Polynomial Solutions of the Ion Velocity Distributions and the Calculation of Incoherent Scatter Spectra in the High-latitude Auroral Ionosphere

In order to describe accurately ion velocity distribution in the auroral ionosphere, the relaxation collision model and the Maxwell molecule collision model is used to describe ion-neutral collisions of Boltzmann equation respectively. The expressions of the ion velocity distribution for 13-moment approximation based on the Maxwell and for 16-moment approximation based on the bi-Maxwell can be obtained by solving the transport equations of the Maxwell molecule collision model and the relaxation collision model respectively. According to Sheffield's theories, the incoherent scatter spectra are calculated using the ion velocity distribution of 13-moment approximation and 16-moment approximation for the relaxation collision model and the Maxwell molecule collision model respectively. Finally, the comparison of results of the incoherent scatter spectra between Maxwell molecule collision model and relaxation collision model are given. It is found that, the Maxwell molecule collision model is better than the relaxation collision model to describe the interaction between ion and neutral component in the ionosphere E layer. The 16-moment approximation is better than 13-moment approximation to describe the ion temperature anisotropy due to increased electric field.