Determination of Optimum Rails Dimensions in Railgun by Lagrange's Equations

One of the methods that are used for increasing accelerator force of projectile in the railgun is the increasing of inductance gradient. Essentially, the inductance gradient is determined by current density in rails and projectile. If we change geometry of the rail, the current density and inductance gradient will be changed. One of the factors that restricts variation domain of rails geometry is the tolerable current of rails. In this paper, we have obtained analytical formulas for the maximum current density and the inductance gradient in terms of rail dimensions using the results that have been obtained by 2-D finite-element method. By these formulas and Lagrange's optimization equations, we determined the optimum dimensions of rail. Tolerable current is bonded for Lagrange's equations.