Calculation of magnetic fields and currents in axisymmetric systems of inductively coupled moving conductors

An algorithm for calculating magnetic fields and currents in axisymmetric systems of inductively coupled moving and stationary conductors is developed using a hybrid method which combines the finite and boundary element methods. The finite element method is used to approximate the unsteady diffusion equation for the $\theta$-component of the magnetic vector potential in the conductors, and the boundary-element method is employed to eliminate the space around the conductors. The proposed method takes into account the connections of the conductors with each other or with external energy sources by means of ideal electrical circuits with lumped parameters $R$, $L$, and $C$. An effective method is developed to take into account the external circuits by an appropriate modification of the mass matrix and the source vector of the obtained system of ordinary differential equations. Examples of using the method to calculate the fields of single- and multi-turn solenoids, magnetic flux concentrators, and induction accelerators with various methods of delivering external electromagnetic energy are considered. The high computational efficiency of the method is shown, in particular, for the case of constant electrothermal properties and sizes of the conductors.