Electric Centrelines and Magnetic Coupling of Superconducting Strands in Assemblies and Cables

Partial coupling or decoupling of superconducting strands in cables is a 3d phenomenon associated with finite conductor lengths or twist pitch. In contrast, 2d modelling of infinitely long strands by variational formulation of the critical state or flux diffusion of non-linear resistivity always results in full coupling even for completed isolated strands. Although 3d modelling of superconducting composites have been realised in various formulations, the computational complexity and cost have limited their application as routine tools for analysing the behaviour of practical conductors and interpreting experimental results. In the present study, we show that full or partial uncoupling of isolated infinite strands can be obtained by imposing within ever strands an electric centre where the current is zero. The net current in a strand determines the position of the electric centre and is a natural parameter for quantifying the strength of coupling. Incorporating electric centres with 2d models for infinite strands of the critical state or power-law non-linear resistivity can be realised by very efficient variational or Brandt's formulations respectively. We show that such 2d models are highly efficient and effective for analysing experimental data on ac losses of complex composite conductors such as Roebel cables of ReBCO tape strands. We show how the electric centres affect the field and current distributions of the 2d models and provide profound insights into the coupling behaviour which is fundamentally a 3d phenomenon. By showing its applicability to arbitrary strands assemblies in either self or applied fields as well both combined, the method is presented as new tool for designing and analysing high field magnets using HTS cables.