Field Quality Study of the LARP Nb$_3$Sn 3.7 m-Long Quadrupole Models of LQ series

After the successful test of the first long Nb$_3$Sn quadrupole magnet (LQS01), the US LHC Accelerator Research Program (LARP) has assembled and tested a new 3.7 m-long Nb$_3$Sn quadrupole (LQS02). This magnet has four new coils made of the same conductor as LQS01 coils, and it is using the same support structure. LQS02 was tested at the Fermilab Vertical Magnet Test Facility with the main goal to confirm that the long models can achieve field gradient above 200 T/m, LARP target for 90-mm aperture, as well as to measure the field quality. These long models lack some alignment features and it is important to study the field harmonics. Previous field quality measurements of LQS01 showed higher than expected differences between measured and calculated harmonics compared to the short models (TQS) assembled in a similar structure. These differences could be explained by the use of two different impregnation fixtures during coil fabrication. In this paper, we present a comparison of the field quality measurements between LQS01 and LQS02 as well as a comparison with the short TQS models. If the result supports the coil fabrication hypothesis, another LQS assembly with all coils fabricated in the same fixture will be produced for understanding the cause of the discrepancy between short and long models.