Abstract. New characteristics of O⁺ ion velocity distribution functions in a background of atomic oxygen neutrals subjected to intense external electromagnetic forces are presented. The one dimensional (1-D) distribution function along the magnetic field displays a core-halo shape which can be accurately fitted by a two Maxwellian model. The Maxwellian shape of the 1-D distribution function around a polar angle of 21 ± 1° from the magnetic field direction is confirmed, taking into account the accuracy of the Monte Carlo simulations. For the first time, the transition of the O⁺ 1-D distribution function from a core halo shape along the magnetic field direction to the well-known toroidal shape at large polar angles, through the Maxwellian shape at polar angle of 21 ± 1° is properly explained from a generic functional of the velocity moments at order 2 and 4.