Mean field correction for ions in kinetic equations

Summary form only given. The kinetics of a system composed of charged particles may be described by an approximate method where a corresponding mean electric field created by the particles is used in place of the actual binary interaction. This assumption provides a self consistent approach and it is usually done in some particular systems of ions where the electric field is the most important one. However, a system composed of interacting particles does not preserve either the energy or the angular momentum distribution, since the collisions redistribute the energy and angular momentum configurations until the equilibrium is reached. For these systems the well known Boltzmann equation, which has a collision term, may be used if the particles interact through a short range potential. In ion dynamics Coulomb collisions are in general the most import kind of interaction. The Coulomb collision is a long range interaction in the sense that it does not have a finite cross section, thus the Boltzmann Equation conditions are not satisfied and it is not possible to introduce such an interaction in the usual one body kinetic equation. This work proposes a novel form to deal with Coulomb collisions in ion dynamics beyond the mean field approach using an effective interaction which provides a correction to the mean electric field. Based on this effective Coulomb interaction, which is a short range interaction, the relation among the impact parameter and the deviation angle during a scattering process is calculated. This relation provides a suitable expression for defining the collision operator of the Boltzmann Equation since it allows relating the velocities of the particles before collision with the outgoing velocities given the energy of the particles, the impact parameter and the range of the interaction. The cross section for the short range effective Coulomb interaction is calculated and analyzed. Results for the effective Coulomb interaction are illustrated by the devi- tion angle in deuteron-deuteron collision for some characteristic conditions found in Inertial Electrostatic Confinement devices (IEC). This equipment is used to confine high energy ions, such as deuteron and triton, in order to produce fusion reaction. Now is underway a study to use the effective interaction together with the Boltzmann Equation to describe the time evolution of the energy and angular momentum distribution of ions in an IEC device.