#### 5.1.2.3 Mechanical and thermal design[^1]

##### 5.1.2.3.1 Magnet structure

###### (a) Magnet support by cryogenic service pipe

The final assembly of the 67.5m length has two parts mounted as a one
unit, the magnet yoke with a conductor cryostat and the cryo-service
line. The 300x5 mm tube of cryo-service line is made from A36 type of
steel and is a housing of all cryogenic pipelines and current return.
The tube serves as a vacuum jacket and as a base for the iron core
assembly, and provides mechanical rigidity of the magnet. The magnet
core is periodically (D=0.5m) welded to the tube to increase assembly
vertical stiffness and to reduce system deflection. The combined
structure is rigid enough that supports every 6m (20') are sufficient to
align the structure. Total magnet weight is \~ 33 tonne (\~500kg/m).

###### (b) Magnet yoke

The laminated magnet yoke consists of upper and lower iron half cores.
Core laminations are stamped from 1.5-mm thick low carbon steel. The
stack of laminations is pressed and welded into a block. Two blocks,
upper and lower, separated by two steel spacer bars are welded to the
stainless steel strips from the inside of the central hole. The welds
provide a prestress no less than 5 tons/m to receive high stability of
the pole geometry near the beam gaps. The side gaps remain open for
magnetic measurements and vacuum chamber installation.

The conductor cryostat is positioned in the center of the core hole. All
gaps between core and cryostat are filled by epoxy. Mechanically, the
magnet core and the cryostat are a monolithic structure.

##### 5.1.2.3.2 Transmission line mechanical analysis

###### (a) Vertical deflection and stress between support points

The magnet is installed on the vertical supports. A distance of 6 m was
chosen between supports. Numerical simulations were done in order to
estimate structural stresses and deformations \[1\]. The maximal
deflection of the magnet under weight load is 1.2 -- 2.1 mm, depending
on the final magnet design. In any case, if the magnet core will be
connected with lower vacuum tube by welds, the vertical sag is close to
1.2 mm and maximal stresses will not exceed 50 -- 60 MPa. For bolted
connection without welds the sag is close to 2.1 mm and maximal stresses
reach 90 MPa.

###### (b) Force to introduce sagitta

Magnet horizontal sagitta is \~15 mm over 67 m length (Lring=232km,
Rring=36.9km). To estimate deformations of the straight magnet structure
introduced by this sag during alignment in the tunnel, the numerical 3D
simulations were performing using 12-m section model \[2\]. Over such a
distance the sag is \~0.5 mm. Both model ends had been restricted from
motion. The model with a distributed weight was loaded by horizontal
force applied to the central supports of the vacuum tube. The result
shows the magnet block moves about 0.9 mm for 1 mm movement of the
vacuum tube. The force needed for 1 mm motion is 150 kg, without
estimating friction. Taking into account the load of \~3 tons for each
support, the friction force may be estimated about 300 kg. [Total force
will be \~450 kg]{.mark} per 1 mm displacement.

Difference in relative movement of the iron halves of the magnet can
reach 30 μm for a support movement of 1 mm.

###### (c) Magnetic forces on transmission line

In the ideal case, the magnetic forces equal zero because of the design
symmetry of the two iron poles surrounding the transmission line.
Nevertheless, the iron saturation effect and incorrect position of
superconducting cable will cause uncompensated magnetic forces \[3\].
The magnet air gaps introduce force gradients of 228 kg/mm in vertical
direction and --100 kg/mm in horizontal direction for 1 m length of
drive conductor at 100 kA current. The return conductor has gradients an
order of magnitude less in both directions. The magnetic forces between
transmission lines with 0.29 m vertical separation in the space between
magnets are 700 kg/m and increase to \~4000 kg/m at 10 mm separation.

###### (d) Thermal stress and thermal forces 

The conductor tubes in the transmission line magnet are made of invar
and consist of continuously welded lines. The cool down shrinkage in
this case will be minimized, but is 65 mm over 135 m distance with 67
MPa of thermal stress. Therefore, two invar conductor pipes (A=200mm^2^)
give \~1400 kg tension force applied on the end of the pipe support at 5
K. The radial force on the invar pipe support for ring shrinkage
compensation is small, \~0.12 kg/m.

All other cryo-lines are made from steel or aluminum and can not be
continuously welded because of high thermal stress level. Table 1
describes the situation for different pipe materials after cool down to
5 K.

Table 1. Pipe at 5 K after cool down from 300 K

+-------------+-------+-------+--------+----------+-------+---------+
| ###         | *∫    | *E    | *σ=E\  | *σyield* | *σyie | *       |
| ## Material | αdt,* | (5K)* | *∫αdt* |          | ld/σ* | ∆L(mm)* |
|             |       |       |        | *MPa*    |       |         |
|             | *     | *GPa* | *MPa*  |          |       | *       |
|             | mm/m* |       |        |          |       | L=135m* |
+-------------+-------+-------+--------+----------+-------+---------+
| > 304 SS    | 3     | 220   | 660    | 600-1200 | 0.    | 405.0   |
|             |       |       |        |          | 9-1.8 |         |
+-------------+-------+-------+--------+----------+-------+---------+
| > 6061 Alum | 4.1   | 80    | 328    | 380      | 1.15  | 553.5   |
+-------------+-------+-------+--------+----------+-------+---------+
| > Invar     | 0.48  | 140   | 67     | 700-1000 | 10.4  | 64.8    |
|             |       |       |        |          | -14.9 |         |
+-------------+-------+-------+--------+----------+-------+---------+

The steel pipes have to be equipped with compensation bellows every
\~33m (135m/(405mm/100mm)) to reduce shrinkage to the level of \~100mm
and to avoid stress build up in the end supports.

###### (e) Yoke deflection under magnetic forces

The dipole magnet at maximum field of 2 T has 25 t/m magnetic force
applied to the poles. The force is zero at injection field and rises
during acceleration cycle. This force is taken across support spacers in
the relatively small \~1 cm distance between the transmission line
vacuum jacket and beam pipe. The yoke assembly has to be rigid enough to
keep the air gap stable. Two welds inside the central bore of the magnet
connect both half-cores together and provide pre-stress \~5 tons/m. The
prestress removes all clearances between spacer bars and half-cores. The
1 m model with outer spacer bars was successfully tested at the room
temperature test stand and no field gradient shift was measured up to
1.7 T \[4\].

The test of a short mechanical model with air gaps open on both sides
showed that the left gap shrinks by 12 μm and the right gap by 6 μm
vertically. The horizontal change was less than 4 μm. These changes were
reproducible. They can only influence the dipole field component and can
be compensated by magnet calibration.

###### (f) Mechanical analysis of support spider 

Loads from transmission line magnetic forces are transmitted from the
drive conductor to the pipe, through the supports (spiders) to the
vacuum jacket, and to the magnet core. A cross-section of the drive
conductor transmission line is shown in [Fig. {5.1.2.2-3}.]{.mark}

In the horizontal direction, the conducting cable is a self-centering
system and does not need strong supports. However, the part of the
conductor inside the magnet is at a point of unstable equilibrium in the
vertical direction. The field gradient gives rise to an instability in
which the current-carrying pipe bends into a sinuous curve with a period
of twice the support distance. Therefore, the support interval 0.5 m has
been optimized for lowest conductor displacement (0.5 mm) chosen for
production accuracy and pipe tolerances \[5\].

The conductor is centrally positioned by spiders made from ULTEM, which
has a low value for the thermal conductivity integral. The spider pegs
have a rectangular cross section 2.5x3.5 mm. A flexible ring unites the
four pegs together and serves as a base for thermal shield assembly.
Perfectly positioned pegs are under compression inside the cryostat. The
compression depends on the leg over-sizing and on the variation in pipe
diameter. A 0.5 mm tolerance is required on the roundness of both pipes.
The pressure range is 20-40 kg. These numbers increase up to 70-100 kg
at cold conditions and under action of magnetic force. For verification,
the prototyped injection-molded supports were exposed to 100,000
mechanical cycles with a load force of 300 kg/m (three times the
expected one). Although a discoloration of the ULTEM was observed, the
supports did not break.

The spider acts as a flexible membrane if the relative axial motion of
the inner-cold conductor line and the outer-warm vacuum jacket tube
occurs without sliding. If motion is \~2 mm, the maximum stress in the
spider material due to bending is \~300 MPa. However, the ultimate
strength for ULTEM is169 MPa, and the fatigue limit for 10^7^ cycles is
100 MPa \[6\]. We therefore have a strong requirement for a longitudinal
anchoring system, since the relative pipe motion can be \~20 mm during
magnet transportation or by temperature variation in the tunnel. This
motion is caused by the difference in thermal contraction between steel
and invar under a 10 K temperature change from 330 K. The sliding range
of the peg needs to be carefully verified. If it is insufficient,
another sliding support system can be used \[7,8,9\].

##### 5.1.2.3.3 Transmission line thermal analysis

Transmission line heat load estimates are divided into two components:
the primary heat load on the 4.5 K system and the heat load to the 50 K
shield system. The calculated heat loads are presented in Tables 2 and 3
\[10\].

Table 2. Estimated Heat Loads into 50 K Shield System\
(all values in W/m)

  ---------------------------- --------- -------------------------- -------
  Transmission Line Shield     0.578     Shield Return Header       0.471

  Conductive Heat Load         0.432     Conductive Heat Load       0.199

  Longitudinal Anchor          0.011     Longitudinal Anchor        0.011

  MLI Heat Load /meter         0.110     MLI Heat Load /meter       0.236

  Instrumentation Leads        0.020     Instrumentation Leads      0.020

  Valve boxes                  0.005     Valve boxes                0.005
  ---------------------------- --------- -------------------------- -------

Table 3. Estimated Heat Loads in 5K at Transmission Line and Return Bus\
(all values in W/m)

  ---------------------------- --------- -------------------------- --------
  Transmission Line 5K Flow    0.048     Return Bus 5K Flow         0.014

  Conductive Heat Load         0.040     Conductive Heat Load       0.006

  Longitudinal Anchor          0.0003    Longitudinal Anchor        0.0003

  Radiation Heat Load          2E-04     Radiation Heat Load        5E-04

  Instrumentation Leads        0.002     Instrumentation Leads      0.002

  Valve boxes                  0.001     Valve boxes                0.001

  Splice heat load             0.004     Splice heat load           0.004
  ---------------------------- --------- -------------------------- --------

##### 5.1.2.3.4 Interconnects, pipes, and bellows 

###### (a) Axial anchoring for transmission line and return line

The magnet anchor system consists of the vacuum barriers, the
force-anchors, the transportation locks and the vacuum jacket anchors.

The vacuum barrier or breaks are used to insulate subsystems in order to
facilitate installation, troubleshooting, and repair. It provides a good
vacuum in the transmission line ring section \[11,12\]. The vacuum
barriers are designed to withstand a differential pressure of 0.15 MPa
(\~1000 kg longitudinal force) and to minimize the heat in-leak. It is
made of an all-welded construction of thin-wall stainless steel tubes.
The barrier is electrically insulated from the invar conductor pipes by
ceramic insulators.

![](media/image1.wmf){width="6.2868055555555555in"
height="2.147222222222222in"}Figure 1. [Anchor system for the]{.mark}
[magnets]{.mark}

All magnet pipes will be physically constrained by the vacuum breaks at
same location. Logically, frequency of break location depends on vacuum
pump distribution and is divisible to the magnet length ([67.75]{.mark}
[m]{.mark}). Distance between breaks is not clear yet. 400-500 m comes
from LHC analogy \[13\]. With a [67.75 m]{.mark} interval, only one
magnet will be damaged if insulation vacuum is accidentally lost. We
assume [a period of *n* magnet lengths, where *n*≤4]{.mark}, is
acceptable.

The pipe force anchor restrains thermal forces from invar pipe shrinkage
(5000 kg) during cool-down and warm-up. This anchor consists of tie rods
and G-10 spider, and connects the invar pipes to the vacuum jacket. The
vacuum break and pipeline anchor can be combined into a single unit.

The vacuum jacket is connected to the ground by the jacket anchors at
the end of the magnets. These points define an immovable magnet
cross-section in case of accidental vacuum loss and jacket thermal
contraction resulting from a cool down to about 250 K \[14\]. The jacket
bellows at the interconnect region compensates for a length change.

The transportation lock is located on the opposite end of the magnet
from the vacuum break. It is mounted in place during production and
removed after magnet installation in the tunnel.

###### (b) Cryostat Interconnection

After magnet alignment, interconnection activities will take place. The
magnet and the cryo-service line need to be connected every \~67.5 m.
There are two interconnection regions between magnets, 3.5 m and 1 m
long.

Both conductors will be spliced at these areas. To compensate magnetic,
thermal and hydraulic forces in the 3.5 m region, where transmission
line conductors make a loop and are located close to each other, an
additional set of special spacers, clamps and tension rods will be used.
The weld on the conductor line can apparently take place directly over
the copper/superconductor structure without damaging it \[15\].

Three carbon steel pipes having stainless bellows will be automatically
orbital welded at both areas. Aluminum thermo-shield made from two
pieces will cover all pipeline connections \[16\]. Multi-layer
insulation blankets are mounted around shield to reduce radiation heat
load. The vacuum jacket is connected by a bellows at 3.5 m region and by
a thin steel skin at 1 m region.

##### 5.1.2.3.5 Beam tube mechanical design

![](media/image2.wmf){width="3.9652777777777777in"
height="2.6909722222222223in"}The vacuum system of the transmission line
magnet is an extruded-aluminum system shown in [FigX]{.mark}.
Non-Evaporable Getter (NEG) strips located in a high-conductance
antechamber (see Fig 2) provide primary pumping \[15\]. Lumped
sputter-ion pumps are required every \~100 m to pump methane and noble
gases, which are not pumped by the NEG strip. To start the NEG, a
temperature of XX°C is required.

Figure 2. Magnet beam pipe

High luminosity operations will require a bakeout of the pipe for
surface outgassing and good pumping efficiency. For an aluminum beampipe
this means that entire lengths of a 67 m pipe must be heated in-situ for
24 hours to either 150°C (for aluminum segments), 300°C (for stainless
steel segments), or 350°C (for stainless steel segments with NEG pumps)
\[17\]. Bellows will be required to compensate for the thermal expansion
of beampipe segments every [67.75 m]{.mark}. The BPMs occur every half
cell ([135.5 m]{.mark}). However, the ELETTRA storage ring has an
experience with no in-situ baked out aluminum vacuum chamber \[18\].

Yielding of the aluminum is an issue because of the elevated bakeout
temperature, the use of high-purity aluminum, and the desire for as thin
an extrusion wall as possible in the region immediately above the beam.
Another issue is the beampipe insertion into the yoke gap from the side.
The elliptical beam chamber has to be vertically squeezed in size by 2
mm along its entire length to pass through the pole shim area on the
magnet core. The wall thickness has to be small enough to allow that,
but big enough for buckling stability under atmospheric pressure.
Buckling stability is achieved by a 2 mm pipe vertical extension after
installation. All of these situations were analyzed by ANSYS program.
Results show reasonable stress level in the wall \[19\].

#### References  {#references .Reference-heading}

\[1\] V.Tsvetkov, "Transmission Line Magnet Mechanics", TD TN XXXX 2001.

\[2\] V.Tsvetkov, "Alignment of the Transmission Line Magnet in the
tunnel", TD TN XXXX 2001

\[3\] V.S.Kashikhin, "Transmission Line Magnet for VLHC. Magnetic Forces
and Magnet Deflection," TD TN XXXX. February 2001.

\[4\] V.S.Kashikhin, "Mechanical model 2 test results", TD TN XXXX.
February 2001.

\[5\] M.McAshan, "Cryogenic System for the 3 TeV Injector Study",
Fermilab TN-XXXX,1997

\[6\] I.Novitski, "Analysis of the spider support", TD TN XXXX 2001

\[7\] E.C.Quimby et al., "VJR/VJRR Design, Construction, Installation,
and Performance," ACE, vol 43, New York, 1998.

\[8\] G.Grygiel et al., "Status of the TTF Cryogenic System," ACE
vol.41, New York, 1996

\[9\] K.Hosoyama et al., "Development of a High Performance Transfer
Line System", ACE vol. 45, 2000

\[10\] G.W.Foster, "Transmission Line Magnet R&D", Second Annual VLHC
Meeting, Danfords, Port Jefferson Long Island, NY, Oct. 16-18, 2000

\[11\] V.Parma et al., "The Insulation Vacuum Barrier for the Large
Hadron Collider Magnet Cryostats", ICEC 18

\[12\] B.Jenny et al., "A Composite vacuum Barrier for the LHC Short
Straight Section", ACE vol.41, New York 1996

\[13\] "Technical Specification for a Compound Cryogenic Helium
Distribution Line for the Large Hadron Collider (LHC)", IT-2399/lhc/lhc,
Geneva, Switzerland, December 1997.

\[14\] M. Chorowski, "Risk analysis of the LHC cryogenic system", ACE
2000

\[15\] G.W.Foster, "Status Report on the Transmission Line Magnet",
Fermilab report, September 1997

\[16\] R.C.Niemann, "Model SSC Dipole Magnet Cryostat assembly at
Fermilab", Supercollider 1, New York 1989.

\[17\] "5.6 Beampipe," URL
http://felix.web.cern.ch/FELIX/Loi/HTML/C5/node7.html

\[18\] A. Gambitta et al., "Experience with Aluminum Vacuum Chambers at
ELETTRA", EPAC 2000, Vienna, Austria.

\[19\] I.Novitski "Beam pipe mechanical design" TD TN XXXX 2001.

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