Nb3Sn Quadrupoles Designs For The LHC Upgrades Page: 2 of 3
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7 :E-usFigure 2: Azimuthal stress distribution due to Lorentz forces at 200 T/m in an infinitely stiff structure with sliding
between layers for two 134 mm aperture cross-sections. Left: Fa L1 = -3.58 MN/m F L2 = -2.46 MN/m - Right: F L1
= -2.7 MN/m Fe L2 = -3.4 MN/mIn the first case (Fig. 1 left), the azimuthal force is much
higher in the inner layer L1 inducing high compressive
stress on the mid-plane. In the second case (Fig. 1 right),
the outer layer L2 exhibits a greater Lorentz force than the
inner layer L1 leading to a more homogeneous stress
distribution in the coil. We clearly see here that the
mechanical stresses induced in the coil depend strongly
on the azimuthal Lorentz forces distribution between layer
1 and layer 2.k a.".
Figure 2: HQ 114 mm aperture cross-section designed by
Vadim Kashinkhin, FNAL
Based on these considerations, a magnetic cross-
section has been designed (Fig. 2) using the conductor
described in Table 1.
The magnet short sample limit parameters at the
operating operation Top = 1.9 K are presented in Table 2.
The critical current density taken into account in the
computation is 3000 A/mm2 at 12 T and 4.2 K.
Table 2: Magnet parameters at Top = 1.9 K
Dimensions Units Values
Gss T/m 234
Bss T 15.39
Iss kA 19.18
F L1/L2 at Iss MN/m 2.5 /2.99
Stored energy MJ/m 1.31The iron yoke is located at 10 mm from the coil. For the
magnetic computation, the outer radius is equal to 260
mm.
MECHANICAL DESIGN
The mechanical structure relies on an aluminum shell
surrounding an iron yoke and four support pads.
The coils are wound around a Titanium pole. For a 114
mm aperture, the aluminum shell is 25 mm thick and the
overall diameter of the magnet is 550 mm. The axial
preload is provided by axial rods, which are pre-tensioned
at room temperature and shrink during cool-down. The
main objectives of this structure are to provide
mechanical support up to the short-sample limit of the
magnet and to implement alignment. The different
components of the mechanical structure are shown in
Figure 3. At 200 T/m, the ANYS 2D simulation shows a
maximum azimuthal stress in the coil of the order of -135
MPa. At the short sample limit, that is to say for a
gradient of 234 T/m, this maximum stress is equal to -177
MPa.
Aluminum Shell
Bolted collar
Iron Yoke
w
Iron Pad Bladder
Axial rods location
Figure 3: HQ mechanical structure
The optimization of this mechanical structure is in
progress in order to incorporate all the accelerator quality
features required for a LHC upgrade (cooling channel,
alignment, LHe containmentt.0000
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Felice, Helene. Nb3Sn Quadrupoles Designs For The LHC Upgrades, article, May 19, 2008; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc932185/m1/2/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.