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AMTEC systems have historically been operated with sodium as the working fluid, in large part because fabrication of beta”-alumina solid electrolyte (BASE) membranes has been substantially easier with sodium than with potassium or other alkali metals1. It has been anticipated that because potassium has a substantially higher vapor pressure for a given temperature, and because the best K-BASE conductivity falls only marginally below that for Na-BASE, potassium AMTEC cells could produce higher power at a given temperature or comparable power at a lower temperature than similar sodium cells. Operation at lower temperatures can reduce materials lifetime or compatibility problems, and for severely heat input constrained systems it could enhance efficiency by reducing parasitic thermal conduction losses. Recently K-BASE tubes have become available as a commercial product2 and conventional experiments to evaluate the performance of complete KAMTEC cells have become much more feasible.

A linear model to predict the dynamics of a free-piston Vuilleumier machine will be presented. The model is based on the linear analysis of free-piston Stirling engines by Berchowitz /4/, where both the motion of the casing and the viscous coupling between the displacers are considered. Closed-form solutions are derived for the frequency, the phase angle and the amplitude ratio. In order to determine the accuracy of the results, they will be compared to the experimental data of a prototype.