Field Quality of the First LARP Nb$_3$Sn 3.7m-Long Quadrupole Model of LQ Series

The US-LHC accelerator research program (LARP) built and tested the first 3.7-m long Nb$_3$Sn quadrupole model of LQ series with a 90 mm bore diameter and a target field gradient of 200 T/m. The LQ series, developed in collaboration among FNAL, LBNL and BNL, is a scale up of the previously tested 1-m long technology quadrupoles of TQ series based on similar coils and two different mechanical structures (shell-based TQS and collar-based TQC), with a primary goal of demonstrating the Nb$_3$Sn accelerator magnet technology for the luminosity upgrade of LHC interaction regions. In this paper, we present the field quality measurements in the first 3.7-m long LQS01 model based on the modified TQS mechanical structure. The results are compared to the expectations from the magnet geometry and magnetic properties of coils and iron yoke. Moreover, we present a comparison between this magnet and the short models previously measured.