Calculation of interstrand coupling losses in superconducting Rutherford cables with a continuum model

Rutherford cables for particle accelerator magnets are subjected to time dependent magnetic fields during the typical accelerator operating cycle, which in turn induce coupling currents flowing in the loops formed at the contacts between different strands. An analysis of the magnitude and losses associated with these coupling currents is relevant to the design of field quality and cryogenic heat loads. The models reported in the literature exhibit some limits related to computational burden when applied to the analysis of interstrand coupling currents for real cable geometries, and conceptual limits when trying to couple different physical simulations. To solve this problem, a continuum model of Rutherford cables was improved to account for the non-uniform contact conductances between the strands along the cable length, also developing a novel strategy for the computation of the induced voltages. Thanks to these features we attain the required level of detail in the description of the short-range interstrand currents, which could not be properly computed with earlier versions of the continuum model. The model was validated by comparison with analytical results available in the literature for simplified case studies with uniform magnetic field applied orthogonal to the cable. Examples of current and loss distributions are presented in the paper, to prove the potential of the model to analyze Rutherford cables of any configuration. A study regarding the proper choice of the boundary conditions of the problem is presented, which suggests the need for experimental investigation on the actual distribution of currents and losses in the long cable lengths used in accelerator magnets.