Scaling laws for plasma armatures in railguns

A methodology for deriving the electrical and thermodynamic properties of plasma armatures in railgun launchers is presented. The methodology is based on the solution to the one-dimensional, quasi-steady equations for the plasma armature. It is shown that the thermodynamic and transport properties for typical armature materials can be adequately represented by power-law curve fits in the temperature and pressure regimes of interest. To illustrate the methodology, detailed computations for both copper and aluminum armatures are performed. Some discussion is also presented for hydrogen armatures. It is shown that the armature properties predicted by the scaling laws agree very well with those derived from more detailed numerical solutions to the governing differential equations. It is shown that, for both aluminum and copper armatures, the electrical conductivity is a strong function of the current per unit rail height and a weak function of launcher geometry. This dependence is shown to be in reasonable agreement with experimental data compiled over a wide range of gun bore dimensions and operating conditions