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New characteristics of O<sup>+</sup> ion velocity distribution functions in a background of atomicoxygen neutrals subjected to intense external electromagnetic forces arepresented. The one dimensional (1-D) distribution function along the magneticfield displays a core-halo shape which can be accurately fitted by a twoMaxwellian model. The Maxwellian shape of the 1-D distribution function around apolar angle of 21 ± 1° from the magnetic field directionis confirmed, taking into account the accuracy of the Monte Carlo simulations.For the first time, the transition of the O<sup>+</sup> 1-Ddistribution function from a core halo shape along the magnetic field directionto the well-known toroidal shape at large polar angles, through the Maxwellianshape at polar angle of 21 ± 1° is properly explainedfrom a generic functional of the velocity moments at order 2 and 4

The auroral O&lt;sup&gt;+&lt;/sup&gt; non-Maxwellian velocity distribution function revisited

The auroral O<sup>+</sup> non-Maxwellian velocity distribution function revisited