General 2D equation for coupling currents in a flat superconducting cable subjected to a time-dependent magnetic field in the face-on orientation

An equation for inter-strand coupling currents induced in a finite piece of flat superconducting cable by the time-dependent magnetic field directed perpendicular to the cable wide surface is derived. Analytical solution of this equation demonstrates longitudinal periodic oscillations in the stationary inter-strand currents. Oscillations are absent only if the sample length coincides with an integer number of cable twist pitches. Due to the boundary influence, stationary strand currents at any sample length are never exactly the same as specified by the uniform solution. Numerical calculations for the harmonically oscillating external magnetic field have been performed and the dependence of the loss per cycle per twist pitch on frequency was obtained. Relation between the loss and the sample length is discussed.