Conformal mapping calculation of railgun skin inductance

The common rail arrangement consisting of two long, parallel, rectangular rails is discussed. The authors calculate the inductance per unit length L´ in the short flight time limit where the skin depth is much smaller than any rail dimensions, the current is all on the rail surface, and the magnetic field does not penetrate the rails. The solution given is based on the Schwartz-Christoffel transformation that maps the boundaries of the problem into a simpler shape