A Detailed Electron Fluid Model
Overview
In simulating the plumes of Hall thrusters, a hybrid approach of treating ions and neutral atoms as particles and the electrons as a fluid is used. Typically the fluid electrons are treated with the Boltzmann relation. However, in this approach, the electrons are modeled using the full electron mass, momentum, and energy conservation equations.
The Boltzmann model  The detailed model  
The Boltzmann model assumes the electrons are isothermal, collisionless, and unmagnetized as well as assuming their pressure follows the ideal gas law. The relation used is then 
The detailed model uses the full electron mass, momentum, and energy conservation equations. They are as follows 

ResultsThe model has been set up for a BHT200 Hall thruster for which several experimental results are available. One of the main differences that arise between the two models is the magnitude of the gradient in electric potential and electron temperature. In particular, the increased potential drop seen in the detailed model leads to a greater acceleration region outside the thruster, thus affecting other properties as well. The Boltzmann ion energy distribution is represented to a fair degree by both models, though it should be noted that the ion exit velocity needed to be increased to about 17 m/s from 13 m/s to achieve this with the Boltzmann model. LIF data shows that the exit velocities are much closer to 13 m/s which is used by the detailed model. Overall, then, it can be seen that the detailed model does offer improvements over the simpler Boltzmann electron fluid model. The cost comes, of course, in computational time. For these simulations, the Boltzmann model ran for roughly 2 hours on a desktop computer while the detailed model required nearly 4 hours. 
Recent Publications
Cai, C. and Boyd, I. D. 3D Simulation of Plume Flows from a Cluster of Plasma Thrusters AIAA20054662, Presented at the 36th AIAA Plasmadynamics and Lasers Conference, June 2005, Toronto, Canada.
Boyd, I. D. and Yim, J. T. Hall Thruster Plume Simulation Using a Detailed Hybrid Model. AIAA20043952, Presented at the 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 2004, Ft. Lauderdale, FL.
Boyd, I. D. and Yim, J. T. Modeling of the near field plume of a Hall thruster. Journal of Applied Physics, May 2004, v.95 i.9 pp.45754584.