Equilibrium lengths of railgun plasma armatures

Recent data have shown that the length of railgun plasma armatures increases with bore size. The mechanisms for plasma growth and mass loss are treated analytically through a simple thermodynamic model in which mass is added through ablation of bore materials and lost through friction. It is assumed that at the bore wall, a thin boundary layer is formed in the plasma in which the velocity is sufficiently slow that the boundary layer is left behind the bulk of the plasma. Using the scaling relations of J.D. Powell and J. Batteh (1983), a functional relationship between the plasma length l_p and bore height h of the form l_p=kh^α, where α≃0.68. Using the model developed in the present work, a linear relationship between l_p and h is derived, but the proportionality factor depends on temperature, plasma conductivity, velocity, and boundary-layer thickness. Predictions of the model are interpreted in the light of available data. The model is shown to predict lengths which are in reasonable agreement with the observed data