Revised formulation of the kinetic plasma theory†

Abstract

Using the Maxwellian macroscopic approach and analysing the formulation of the dielectric constant, it is shown that the concept of energy has not been properly incorporated into the current kinetic plasma theory. The difficulties are due to the Boltzmann collisional term (∂F/∂t)_coll which accounts for a change in the velocity distribution due to collisions alone. If one attempts to rephrase the Boltzmann-Vlasov theory in terms of the Maxwcllian macroscopic formulation, one obtains an expression for energy which is not consistent with the meaning of this concept in generalized dynamics. In a revised version developed in this analysis the Boltzmann collisional term has been eliminated and an appropriate collisional operator is introduced which is believed to describe more adequately collisional processes in a plasma. It is assumed that the collisional operator can be applied directly to the electrical intensity of the field interacting with the plasma and is effective in transforming the intensity in a collisionless plasma into a corresponding intensity in a collisional plasma. At the same time the relationship between the electron velocity distribution function and the field intensity is considered to be the same, whether there are collisions or not. In other words, not only a collisionless but also a collisional plasma are assumed to be controlled by a Vlasov type mechanism which does not take into account explicitly the Boltzmann term (∂F/∂t)_coll.