The Decay of the Field Integral in Superconducting Accelerator Magnets Wound with Rutherford Cables

The field integral in superconducting accelerator magnets wound with Rutherford cable decays slowly when the magnet current is constant. This is believed to be caused by the decrease of the filament m agnetization of the cable strands due to current redistribution. In this paper the decrease is calculated for changes of the self-field of the strand and for changes of the external field due to the o ther strands. It is shown that the self field can only contribute significantly if the current change redistributes homogeneous by over the strand cross-section. However, none of the current redistrib ution mechanisms studied, including the quality index number of the critical current transition, gave a sufficiently large redistribution. Only the external field changes can explain the large decreas e (about 20%) of the filament magnetization observed on LHC prototype dipole magnets. An analytical model shows that the average decrease always lies between 1 and 2 times the absolute value of the av erage external field change in the windings, provided that the field is periodic over the length of the cable.