Coupling between the F-region and protonosphere: Numerical solution of the time-dependent equations

This paper describes a new method of solution of the time-dependent continuity and momentum equations for H⁺ and O⁺ in mid-latitude magnetic field tubes from the F-region to the equator. For each ion the equations are expressed as an integro-differential equation. This equation is treated as an ordinary differential equation and solved by a searching method. By means of this method, the distribution of H⁺ in the O⁺?H⁺ transition region and the protonosphere can be investigated and the influence of H⁺ fluxes on the F layer examined.As an example of application of the method a suggestion by Park (1971) about observed night-time enhancements of N_mF2 is examined. He suggested that lowering of the F layer some hours after a magnetic substorm may cause N_mF2 to increase because of increased ion influx from the protonosphere. In the present calculations the Flayer is maintained around a constant height for some time and then abruptly lowered. Under the conditions adopted the resulting increase in downward H⁺ flux is sufficient to maintain N_mF2 against the increased recombination but not to increase N_mF2 significantly. It is emphasised that these results are not conclusive.