Using 3D finite element method (FEM) modelling, the present work investigates the coupling effect between two finite superconductors through a resistive matrix. This effect, related to the finite length of the conductors, is typically three-dimensional and cannot be analysed by the widely utilized 2D models. Superconductors are modelled with the nonlinear power-law E = E c (J /J c ) n , which has been implemented in the FEM software. The main focus is to demonstrate the feasibility of such calculations and to establish the correlation between the coupling effect and the aspect ratio of the conductor cross-section, in order to extend the existing theory, which is only precise for superconductors of infinite slabs, fully penetrated by the magnetic field. The effect of other parameters such as the conductor length and the gap between the superconducting filaments is also considered. The latter is a parameter which does not feature in the approximate theories.

An integral formulation based on the stream function of sheet currents is applied to finite length superconductors to model the coupling through a normal matrix. This formulation is an extension of Brandt’s 2D formulation for modelling a 3D problem. Thin discs and infinite slabs were studied and the critical was obtained as a function of applied field. While an excellent agreement for fully penetrated infinite slabs was found with existing theories, original results are presented for partially penetrated slabs as well as for thin discs in a wide range of applied fields.