**Coil End Design for the**

**LHC IR Quadrupole Magnet**

Jeffrey S. Brandt, Anthony L. Simmons

*Fermi National Accelerator Laboratory*

November 8, 1996

**Abstract**

This paper describes the design of the coil ends for the LHC IR
Quadrupole magnet, intended for use at the CERN European Laboratory for
Particle Physics in Switzerland. These magnets will be produced by Fermi
National Accelerator Laboratory. The superconducting cable paths are
determined from both magnetic and mechanical considerations. The coil
end parts used to shape and constrain the conductors in the coil ends
are designed using the developable surface, grouped end approach. This
method allows the analysis of strain energy within the conductor groups,
and the optimization of mechanical factors during the design. Design
intent and implementation are discussed, and design challenges are
detailed.

**Developable Surface, Grouped End Design**

***Mathematically least-strain***

The optimal coil end design provides consistent containment for each
conductor in the end, while optimizing strain energy and minimizing
mechanical and magnetic disturbances. Fermilab has progressed through
many methods of specifying the positions of conductors in coil ends
\[1\]. Starting with the SSC dipole program, in which Fermilab designed
and produced several magnets, a method termed developable surface,
grouped end was tried \[2, 3\].

Each coil cross-section contains sub-groups of conductors, or current
blocks. The grouped end design method treats each current block as a
group of conductors that originate at the end of the coil straight
section and maintain conductor-to-conductor contact as they wind around
and over the mandrel. The group is a mathematically determined
configuration that attempts to minimize the strain energy of individual
conductors within the group, and is created by a computer program, BEND,
written by Joe Cook \[4, 5\].

This program is the heart of a complete coil end design system which
consists of using BEND to create and optimize the groups, combining the
BEND group files into files which define the coil end parts, and reading
these files into a CAD package to produce the part geometry. This
geometry is then used to make individual drawings of the parts, CAM
toolpaths for manufacturing them, and computerized inspection paths for
measuring them. This design system was first applied to the SSC Dipole
magnets \[6\], then to an alternate coil end design for the LHC Dipole
magnets \[7, 8\], and now to the LHC IR Quadrupole magnets.

***Unique winding surfaces***

One distinct advantage of this design system is the unique set of
rulings, or fold lines, contained within the winding surfaces of the
parts (see Figure 1). These fold lines define a surface that is more
naturally windable than any of the other part surfaces we have
experienced. The conductor bends around these fold lines in a way that
minimizes its strain energy, and allows it to conform to the radius of
the winding mandrel. After winding, the conductor experiences no
tendency to lift off the mandrel and ride up the nose of the part. This
was demonstrated while winding outer coils for the LHC dipoles at CERN
\[8\].

***Fewest number of parts***

Another advantage to this design system is that it defines the fewest
number of parts required to produce a magnet. There are a total of
fifteen different coil end parts for the LHC IR quad magnets: three
return end parts and five lead end parts for an inner coil, and three
return end parts and four lead end parts for an outer coil. Because the
conductors are allowed to group together, there are no fan-outs or turn
separators in either of the coils.

![](media/image1.emf){width="5.000694444444444in"
height="3.352777777777778in"}

**Based on Caspi\'s Initial Magnetic Design**

***First group lengthened by 8.00mm***

An initial magnetic analysis for the IR quad coil end was performed by
Shlomo Caspi of LBL in April of 1996. We received by telephone a set of
A-lengths and origin differences for the four groups of the coil return
ends. The groups are created within a right-hand Cartesian coordinate
system that has the Z--axis coincident to the beam tube centerline, and
the Y--axis passing through the pole center. A group\'s A-length is the
value of the Z-coordinate on the inside group surface, on the coil outer
radius, in the Y--Z plane.

The 0,0,0 origin of the coil end is located on the beam tube centerline
at the point which the coil straight section ends. Not all the groups in
an end need to originate at this 0,0,0 point, and magnetic field
disturbances in the end can be minimized by shifting the origin of
certain groups away from the 0,0,0 point along the Z--axis. The origin
difference of a group is the distance the X,Y,Z coordinate system of the
group is shifted along the Z-axis from the 0,0,0 origin of the coil end,
effectively lengthening the straight section for that current block.
Here are the initial values received from Shlomo, and the modifications
we had to make during the design process:

First-wound inner coil groups:

Shlomo\'s A-length 10mm + Shlomo\'s origin difference 0mm = 10mm

Fermilab\'s A-length 18mm + Fermilab\'s origin difference 0mm = 18mm
(+8mm)

Second-wound inner coil groups:

Shlomo\'s A-length 29mm + Shlomo\'s origin difference 44mm = 73mm

Fermilab\'s A-length 35mm + Fermilab\'s origin difference 46mm = 81mm
(+8mm)

First-wound outer coil groups:

Shlomo\'s A-length 35mm + Shlomo\'s origin difference 0mm = 35mm

Fermilab\'s A-length 43mm + Fermilab\'s origin difference 0mm = 43mm
(+8mm)

Second-wound outer coil groups:

Shlomo\'s A-length 40mm + Shlomo\'s origin difference 20mm = 60mm

Fermilab\'s A-length 68mm + Fermilab\'s origin difference 0mm = 68mm
(+8mm)

![](media/image2.emf){width="5.000694444444444in" height="3.75in"}

***Relative group positions maintained***

As shown above, several of the values provided by Shlomo were changed in
the Fermilab design. The first-wound inner coil groups were not able to
be optimized with a 10.00mm A-length. We increased the value until we
got successful groups at 18.00mm. The additional 8.00mm was then added
to the combined A-length / origin difference for all the other groups,
maintaining the relative positions of the four groups. A cross-section
through the return end of a coil set is shown in Figure 2.

The second-wound inner coil groups were also not possible at 29.00mm, or
at 81.00mm without an origin difference. These groups ended up with an
A-length of 35.00mm, and the origin difference was adjusted to maintain
the groups\' relative position within the end. The first-wound outer
coil groups behaved fine at the modified A-length of 43.00mm, and the
second-wound outer coil groups were able to be defined with a 68.00mm
A-length, avoiding the need for an origin difference.

**Specific Mechanical Considerations**

Based on experience, the return end groups and lead end groups required
in a coil are designed in parallel. Lead end groups often require longer
A-lengths to distribute the larger twist values encountered in turns
that transition from one current block, across a wedge to the next-wound
current block. Lead end groups are designed to utilize and match
existing return end geometry (see Figures 3 and 4). If the design work
is not done in parallel, the work of defining return end group geometry
will sometimes have to be redone. On the inner coil for this magnet, the
lead end design was very sensitive to the A-lengths specified for the
return end groups.

The wide conductor widths and small strand diameters specified for this
magnet were a concern. LBL produced several spools of preliminary
conductor that were sent to Fermilab for practice winding \[9\]. These
winding experiments revealed that the stability of the conductors were
such that both coils should be wound in the favorable direction ---
clockwise for the left-hand lay outer cable. Since the inner and outer
coils need to be wound in opposite directions, a right-hand lay inner
cable was later produced to allow inner coils to be wound in the
favorable counter-clockwise direction.

***First-wound inner coil groups***

The extremely narrow key width made bend radii a primary consideration
for the design of these groups. Small A-lengths made the lead end groups
buckle, and large A-lengths produced large X--axis bulge values. An
18.00mm A-length provided the smallest bulge values without buckling the
lead end groups. Program BEND produced a final edge angle of 7.750° at
the inside of the first-wound return end group. This angle was steep
enough to preclude the need for a shelf under these groups.

On the three-conductor return end group, the guiding strip was placed
with 0 conductors inside and 3 conductors outside to provide the largest
possible radii in the group, since conductors stacked on the inside of
the guiding strip tend to force the radii smaller. No origin difference
was used. The shift value used was 2.386, the blunt value was 0.288, and
the narrow value was 0.000.

On the two-conductor lead end group, the guiding strip was placed with 0
conductors inside and 2 conductors outside. No origin difference was
used. The shift value used was 1.000, the blunt value was 0.250, and the
narrow value was 0.000. The inside group final edge angle was made
7.750° to match the return end group. On the one-conductor lead end
group, the guiding strip was placed with 0 conductors inside and 1
conductor outside. No origin difference was used. The shift value used
was -1.500, the blunt value was 0.462, and the narrow value was 0.000.
The outside group final edge angle was made 7.161° to match the return
end group.

The inside-group surface of the one-conductor group had to be designed
with the outside-group surface of the two-conductor group in mind. These
two group surfaces define the geometry of the lead end filler between
them. The filler must start at the 0,0,0 origin matching the wedge shape
of the coil cross-section, and feather to 0.00mm thickness at the nose.
This filler was fairly easy to design. At first, the inside filler
surface did cross through the outside surface, but a fair amount of work
with the variables blunt and shift provided a smooth transition of the
filler free edge thickness.

![](media/image3.emf){width="5.280555555555556in"
height="3.7847222222222223in"}

***Second-wound inner coil groups***

Finding an A-length that would avoid large X--axis bulge values and
still provide reasonable strain energy values was a real problem for the
second-wound groups. A large number of A-length and guiding strip
positions were tried before an acceptable combination was found. These
groups have a fairly narrow width and a large amount of twist to
distribute because of the angle from vertical of the outside wedge
surface. An inside group A-length of 35.00mm produced the most stable
groups with the smallest strain energy and error magnitudes.

Program BEND produced a final edge angle of 21.087° on the inside of the
second-wound return end group. This angle is steep enough to make the
shelf under these groups very thin, but not steep enough to eliminate
the need for a shelf. Shallowing this angle manually to thicken the
shelf would have increased the twist even more, and steepening it to
eliminate the shelf would have produced the same problems encountered in
the LHC dipole second-wound inner coil groups, which later had to be
redesigned.

The decision was made to accept the BEND final edge angle, and allow the
shelf to exist under this eleven-conductor group. The shelf thickness
was 0.42mm at the nose, tapering down to 0.29mm at the front of the
shelf. This is thinner than any shelf we have allowed in the past, but
too thick to ignore. The shelf gets thicker as it wraps around the tube
radius and before it feathers out to 0.00mm thickness. The maximum shelf
thickness was 0.55mm at ruling number 28.

One other feature of shelves should be discussed. At the time the idea
of shelves was first tried, the cable shape changes seen in coil ends
were not yet understood. It was theorized that as-wound conductors would
be \"fluffy\" and would produce groups that would later be compressed
during the curing process. For this reason, shelves contained an
extension on the front, which would allow the wound conductors to take
up more space than they would need after curing, and not fall off the
front of the shelf while winding.

Since then, it has been shown that axial curing forces do very little to
push as-wound conductors into a tighter package after curing. If the
conductors are not well packaged during the winding process, they will
not be made to do so by curing forces. In addition, the larger amount of
room required by as-wound conductors in the coil ends is now better
understood to be directly related to cable shape changes. We recognize
that the amount of compaction we get in the coil ends is not as large as
in the coil straight section, but conductor containment can still be
very good if appropriate cable shape changes are applied in group
design.

Shelf extensions are very costly, requiring an additional surface to be
machined in each shelf, and two additional undercut surfaces to be
machined in the part in front of the shelf. These undercut surfaces are
difficult to define in the machine shop, require an additional part
setup, and sometimes break through an unrelated part surface during
their manufacture.

Because of this, the conceptual understandings mentioned above, and the
LHC dipole program experience \[8\], shelf extensions and undercuts will
be eliminated from the LHC IR quadrupole end parts. The shelves will end
at the inside surface of the part in front of them, allowing the machine
shop to use the same toolpath to cut both the part in front, and the
front shelf surface. Visual inspection of the mating surfaces will be
easy, and all related problems with undercuts and part mating will be
eliminated.

The dangers of this decision are that the as-wound conductors truly will
overhang the front of the shelf and become pinched by the installation
of the part in front, or that the part in front will bottom out against
the shelf front, not allowing full compaction of the group. The
experience with the LHC dipole coils makes us confident that these
potential dangers will not be a problem, and similar cable dimensions
give us additional confidence in our ability to predict cable shape
changes. We feel that these designed groups will be very close fits to
actual groups of as-wound LHC IR quad conductor.

On the eleven-conductor return end group, the guiding strip was placed
with 2 conductors inside and 9 conductors outside. Again, this position
was chosen to minimize the magnitudes of the X--axis bulge and strain
energy values. An origin difference of 46.00mm was used to maintain the
relative position of this group within the end. The shift value used was
0.844, the blunt value was 0.260, and the narrow value was 0.000.

No filler is required for the last-wound groups in a coil lead end, but
the last turn exits the coil package at the parting plane instead of
continuing around the end. Two additional groups were created for the
lead end that used the same relative guiding strip position as the
return end. One group had 1 conductor inside and 9 conductors outside. A
46.00mm origin difference was used. The shift value used was 0.281, the
blunt value was 0.279, and the narrow value was 0.000. The inside group
final edge angle was made 21.087° to match the other lead end group. The
group near the lead exit had 2 conductors inside and 8 conductors
outside. A 46.00mm origin difference was used. The shift value used was
0.605, the blunt value was 0.260, and the narrow value was 0.000.
Program BEND produced a final edge angle of 21.087° on the group inside,
which is the same angle as that produced on the return end group.

***First-wound outer coil groups***

There is only one conductor in the first-wound outer coil groups, a
condition which simplifies the end part design in three ways. First,
there is only one lead end group to design instead of the usual two.
Second, this lead end group transitions directly into the second-wound
group, eliminating the need for a filler in the outer coil. Since filler
design is usually quite complicated because of the two defining groups
crossing into each other, this was a significant simplification. Third,
a one conductor group is usually easier to optimize than a
multi-conductor group.

For both one-conductor groups, a 43.00mm A-length was used to maintain
the relative position of these groups within the end without the need
for an origin difference. Program BEND produced a final edge angle of
15.982° at the inside of the first-wound return end group. This angle
was steep enough to preclude the need for a shelf under these groups,
impractical for one-conductor groups anyway.

On the one-conductor return end group, the guiding strip was placed with
0 conductors inside and 1 conductor outside to provide the largest
possible radii in the group. No origin difference was used. The shift
value used was 0.661, the blunt value was 0.292, and the narrow value
was 0.000. On the one-conductor lead end group, the guiding strip was
placed with 0 conductors inside and 1 conductor outside. No origin
difference was used. The shift value used was 0.891, the blunt value was
0.267, and the narrow value was 0.000. The inside group final edge angle
was made 15.982° to match the return end group.

![](media/image4.emf){width="5.147222222222222in"
height="4.1097222222222225in"}

***Second-wound outer coil groups***

Finding a guiding strip position that would avoid X--axis bulge errors
was the only optimization problem for the second-wound groups. These
groups have a large number of conductors, which puts some cables far
from the guiding strip, but the larger coil radii and pole width made
them fairly easy to design. An inside group A-length of 68.00mm was used
to maintain the relative position of these groups within the end without
the need for an origin difference.

Program BEND produced a final edge angle of 23.297° at the inside of the
second-wound return end group. Again, this angle is steep enough to make
the shelf under these groups very thin, but not steep enough to
eliminate the need for a shelf. The decision was made to accept the BEND
final edge angle, and allow the shelf to exist under this
fifteen-conductor group. The shelf thickness was 0.72mm at the nose,
tapering down to 0.56mm at the front of the shelf. The shelf gets
thicker as it wraps around the tube radius and before it feathers out to
0.00mm thickness. The maximum shelf thickness was 0.80mm at ruling
number 28. As on the inner coil, shelf extensions and undercuts were
eliminated.

On the fifteen-conductor return end group, the guiding strip was placed
with 3 conductors inside and 12 conductors outside. Again, this position
was chosen to minimize the magnitudes of the bulge and stain energy
values. No origin difference was needed to maintain the relative
position of this group within the end. The shift value used was 0.724,
the blunt value was 0.190, and the narrow value was 0.000.

No filler is required for the last-wound groups in a coil lead end, but
the last turn exits the coil package at the parting plane instead of
continuing around the end. Two additional groups were created for the
lead end that used the same relative guiding strip position as the
return end. One group had 2 conductors inside and 12 conductors outside.
No origin difference was used. The shift value used was 0.803, the blunt
value was 0.215, and the narrow value was 0.000. The inside group final
edge angle was made 23.297° to match the other lead end group. The group
near the lead exit had 3 conductors inside and 11 conductors outside. No
origin difference was used. The shift value used was 0.668, the blunt
value was 0.199, and the narrow value was 0.000. Program BEND produced a
final edge angle of 23.297° on the group inside, which is the same angle
as that produced on the return end group.

**Cable Shape Changes**

***LHC dipole analysis***

The presence of a fifteen-conductor group in this coil end design was
cause for concern. Another fifteen-conductor group in the LHC dipole
program behaved in an unexpected way, showing fairly large gaps in a
localized area on the underside of the outer coils. Program BEND allows
the cable shape to change in a smooth way as the conductors wind around
the end parts. If desired, the conductors may be allowed to change in
mid-thickness and in keystone angle. Based on SSC experience, the
conductors for the LHC dipole were allowed to get thicker at the group
mid-point and the nose, and to become less keystoned.

The BEND variable KEY1 is a multiplier that specifies the change to the
nominal conductor keystone angle at the mid-point in the group, while
KEY2 specifies the change at the group termination, or nose of the end
part. The conductor keystone angle is allowed to become smaller, because
previous magnet designs show that the conductors in the ends appear to
do so. For the LHC dipole program, KEY1 was set to be 0.1, and KEY2 was
set to be 0.2, allowing the conductors to become very nearly
rectangular.

It has been theorized that the conductor becomes more rectangular
because of hard-way bend within the cables. The direction of this
hard-way bend has always been assumed to be around the mandrel, placing
the cable radially inner edge into compression, and causing it to
increase in width, making the conductor more rectangular. This idea has
been supported by actual sectioned coil ends, and by BEND output.
Program BEND outputs the highest values of hard-way bend in a group.
These values are known as ∆L/L\'s, and are negative in sign when
hard-way bends are in the direction to make the conductor more
rectangular.

The highest ∆L/L values output by program BEND are always negative in
sign. However, not all values within a group are output, only the
highest. After seeing the gaps in the LHC dipole ends, it was theorized
that perhaps the hard-way bend in the affected areas of these groups was
in the opposite direction, causing the radially inner edges of the
conductors to become thinner, making the cable more keystoned or at
least less rectangular than predicted.

***New Joe Cook program, DELCOR***

To allow a detailed analysis of the ∆L/L\'s within the LHC dipole group,
Joe Cook wrote a program named DELCOR, which reads the BEND.COR file of
any group and displays all the ∆L/L\'s of each conductor at all fifty
points. In this way, it was seen that the fifteen-conductor group which
showed the unexplained gaps had a section at mid-group, in which the
∆L/L\'s of each conductor were indeed positive.

This evidence was further supported by examining the LHC dipole
second-wound eleven-conductor group. This group showed no sign of
similar gaps, though it too contained a large number of conductors, and
had been designed with the same KEY1 and KEY2 values as the
fifteen-conductor group. This second group showed that all the ∆L/L\'s
of each conductor at all fifty points were negative. Using the
fifteen-conductor LHC dipole group as a model, a study of the effect of
changing the value of KEY1 was made. This led to the creation of a new
version of program BEND, in which the value of KEY1 was changed from 0.1
to 0.5.

***LHC IR quadrupole requirements***

We used program DELCOR to analyze the corner files for all the groups
designed for the LHC IR quad. This analysis showed that nearly every
group in this magnet contained a section in which the primary value of
the ∆L/L\'s was positive. For this reason, the new version of program
BEND was used in the creation of all groups for the LHC IR quad, except
for the two first-wound inner coil lead end groups, and the two
first-wound outer coil lead and return end groups. It is hoped that this
change will avoid the kind of gaps seen in the fifteen-conductor LHC
dipole group.

**Preform Design Integration**

***Preform surfaces defined***

The design of the pole splice for the LHC IR quad is described in
TS-96-014 \[10\]. This splice is made in a similar way to the SSC dipole
and low beta quad magnets previously designed at Fermilab. The spliced
area is part of a soldered preform area that must be partially contained
within the inner and outer coil lead end keys. This preform geometry has
typically been defined by 2-D geometric shapes which have several
shortcomings.

First, this 2-D geometry is not easily applied to a 3-D end part in
which the preform geometry specified must be machined into a tube that
is dropping away out of the 2-D plane. This problem has resulted in end
part shapes which are a poor match to the shapes produced by the preform
fixture. A slot has typically been cut into the end parts to accept the
insulated preform. Too little end part material removed results in a
slot too small, with obvious assembly difficulties and damaged
insulation. Too much material removed results in preforms which are not
firmly constrained within the end parts, and a source of many quenches.

Second, the slot geometry itself is difficult to define, and is subject
to much misinterpretation by manufacturers. The surfaces required in the
end parts must allow for an insulated preform, while the preform
soldering fixture must be defined around bare cable. These problems have
always resulted in a poor fit of the preform within the end parts,
leaving room for the cable to move regardless of how firmly the preform
slots are packed with insulation or filler material.

For these reasons, and others described in TS-96-014 \[10\], the preform
geometry for the LHC IR quad magnets was designed differently. Another
program written by Joe Cook, called LEAD, allows the design of preform
shapes that are completely defined along their entire lengths. A 2-D
geometry layout from Fred Nobrega was used as a basis for this preform
design, and contained certain length and minimum curvature definitions
which were retained. Program LEAD was then used for the creation and
optimization of the preform sections required, producing both the bare
geometry required in the preform fixture, and the insulated geometry
required in the end parts.

***Wind and cure around G-10 keys***

In past magnet designs, coils have been wound around mold-released steel
keys. After curing, these steel keys are removed and appropriate
non-conductive keys are inserted. This compounds the problem of the
preform geometry not being well contained within the end parts. Now the
preform slots must be large enough to clear the insulated preform, and
also allow for the removal and insertion of the keys into the coil
package. Another related problem with this procedure is that the
critical first turn is no longer seated firmly against the surface it
was cured around, and the replacement part surface is never a perfect
match to the steel surface.

These difficulties produce a strong desire to wind and cure around the
G-10 or Ultem keys, to make sure that all the end parts are firmly
bonded into the cured coil package. The feasibility of this idea was
proved in the SSC dipole program, and again in the LHC dipole program.
The surfaces defined by program LEAD will be machined into a two-piece
lead end key, each piece containing one side of the appropriate
insulated preform shape (see Figure 5). The accurate definition of these
surfaces will ensure a good fit to the preform shape. The surfaces will
be coated with an appropriate adhesive, assembled around the preform,
and bolted and pinned to the winding mandrel while being clamped firmly
together. This will produce a cured coil in which the preform shape is
in intimate contact with the coil end parts, and is firmly bonded into
the coil package.

![](media/image5.emf){width="4.290277777777778in"
height="2.723611111111111in"}

On the outer coils, there will be an additional slot which will be
filled with a steel mold-released shim during winding and curing. This
shim will be removed later to allow the inner coil preform to pass up
though the outer coil key and into splicing position. This slot will
then be filled with a machined shim of the appropriate end part
material, leaving only a short length of inner coil preform with
non-cured containment. The shim will be dimensioned to hold this short
length of inner preform as tightly as assembly will allow. We feel that
these design features will result in the best preform containment ever
achieved.

**References**

  -------- ------------------------------------------------------------------
  \[1\]    R. C. Bossert, J. S. Brandt, J. A. Carson, H. J. Fulton, G. C.
           Lee, \"Analytic Solutions to SSC Coil End Design,\" in *IISSC,
           Supercollider 1*, M. McAshan, editor, New York: Plenum Press,
           1989.

           

  \[2\]    R. C. Bossert, J. M. Cook and J. S. Brandt, *End Designs for
           Superconducting Magnets*, presented at Breckenridge Workshop,
           August 14-24, 1989.

           

  \[3\]    R. C. Bossert, J. S. Brandt, J. A. Carson, C. E. Dickey, I.
           Gonczy, W. A. Koska and J. Strait, \"SSC 40mm Short Model
           Construction Experience,\'\' in *Supercollider 2*, M. McAshan,
           editor, New York: Plenum Press, 1990.

           

  \[4\]    J. M. Cook, \"An Application of Differential Geometry to SSC Coil
           End Design,\'\' SSC Laboratory SSCL-N-720, FERMILAB-TM-1663, Fermi
           National Accelerator Laboratory, Batavia, IL, 1990.

           

  \[5\]    J. M. Cook, \"Strain Energy Minimization in SSC Magnet
           Winding,\'\' in *IEEE Transactions on Magnetics*, vol. 27,
           pp.1976-1980, March 1991.

           

  \[6\]    J. S. Brandt, \"Coil End Design for the SSC Collider Dipole
           Magnet,\" FERMILAB-TM-1735, FERMILAB-Conf-91/196, Fermi National
           Accelerator Laboratory, Batavia, IL, July 1991.

           

  \[7\]    J. S. Brandt, \"Inner Coil End Design for the LHC Dipole Magnet,\"
           Fermilab Technical Support Technical Note #TS-95-010, Fermi
           National Accelerator Laboratory, Batavia, IL, November 1995.

           

  \[8\]    J. S. Brandt, \"Coil End Design for the LHC Dipole Magnet,\"
           FERMILAB-TM-1954, Fermi National Accelerator Laboratory, Batavia,
           IL, May 1996.

           

  \[9\]    J. S. Brandt, \"LHC IR Quad Cable Test Winding Results,\" Fermilab
           Technical Support Technical Note #TS-96-010, Fermi National
           Accelerator Laboratory, Batavia, IL, February 1996.

           

  \[10\]   J. S. Brandt, \"Preform and Pole Splice Design for the LHC IR
           Quadrupole Magnet,\" Fermilab Technical Support Technical Note
           #TS-96-014, Fermi National Accelerator Laboratory, Batavia, IL,
           November 1996.
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