Non-Maxwellian velocity distribution functions and incoherent scattering of radar waves in the auroral ionosphere

For studies or the high latitude ionosphere it is important to calculate the effect of convection electric fields on the velocity distribution functions. At an altitude where the plasma is weakly ionized, the appropriate Boltzmann equation is solved in the spatial homogeneous case. We discuss the characteristics of the ion non-equilibrium steady state reached for large electric fields, from the macroscopic point of view. From the microscopic point of view, we show that the Grad expansion fails to converge rapidly for large electric fields. Generalized polynomial expansions are developed for different models of ion-neutral interactions. The consequences of these non-Maxwellian ion distribution functions on radar waves are presented and erroneous interpretations of measurements are discussed.