Two-dimensional plasma model for the arc-driven rail gun

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Abstract
A previously developed one-dimensional model for studying the fluid-mechanical electrodynamical properties of the plasma in an arc-driven rail gun is extended to two dimensions. The analysis includes deriving a set of general, time-dependent equations, the solution of which yields the associated properties of the arc. These equations are then solved under the assumptions that the flow variables are steady in a frame of reference which accelerates with the arc, and that the effect of the arc’s acceleration upon these variables can be neglected. Numerical calculations are carried out to analyze arcs in recent experiments. In addition to the numerical calculations, some approximate analytic solutions, which are applicable under certain limiting conditions, are also worked out. These limiting-case solutions are then used to derive a set of scaling relations which indicate how the arc properties vary with gun size, projectile mass, and acceleration characteristics. Considerable discussion of the assumptions and the results is given emphasizing particularly the physical reasons for the differences with previous one-dimensional calculations.