Key Factors in Fluid Modelling of Plasmas and Swarms

In this paper we start with general fluid equations for both ions and electrons in neutral gases, obtained as velocity moments of Boltzmann's cquation. Two distinct approximations are required for these exact equations to be of allY practical use: 1. The collision transfer terms (right hand side of the fluid equations) must be approximated, and II. Some closure ansatz (hypothesis) is required for the "streaming terms" (left hand side of the fluid equations), to ensure that the number of equations corresponds to the number of unknowns. For step I, swarm (frce diffusion) limit results using, e.g., momentum transfer theory, may be taken over directly to low temperature plasmas, but step II remains problematic, with little guide from swarm physics, and serious doubts about existing assumptions in the plasma literature. We focus on electron fluid equations with closure at the level of momentum and energy balance, which requires an accurate heat flux ansatz in order to produce physically meaningful results. The crucial nature of this ansatz is illustrated using a simple benchmark calculation for infinite plane parallel geometry, where we show for the first time how periodic spatial structures (Franck-Hertz oscillations) may be generated from fluid equations