Role of the mirror force on the collision rate due to relativistic electron precipitation

We numerically evaluate the role of the mirror force on the collision rate due to the relativistic electron precipitation into the ionosphere. We compute the motion of individual precipitating electrons with the mirror force, considering collisions with neutral gas by the Monte Carlo method. We examine the effect of the mirror force on the altitude profile of the ionization rate by comparing the results with those without the mirror force. Simulation results demonstrate that larger kinetic energy lowers the altitude profiles of the collision rate, which is consistent with previous studies. The simulation results also show 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. Electrons with kinetic energies above 100 keV form a secondary peak of the collision rate near the mirror point. The formation of the secondary peak can be explained by the stagnation of electrons around the mirror point 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.