  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.
