“…Other studies have considered the collisionless plasma outflows in the polar wind and auroral regions and have included the effect of wave-particle interactions. These studies have replaced the Fokker-Planck collision term in the Boltzmann equation by the effect of wave-particle interactions (e.g., Retterer et al, 1987Retterer et al, , 1994Crew et al, 1990;Barghouthi et al, 1998Barghouthi et al, , 2007Barghouthi et al, , 2008; Barghouthi and Atout, 2006;Barghouthi, 1997Barghouthi, , 2008Bouhram et al, 2003aBouhram et al, , b, 2004. In these studies the ion motion was followed along geomagnetic field lines under the effects of external forces (gravity and polarization electric field) and the interactions between the ion and the electromagnetic waves observed in those regions.…”