The Compact Muon Solenoid (CMS) is a general purpose detector, designed to run at the highest luminosity at the CERN Large Hadron Collider (LHC). Its distinctive features include a 4 T superconducting solenoid with 6-m-diameter by 12.5-m-length free bore, enclosed inside a 10000-ton return yoke made of construction steel. The return yoke consists of five dodecagonal three-layered barrel wheels and four end-cap disks at each end comprised of steel blocks up to 620 mm thick, which serve as the absorber plates of the muon detection system. Accurate characterization of the magnetic field everywhere in the CMS detector is required. To measure the field in and around the steel, a system of 22 flux-loops and 82 3-D Hall sensors is installed on the return yoke blocks. Fast discharges of the solenoid (190 s time-constant) made during the CMS magnet surface commissioning test at the solenoid central fields of 2.64, 3.16, 3.68 and 4.01 T were used to induce voltages in the flux-loops. The voltages are measured on-line and integrated off-line to obtain the magnetic flux in the steel yoke close to the muon chambers at full excitations of the solenoid. The 3-D Hall sensors installed on the steel-air interfaces give supplementary information on the components of magnetic field and permit to estimate the remanent field in steel to be added to the magnetic flux density obtained by the voltages integration. A TOSCA 3-D model of the CMS magnet is developed to describe the magnetic field everywhere outside the tracking volume measured with the field-mapping machine. The results of the measurements and calculations are presented, compared and discussed.
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