A possible explanation of the problem of ramp rate limitation in large superconducting magnets

Unexpected ramp rate limitations were found in large superconducting magnets for fusion experiments as well as in accelerator magnets. In this paper it is shown that a variation of the field sweep rate dB/dt along the length of a superconducting cable induces superposed extra coupling currents flowing over long lengths. These "supercurrents" lead to a highly nonhomogeneous current distribution in the cable and to additional coupling losses ("supercurrent losses"), even in magnet sections with dB/dt=0. These both effects may drastically reduce the stability of a magnet during fast ramp up. The solution of the diffusion equation allows us to calculate the space and time dependence of supercurrents as well as of supercurrent losses. The time constants of supercurrents are many orders of magnitude larger than typical coupling time constants of a superconducting cable. The proposed model can explain typical results of ramp rate limitations in large magnets.