Multipoles Induced by Inter-Strand Coupling Currents in LARP Nb$_{3}$Sn Quadrupoles

The U.S. LHC Accelerator Research Program has been developing Nb_3Sn quadrupole magnets of progressively increasing performance and complexity for the High-Luminosity LHC project. The magnets are wound with Rutherford cables following the wind-and-react process. The resulting inter-strand coupling can generate strong field distortions during current ramp. The latest series of 120 mm aperture magnets (HQ) are designed and built for high field quality, offering an opportunity for detailed studies of these effects. Magnetic measurements of first-generation HQ magnets showed strong ramp-rate dependence. A stainless-steel core was introduced for the second generation of magnet coils to control the inter-strand coupling currents and the resulting dynamic multipoles. We report the observed dynamic effects and compare with calculations taking into account the coil geometry and cross-contact resistance in the Rutherford cable. In particular, the dependence of field quality on width and position of the stainless steel core is discussed.