[^1]

*Abstract*---The 3.7 m long quadrupole magnet LQS01 represents a major
step of the US LHC Accelerator Research Program (LARP) towards the
development of long Nb3Sn accelerator quadrupole magnets for a LHC
Luminosity upgrade. The magnet support structure is a scale up of the 1
m long Technology Quadrupole TQS design with some modifications
suggested by TQS model test results. It includes an aluminum shell
pre-tensioned over iron yokes using pressurized bladders and locking
keys (bladder and key technology). The axial support is provided by two
stainless steel plates compressed against the coil ends by four
stainless steel rods. The structure, instrumented with strain gauges,
has been fabricated and assembled around four aluminum "dummy coils" in
order to determine pre-load homogeneity and mechanical response during
cool-down. After presenting the main magnetic and mechanical parameters
of LQS01, we report in this paper on design, assembly, and test of the
support structure, with a comparison between strain gauges results and
3D numerical predictions.

*Index Terms*--- LARP, Nb~3~Sn, Quadrupole magnet

# INTRODUCTION

[AS]{.smallcaps} part of the LHC Accelerator Research Program (LARP
\[1\]), three US national laboratories (BNL, FNAL, and LBNL) are
currently engaged in the development of Nb3Sn superconducting magnets
for a future upgrade of the LHC Interaction Regions (IR). In order to
contain the superconducting coils during magnet excitation and minimize
conductor motion induced by electro-magnetic forces, LBNL has developed
shell-based support structures for quadrupole magnets. The main
components and features of these structures are the following.

![](media/image1.png){width="2.5256944444444445in"
height="2.5256944444444445in"}

Fig. 1. LQS01 cross-section.

• An external aluminum segmented shell (solid tube).

• A 4-piece iron yoke with gaps open during all magnet operations.

• Assembly performed through two sub-assemblies.

• Pre-loading obtained with water pressurized bladders.

• Maximum coil stress reached after cool-down.

• Axial coil support provided by end-plate and axial rods.

These support structures have been originally adopted by the LBNL
Superconducting Magnet Program to cope with the needs of high field
Nb3Sn magnets, which, because of large e.m. forces acting on a brittle
superconducting material, require a precise control of the coil pre-load
\[2-3\]. In this paper with give an overview of how these structures
have been applied to quadrupole magnets, we describe their main
principles of operation and finally we present how, through LARP,
accelerator quality features are in the process of being included in the
design.

# Magnet Design and Parameters

The structure LQS structure is based on an aluminum shell pre-tensioned
with pressurized bladders \[6B.1-6B.10\]. The design (Fig. 6B.1)
comprises an iron yoke surrounded by a 20 mm thick aluminum shell, and
includes four pads and four coils wound around titanium poles. Between
each pad and yoke two interference keys are used to balance the
azimuthal tension in the outer shell with the azimuthal compression in
the inner coils. The 3D design (Fig. 6B.2) is characterized by:

Stainless steel or iron pad laminations (50 mm thick)

Iron masters (1.6 m long)

Iron yoke laminations (50 mm thick)

4 aluminum shell segments (0.820 m long)

Axial rods and tie rods 3.3 m long

Based on detailed FEA analysis, and taking into account the requirements
for a long structure and the TQS program experience, several
improvements and optimizations were included in the LQS design: Load
keys are located closer to the mid-plane, resulting in optimal coil
stress distribution Two bladders per quadrant provide larger surface and
better control during assembly Axial rods located next to the coils
reduce the end plate deflections and overall thickness Iron masters
located between pad and yoke provide a flat and precise surface for
bladders and keys. This solution is compatible with the use of laminated
pads and yokes, and is suitable for providing structure alignment during
assembly, cool-down and operation. Aluminum shell thickness of 20 mm was
selected for optimal balance between pre-load at room temperature,
cool-down and operation, taking into account the assembly requirements.
Further optimization may include the use of stamped laminations for the
pads and yokes, resulting in more accurate tolerances and cost
reductions for a larger production.

TABLE I Magnet Design Parameters

  ---------------------------------- ------------------- ----------------
  **Parameter**                      **Unit**            

  Strand diameter                    mm                  0.8

  No. strands                                            51

  Cable width (bare)                 mm                  22.000

  Cable thickness (bare)             mm                  1.400

  Insulation thickness               mm                  0.110

  No. turns/quadrant (layer 1)                           24

  No. turns/quadrant (layer 2)                           30

  Short sample current               kA                  17.3

  Maximum dipole field               T                   15.8

  Coil peak field                    T                   15.0

  Stored energy                      MJ/m                0.84

  Inductance                         mH/m                5.6

  Fx / Fy layer 1 (per quadrant)     MN/m                \+ 2.3 / - 0.3

  Fz layer 1 (per quadrant)          kN                  90

  Fx / Fy layer 2 (per quadrant)     MN/m                \+ 3.3 / - 2.2

  Fz layer 2 (per quadrant)          kN                  126
  ---------------------------------- ------------------- ----------------

![](media/image2.png){width="3.1680555555555556in"
height="1.9854166666666666in"}

Fig. 2. LQS01 end region design.

# Magnetic Analysis

## Cross-section

The field in the conductor has been computed by a 2D magnetic model of
the magnet cross-section (Fig. 3B.1), where each individual turn has
been considered. The assumed current density of 2800 A/mm2 (12 T, 4.2 K)
is based on measurements from the TQS02 magnet, which used the same
conductor and heat treatment as presently envisioned for LQ. The highest
field of 13.4 T (Fig. 3B.2), at the 1.9 K short sample current is
located in layer 1 on the pole turn. Layer 2 has a margin of \~ 2 T.

LQS01 magnet parameters

![](media/image3.wmf){width="3.34375in" height="0.8395833333333333in"}

## Ens region

In order to investigate the field in the end and its dependence on the
iron design, we analyzed several cases using different yoke, pad and
master configurations and materials. A modeled coil length of 1 m is
sufficient to perform the end field analysis. In Fig. 3B.2 we show
several pictures of the model aimed at investigating the difference
between the peak field in the coil straight section and the peak field
in the end with different yoke and master length (for the stainless
steel pad case). The results are given in Table 3B.4.

The final choice is shown in Fig. 3B.3, with stainless steel pads
covering the coil end region. In these conditions, the peak field in the
end region, which is located in the pole turn of layer 1 (right below
the region where the pole turn of layer 2 is bent around the pole, as
shown in Fig. 3B.4), is the same as the peak field in the straight
section.

![](media/image4.png){width="2.71875in" height="2.111111111111111in"}

Fig. 3. LQS01 end region design.

# Mechanical Analysis

## Cross-section

A 2D mechanical analysis of the cross section was performed for both
cases. We computed the stresses assuming no separation at 240 T/m (for
both cases) between coil and pole in layer 1 (see Fig. 6B.3). The
material properties used in the model are given in Table 6B.1, the
electromagnetic forces are given in Table 6B.2, and a summary of the
results of the analysis is given in Table 6B.3. The load key position
(21 mm from the mid-plane) has been optimized to minimize stresses and
to have the same peak stress after cool-down and during excitation.

Magnet parameters and electromagnetic forces at 240 T/m

![](media/image5.wmf){width="2.6590277777777778in"
height="2.317361111111111in"}

Table 6B.3

Summary of the 2D mechanical analysis

![](media/image6.wmf){width="3.098611111111111in" height="2.11875in"}

Fig. 2. LQS01 end region design.

![](media/image7.wmf){width="3.1083333333333334in" height="2.125in"}

Fig. 2. LQS01 end region design.

## Ens region

Two finite element model were used for the 3D mechanical analysis of
LQS: a 1 m long model (TQS length, Fig. 6B.14) and a 3.3 m long model
(Fig. 6B.15). The following computational steps were considered:

o Key insertion

o Cool-down

o Excitation

The surfaces of the impregnated coil are bonded, while all the other
surfaces are modeled under the assumption of "sliding with separation
allowed" with a friction factor of 0.2. The axial pre-load has been
chosen in order to provide full contact between coil and end parts when
the electro-magnetic forces for a gradient of 240 T/m are applied (Fig.
6B.16). In the end the contact area between pole turn and pole in layer
2 in the end region is the one more likely to separate because of the
e.m. axial forces (Fig. 6B.17). The axial support is provided by 4
stainless steel rods with a diameter of 25.4 mm, connected to a 50 mm
thick end plate made of Nitronic 40 stainless steel.

According to the 3D analysis

o about 65 MPa of coil-pole contact pressure are necessary to prevent
separation in the end of layer 2 (Fig. 6B.18)

o in order to withstand a total electromagnetic axial force of 474 kN,
25.4 mm diameter stainless steel axial rods are pre-tensioned to 88 MPa,
corresponding to 180 kN of total axial force, to reach after cool-down a
tension of 240 MPa, corresponding to 480 kN of total axial force (Fig.
6B.19 and Fig. 6B.20).

![](media/image6.wmf){width="3.098611111111111in" height="2.11875in"}

Fig. 2. LQS01 end region design.

![](media/image7.wmf){width="3.1083333333333334in" height="2.125in"}

Fig. 2. LQS01 end region design.

# Assembly Procedure and Tooling

# Cool-down Test 

The shell was instrumented with half-bridge strain gauges placed on the
right side and left side of the magnet mid-plane (see Fig. 2). The
gauges measure the azimuthal and axial strain at six longitudinal
stations along the shell: station 1 is near the lead end and station 5
is at the shell's longitudinal center. In total, 24 gauges, all
thermally compensated by gauges mounted on stress-free aluminum
elements, were mounted on the shell. The gauges in stations 1 and 2 (end
gauges) were used to monitor end effects, whereas the ones in stations 3
to 6 (central gauges) measured strain variations in the central part of
the magnet. The measured strain in the azimuthal and axial directions (
and *~z~*) was converted into stress ( and *~z~*) using the relation

$\sigma_{\theta,z} = \frac{E}{\left( 1 - \nu^{2} \right)}\left( \varepsilon_{\theta,z} + \text{νε}_{z,\theta} \right)$,
(1)

where *E* and are, respectively, the elastic modulus (79 GPa at 4.5 K)
and the Poisson's ratio (0.34) of aluminum.

![](media/image8.png){width="3.3152777777777778in"
height="2.276388888888889in"}

![](media/image8.png){width="3.3152777777777778in"
height="2.276388888888889in"}

![](media/image8.png){width="3.3152777777777778in"
height="2.276388888888889in"}

![](media/image8.png){width="3.3152777777777778in"
height="2.276388888888889in"}

# Status of the Fabrication

# Conclusions

# Conclusions

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[^1]: ^^Manuscript received 19 August 2008. This work was supported by
    the Director, Office of Energy Research, Office of High Energy and
    Nuclear Physics, High Energy Physics Division, U. S. Department of
    Energy, under Contract No. DE-AC02-05CH11231.

    P. Ferracin, S. Caspi , D.W. Cheng, D. R. Dietderich, S. A. Gourlay,
    A. R. Hafalia, C.R. Hannaford, A. F. Lietzke, and G. L. Sabbi are
    with Lawrence Berkeley National Lab, Berkeley, CA 94720, USA (phone:
    510-486-4630; fax: 510-486-5310; e-mail: <pferracin@lbl.gov>).

    G. Ambrosio, E. Barzi, A.R. Nobrega, and A.V. Zlobin are with
    Fermilab National Accelerator Laboratory, Batavia, IL 60510, USA.

    M. Anerella, J. Schmalzle, and P. Wanderer are with Brookhaven
    National Laboratory, Upton, NY 11973-5000, USA.