Auroral ion velocity distribution function: The Boltzmann model revisited

The velocity distribution of ion populations is calculated for auroral conditions where strong convection electric fields exist. The Boltzmann equation has been solved for the E and F regions of the ionosphere where plasma is weakly dense, weakly ionized and where the ion-neutral collision frequency is small in regard to the ion cyclotron frequency. The ion distribution function has been expanded in a generalized orthogonal polynomial series about a bi-Maxwellian “temperature” varying weight function. This generalized Grad solution expansion enables us to obtain good approximations for electric field strengths as large as 75 mV m^?1 and 115 mV m^?1 respectively, for both the resonant charge exchange and the polarization collision models. The instability threshold of these distribution functions appears to be higher than the two respective electric field strengths considered above.