Charged particles are deflected in a magnetic field due to the Lorentz force. The resulting path is helical propagating along a circular path in the bending plane and following the field direction (figure2.6).
The ATLAS magnet system uses superconductive magnets to provide high fields to the detector (above 2 T). To provide the optimised magnetic field configuration for particle bending in a light and open structure, ATLAS chose different types of magnets:
a central solenoid with small radius and thin walls, surrounded by three large air-core toroids, generating the magnetic field for the muon spectrometer.
A scheme of the complete system can be seen in figure2.7.
Figure 2.6: Inside a magnetic field the trajectories of the particles are deflected due to the Lorentz force describing a helical path.
Figure 2.7: Three-dimensional view of the bare windings of the ATLAS magnet system:
the central solenoid, the 8 coils of the barrel toroid and the 2×8 coils of the end-cap toroids.
•
Central Solenoid: Surrounding the Inner Detector, the solenoid produces a 2 T magnetic field in the central tracking volume . This high magnetic field bends particles around the direction of the incoming LHC beams (even very energetic particles). Below 400MeV
of momentum, particles will be curved so strongly and they will loop repeatedly in the field and most likely not be measured; however, this energy is very small compared to the several TeV of energy released in each proton collision.To decrease particle scattering effects, the superconducting solenoid is based on a thin-walled construction and the material of the system is reduced sharing its cryostat with the liquid argon calorimeter. The solenoid is made as a single
2.3 The ATLAS Detector 25
layer coil so it generates a nearly uniform field inside the windings and a comparably weak and divergent field outside. The direction of the magnetic field and the field lines can be seen in figures2.8and2.9respectively.
Figure 2.8: Magnetic field (B) inside a solenoid.
Figure 2.9: Field lines inside a solenoidal magnetic field.
An schematic bird’s eye view of the solenoid is depicted in figure2.10. Solenoidal fields give very good momentum resolution at large angles.
Figure 2.10: Schematic bird’s eye view of the ATLAS central solenoid.
•
Toroid Magnets: Each of three ATLAS toroid systems consists of eight coils, assembled radially and symmetrically around the beam axis. A scheme of the complete system design can be seen in figure2.11. In order to obtain a better momenta and position measurement, the toroids have been built “in air”.The magnetic field inside a toroid is directed tangentially and depends on the radius of the toroid (figure2.12). The field lines created by a toroidal magnet
Figure 2.11: Schematic view of the ATLAS toroid magnet system design. It consists of two inserted end-cap toroids and a long barrel toroid that comprises eight separate cryostats.
can be seen in figure2.13.
Figure 2.12: Magnetic field (B) inside a toroid.
Figure 2.13: Field lines inside a toroidal magnetic field.
Toroids contain closed B field lines (figure2.14), thus there is no need for extra yokes, avoiding the resulting multiple scattering.
With a toroid field particles will cover the complete pseudorapidity range being almost perpendicular to the field. This means that the field integralR
BdL, which is the important factor for momentum resolution, can be kept high even in the forward direction.
2.3 The ATLAS Detector 27
Figure 2.14: Simulation of the magnetic field lines generated by the magnet system. The magnet system provides an optimised magnetic field configuration for particle bending in the inner detector and the muon spectrometer.
The system is composed by two end-cap toroids (figure 2.15) and a 25 m long barrel toroid (figure 2.16). The Barrel system comprises eight separate cryostats. Each of the toroids carries a current of 20 kA, generating a magnetic field of 4 T. This magnet system provides strong bending power in a large volume (3 Tm in the barrel and 6 Tm in the end-caps) and this force is independent on the track angle since the magnetic field acts on
p
and notp
T.The type of the magnets used is one of the differences between CMS and ATLAS.
CMS is smaller and heavier than ATLAS, for this reason CMS uses a strong solenoidal magnetic field to bend the trajectories of the particles. On the contrary, ATLAS opts for a larger and lighter configuration using a smaller central solenoid but adding toroidal magnets in the outer part.
The combination of the solenoid and the toroid magnets provides a high-precision stand-alone momentum measurement of muons. In collider experiments often the sagitta s is measured inside the magnet region. The precision of the sagitta measurement is a direct measure for the precision of the muon momentum. The sagitta method is depicted in figure2.17.
In general a charged particle track is measured using several (N) position-sensitive detectors. At least three coordinate measurements are necessary. For
N
equidistant measurements, the momentum resolution is described by the Gluckstern formulaFigure 2.15: Endcap toroid system inserted in ATLAS. It consists of eight flat coils assembled radially and symmetrically around the beam axis. The magnet system provides a peak field of 4.1 T.
Figure 2.16: Barrel toroid system inserted in ATLAS. It consists of eight flat coils assembled radially and symmetrically around the beam axis. The magnet system provides a peak field of 3.9 T.
(1963) [28]. Assuming that each detector measures the coordinates of the track with a precision of
σ
x, the approximate parametrization of the resolution is:σ
pTp
T≈
r A
NN + 4
σ
xp
T0.3BL
2(2.6)
2.3 The ATLAS Detector 29
Figure 2.17: The sagitta s of the curvature of the track is often measured on collider experiments. The precision of the sagitta measurement is a direct measure for the precision of the muon momentum p.
with
A
Nstatistical factor equal to 720 [28].According to the above equation, the momentum resolution depends on the amount of material the particle has to traverse (L), the magnetic field strength (B) and the position resolution (
σ
x). A sketch of two muon tracks bending under the presence of the ATLAS magnet system can be seen in figure2.18.Figure 2.18: Sketch of two muon tracks bending under the presence of the ATLAS magnet system.
The ATLAS magnet system generates a stable, precise and predictable magnetic field in an enormous volume and is fully integrated with the detectors in an overall
20 × 20 × 25 m
3 assembly. In table 2.4 the main parameters of the CMS and ATLAS magnet systems are presented.CMS ATLAS
Parameter Solenoid Solenoid Barrel Toroid End-cap Toroids
Inner diameter 5.9 m 2.4 m 9.4 m 1.7 m
Outer diameter 6.5 m 2.6 m 20.1 m 10.7 m
Axial length 12.9 m 5.3 m 25.3 m 5.0 m
Number of coils 1 1 8 8
Number of turns per coil 2168 1173 120 116
Conductor size (
mm
2) 64 x 22 30 x 4.25 57 x 12 41 x 12Bending power 4 Tm 2 Tm 3 Tm 6 Tm
Current 19.5 kA 7.7 kA 20.5 kA 20.0 kA
Stored energy 2700 MJ 38 MJ 1080 MJ 206 MJ
Table 2.4: Main parameters of the CMS and ATLAS magnet systems. CMS uses strong solenoidal magnets on a compact structure while ATLAS combines lighter solenoidal and toroidal magnetic fields in an open structure.
Table2.5shows a summary of the expected combined1and stand-alone2performance at two typical pseudorapidity values (averaged over azimutal) of the CMS and ATLAS experiments. The ATLAS muon stand-alone performance is excellent over the whole pseudorapidity3(
η
) range.Combined (stand-alone) momentum resolution at ATLAS CMS
- p = 10 GeV and
η ≈
0 1.4%
(3.9%
) 0.8%
(8%
)Table 2.5: Summary of the expected combined and stand-alone performance at two typical pseudorapidity values (averaged over azimutal) of the CMS and ATLAS experiments.
1Muons are reconstructed with the muon spectrometer and the inner detector.
2Muons are reconstructed with the muon spectrometer stand-alone; the muon momentum is corrected for the energy loss in the calorimeters by the expected energy loss.
3In experimental particle physics, pseudorapidity (η) is related with the azimuthal angleθ(i.e. it is related with the angle of a particle relative to the beam axis) as follows:η = −ln[tanθ
2]
2.3 The ATLAS Detector 31