Long range collision effects for drifting velocity distributions

The interparticle force acting during a binary encounter is usually modeled by a potential of the inverse power law form. The influence of one particle on the other decays with distance and here the effects felt around the so called cutoff distance are considered. Attention is given to the Fokker–Planck model in generalized and restricted forms to describe the collisional consequences of this sort of interaction. Particular emphasis is placed on the peculiar details of the Coulomb collision theory overlooked in earlier works on this matter as: (a) the form of the collision term, (b) the definition of the Coulomb logarithm and (c) the value of the effective cross section. Only the long range effects are focused. To combine close and long ranges into a unique collision term the cross section corresponding to each range must be added. The classical use of the same expression for the cross section in both ranges is shown to be inappropriate. The proposed approach is valid regardless the form of the distribution function, on the magnitude of the flow velocity, besides being applicable to other types of interparticle forces as Maxwell molecule interactions. The material is relevant for solar plasma, interplanetary transport and planetary magnetosphere studies.