Current and magnetic field distribution in finite superconducting cables

The general diffusion equation for the magnetic field penetration into cables is used to find the solutions for the induced currents in the strands of finite cables in the low frequency limit. The homogeneous magnetic field is applied on the whole cable length l. These results are compared with the properties of infinite cables in the same homogeneous applied magnetic field. The current distribution in the strands close to the central part of the cable is strongly influenced by the total length of the cable, l. On the other hand, the current distribution in a large part of the cable is nearly the same as that close to the ends, determined by the boundary condition of zero current at the ends. The maximum amplitude of the induced currents in finite cables is two times higher than that in the infinite one. This enhancement of the induced current, decreasing the critical current of the cable, can be important for the stability of some magnets. The magnetic field due to the induced currents is also changing strongly along the cable axis, nearly periodically with the period of the cabling pitch. Therefore, the measurements of the local magnetic induction or local magnetic moment can lead to misinterpretation of the magnetic flux distribution and the electromagnetic properties of the cables. To avoid this, one should always perform some measurements of these quantities also at different positions along the axial direction of the cable. (author)