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Calculation of Forces on the High Granularity Calorimeter Stainless Steel Absorber Plates in the Compact Muon Solenoid Magnetic Field

The general-purpose Compact Muon Solenoid (CMS) detector at the Large Hadron Collider (LHC) at CERN includes the hadronic calorimeter to register the energies of the charged and neutral hadrons produced in the proton-proton collisions at the LHC at a centre of mass energy 13.6 TeV. The calorimeter is located inside the superconducting solenoid of 6 m in diameter and 12.5 m in length creating the central magnetic flux density of 3.8 T. For operating optimally in the high pileup and high radiation environment of the High Luminosity LHC, the existing CMS endcap calorimeters will be replaced with a new high granularity calorimeter (HGCal) comprising of an electromagnetic and a hadronic section in each of the two endcaps. The hadronic section of the HGCAL will include 44 stainless steel absorber plates with a relative permeability value well below 1.05. The volume occupied by 22 plates in each endcap is about 21 m$^{3}$. The calculation of the axial electromagnetic forces on the absorber plates is a crucial element in designing the mechanical construction of the device. With a three-dimensional computer model of the CMS magnet, the axial forces on each absorber plate are calculated and the dependence of forces on the central magnetic flux density value is presented. The method of calculation and the obtained results are discussed.