  The Compact Muon Solenoid (CMS) detector is a general-purpose experimental
setup at the Large Hadron Collider (LHC) at CERN to investigate the production
of new particles in the proton-proton collisions at a centre of mass energy 13
TeV. The third run of the data taken is started in April 2022 and will continue
till the end of 2025. Then, during a long shutdown time, the existing CMS
hadron endcap calorimeter will be replaced with a new high granularity
calorimeter (HGCal) designed for the higher LHC luminosity. The HGCal contains
the stainless-steel absorber plates with a relative permeability limited by a
value of 1.05 from estimation of the electromagnetic forces acting on this
slightly magnetic material. To exclude the surprises with possible perturbation
of the inner magnetic flux density in the region of the charged particle
tracking system, an influence of this additional material onto the quality of
the magnetic field inside the inner tracker volume is investigated at this
limited value of the permeability of stainless steel . The three-dimensional
model of the CMS magnet is used for this purpose. The method of the magnetic
field double integrals characterizing the charged particle momentum resolution
the first time is applied to the CMS detector and the first time is described
in the journal publication. The results obtained with this method are presented
in detail and discussed.
