[^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
\[1\], \[2\]), three US national laboratories (BNL, FNAL, and LBNL) are
developing the Long Quadrupole magnet LQ, the first 4 m long Nb3Sn
quadrupole magnet ever built and a fundamental step toward the
development of Nb3Sn magnet for a future LHC luminosity upgrade. LQ will
implement four cos-theta type coils fabricated at BNL and FNAL
\[3\]-\[5\], at it will be firstly tested in a shell-based support
structure designed, fabricated, and assembled at LBNL. Shell-based
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
\[6\], \[8\]. The main components and features of these structures are
the following:

-   external segmented aluminum shell;

-   4-piece iron yoke with gaps open during all 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.

The LQ support structure design builds upon several shell type support
structure adopted by the LARP Program. The Sub-scale Quadrupole magnet
SQ \[9\]-\[12\], developed in 2005, was the first racetrack quadrupole
magnet assembled in a shell-based structure, with alignment of all the
components. The Technology Quadrupole Shell-type magnet TQS
\[13\]-\[19\], assembled and tested in 2005, featured 4 cos-theta type
coil in a shell-based structure. In 2006 the Long Racetrack shell-type
magnet LRS \[20\]-\[24\] was fabricated: it was the first magnet
adopting these types of structure with 3.6 m long racetrack coils
assembled in a common-coil configuration. The structure designed for the
LQ is going to apply the design features of the previous structure to
3.5 m long cos-theta type coils, and with some additional components to
improve coil stress distribution and facilitate alignment and assembly
of the 4 m long structure. The alignment of the coil with the structure,
not addressed in the LQ magnet, is under study as part of the
development of the HQ magnet \[25\], \[26\].

In this paper, we provide a detailed description of the magnet and cable
design in Sec. II. The results of the magnetic and mechanical analysis
are presented in Sec. II and Sec. III, while the assembly procedure is
discussed in Section IV. Finally, Sec. IV deals with the results of a
cool-down test of a 0.8 m long version of the structure assembled with
aluminum dummy coils.

# Cable and Magnet Design 

The LQ magnet features the same coil cross-section design as the TQ
program, with three conductor block wound around Titanium alloy pole
pieces. The strand and cable parameters are given in Table I.

TABLE I Cable Design Parameters

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

  Strand diameter                    mm                  0.7

  Process                                                RRP

  Stack                                                  54/61

  No. strands                                            27

  Cable width (bare)                 mm                  

  Cable thickness (bare)             mm                  

  Insulation thickness               mm                  

  No. turns/quadrant (layer 1)                           

  No. turns/quadrant (layer 2)                           
  ---------------------------------- ------------------- -----------------

The support structure (see Fig. 1) comprises of four main components:
iron pads, iron masters, iron yokes, and aluminum outer shell. As a
first step in the assembly, the four pads are bolted around the coil,
while the yoke pieces are inserted inside the 20 mm thick shell (with an
outer diameter of 496 mm) and locked by gap keys. The coil-pad assembly
is then inserted into the shell-yoke sub-assembly. To provide alignment
between the coil-pack and the shell/yoke subassemblies, a set of
"master" assemblies are incorporated. These masters are matched and
nested into precision-machined features in the load pads and yokes. A
central key provides alignment between the two masters, while four pins,
located at the four mid-planes, align azimuthally the yokes with the
shell.

![](media/image1.png){width="3.4923611111111112in"
height="2.6847222222222222in"}

Fig. 1. LQS01 cross-section.

Based on the experience learned from LRS magnet LR tests \[23\], \[24\],
in order to improve coil stress homogeneity along the longitudinal axis,
the shell has been segmented in four equal-length parts (segment). The
50 mm thick yoke and pad laminations are stacked and pre-compressed by
full-length stainless steel tie rods. In order to provide continuous
surfaces for the pairs of water pressurized bladders (used to
azimuthally preload the structures) and the load keys (used to lock-in
the preload) the masters are machined from 1.8 m long iron plates.

The coil end support system, similarly as the one previously implemented
in the HD1 magnet \[27\], is composed by four aluminum rods, with a
diameter of 25.4 mm, inserted in the four holes of the pads, and bolted
to two 50 mm thick stainless steel end plates (see Fig. 2). The rods are
pre-tensioned with an axial piston at room temperature.

![](media/image2.png){width="3.4993055555555554in"
height="2.4006944444444445in"}

Fig. 2. LQS01 structure end design.

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 an improved 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.

# Magnetic Analysis 

The field in the conductor has been computed by a 2D finite element
magnetic model of the magnet cross-section, where each individual turn
has been considered. The assumed critical current density in the
superconductor of 2800 A/mm^2^ (12 T, 4.2 K) is based on measurements
from the TQS02 magnet \[18\], which used the same conductor and heat
treatment as the one considered for LQ. The highest field of 13.4 T (see
Table II) at the 1.9 K short sample current is located in layer 1, on
the pole turn. The peak field in layer 2, also located in the pole turn,
is about 2 T then layer 1. For a field quality measurements performed on
the TQ series we refer to \[28\]-\[30\].

TABLE II Magnetic Design Parameters

  ------------------------------- ---------- ---------- ---------- ----------
  **Parameter**                   **Unit**   **4.5 K**  **4.2 K**  **1.9 K**

  Short sample current I~ss~      kA         13.76      13.96      15.16

  Gradient at I~ss~               T/m        240        244        262

  Coil peak field (layer 1) at    T          12.29      12.46      13.43
  I~ss~                                                            

  Coil peak field (layer 2) at    T          10.52      10.66      11.48
  I~ss~                                                            

  Stored energy at I~ss~          kJ/m       457        479        559

  Inductance                      mH/m       4.9                   
  ------------------------------- ---------- ---------- ---------- ----------

Values computed assuming critical current density in the superconductor
of 2800 A/mm^2^ (12 T, 4.2 K).

In order to investigate the field in the end and its dependence on the
iron design, we analyzed with a 3D magnetic finite element model several
cases using different yoke, pad and master configurations and materials.

![](media/image3.png){width="3.495833333333333in"
height="0.8583333333333333in"}

Fig. 3. LQS01 coil end region design.

The final choice is shown in Fig. 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, is the
same as the peak field in the straight section.

# Mechanical Analysis

## Cross-section

The stresses in coil and support structure were computed with a 2D
finite element mechanical model. The contact surfaces of the impregnated
coil (i.e. coil blocks and pole pieces) are assumed bonded, while all
the other surfaces are modeled under the assumption of "sliding with
separation allowed" with a friction factor of 0.2. The shell pre-load is
chosen so that the contact region between the pole turns and the pole
pieces does not exhibit tension larger than 20 MPa when electro-magnetic
forces, generated at a gradient of 240 T/m, are applied. The e.m forces
are given in Table III, and the computed stresses for shell and coil
layer 1 (where higher stresses are observed) are plotted in Fig. 4, Fig.
5, and Fig. 6. During bladder operation the shell is pre-tensioned to 51
MPa and the coil compressed to a maximum stress of 99 MPa. Once the load
keys are inserted and the bladder deflated, a spring-back is expected in
the structure, due to the clearance necessary to slide the keys between
the masters.

TABLE I Electro-magnetic Forces

  --------------------------- ---------- ---------- ---------- ---------- --------
                              **Unit**   **F~x~**   **F~y~**   **F~r~**   **F**

  Layer 1                     N/mm       +1673      -1124      +1148      -1503

  Layer2                      N/mm       -32        -1039      -311       -1018
  --------------------------- ---------- ---------- ---------- ---------- --------

Values are computed for a gradient of 240 T/m.

![](media/image4.wmf){width="3.1555555555555554in"
height="2.589583333333333in"}

Fig. 4. Shell azimuthal stress during bladder operation, after key
insertion and bladder deflation, after cool-down and at 240 T/m.

![](media/image5.wmf){width="3.1930555555555555in"
height="2.589583333333333in"}

Fig. 5. Coil azimuthal stress in layer 1 pole area during bladder
operation, after key insertion and bladder deflation, after cool-down
and at 240 T/m.

![](media/image6.wmf){width="3.25in" height="2.589583333333333in"}

Fig. 6. Coil azimuthal stress in layer 1 mid-plane during bladder
operation, after key insertion and bladder deflation, after cool-down
and at 240 T/m.

After cool-down, the shell tension increases to 159 MPa, while the coil
pole reaches a peak stress of 139 MPa. As the e.m. forces are applied
the unloading of the coil pole results in a increase of stress on the
mid-plane, while marginal variation of shell stress are observed.

## End region

The mechanical behavior of the magnet ends was analyzed with a 3D finite
element mechanical model, following the integrated modeling technique
described in \[31\]. Similarly to the 2D model, the axial pre-load
provided to the coil by the end support has been chosen in order to
minimize the contact tension between coil and end parts when the
electro-magnetic forces (directed outwardly in the longitudinal
direction) for a gradient of 240 T/m are applied. According to the
model, the contact area between layer 2 pole turn and pole piece in the
end region (see Fig. 3) is the one more likely to undergo high tension
separate under the action of the e.m. axial forces. In order to
withstand a total e.m 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. 7). The force
provided by the rods compress the pole turn against the pole piece with
a contact pressure of 65 MPa, which reduces to 7 MPa at 240 T/m. As
observed in the shell, minimum rod stress variations are observed during
excitation.

![](media/image7.wmf){width="3.1930555555555555in"
height="2.5902777777777777in"}

Fig. 7. Axial rod stress after loading at 293 K and as a function of the
fraction of e.m. force with respect to the 240 T/m level.

![](media/image8.wmf){width="3.1930555555555555in"
height="2.5902777777777777in"}

Fig. 8. Contact pressure between layer 2 pole turn and pole piece after
loading at 293 K and as a function of the fraction of e.m. force with
respect to the 240 T/m level.

# Assembly Procedure and Tooling

The LQ magnet support structure is composed of four, equal-length
yoke-shell, or segments. Each of these segments are individually
assembled and pre-loaded, and then combined in a full-length structure.
The assembly procedure starts by pre-assembly four 0.8 m long stacks of
pad and yoke laminations (see Fig. X, top). The laminations aligned with
bushings and compressed with an hydraulic cylinder. The pre-load is
locked-in with stainless steel tie-rods and nuts. The yoke-stacks are
aligned and keyed in place within the shell near both ends of the
subassembly by internal alignment pins (see Fig. 1) set in
precision-machined grooves in each of the yoke laminations and shell
inside diameter. The pad stacks are instead bolted around four aluminum
dummy coils. The coil-pack subassembly used to preload each shell/yoke
segment (see Fig. X). The yoke stacks are locked into place with
yoke-gap keys via pressurized bladder & key operations around the
pre-assembled 1-m dummy coil-pack sub-assembly.

![](media/image9.png){width="3.49375in" height="3.178472222222222in"}

Fig. X. Assembly steps: pad lamination stacking (top left); yoke
lamination stacking (top right); assembly of first segment (center);.

The same operation is executed for the second shell-yoke segment. In
order to accurately support and handle each assembled segment, they are
mounted on aluminum cradles which are bolted to a specially designed and
fabricated "air pallet". This air pallet will raise the full weight of
the 1000 kg \[2200 lb.\] subassembly approximately 0.07 mm on a cushion
of air at 500kPa \[70 psi). A rotary assembly was designed to
hydraulically raise the shell/yoke segments to orient the
segment-to-segment alignments pins, azimuthally so that each segment can
engage the other as they were floated together on the air pallets. After
removing the 0.8 m long tie rods, the first two Shell/Yoke Segments are
drawn together with the 2-m tie-rods by using a hydraulics array. .

The following describes the 2-segment assembly process. The 1-m yoke
tie-rods are removed from each of the two segments. The completed
Segment 2 subassembly, mounted on its air pallet support, is floated to
the stationary Segment 1, also mounted on its air pallet support. The
hydraulics of the rotary assembly on Segment 2 is energized to allow
rotation of the shell to align and engage the four segment-to-segment
pins.

Once the pins are engaged, the eight, temporary 2-m yoke tie-rods are
inserted and the two segments are drawn together by the hydraulics array
assembly. then the nuts are tie-rod nuts are torqued and the hydraulics
assembly depressurized and removed. The same procedure is used on
Segments 3& 4.

For the full-length assembly, the same procedure is performed except the
air pallets supporting Segments 3 & 4 subassembly are pressurized
simultaneously and floated into alignment with the Segment 1 & 2
subassembly. The 4-m yoke tie-rods are inserted and the hydraulics array
is used, again, to draw the total assembly together

The full-length dummy coil pack is assembled on a specially designed
"insertion" structure that is accurately placed in line with the fully
assembled shell/yoke structural subassembly. (Fig)

The completed coil-pack subassembly is pulled into the full-length
shell/yoke structure on the keys in the bottom master key blocks
(already installed in the shell/yoke structure) with a powered winch
assembly. (Fig)

Next, the sides and top master key blocks, alignment keys and bladders
with pull shims are inserted from both ends of the assembly.

Preloading of the magnet structure is done in three phases. Phase One is
a nominal azimuthal preload operation -- done with the bladders and load
keys. This operation seats ("de-fluffs") all the components in the
structure. Phase Two is the axial loading procedure -- where the final
end preload is applied to the coils in the coil-pack. Phase Three is the
final azimuthal loading applied by the bladders and keys.

Before pressurizing the bladders for Phase One, the strain gage
monitoring system is connected to the strain gage arrays mounted to the
shells and coils to monitor strain states during all the phases of
loading.. The bladders are then pressurized to exert a nominal preload
on both the coilpack and the shell/yokes until the yoke keys are loose.
The gap keys are left inserted as a safety stop if there is a bladder
failure The pressure is held until more shims are inserted at the load
keys. Then, pressure is incrementally increased and more load pad shims
are inserted until the target shell strain is attained. Then the yoke
gap keys are removed.

To axially preload the four quadrupole coils held inside the coil-pack,
four 4 m, 19.05 mm \[.75"\] diameter, stainless steel axial load rods
are inserted in the clearance cavities created by the assembled
coil-pack. (Fig) Then the axial load endplate assemblies are inserted
over the rods at both ends with the "bullets" engaged in insulated,
load-bearing receptacle-blocks attached to each coils' end shoes. The
bullets are screwed into the endplates for adjustment. (Fig) These
endplates and bullets are temporarily held against the coils with nuts.

A 25-ton capacity, hydraulic cylinder assembly is installed on the lead
ends of the axial rods. The hydraulic cylinder will pull/stretch the
axial rods, as it bears against the endplate, thus simultaneously
compressing the coils axially.

![](media/image10.jpeg){width="1.6in" height="2.401388888888889in"}
![](media/image11.jpeg){width="1.7902777777777779in"
height="2.3979166666666667in"}

Fig. 8. Section 2 dummy coil--pad sub-assembly (left) and yoke-shell
sub-assembly (right) instrumented for cool-down test.

# Cool-down Test 

A 0.8 m long segment (Segment 2) of the structure was assembled with
four aluminum dummy coils and cooled-down to 77 K to characterize the
structure. The shell was instrumented with four half-bridge strain
gauges placed on the the four magnet mid-planes. An identical strain
gauge set-up was mounted on the dummy coils.

The gauges measured the azimuthal and axial strain at the shell's
longitudinal center. In total, 16 gauges, all thermally compensated by
gauges mounted on stress-free aluminum elements, were mounted on the
structure. 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 (78 GPa at 77 K)
and the Poisson's ratio (0.34) of aluminum. The gauge measurements of
the shell and dummy coil gauges, both in term of micro-strain and
stress, are shown in Fig. X to Fig. X (markers), and compared with
values expected from a 3D finite element model of the segment (dashed
line). After cool-down the shell stress in the shell raised to +138 6
MPa (1 rms) and +41 13 MPa , in the azimuthal and axial direction, while
the stress in the dummy coils reached azimuthally -231 23 MPa and
axially +74 7 MPa. In both case data are weel reproduced by model
results.

![](media/image12.png){width="3.2777777777777777in" height="2.60625in"}

Fig. 8. Gauge measurements of azimuthal and axial strain in the shell
(markers) and comparison with computed values (dashed lines).

![](media/image13.png){width="3.3152777777777778in" height="2.60625in"}

Fig. 9. Gauge measurements of azimuthal and axial strain in the dummy
coils (markers) and comparison with computed values (dashed lines).

![](media/image14.png){width="3.2777777777777777in" height="2.60625in"}

Fig. 8. Gauge measurements of azimuthal and axial stress (MPa) in the
shell (markers) and comparison with computed values (dashed lines).

![](media/image15.png){width="3.2777777777777777in" height="2.60625in"}

Fig. 8. Gauge measurements of azimuthal and axial stress (MPa) in the
dummy coils (markers) and comparison with computed values (dashed
lines).

# Conclusions and Next Steps

The LQS magnet is goin to be the first long cos-theta type quadrupole
assembled in a shell-type support structure. At 4.5 K, the quadrupole is
expected to generate a gradient of 240 T/m, with peak field in the
straight section of the layer 1 pole turn. The structure provides enough
support to the coil so that no separation is expected between conductor
and pole pieces both in the straight section and in the ends. A new
assembly procedure featuring four 0.8 m long segment of the structure
pre-assembled individually and then combined together. Excellent
agreement has been obtained between model prediction and strain gauge
measurements performed during cool-down of a short section of the
structure. At the time of the submission of this paper, all the
components of the structure have been fabricated. Two yoke-shell
segments (1 and 2) have been assembled. As a next step the two
sub-assemblies will be connected with 2 m long tie rods. Segments 3 and
4 shall be pre-assembled the same way. Both segment pairs will be
connected by the final 4-meter long yoke tie-rods. Before the final
pre-load with the LQS01 coils, a completed, full-length, dummy coil-pack
subassembly will be pulled in and bladder operation will be performed.

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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.