Abstract. A new theoretical model of the Earth’s low- and mid-latitude ionosphere and plasmasphere has been developed. The new model uses a new method in ionospheric and plasmaspheric simulations which is a combination of the Eulerian and Lagrangian approaches in model simulations. The electron and ion continuity and energy equations are solved in a Lagrangian frame of reference which moves with an individual parcel of plasma with the local plasma drift velocity perpendicular to the magnetic and electric fields. As a result, only the time-dependent, one-dimension electron and ion continuity and energy equations are solved in this Lagrangian frame of reference. The new method makes use of an Eulerian computational grid which is fixed in space co-ordinates and chooses the set of the plasma parcels at every time step, so that all the plasma parcels arrive at points which are located between grid lines of the regularly spaced Eulerian computational grid at the next time step. The solution values of electron and ion densities Ne and Ni and temperatures Te and Ti at the Eulerian computational grid are obtained by interpolation. Equations which determine the trajectory of the ionospheric plasma perpendicular to magnetic field lines and take into account that magnetic field lines are "frozen" in the ionospheric plasma are derived and included in the new model. We have presented a comparison between the modeled NmF2 and hmF2 and NmF2 and hmF2 which were observed at the anomaly crest and close to the geomagnetic equator simultaneously by the Huancayo, Chiclayo, Talara, Bogota, Panama, and Puerto Rico ionospheric sounders during the 7 October 1957 geomagnetically quiet time period at solar maximum. The model calculations show that there is a need to revise the model local time dependence of the equatorial upward E × B drift velocity given by Scherliess and Fejer (1999) at solar maximum during quiet daytime equinox conditions. Uncertainties in the calculated Ni , Ne , Te , and Ti resulting from the difference between the NRLMSISE-00 and MSIS-86 neutral temperatures and densities and from the difference between the EUV97 and EUVAC solar fluxes are evaluated. The decrease in the NRLMSISE-00 model [O]/[N₂] ratio by a factor of 1.7–2.1 from 16:12 UT to 23:12 UT on 7 October brings the modeled and measured NmF2 and hmF2 into satisfactory agreement. It is shown that the daytime peak values in Te , and Ti above the ionosonde stations result from the daytime peak in the neutral temperature. Our calculations show that the value of Te at F2-region altitudes becomes almost independent of the electron heat flow along the magnetic field line above the Huancayo, Chiclayo, and Talara ionosonde stations, because the near-horizontal magnetic field inhibits the heat flow of electrons. The increase in geomagnetic latitude leads to the increase in the effects of the electron heat flow along the magnetic field line on Te . It is found that at sunrise, there is a rapid heating of the ambient electrons by photoelectrons and the difference between the electron and neutral temperatures could be increased because nighttime electron densities are less than those by day, and the electron cooling during morning conditions is less than that by day. This expands the altitude region at which the ion temperature is less than the electron temperature near the equator and leads to the sunrise electron temperature peaks at hmF2 altitudes above the ionosonde stations. After the abrupt increase at sunrise, the value of Te decreases, owing to the increasing electron density due to the increase in the cooling rate of thermal electrons and due to the decrease in the relative role of the electron heat flow along the magnetic field line in comparison with cooling of thermal electrons. These physical processes lead to the creation of sunrise electron temperature peaks which are calculated above the ionosonde stations at hmF2 altitudes. We found that the main cooling rates of thermal electrons are electron-ion Coulomb collisions, vibrational excitation of N₂ and O₂, and rotational excitation of N₂. It is shown that the increase in the loss rate of O⁺(⁴S) ions due to the vibrational excited N₂ and O₂ leads to the decrease in the calculated NmF2 by a factor of 1.06–1.44 and to the increase in the calculated hmF2, up to the maximum value of 32 km in the low-latitude ionosphere between –30 and +30° of the geomagnetic latitude. Inclusion of vibrationally excited N₂ and O₂ brings the model and data into better agreement.

Key words. Ionosphere (equatorial ionosphere; electric fields and currents, plasma temperature and density; ion chemistry and composition; ionosphere-atmosphere interactions; modeling and forecasting)