Sources and resultant radiations of extremely low frequency (ELF) electromagnetic waves can be effectively generated via modulated heating of the ionosphere by powerful high-frequency (HF) waves. With fundamental equations of magneto-hydrodynamics

the radiation field of the ELF radiation source in the ionosphere is derived. The dispersion relation of ELF waves propagating in the ionosphere is then obtained and the downward propagation attenuation model is established. According to this model

the differences of propagation attenuation in distinct latitudes and influences of transmitting frequency and ambient ionospheric parameters on propagation attenuation are analyzed. It is shown that the relative attenuation rate is raised with increase of the geomagnetic inclination and firstly rises and then falls with increase of the transmission frequency

resulting in an optimal transmission frequency value at which the relative attenuation rate reaches minimum. With enhancement of electron density or electron temperature

the relative attenuation rate rises and its growth rate drops.