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The high field superconducting magnets required for ongoing and planned upgrades to the Large Hadron Collider (LHC) will be wound with Nb3Sn Rutherford cables for which reason studies of Nb3Sn strand, cable, and magnet properties will continue to be needed. Of particular importance is field quality. The amplitudes of multipoles in the bore fields of dipole and quadrupole magnets, induced by ramp-rate-dependent coupling currents, are under the control of the interstrand contact resistances-crossing-strand, $R-{c}$, adjacent strand, $R-{a}$ , or a combination of them, $R-{{\text{eff}}}$. Although two decades ago it was agreed that for the LHC $R-{c}$ should be in the range 10-30 μ, more recent measurements of LHC quadrupoles have revealed $R-{c}$ values ranging from 95 to 230 μ. This paper discusses ways in which these values can be achieved. In a heavily compacted cable $R-{{\text{eff}}}$ can be tuned to some predictable value by varying the width of an included stainless steel (effectively 'insulating') core. But cables are no longer heavily compacted with the result that the crossing strands of the impregnated cable are separated by a thick epoxy layer that behaves like an insulating core. If a stainless steel core is actually present, $R-{{\text{eff}}}$ must be independent of core width. Since there is no guarantee that a fixed predetermined amount of interlayer separation could be reproduced from winding to winding it would be advisable to include a full width core.

Calorimetric measurement of coupling loss versus frequency has been measured on two sets of cored and uncored large Hadron Collider Accelerator Research Program high gradient quadrupole Nb3Sn Rutherford cables. Studied are the responses of the resulting interstrand contact resistances (ICR) to variation of stainless-steel (SS) core width and position and to variation of reaction-heat-treatment (RHT) condition. One pair of cables (an early HQ-series type) with and without core had received RHT under 20-MPa uniaxial face-on pressure. Another set of cables (recent QXF type) furnished with SS cores of various widths had received RHT under ambient pressure. The results were displayed as cable-cross-sectional micrographs and plots of ICR versus percent core coverage (W). The HQ cables were tightly compacted and produced results consistent with a previously expected continuous ICR versus W variation. On the other hand, the QXF cables were uncompacted such that their upper and lower layers were separated by what is referred to as a full-width 'pseudocore;' as a result, their ICRs were independent of the widths of the SS cores. Compaction versus noncompaction is discussed and future research directions are suggested.

Persistent magnetization currents are induced in superconducting filaments during the current ramping in magnets. The resulting perturbation to the design magnetic field leads to field quality degradation, particularly at low field, where the effect is stronger relative to the main field. The effects observed in NbTi accelerator magnets were reproduced well with the critical-state model. However, this approach becomes less accurate for the calculation of the persistent-current effects observed in Nb3Sn accelerator magnets. Here, a finite-element method based on the measured strand magnetization is validated using three state-of-the-art Nb3Sn accelerator magnets featuring different subelement diameters, conductor critical currents, magnet designs, and test temperatures. The temperature dependence of the persistent-current effects is reproduced. Based on the validated model, the impact of conductor design on the persistent-current effects is discussed. The strengths, limitations, and possible improvements of the approach are also discussed.