Improved Transport Equations for Fully Ionized Gases

Abstract

We have developed fluid transport equations for fully ionized gases that improve the description of Coulomb collisions. The aim has been to develop simple and versatile equations that can easily be implemented in numerical models and thus be applied to a large variety of space plasmas, while they still accurately describe thermal forces and energy flows in collision-dominated plasmas. Based on exact solutions to the Boltzmann equation in the collision-dominated limit, the correction term to the velocity distribution function that account for particle flows is assumed to be proportional to the third power of the velocity, leading to a near isotropic core distribution. Applying the fluid equations derived from this new velocity distribution to a collision-dominated electron-proton plasma with a small temperature gradient, the resulting electron heat flux, as well as the thermal force between electrons and protons, deviate less than 25% from the exact results of classical transport theory. The new equations predict a factor of 4 reduction in the thermal force acting on heavy, minor ions caused by an imposed heat flux, compared with fluid equations that are in common use today. The improved description of thermal forces is expected to be important for modeling the composition of stellar atmospheres.