We study the effect of the mirror force on the collision rate due to the energetic electron precipitation into the ionosphere. We solve the motion of individual precipitating electrons with the mirror force, where collisions with neutral gas are computed by the Monte Carlo method. By comparing the results with those without the mirror force, we examine the effect of the mirror force on the altitude profile of the ionization rate. First, we carry out simulations of mono-energetic precipitation of 3 keV electrons whose initial pitch angle is 70 degrees at 400 km at L = 6.45. We find that the collision rate peaks at around 120 km altitude and that the duration of the collision is scattered in time with a delay of about 5 ms compared with the result without mirror force. Next, we perform mono-energetic precipitation of the different energy and pitch angle ranges. Simulation results demonstrate that larger kinetic energy lowers the altitude profiles of the collision rate, consistent with previous studies. We also find that the upward motion of electrons bounced back from their mirror points results in the upward broadening of the altitude profile of the collision rate. Simulation results for electrons with kinetic energies above 100 keV show that a secondary peak of the collision rate is formed near the mirror point. The formation of the secondary peak can be explained by the stagnation of electrons around the mirror point at 130 km altitude, because the relatively long duration of staying in neutral gas increases the number of collisions. Simulation results show that under the precipitation of electrons in the kinetic energy range larger than tens of keV with the pitch angle close to the loss cone, the maximum collision rate in the altitude range lower than 100 km becomes one order of the magnitude smaller. The results of the present study suggest the importance of the mirror force for the precise modeling of ionospheric response due to the energetic electron precipitation caused by the pitch angle scattering through wave–particle interactions. Graphical Abstract

We study the effect of the mirror force on the collision rate due to the energetic electron precipitation into the ionosphere. We develop a simulation code for the motion of energetic electrons with the mirror force to solve the variation of the pitch angle of electrons during their precipitation. In this code, a module computing the collision between precipitating energetic electrons and neutral gas using the Monte Carlo method is employed. By combining the developed modules, altitude profiles of the collision rate due to energetic electron precipitation in the keV energy range are investigated, and the effect of the mirror force acting on precipitating electrons is examined. The simulation results show that the influence of the mirror force on the altitude profile of the collision rate is significant for electrons with a high initial pitch angle, corresponding to the pitch angle close to the loss cone. The effect of the mirror force results in the broadening of the altitude profile of the collision upward due to the reflection of mirroring electrons. Simulation results for energetic electrons with kinetic energies above 100 keV show that a secondary peak near the mirror point is formed in the altitude profile of the collision rate. The formation of the secondary peak can be explained by the stagnation of electrons around the mirror point. The relatively long duration staying in neutral gas results in the increase of the collision rate around the mirror point, against the smaller collision cross-section in the higher energy range. Simulation results reveal that the maximum collision rate in the altitude range lower than 100 km becomes one order of magnitude smaller if electrons in the kinetic energy range larger than tens of keV precipitate with the pitch angle close to the loss cone. The results of the present study emphasize the importance of the mirror force for the precise modeling of ionospheric response due to the energetic electron precipitation.