar flare effect on the ionosphere is being studied, although the variability of model parameters could affect the simulation results. The changes in conductivity influence on the penetration depth of the low-frequency electromagnetic field into the conducting ionosphere, which results in a slight increase in the frequencies of the Schumann resonances. The theory explains the relationship between the intensity of X-ray radiation and the change in the weighted average frequency of Schumann resonances, which was observed for a number of solar flares of various classes.