Time-Varying Inductance Gradient in Rails Based on Geometric Mean Distance

The inductance gradient is one of the most critical parameters in the electromagnetic rail launcher (ERL). It determines the electromagnetic force and efficiency in the ERL. In general, the inductance gradient in the rails is treated as a constant. However, the inductance gradient in the rails changes dynamically during the launching process. It is very important for the electromagnetic driving force in the launching process to accurately solve the time-varying inductance gradient. For this reason, a method for establishing the analytical calculation of the time-varying inductance gradient is proposed in this article. The results show that the application conditions of the proposed method are ( $s/w>2$ and $s/h>1$ ), and the shortest side length of the rail must be greater than 20 mm. At last, in order to verify the applicability of this method, the inductance gradients in five different ERLs injected with the pulse current are calculated and the results obtained are compared with the FEA. The research shows that the inductance gradient in the initial stage changes significantly due to the rapidly changing current frequency. After an interval, it tends to be a constant, which is the result of the stabilization of the current. It is consistent with the results reported in the literature. And if the rail dimensions meet the applicable conditions, the maximum error between the method in this article and the FEA is less than 5%.