1 Influence of the high granularity calorimeter stainless steel absorbers onto the C ompact Muon Solenoid inner magnetic field

2025-04-27 0 0 670.14KB 8 页 10玖币

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Influence of the high granularity calorimeter stainless steel absorbers onto

the Compact Muon Solenoid inner magnetic field

Vyacheslav Klyukhin1,2 for the CMS Collaboration

1*Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, RU-119991, Moscow, Russia

2CERN, CH-1211, Geneva 23, Switzerland

*Corresponding author. E-mail : Vyacheslav.Klyukhin@cern.ch; ORCID: 0000-0002-8577-6531

Abstract

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.

Keywords : electromagnetic modelling, magnetic flux density, magnetic field integrals, superconducting coil,

charged particle momentum resolution, inner tracker.

Article Highlights

• The method of the magnetic field double integrals to investigate a quality of the magnetic field in the

particle detector is fully described.

• The possible perturbation of the magnetic field inside the Compact Muon Solenoid inner tracker with the

replacement of the endcap hadronic calorimeter is investigated.

• The estimations on the degradation of the charged particle momentum resolution are presented.

1 Introduction

The Compact Muon Solenoid (CMS) detector [1] at the Large Hardon Collider (LHC) [2] is a multi-purpose

experimental setup to register the charged and neutral particles created in the proton-proton collisions at a center

of mass energy 13 TeV. The detector includes a wide-aperture superconducting thin solenoid [3] with a diameter

of 6 m and a length of 12.5 m operated with a direct current of 18.164 kA to create the central magnetic flux

density B0 of 3.81 T. Inside the superconducting coil, the major subdetectors of particles are located around the

interaction point of proton beams: a silicon pixel and strip tracking detectors to register the charged particles in a

cylinder volume with a diameter of 2.27 m and a length of 5.6 m; a solid crystal electromagnetic calorimeter to

coil in the muon spectrometer.

After finishing Run 3 of data taken at the LHC in the end of 2025, the existing CMS plastic scintillator-based

hadron endcap calorimeter will be replaced by a new High Granularity Calorimeter (HGCal) containing the silicon

sensors and stainless-steel absorber plates [4]. The relative permeability of the stainless steel is assuming to be

well below 1.05 that is limited by the axial forces attracting the absorber plates to the center of the CMS

superconducting solenoid. This study investigates the influence of the HGCal absorber plates with an extreme

permeability value of 1.05 onto the CMS solenoid inner magnetic field in the location of the pixel and strip tracking

detectors. The study is based on the calculation and comparison of the magnetic field double integrals

characterizing the resolution in the charged particle momentum measurements.

The method of the magnetic field double integrals has been proposed in 1993 [5] and was used in the

investigation of the magnetic field quality in the different options [6–8] of the magnetic system for the FCC-hh

detector [9] at the proposing Future Circular Collider [10].

The structure of this article is as follows: in Section 2 the method of the magnetic field double integrals applied

to the CMS inner magnetic field is described in detail; in Section 3 the model of the HGCal stainless steel absorber

plates is presented and the expressions for the axial force calculations are displayed; in Section 4 the results of the

study are drawn and discussed, and finally, Section 5 contains a conclusion.

2 Magnetic field double integrals and particle momentum resolution

In a center of mass reference system of the colliding particle beams, consider a trajectory of a charged particle

emitted in the radial RZ-plane, at angle θ to the beam Z-axis, from the nominal beam crossing point. For a small

step dl along the direction of the particle motion in an ideal (homogeneous) solenoid the change to the turning

angle of the track dα lies in the transverse plane and is given by



  

where l is in meters, pT is the particle transverse momentum of the constant value in GeV/c, and B is the constant

vector of the magnetic flux density in Tesla. In general, for inhomogeneous field, where the vector B changes its

value and direction, the track is turning according to, and in the direction of, the vector product dl×B [5].

For energetic particles, the magnetic deflection is small compared to the track length, thus the distance along

the trajectory can be approximated by l = r / sinθ, where r is the transverse radius (the orthogonal distance from

the beam axis to l in the radial RZ-plane), and small angle approximations are valid. At a track length l in the RZ-

plane, the relative angle α of the track with respect to its initial direction in transverse projection is given by



  





Here the polar angle θ (dl, B) represents the longitudinal component of the angle between the track projection to

the RZ-plane and the field vector, i. e. both the track length and the magnetic flux density vector are considered

to lay in the RZ-plane.

Fig. 1: The trajectory of a charged particle (magenta dashed line) with a transverse momentum pT of 100 GeV/c emitted in a

plane transverse to the axis of the interacting particle beams. Here: Rt (blue line) is a radius of the particle trajectory; S (an end

part of blue line) is a distance from the center of the arc to the center of its base (sagitta); α (red line) is a particle final turning

angle; transverse deflection x (green lines) is determined with Eq. (3); L is the total track length in the RZ-plane. The magnetic

flux density vectors are orthogonal to the plane of the plot and correspond to the distribution of the magnetic flux in the existing

CMS configuration. The sagitta S is calculated in two ways: with the exact formula (in blue) and with the transverse deflections

x (in green). The difference between two calculated values is within 0.8 %. The scale of the vertical axis distorts the trajectory

radius turning angle, half of which is also equal to α.

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摘要：

1InfluenceofthehighgranularitycalorimeterstainlesssteelabsorbersontotheCompactMuonSolenoidinnermagneticfieldVyacheslavKlyukhin1,2fortheCMSCollaboration1*SkobeltsynInstituteofNuclearPhysics,LomonosovMoscowStateUniversity,RU-119991,Moscow,Russia2CERN,CH-1211,Geneva23,Switzerland*Correspondingauthor.E-...

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1 Influence of the high granularity calorimeter stainless steel absorbers onto the C ompact Muon Solenoid inner magnetic field

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