Critical Current in High-J $ _{\rm c}$ Nb $_{3}$Sn Rutherford Cables Affected Substantially by the Direction of the Applied Magnetic Field

Recently several Rutherford-type Nb Sn cables for possible use in new magnets for upgrades of the LHC have been measured at CERN. A summary is provided including a comparison of the critical current (I
_c
) of various cable types and strand materials versus their respective extracted strand measurements. The conductors were cabled at CERN and Lawrence Berkeley National Laboratory. The summary shows an unsurprising linear relation between the strand and the cable performance. However, assuming that the local peak magnetic field in the conductor is the relevant factor for determining the I
_c
(B) relation, a discrepancy is found when results from different directions of applied magnetic field on the cable are compared. In this paper it is shown that the critical current as a function of the peak magnetic field in the conductor can change in the range of 7-12% depending on the direction of the applied magnetic field. This effect originates from the superposition of the self field of the conductor and the applied magnetic field. When the direction of the applied magnetic field is changed, the position of the peak magnetic field in the conductor shifts. Mechanical degradation during the cabling process can create a local reduction in the critical current. When the position of the peak magnetic field shifts from a more degraded to a less degraded area, the measured I
_c
(B) curve of the conductor will change accordingly. The measured effect is in principle present in all cables exhibiting non-uniform cabling degradation but is substantially present in Nb
₃
Sn conductors for the reasons mentioned.