#  Stage 1 Components

## 5.1 Magnets {#magnets .unnumbered}

### 5.1.1 Introduction {#introduction .unnumbered}

The magnet system of the 20 TeV Stage-I VLHC is one of the main
components of the collider, and has a strong influence on the total cost
of machine. For these reasons, the general design goal is to reduce the
cost per Tesla-meter of the collider. The arcs of VLHC-1 are based on
warm-iron, combined function gradient dipole magnets\[1-3\], which are
excited by a single turn 100 kA superconducting transmission line. A
cross-section of the magnet, including the cryogenic service line and
return bus, is shown in Figure 5.1. The flux lines surrounding the
transmission line are shaped by an iron yoke, and two gaps in the yoke
provide the apertures for the two beams. The 20 TeV bending field is
1.966 T. The magnets have a field gradient of ±4.73%/cm,

![](media/image1.png){width="5.830555555555556in"
height="4.324305555555555in"}

Figure 5.1. Cross-section of the gradient dipole magnet used in the arcs
and dispersion suppressor of the Stage-1 VLHC.

which provides focusing and eliminates the need for separate
quadrupoles. The 135.5 m long half-cell is made of two 65.75 m long
gradient magnets.

At the end of each half-cell, where the beta function is maximum in one
plane and minimum in the other, a 3.5 m long space is left open for
correction coils. The transmission line is diverted into the cryogenic
service pipe, near the return bus, allowing the use of conventional,
room temperature, air cooled iron magnets, as shown in Figure 5.2. Three
correctors are installed at each location: a vertically or horizontally
steering dipole, a quadrupole and a sextupole corrector.

make white background:

![](media/image2.png){width="6.4875in" height="2.729861111111111in"}

Figure 5.2. Correction coils placed at each half-cell.

The dispersion suppressor sections are made in a similar fashion. Here
the 101.6 m long half-cell is made of two 48.81 m long dipoles, with a
field at 20 TeV of 1.766 T and an increased gradient of ±9.449 %/cm.
Correctors are employed at each half cell as in the arcs.

In the long straight sections, the space not occupied by the interaction
regions or machine utilities are FODO channels made from conventional
water cooled quadrupoles. Two 6.1 m long, 70 T/m quadrupoles make one
half-cell. Special optics for the machine utilities -- injection, abort,
the RF system, and beam cleaning, are constructed using quadrupoles of
the same design but with special lengths. The matching section for the
low-beta insertions at the interaction regions are also constructed from
the same quadrupoles. The low-beta triplets themselves utilize 300 T/m
cos2θ superconducting quadrupoles made from Nb~3~Sn cable. Special
dipole magnets, similar in design to the gradient magnets in the arcs
and excited by the transmission line, are used to bring the beams into
collision at the interaction regions, to separate the beams to implement
independent RF systems for the two beams, and to cross the beams over at
two opposite points in the ring to ensure equal path lengths for the two
beams.

Table 5.1 summarizes the main parameters of the magnets used in the
VLHC-1 design.

The arc dipoles will clearly dominate the system cost. During the past
three years, most of the R&D effort has concentrated on the dipole
design, with considerable attention focused on the 100 kA
superconducting transmission line cable. The arc dipole design has been
refined through intense prototyping of the major magnet components, and
various types of transmission line cables were tested at a 17m length
superconducting test stand \[4\]. Several short magnet iron core
configurations were tested, using a room temperature test stand \[5\].
Two 6 m magnet prototypes have now been manufactured to confirm the main
technical decisions.

Section 5.1.2 describes the combined function arc and dispersion
suppressor magnets in detail, including magnetic design, design of the
100 kA transmission line, and the mechanical and thermal designs. The
correctors are described in section 5.1.3 and the interaction regions in
section 5.1.4. Section 5.1.5 presents the various special magnets,
including straight section quadrupoles; beam separation, recombination
and cross-over dipoles; and injection and abort system magnets.
Production of the 66 m long gradient dipoles and the testing and
measuring of them are described in sections 5.1.6 and 5.1.7
respectively. Transport, installation and alignment methods are
summarized in section 5.1.8.

Table 5.1. Main parameters of magnets in the Stage-1 VLHC.

+--------------+--------+--------+--------+--------+-------------------+
| Magnet Type  | B~nom~ | G~nom~ | L~mag~ | Number | Notes             |
|              | (T)    | (T/m)  | (m)    | of     |                   |
|              |        |        |        | el     |                   |
|              |        |        |        | ements |                   |
+--------------+--------+--------+--------+--------+-------------------+
| Gradient     | 1.97   | 9.73   | 65.75  | 3136   |                   |
| dipole (arc) |        |        |        |        |                   |
+--------------+--------+--------+--------+--------+-------------------+
| Gradient     | 1.80   | 16.88  | 48.81  | 160    |                   |
| dipole (DS)  |        |        |        |        |                   |
+--------------+--------+--------+--------+--------+-------------------+
| Special      | 1.95   |        | 25 -   | 52     | Separation,       |
| dipoles      |        |        | 35     |        | recombination,    |
|              |        |        |        |        | and cross-over    |
+--------------+--------+--------+--------+--------+-------------------+
| Straight     |        | 70     | 4.8 -  | 464    |                   |
| sect quads   |        |        | 6.8    |        |                   |
+--------------+--------+--------+--------+--------+-------------------+
| Low β        |        | 300    | 9.2 -  | 8      |                   |
| quadrupoles  |        |        | 10.9   |        |                   |
+--------------+--------+--------+--------+--------+-------------------+
| Correctors   |        |        |        |        |                   |
+--------------+--------+--------+--------+--------+-------------------+
| > Dipole     | 1.0    |        | 0.50   | 1648   |                   |
| > (horiz.)   |        |        |        |        |                   |
+--------------+--------+--------+--------+--------+-------------------+
| > Dipole     | 1.0    |        | 0.50   | 1648   |                   |
| > (vert.)    |        |        |        |        |                   |
+--------------+--------+--------+--------+--------+-------------------+
| > Quadrupole |        | 25     | 0.50   | 3296   |                   |
+--------------+--------+--------+--------+--------+-------------------+
| > Sextupole  |        | 1750   | 0.80   | 3296   | Gradient in       |
|              |        |        |        |        | T/m^2^            |
+--------------+--------+--------+--------+--------+-------------------+

### 5.1.2 Combined function Arc Magnets {#combined-function-arc-magnets .unnumbered}

The 20 TeV Stage-I VLHC is based on superferric (\~2 Tesla),
twin-aperture superconducting transmission line magnets \[1-7\], as
shown in Figures 5.1 and 2.6. The low parts cost and simple
manufacturing process for these magnets are expected to compensate for
the cost of the long circumference of this machine. All bending magnets
share a common single turn excitation transmission line winding. The
return bus, located within the cryogenic service pipe, is 290 mm below
the drive bus. There are several advantages of this the single turn
winding system: simple construction, low cost, low field in the
superconductor area, absence of turn to turn insulation, low magnetic
forces and heat leak, high stability and simple quench protection.
Nevertheless there are some negative effects associated with the
external return bus: a non-negligible fringe field, asymmetric
saturation of the lower and upper iron half-cores, and uncompensated
magnetic forces on the drive and return busses. It is possible to
optimize the magnet geometry and return bus position to minimize but not
eliminate these effects.

Section 5.1.2.1 describes the magnetic design. The transmission line
design is presented in section 5.1.2.2. The mechanical and thermal
designs are described in section 5.1.2.3, including the magnet
structure, the transmission line, the cryogenic service pipe and
cryostat, and the beam pipe. The magnet ends, where space is provided
for the correction magnets and interconnections from one magnet to the
next are made, is described in section 5.1.2.4.

#### 5.1.2.1 Magnetic design {#magnetic-design .unnumbered}

The combined function gradient dipole is an iron-dominated magnet, in
which the field quality is determined mainly by the shape of the yoke
and the properties of the iron from which it is made. One of the
challenges in this design is obtaining a high quality magnetic field
magnet over a large range of field variations (0.1 - 2.0 T), in
particular dealing with field distortions induced by strong saturation
of the iron at high field. The saturation effects are controlled in the
current design with a set of holes placed in the iron near the poles.
Magnetic measurements have confirmed the attractiveness of the poles
with holes technique.

Table 5.2 shows the main parameters of the dipole magnets. Both the main
and dispersion suppressor magnets are excited by the common transmission
line. Due to the larger gradient required in the dispersion suppressor
magnets, the gap height at the nominal beam position must be opened
somewhat, such that at the narrow edge of the tapered gap the separation
is about the same as in the main magnets, so as to control the
saturation effects. Consequently the operating field is decreased
relative to the main dipoles.

Table 5.2. Main Parameters of Dipole Magnets

  ----------------- ----------- ---------------------- ---------------------
                                *Main dipole*          *Dispersion
                                                       Suppressor*

  Beam gaps (height             18 mm x 28 mm          
  x width)                                             

  Magnet air gap in             20 mm                  22.26 mm
  the orbit center                                     

  Two beams                     150 mm                 
  separation                                           

  Magnet length                 65.74 m                48.81 m

  Half-cell length              135.5 m                101.6 m

  Gradient                      ± 4.73 %/cm            ± 9.449%/cm

  Magnetic field:   injection   0.1 T                  0.09 T

                    maximum     1.966 T                1.766 T

  Good field        injection   20 mm                  
  diameter (0.02%):                                    

                    maximum     10mm                   

  Maximum current               90 kA                  

  Magnetic field                790 kJ                 473 kJ
  energy                                               

  Superconducting               Braided NbTi           
  cable                                                

  Peak Operating                6.5-7 K                
  Temp.                                                

  Iron Core                     Low carbon Steel (AISI 
                                1008)                  
  ----------------- ----------- ---------------------- ---------------------

The crucial problem in the magnetic design is the control of iron
saturation induced field errors at high field. This determines the
strength of the correction system required to compensate these effects
and sets the maximum field, and hence the maximum beam energy, that can
be achieved. The parameters shown in Table 5.2 correspond to preliminary
designs, which have not been fully optimized yet. To indicate the field
quality that can be expected when the optimization is complete, an
earlier, fully optimized design is presented here\[6\]. It has a smaller
gradient of ±3%/cm, corresponding to an earlier lattice with 60°/cell
phase advance, and a smaller spacing of 140 mm between beam apertures
than the current value of 150 mm. It is anticipated that performance
similar to that described here will be achieved for the current designs
when their optimization is complete.

Figure 5.3 shows a detailed cross-section of the magnet, with an inset
showing the dimensions and placement of the saturation control holes.
The laminated core consists of upper and lower iron half cores, which
are stamped from 1.5 mm thick low carbon steel. The upper and lower
laminations are stacked and welded into 6 m long yoke blocks, which are
then assembled into the complete yoke structure. The precise spacing
between the two yoke halves is provided by non-magnetic 316L stainless
steel spacer bars, and the two halves are welded together with
non-magnetic steel plates at the inner radius. The weld is done inside a
press, and the weld shrinkage provides the prestress necessary to assure
precise and stable contact between all of the laminations and the spacer
bar.

The return conductor is placed 290 mm below the drive conductor. This
conductor generates a fringing field, which saturates the lower core
more than the upper, which in turn decreases the field quality in the
gaps and increases the magnetic force on the drive conductor. This can
be countered by increasing the thickness of the lower half core, and it
is possible to optimize this thickness and the position of the return
bus, such that the magnetic force on both the drive and return
conductors is zero when they are at their nominal position.

![](media/image3.png){width="4.194444444444445in"
height="4.8125in"}![](media/image4.png){width="2.2152777777777777in"
height="1.9090277777777778in"}

Figure 5.3. Cross-section of transmission line magnet showing yoke
details.

The classic technique of correction holes in the pole tips was used to
minimize saturation field distortions. Field quality optimization calls
for a larger number of holes, while field strength and mechanical
considerations favor a smaller number of holes. The combined optimum was
found to be three holes per pole, as shown in Figure 5.3. The field
optimization objective function was the integral field homogeneity
around a circular aperture. The optimization process was carried out
simultaneously for three field levels (1 T, 1.7 T and 2.0 T). The
optimization was done using an ANSYS Subproblem Optimizer, and a large
number of local minima were investigated. The best solution was tested
by OPERA 2D and had ±0.02% field quality within a 20 mm diameter
aperture for 0.1 ≤ B ≤ 0.8 T, 15 mm for 0.8 \< B ≤ 1.5 T, and 10 mm for
1.5 T \< B \< 2.0 T. This shrinkage of good field region is acceptable
since the beam is \~4x smaller at full energy than at injection.

Figure 5.4 shows the computed B versus I characteristic. The 20 TeV
design field of 1.966 T is achieved at 98.4 kA. Figure 5.5 shows the
effects of putting the correction holes in the pole laminations on the
saturation of the sextupole. Figure 5.6 compares the calculated and
measured shift in the quadrupole moment as a function of excitation for
a prototype yoke stack. The quadrupole and sextupole errors are ±2 units
in the field range 0.1T - 1.85T and both are about -8 units at 1.95T.
The correction system described in section 5.1.3 is capable of
compensating up to 4.8 and 5.4 units of quadrupole and sextupole error.

![](media/image5.wmf){width="5.302777777777778in"
height="3.3340277777777776in"}

Figure 5.4. Calculated magnetic field strength as a function of
transmission line current..

![](media/image6.wmf){width="5.425694444444445in"
height="3.8152777777777778in"}

Figure 5.5. Effect of Slots in the Pole on Saturation Sextupole as a
function of transverse position in the Transmission Line Magnet

![](media/image7.wmf){width="5.479166666666667in"
height="4.176388888888889in"}

Figure 5.6. Effect of Slots in the Pole on the Gradient Shift in the
Transmission Line Magnet

#### 5.1.2.2 Superconducting Transmission Lines  {#superconducting-transmission-lines .unnumbered}

The magnetic field in the superferric transmission line magnet is
generated by a current carried in a drive conductor centrally positioned
between the two stacks of iron laminations as shown in Figure 5.1. The
transmission line consists of a cylindrical superconducting braid cooled
by supercritical 4.5-6.0 K helium, which is placed inside a co-axial
cryostat, which in turn is placed at the center of the room temperature
iron yoke. A three dimensional view of a drive conductor transmission
line is shown in Figure 5.7. The transmission line consists of (from
inside out) a perforated invar tube, the conductor cable itself, the
cold pipe support, a cryoshield, the superinsulation blanket, and the
vacuum jacket. The cold pipe support sets conductor cable centrally to
the vacuum jacket which in turn is placed centrally inside the magnet
lamination. It also supports the cryoshield pipe which in turn supports
the superinsulation blanket.

In order to suppress distant magnetic fringe fields and minimize the
system inductance, a return conductor is placed outside the magnet
laminations. At the mid point of the accelerator, the drive conductor
returns back through the first half of the magnets (but outside the
lamination stack). At the points where the beams cross each other -- at
the interaction regions and the beam cross-over insertions -- the drive
and return busses trade places. For the VLHC Stage 1 accelerator, the
continuous length of the superconducting bus is about 464 km.

Three distinct transmission line designs are utilized. The transmission
line that excites the dipole is optimized for minimum size consistent
with operation at 100 kA in a \~1 T self-field. The return bus, which
has essentially the same self-field as the drive conductor, is larger to
provide a larger flow area. The cryogenic system (see section 5.2.1) is
designed such that the maximum temperature is 6.0K in both the drive and
the return bus. Where the drive conductor is diverted to make space for
the correction magnets (see Figure 5.2), a special bus section is
required for both the drive and return buses. Here, due to the proximity
to the return bus, the peak field rises to 1.5 T, requiring more
superconductor to carry the 100 kA current. A different design is also
required due to the need to place pressure relief ports in this region.
The main parameters of the three bus types are summarized in Table 5.3.

![](media/image8.jpeg){width="5.4in" height="3.9965277777777777in"}

Figure 5.7. A 3D view of the drive conductor transmission line.

The superconductor for the drive and return busses are sandwiched
between an inner perforated invar pipe, which serves as a liquid helium
channel, and an outer invar pressure pipe which closes the helium space.
The design is based on strands of the dimension of the SSC outer dipole
layer design and current prototypes use actual SSC strand. For VLHC-1 it
is planned to use a more cost effective wire optimized for the lower
fields seen here and without the constraint of small filament size. A
braided conductor is used for the main drive and return buses. It
consists of 288 NbTi strands arranged in a pattern of two sets of 24
crossing bundles with opposite pitch angle about the tube. This yields a
"tight" braid for the drive conductor, and a looser braid, with more
void space for the return bus. Alternatively the return bus braid could
be made of a larger number of smaller wires, which preserves the area of
superconductor in the cross-section. There is also a copper braid placed
underneath the conductors that provides an additional copper for
carrying current during a quench. The conductor braid is secured in
position by swaging the inner pipe against the outer one by drawing a
series of carbide steel balls through the pipe.

For the bus in the corrector magnet space an assembly of 9 SSC inner
dipole Rutherford cables is proposed. Cables are used here rather than
braid to allow openings to be made for in the superconductor assembly
for pressure relief ports, which are placed at every 4th half-cell
(542 m). The cables are secured in place by welding the outer invar clam
shell under pressure.

A cross-section of the drive conductor cryostat is shown in Figure 5.8.
The support spider consists and injection molded ULTEM ring with two
pairs of pegs pointing up and down, the direction of the magnetic force.
The inner pair of pegs support the cold pipe, while the outer pegs
contact the vacuum shell. The conductor must be placed precisely on the
central line of the magnet to minimize the de-centering force. Offsets
of the order of 0.5 mm, which can be expected due to part tolerances,
lead to de-centering forces on the order of 100 kg/m. The supports must
withstand 100,000 mechanical cycles during the accelerator lifetime.
Laboratory tests these supports withstood 100,000 mechanical cycles of
300 kg/m force, three times that of the design requirement. Further
design development, however, may be required to optimize the spider
design with respect to axial motion, expected under thermal cycling.
(See section 5.1.2.3.)

The cryo-shield is made of extruded aluminum pipe segments \~50 cm long,
which slide over opposite ends of each support spider. The 6.4 mm
diameter invar pipe that is used to provide the 50 K pressurized helium
is "snapped in" to the cavities at the top and the bottom of both the
shield and the supports once a magnet's length of shield has been
assembled. The shield pipe is wrapped with 40 layers of a dimpled
superinsulation blanket. The vacuum jacket is made of extruded aluminum,
and it is of a "squared" shape to firmly fix its position inside the
iron laminations. This also helps to prevent potential rotation (and/or
twist) of the cold pipe supports.

Table 5.3. Main parameters of the transmission line conductors.

+-----------------+-------------+-----------------+-------------------+
|                 | > **Drive   | > **Return      | > **Bus in Corr.  |
|                 | > Bus**     | > Bus**         | > Space**         |
+-----------------+-------------+-----------------+-------------------+
| > Cu/SC ratio   | > 1.8       | > 1.8           | > 1.3             |
+-----------------+-------------+-----------------+-------------------+
| > Diameter (mm) | > 0.648     | > 0.648         | > 0.808           |
+-----------------+-------------+-----------------+-------------------+
| > Cond.Type     | > Braid     | > Braid         | > 9 Rutherford    |
|                 |             |                 | > Cables          |
+-----------------+-------------+-----------------+-------------------+
| > Number of     | > 288       | > 288           | > 270             |
| > strands       |             |                 |                   |
+-----------------+-------------+-----------------+-------------------+
| > Cu Wire dia.  | > 0.64      | > 0.64          | > 0.64            |
| > (mm)          |             |                 |                   |
+-----------------+-------------+-----------------+-------------------+
| > Number of     | > 240       | > 288           | > 288             |
| > wires         |             |                 |                   |
+-----------------+-------------+-----------------+-------------------+
| > Inner Pipe ID | > 25.3      | > 36.8          | > 36.8            |
| > .(mm)         |             |                 |                   |
+-----------------+-------------+-----------------+-------------------+
| > Outer Pipe OD | > 38.1      | > 47.1          | > 50.1            |
| > (mm)          |             |                 |                   |
+-----------------+-------------+-----------------+-------------------+
| > Max working   | > 40        | > 40            | > 40              |
| > Pressure      |             |                 |                   |
| > (bar)         |             |                 |                   |
+-----------------+-------------+-----------------+-------------------+

> ![](media/image9.jpeg){width="5.194444444444445in"
> height="2.9916666666666667in"}

Figure 5.8. The details of the drive conductor cryostat.

The return conductor is located inside the cryogenic service pipe. Its
is part of the cryostat that also includes the helium cooling lines,
which is described in Section 5.2.2.

The critical temperature vs. current for the braided conductor is shown
in Figure 5.9. The data point is the measured performance of the
conductor used in the prototype, and the diagonal line is the computed
performance using the properties of NbTi and the self-field as a
function of current. At 90 kA current the critical temperatures is 6.8
K. The temperature margin of 0.7 K with respect to the maximum helium
temperature of 6.1 K (see Section 5.2.1) is sufficient both for
stability of the superconductor and for operational "head room." The
margin for the braided conductor, normalized to its higher self-field in
the space between dipoles, is slightly larger than for the main
conductor.

The quench propagation velocities were measured in a 17 m long conductor
loop\[4\]. It was found that in a forced quench by a local heating of
\~10 K, quench propagation velocity rises linearly with current, and it
reaches about (10-12) m/s value at \~80 kA. Above this current, it rises
exponentially reaching about (30-40) m/s value at 100 kA. This indicates
that by applying a current dump circuit of a time constant of 1 s, the
stored magnetic energy released in a quench would be at most that of a
half length of a dipole magnet (34 m), thus not exceeding 1 MJ value.
Detailed thermohydraulic simulations have also been performed on many
quench scenarios with a number of different configurations of the
transmission line\[8\]. The simulations use a 1 V quench detection
threshold and a 1 second decay time constant (see Section 5.2.2.3) *{is
this the right section?}*. The calculations demonstrate that, for
conceivable worst-case scenarios, the peak temperature remains low
(\<60 K) and, with relief valves spaced every four half-cells, the peak
pressure is below the 40 bar maximum for which the invar pipe is rated
without taking credit for the increased strength at low temperature. The
simulations also show that the additional copper stabilizer braid is
essential. Without it the peak temperature can reach 250 K, and the
higher temperature can result in peak pressure above 40 bar.

![](media/image10.wmf){width="5.354861111111111in"
height="3.3854166666666665in"}

Figure 5.9. The critical temperature vs. current for main drive and
return conductors.

#### References {ed. note -- for Secs 5.1.0 -- 5.1.2.2} {#references-ed.-note-for-secs-5.1.0-5.1.2.2 .unnumbered}

\[1\] R.R. Wilson, Proceedings of Snowmass 1982.

\[2\] "The Pipetron: a Low-Field Approach to a Very Large Hadron
Collider," Snowmass '96.

\[3\] G.W.Foster, "Transmission Line Magnet Status Report", VLHC
Information Packet for HEPAP Subpanel, Fermilab 1998.

\[4\] G.W.Foster, V.S.Kashikhin, E.Malamud, P.Mazur, H.Piekarz,
J.Fuerst, R.Rabehl, P.Schlabach, J.Volk, "The 100 kA VLHC Transmission
Line Magnet Superconducting Cable Test Facility," MT-16, IEEE Trans. of
Applied Superconductivity, Vol.10, No.1, March 2000, pp.318-321.

\[5\] J.DiMarco, G.W.Foster, V.Kashikhin, A.Makarov, P.Schlabach,
"Measurements of a Crenellated Iron Pole Tip for the VLHC Transmission
Line Magnet," PAC 99, pp. 3327 -- 3329.

\[6\] G.W.Foster, V.S.Kashikhin, I.Novitski, "Design of a 2 Tesla
Transmission Line Magnet for the VLHC," MT-16, IEEE Trans. of Applied
Superconductivity, Vol.10, No.1,March 2000, pp.202-205.

\[7\] G.W. Foster, V.S.Kashikhin, V.V.Kashikhin, "Pole Profile
Optimization of VLHC Transmission Line Magnet," EPAC 98.

\[8\] N. A. Shatil, "Quench Simulation of VLHC Transmission Line Magnet
(Final Report)", TD-01-025, February, 1999; N. A. Shatil, "Quench
Simulation of VLHC Transmission Line Magnet (Task 2)", TD-01-026,
October, 1999.

#### 5.1.2.3 Mechanical and thermal design {#mechanical-and-thermal-design .unnumbered}

##### 5.1.2.3.1 Magnet structure {#magnet-structure .unnumbered}

###### (a) Magnet support by cryogenic service pipe {#a-magnet-support-by-cryogenic-service-pipe .unnumbered}

The final assembly of the 67.75 m long magnet has two parts mounted as
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 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. The
magnet core is periodically (D=0.5m) welded to the tube to increase the
vertical stiffness of the assembly and to reduce system deflection. The
combined structure is rigid enough that supports every 6 m are
sufficient to align the structure. Total magnet weight is \~ 33 tonne
(\~500 kg/m).

###### (b) Magnet yoke {#b-magnet-yoke .unnumbered}

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 achieve 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 {#transmission-line-mechanical-analysis .unnumbered}

###### (a) Vertical deflection and stress between support points {#a-vertical-deflection-and-stress-between-support-points .unnumbered}

The magnet is installed on the vertical supports. A distance of 6 m was
chosen between supports \[1\]. 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 the lower
vacuum tube by welds, the vertical sag is close to 1.2 mm and maximal
stresses will not exceed 50 -- 60 MPa.

###### (b) Force to introduce sagitta {#b-force-to-introduce-sagitta .unnumbered}

The magnet horizontal sagitta is \~15 mm over its 67 m length. To
estimate deformations of the straight magnet structure introduced by
this sag during alignment in the tunnel, numerical 3D simulations were
performing using a 12-m section model \[2\]. Over such a distance the
sag is \~0.5 mm. Both model ends were 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 450 kg. Difference in relative movement of the
iron halves of the magnet can reach 30 μm.

###### (c) Magnetic forces on transmission line {#c-magnetic-forces-on-transmission-line .unnumbered}

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 the
vertical direction and --100 kg/mm in the 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 the 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  {#d-thermal-stress-and-thermal-forces .unnumbered}

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 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 of steel or aluminum and can not be
continuously welded because of high thermal stress level. Table 5.4
describes the situation for different pipe materials after cool down to
5 K.

Table 5.4. Pipe at 5 K after cool down from 300 K

+-------------+-------+-------+--------+----------+-------+---------+
| #####       | *∫    | *E    | *σ=E\  | *σyield* | *σyie | *       |
|  Material { | αdt,* | (5K)* | *∫αdt* |          | ld/σ* | ∆L(mm)* |
| #material . |       |       |        | *MPa*    |       |         |
| unnumbered} | *     | *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 |         |
+-------------+-------+-------+--------+----------+-------+---------+

If the steel pipes will be equipped with compensation bellows every \~33
m to reduce shrinkage to the level of \~100 mm, the convoluted length of
the bellow is 100/0.25 = 400 mm. The force to expand the bellows by 50
mm is 300 kg for the bellows' spring constant 6 kg/mm. The bellows'
stability problem is solved by using the internal tube liner and the
outer protecting skin.

###### (e) Yoke deflection under magnetic forces {#e-yoke-deflection-under-magnetic-forces .unnumbered}

The dipole magnet at the maximum field of 2 T has 25 tonne/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  {#f-mechanical-analysis-of-support-spider .unnumbered}

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. 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 \[5\].

Spiders made of ULTEM centrally position the conductor. 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 that
expected). 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. This motion can cause high stress in the spider
material \[6\]. 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. 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-thermal-analysis .unnumbered}

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 Table 5.5-6
\[10\].

Table 5.5. 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 5.6. 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  {#interconnects-pipes-and-bellows .unnumbered}

###### (a) Axial anchoring for transmission line and return line {#a-axial-anchoring-for-transmission-line-and-return-line .unnumbered}

The magnet anchor system consists of the vacuum barriers, the
force-anchors, the transportation locks and the vacuum jacket anchors,
as shown in Figure 5.10.

![](media/image11.wmf){width="5.99375in" height="1.9006944444444445in"}

Figure 5.10. Anchor system for the magnets

All magnet pipes will be physically constrained by vacuum barriers, or
breaks, at the same location. The vacuum 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 and to minimize the heat in-leak \[13\]. They are
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. Distance between breaks is 270 m.

The pipe longitudinal anchor is located close to the vacuum barrier to
prevent damage of the ceramic insulators. The pipe force anchor
restrains thermal forces from invar pipe shrinkage and stainless steel
bellows expansion (\~3000 kg) during cool-down and warm-up. This anchor
consists of carbon tie rods and a G-10 spider, and connects all the
pipes to the vacuum jacket.

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 {#b-cryostat-interconnection .unnumbered}

After magnet alignment, interconnection activities will take place. The
magnet and the cryo-service line must be connected every \~67.75 m at
the 3.5 m and 1 m interconnection regions, as shown in Figure 5.11.

![](media/image12.wmf){width="5.990277777777778in"
height="2.4027777777777777in"}

Figure 5.11. Magnet interconnections

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

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

Beam pipes are connected by bellows every 135 m in the space between
corrector magnets to compensate \~25 mm motion of the magnets from
expected temperature excursions in the tunnel.

#### References *{ ed. note -- for Sec. 5.1.2.3}* {#references-ed.-note-for-sec.-5.1.2.3 .Reference-heading .unnumbered}

\[1\] 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.

\[17\] I.Novitski "Beam pipe mechanical design" TD TN XXXX 2001.

### 5.1.3 Correctors {#correctors .unnumbered}

The purpose of the correction system is to correct the closed orbit.
Sources of orbit distortions include dipole, gradient and sextupole
field strength errors. Various factors and effects (main magnet
manufacturing and installation, iron core saturation, fringing fields,
residual fields, and magnet displacements with time) cause all these
errors. The accelerator lattice design includes a space 3.5 m between
combined function magnets at the end of each half-cell, and a 1 m space
in the middle of the half-cell. Dipole, quadrupole and sextupole
correctors will be placed there (see Figure 5.2). There are several ways
to optimize corrector strengths. A rather promising approach is to
optimize pole profiles and correction hole positions of the main dipoles
for the minimum and maximum fields. In this case, correctors will work
at full power for only a short period of time during the acceleration
cycle. This will reduce the operational cost of the corrector power
supplies and the ventilation system. At maximum field they will
compensate residual effects after magnet calibrations.

The main design issue for the correction system is the high fringing
field generated by the straight and return 100 kA conductors in the
drift space between dipole magnets. This field has a level of 0.3 T in
the vacuum chamber areas and causes large magnetic forces of 1000 kg/m
on the superconducting cable. The distance between the outer shell of
the superconducting transmission line and the vacuum chamber center is
only 30 mm; it is a nontrivial task to form the needed correction field
in this area. There are several options to solve this problem:

1.  Cold ferromagnetic screen with superconducting windings \[*need
    ref:* TD Note N.Andreev\]

2.  Room temperature horizontal and vertical dipole correctors with iron
    core as a ferromagnetic screen

3.  Nearly coaxial configuration of the transmission line and return bus
    in the space between magnets and room temperature air-cooled
    correctors (see below)

4.  Main dipole pole windings ( very effective at injection )

5.  Iron-dominated correctors ( low power, stepping motor drive)

6.  Permanent magnet correctors (rotational multipoles, stepping motor
    drive)

All of these options were investigated. From the point of view cost and
operations, the most convenient magnets are conventional room
temperature air-cooled magnets (Option 3 above). The other options may
be used only if their total cost will be less than Option 3.

One of the options to eliminate the fringing field of the transmission
lines is to bend the main transmission line and place it as close as
possible to the return bus (see Figure 5.11). Electrical insulation
capable of withstanding \~5 kV during quench should be applied in the
space between the two lines. The collar around both lines should
accommodate large magnetic forces. Conventional dipole and multipole
correctors can be installed in the field free space between the main
dipole magnets. For easy installation and replacement, all the
correctors can be separated in the median plane. Correctors will
dissipate power in the tunnel and will produce an extra heat load for
the ventilation system. Magnets will have separate power supplies placed
nearby to reduce the cost of cables and operational cost.

Table 5.7. Corrector Parameters

+--------------------------------+---------+-------+--------+---------+
| Corrector type                 | Hor     | Ver   | Quadr  | Se      |
|                                | izontal | tical | u-pole | xtupole |
|                                |         |       |        |         |
|                                | dipole  | d     |        |         |
|                                |         | ipole |        |         |
+--------------------------------+---------+-------+--------+---------+
| Quantity                       | 3420    | 3136  | 3136   | 3136    |
+--------------------------------+---------+-------+--------+---------+
| Maximum magnet strength        | 1.0 T   | 1.0 T | 25 T/m | 1750    |
|                                |         |       |        | T/m²    |
+--------------------------------+---------+-------+--------+---------+
| Field quality, 18 mm diameter  | 1.0     | 1.0   | 1.0    | 1.0     |
| area, %                        |         |       |        |         |
+--------------------------------+---------+-------+--------+---------+
| Effective magnet field length, | 0.5     | 0.5   | 0.5    | 0.8     |
| m                              |         |       |        |         |
+--------------------------------+---------+-------+--------+---------+
| Integrated field at r = 1 cm,  | 0.5     | 0.5   | 0.125  | 0.14    |
| T\*m                           |         |       |        |         |
+--------------------------------+---------+-------+--------+---------+
| Half-cell integrated field at  | 260     | 260   | 260    | 260     |
| 1 cm, T\*m                     |         |       |        |         |
+--------------------------------+---------+-------+--------+---------+
| Half-cell field correction at  | 19      | 19    | 4.8    | 5.4     |
| 1 cm, units                    |         |       |        |         |
+--------------------------------+---------+-------+--------+---------+
| Magnet core length, m          | 0.48    | 0.48  | 0.5    | 0.5     |
+--------------------------------+---------+-------+--------+---------+
| Current, A                     | 25      | 25    | 1.0    | 1.0     |
+--------------------------------+---------+-------+--------+---------+
| Voltage, V                     | 23      | 23    | 140    | 175     |
+--------------------------------+---------+-------+--------+---------+
| Power, W                       | 600     | 600   | 150    | 200     |
+--------------------------------+---------+-------+--------+---------+
| Number of coils per magnet     | 1       | 1     | 4      | 6       |
+--------------------------------+---------+-------+--------+---------+
| Number of turns per coil       | 640     | 640   | 1240   | 633     |
+--------------------------------+---------+-------+--------+---------+
| Copper conductor, mm           | 5 x 5   | 5 x 5 | ǿ 1    | ǿ 1     |
+--------------------------------+---------+-------+--------+---------+
| Copper weight, kg              | 250     | 250   | 40     | 50      |
+--------------------------------+---------+-------+--------+---------+
| Core weight, kg                | 300     | 220   | 30     | 50      |
+--------------------------------+---------+-------+--------+---------+

The bent sections of the transmission line at the arc magnet ends will
be forced to the closest iron corrector cores. Longitudinal anchors
should accommodate uncompensated forces. Cross-sections of the dipole,
quadrupole and sextupole correctors are shown in Figure 5.12-13.

All the correctors can be installed and removed without breaking the
beam pipe vacuum. The corrector assemblies installed in 3.5 m space will
have the common support structure but separate position adjusting
mechanics. Three correctors assembly will be transported into the tunnel
as one unit with previously mounted beam pipes and installed when all
the main dipole connections are made.

![](media/image13.wmf)

Figure 5.12. Horizontal dipole correctors

![](media/image14.wmf)

Figure 5.13. Quadrupole correctors.

![](media/image15.wmf){width="4.145138888888889in"
height="2.2819444444444446in"}

Figure 5.14. Sextupole correctors.

### 5.1.4 Interaction Regions {#interaction-regions .unnumbered}

VLHC has provisions for two large colliding experiments located on the
present Fermilab site. The beam interaction points will be located
symmetrically from the two non-interaction beam crossing points. The
closest crossing point is 13 half cells or 1700 meters from the
interaction points.

A system of magnets on each side of the interaction regions is required
to bring the beams into collision. With these magnets comes additional
requirements for the accelerator including power supplies, beam
absorbers to protect the magnets and prevent activation of the tunnel,
and an alignment system for the magnetic elements. For the
superconducting magnets there is quench protection system, cryogenics,
and interconnects for room temperature to cold transitions of
instrumentation and powering.

Figure 5.15 shows a schematic of the interaction regions magnetic
elements. Each interaction region spans a space of 6 half cells, from 20
meter to approximately 810 meters from the interaction points. The
interaction regions consist of four high gradient "inner triplet"
quadrupoles, two separation dipole elements, and an outer system of
lower gradient quadrupoles. There will also be orbit and local field
corrector magnets. The separation dipoles, "outer" quadrupoles and
correctors are used in other parts of the accelerator and are thus
described in section 5.1.5. The high gradient inner triplet quadrupole
is described below.

![](media/image16.wmf){width="4.897222222222222in"
height="2.5444444444444443in"}

Figure 5.15. Principal magnetic elements for the VLHC-1 interaction
region.

#### 5.1.4.1 Low-beta IR quadrupoles {#low-beta-ir-quadrupoles .unnumbered}

These magnets form the final focus at the two collision points. The
required gradient is 300 T/m with a length of 10 meters and a single
aperture of \~80 mm. The field quality must be very good because the
beams could be separated by as much as 12.5 mm due to the crossing
angle.

A design developed by INFN-LASA for a possible upgrade of the LHC low-β
quadrupoles, with an aperture of 85 mm \[1\], can be used as a starting
point to meet these requirements. The basic design as shown in Figure
5.16 has two Nb~3~Sn layers in a cos (2Θ) geometry, wound using the
cable described in Table 5.8. The cable has a target critical current
density of 3000 A/mm^2^ @ 4.2 K, 12 T \[2\]. Internal splices can be
avoided using the double pancake technique. The main characteristics of
the magnetic design are reported in Table 5.9. The field quality of the
basic design (aperture = 85 mm) gives acceptably low values for the
allowed harmonics. The value of the b6, b10 and b14 multipoles,
normalized to the gradient and using a 10 mm reference radius are
respectively 1.5 e-6, 1.6 e-8 and \< 1.0 e-9. The relative field error
is lower than 1.1 e-5, at 12.5 mm from the center on the midplane. Iron
saturation effect has to be studied.

Table 5.8: Conductor characteristics

  ------------------------------------------ ----------------------------
  Superconductor                             Nb~3~Sn

  Critical current non Cu (@ 4.2K 12T)       3000 A/mm^2^

  Strand diameter                            0.825 mm

  α = Cu/nonCu                               1.3

  Number of strands                          36

  Cable dimension                            1.34 ÷ 1.60 x 15.0 mm^2^

  Effective filament diameter                \< 40 μm
  ------------------------------------------ ----------------------------

![](media/image17.wmf){width="3.298611111111111in"
height="2.040277777777778in"}

Figure 5.16. Basic design cross section with field quality at maximum
gradient

> Table 5.9: Magnetic design characteristics at short sample limit

  -------------------------------------- --------------------------------
  Aperture                               85 mm

  Gradient                               300 T/m

  Current                                20218 A

  Self inductance                        4 mH/m

  Stored energy                          820 KJ/m

  Horizontal Magnetic force (per octant) 2.78 MN/m

  Vertical Magnetic force (per octant)   3.43 MN/m

  Number of turns                        10 + 4 + 19

  Collars thickness                      20 mm

  Iron inner radius                      93.5 mm
  -------------------------------------- --------------------------------

The quench protection has been studied at an operating current
corresponding to 93% of the short sample limit. Simulations were
performed using a version of the QLASA code \[3\] modified at Fermilab
\[4\] for the study of FNAL Nb~3~Sn high field magnets. These studies
show that full coil coverage by heaters on both layers is required, and
the delay time between the spontaneous quench start and the beginning of
the heater-induced quench must be very short. This solution has an
impact on magnet technology, because if the insulation of the heaters
between the inner and outer layers cannot withstand the conductor heat
treatment, the double pancake technique must be abandoned. Furthermore,
protection redundancy will not be possible (or at least very
complicated) and fault scenarios have to be addressed. The short time
delay necessary to avoid excessive hot spot temperature and the lack of
protection redundancy should be the object of an appropriate R&D.

A possible solution for the mechanical design is the one proposed for
the upgraded version of the LHC IR low-beta quadrupoles presented in
\[5\]. It uses 20 mm thick stainless steel collars, which can provide
part of the required prestress and magnetic force containment. The rest
of prestress and support are provided by a thick skin. The yoke is only
in contact with the collars close to the midplanes, in order to transfer
the stress from the skin to the coils where it is most necessary. The
effectiveness of this design for the higher forces developed in the VLHC
IR quadrupoles is still under investigation. A finite element analysis
of coils and collars, simulating the rest of the mechanical structure by
use of an external load, showed that the maximum stress in the coil can
be kept below 160 MPa. The design of yoke, skin and contact regions must
still be optimized to provide the required support on the coils.

In summary, it can be concluded that a two layer design using Nb~3~Sn at
4.2 K is a good candidate to meet the requirements for these magnets, if
the critical current target is reached. Some design optimization will be
required for the quench protection and mechanical design.

#### 5.1.4.2 Interaction Region Subsystems {#interaction-region-subsystems .unnumbered}

Most of the 800 meters of the interaction region will be in the standard
VLHC tunnel. Since these magnets elements need to be "tunable" they
require a special gallery to handle the power supply and electronics of
these magnets. There will likely be a global alignment system that
connects the experiments to the final focussing elements. Finally, the
tunnel will need to be wider near the IP to accommodate the extra
shielding and vacuum connections and instrumentation associated with the
collision detection and IP interconnect.

Four independent power systems are required for each side of an
interaction region: one for the inner triplet, one for each separation
dipole and one for the outer quadrupoles. Additional quadruples in the
IR region will likely be powered in series with other straight section
quadrupoles in the accelerator and are not include here. The high
gradient quadruples require a 25 kA, 10 Volt supply, the conventional
separation dipoles require 1 kA, 100 Volt supplies while the
conventional outer quadrupoles need a 7kA, 10 volt supply. Correctors
will be powered independently with supplies comparable to the outer
quadrupole conventional magnets.

Superconducting circuits will rely on quench heaters for protection.
With the relatively small amount of stored energy (50 MJ) and small
number of magnets/circuit (4 or less) it is not clear whether the
complications of an extraction circuit and bypass diodes are worth the
effort. Thus, in the event of a detected spontaneous quench, the circuit
power converter will be phased off, all quench protection heaters on all
the magnets in a circuit will be energized.

As stated, inner triplet quadruples will likely need protection levels
comparable to or greater than a similarly sized LHC IR quadrupole
magnet. Thus 4-8 quench heater circuits plus the requisite electronics
are required for each magnet. The total space for power supplies and
electronics required for each quench heater circuit is approximately 2
6U VME crates. Thus a space of approximately 70 6U crates are required
for each side/IR.

LCW and electrical power will be required for the power supplies and
conventional magnet. The LCW system will be required to deliver several
hundred liters/minute per IR.

Superconducting magnets rely on 4.5 K helium. The estimated dynamic heat
load/side/IP will be approximately 600 Watts or 2.4 kW for both
interaction regions \[6\]. Local heating in the quadrupoles could be
quite large due to the strong focusing elements (G.dl \~ 3000 T/m \*m).
This could be a non-negligible load on the Phase I cryogenic
requirements.

This heat load, if taken directly by the 4.5 K helium will require
approximately ½ of a VLHC-1 power plant. Thus the cryogenic plant
located on site would have to be upsized. Since the IR temperature and
pressures profiles and requirements will differ from the transmission
lines, there will likely be a need to be a separate transfer line from
the cryogenic system. The helium requirements might be reduced by
carrying away some of the heat load by actively cooled absorbers in the
80 mm beam tubes.

A distribution box will be required in order to make a connection
between the room temperature and cryogenic electrical elements, as well
as supply the cryogens to the magnetic elements. Elements include
voltage taps, strip heater leads, thermometry and other cryogenic
instrumentation. 25-30 kA HTc leads would be used to supply the
excitation currents.

A particle absorber system will be required to protect the IR magnets
from the excessive radiation from particles produced from the
interaction region. Using the LHC as a guide, the system will require a
hadron and neutral particle absorber. The primary hadron absorber will
be located on the IP side of the inner triplets. The size of the
absorber will be comparable to the LHC absorber but will have
significantly larger heat loads, estimated to be 2 kW per IR \[7\]. Thus
an actively cooled absorber will likely be necessary. The neutral
absorber, located between the separation dipoles would be necessary to
protect the outer quadrupoles, possibly the transmission line magnets
and the walls of the tunnel from activation. It, too, will likely need
to be actively cooled. If water cooled the requirements would be modest
and would be parasitic to the magnet and power supply LCW system.

Alignment tolerances are likely to be comparable to those of the LHC
Interaction region. Transverse alignment tolerances will thus need to be
on the order of 100-300 microns over both sides of the IP. Thus an
alignment system will be required to tie together the two sides of the
IR and the detector.

#### References *{note -- for sec. 5.1.4}* {#references-note-for-sec.-5.1.4 .Reference-heading .unnumbered}

\[1\] G. Ambrosio et al. *"Preliminary Proposal of a Nb3Sn Quadruple
Model for the Low-beta Insertions of the LHC"* INFN Report,
INFN/TC-95/25, Sept. 13, 1995.

\[2\] R. Scanlan, *"Conductor Development Program"* Low Temperature
Superconducting Workshop, Santa Rosa (CA), Nov. 8-10, 2000.

\[3\] M. Canali, L. Rossi, *"DYNQUE: a computer code for quench
simulation in adiabatic multicoil superconducting solenoids"*, INFN
Report, INFN/TC-93/06, 1993

\[4\] L. Imbasciati, G. Ambrosio, P. Bauer, V. Kashikhin, A. Zlobin,
*"Quench Protection of the Common Coil Racetrack (CCRT-1)-Results of
Adiabatic Model Calculations",* TD-00-056, FNAL (Sept. 2000)

\[5\] G. Ambrosio, G. Bellomo and L. Rossi, *"A 300 T/m Nb3Sn Quadrupole
for the Low-beta Insertions of the LHC"*, Proc. of EPAC96, Sitges
(Barcelona), p. 2290.

\[6\] Nikolai Mokhov, private communication

\[7\] Bill Turner, private communication

### 5.1.5 Special Collider Ring Magnets {#special-collider-ring-magnets .unnumbered}

This section describes several different magnets installed in the
straight sections of the ring. There are a total of 10 straight
sections, 5 in each half of the ring. On the Fermilab site there are two
Interaction Region straight sections, two Utility straight sections and
one Beam Crossing straight section. The straight sections on the
opposite side of the collider are basically the mirror reflection of
what is on the Fermilab site, except that there are no IRs or utility
equipment installed in this area. As a transition from an arc to a
straight section, a matching dispersion suppression section cell is
used, described in section 3.2 *{check ref}*.

Beam focusing in the straight sections is provided using a classical
quadrupole triplet cell made of four quadrupoles of equal integrated
strength of 422.93 T. The basic cell half-length is about 135.46 m. This
is the amount of space that can be used to install the required
equipment. The triplets quadrupoles are installed back-to-back in both
rings, providing focusing in different directions for each ring. The
basic beam-beam spacing of 150 mm and the required beam pipe size of 20
mm implies certain restrictions on the achievable quadrupole field
gradient. The chosen reference gradient of 69.333 T/m results in the
basic quadrupole length of 6.1 m. Taking into account this length and
the space between the quadrupoles in the focusing cell, only a 100 m gap
is available for the utility equipment. When this space is not enough,
or when some special features are to be introduced into the beam optics,
modifications of the focusing lattice are to be done.

#### 5.1.5.1 Straight section quadrupole {#straight-section-quadrupole .unnumbered}

The focusing quadrupole has been designed so that a pair of them can be
installed back-to-back in both rings. This gives a certain flexibility
when increased beam separation is used in the Utility section. The lens
uses water-cooled windings. The preliminary magnetic design indicates
that field quality is not going to be a problem for this lens: there is
plenty of space to make the needed pole shaping. The magnetic field in
the steel is acceptable, reaching 1.9 T at the pole base, but there are
regions in the minimal pole separation area where the field exceeds 2.0
T at 70 T/m, so good quality low carbon steel must be used for lens
fabrication. A cross-section of the quadrupole is shown in Figure 5.17.
summarizes the quadrupole features.

![](media/image18.wmf){width="3.347916666666667in" height="2.20625in"}

Figure 5.17. Straight section focusing quadrupole

Table 5.10. Parameter list of a conventional straight section quadrupole

  --------------------------------------------------------- -------------
  Gradient, T/m                                             70

  Pole spacing, mm                                          22

  Length, m                                                 6.1

  Width, mm                                                 148

  Height, mm                                                168

  Number of coils per winding                               4

  Number of turns per coil                                  12

  Conductor cross section area, mm^2^                       61.5

  Resistance of the winding, Ohm                            0.18

  Rated current, A                                          285

  Voltage drop, V                                           53

  Power consumption, kW                                     15

  Conductor hole diameter, mm                               5

  Water temperature rise at 1 MPa (deg. C)                  12

  Water flow per quadrupole (l/min)                         17
  --------------------------------------------------------- -------------

The number of quadrupoles required for each straight section depends on
its design. For the Far End straight sections (except the Beam Crossing
section), a total of 22 focusing cells are used that require 176 of the
6.1-m quadrupoles, equivalent to 1074 m of quadrupole length.

Conventional quadrupoles provide some flexibility and freedom in high
radiation areas, where the use of superconducting magnets may be
precluded. Nevertheless, superconducting quadrupoles have an advantage
of higher gradient and can be used when appropriate or when space
requirements become a critical issue \[1\].

#### 5.1.5.2 Beam Cross-Over Section {#beam-cross-over-section .unnumbered}

The two beam cross-over regions in the collider are introduced to make
the perimeters of the counter-rotating rings equal. To accommodate the
magnets in the cross-over region, a short straight section is used that
consists of a focusing cell that differs from the standard focusing
cell. At the entrance to the cross-over region, the two beams are in the
horizontal plane, separated by 150 mm. To make a cross-over, it is
necessary to bring the beams together horizontally, separate them
vertically before the crossing, and make the opposite transformation
after the crossing. The vertical shift of each beam required to
eliminate beam-beam interaction effects is 4.5 mm, which results in a
beam-beam separation of 9 mm, more that 18 σ. To reduce the number of
magnets required for beam manipulation, tilted dipoles are used to bend
beams both horizontally and vertically. The cell layout is shown
schematically in Figure 5.18.

{still need some refining of the text for the remainder of Sec. 5.1.5
from this point on.}

Magnet length L~m~ and tilt angle θ can be found based on nominal
magnetic field and length of gaps between the magnets in the string. As
it is in the arc dipoles, transmission line is used for magnet
excitation. More over, because of the large required pole width of the
magnet, return line is also used as active part of the magnet excitation
wiring. To minimize iron core saturation effects, magnetic field
B~m~=1.95 T was chosen, as it was for the arc dipoles. With two-meter
gaps introduced between the magnets to allow some space for
repositioning of the transmission line, this results in magnet length of
34.95 m and tilt angle of θ = ± 6.84°.

![](media/image19.wmf){width="4.102083333333334in"
height="2.2680555555555557in"}

Figure 5.18. Cross-over straight section layout

The total length of the beam cross-over magnetic system is about 150 m.
Magnet cross-section is shown in Figure 5.19. The dipole gap is 44 mm to
accommodate (while tilted) the two beams with their vacuum pipes. Pole
width provides good field region for beams separated by 150 mm. Because
of big difference in the gap thickness for the pole and flux return
regions, force applied to the cable is significant, up to 2000 kg/m for
this magnet. Special measures must be undertaken to strengthen the cable
\"spider\" to the needed level at this location.

![](media/image20.wmf){width="4.225in" height="2.7069444444444444in"}

Figure 5.19. Beam crossing dipole

To allow 150-m gap for the tilted magnet installation, basic focusing
cell was modified, that resulted in increased length of the cell
quadrupoles: 18.96 m for each of the two inner quadrupoles and 16.94 m
for each of the two outer quadrupoles. Significantly increasing the
basic quadrupole length above 6 m would result in the increased cooling
water temperature rise, so the total required focusing strength can be
obtained mostly by increasing the number of quadrupoles. The total
length of quadrupoles installed in the two rings for each of the two
cross-over sections is 143.6 m.

#### 5.1.5.3 Conventional Magnets for Interaction Region {#conventional-magnets-for-interaction-region .unnumbered}

As described in section 5.1.4, the IR straight section requires certain
beam manipulation to allow using of low-beta high gradient quadrupoles.
For this purpose, so called \"separation/recombination\" dipoles are
used that bring the two beams together within the low-beta lens string
region and place the beams onto the nominal orbits before they go into
the regular part of the straight section (see Figure 5.15).

Like it was made in the cross-over section, existing transmission line
cable is used for excitation of these magnets and 1.95 T maximal
magnetic field in the dipoles has been chosen. As it follows from
section 2.1.1, gap available for the bending magnets installation is
about 125 meters. Leaving some space for the transfer line position
manipulation, magnet length of 28 m was chosen that insure a 75-mm beam
shift within the 120-m gap in the lattice. Beam displacement inside the
dipole of the specified length is about 12 mm. This displacement must be
taken into account when good field region of the dipoles is being
specified.

To bring the beams together, the \"recombination\" dipole bends
simultaneously the two beams separated by 150 mm. This requires one
direction of bending field for both beams. \"Separation\" dipole
separates beams moving in the opposite directions. Final beam separation
at the outer edge of the magnet is 24 mm. To reduce force applied to the
transmission line and to avoid field asymmetry, a symmetrical iron core
configuration was chosen. The magnet cross-section is shown in Figure
5.20. Good field region area for this dipole is 35 x 20 mm, which is
enough to accommodate the two shifted beams.

![](media/image21.wmf){width="3.098611111111111in"
height="2.204861111111111in"}

Figure 5.20. Separation dipole.

The double-channel separation dipole makes use of both arc dipole
excitation line and return transmission line. As it was for the single
aperture dipole, gap height is 26 mm. Maximal force applied to the
superconducting cable is about 65 kg/m at maximal field strength. Magnet
cross-section is similar to shown in Figure 5.19 above, except the pole
gap and pole width are smaller resulting in a more compact magnet with
650 x 350 mm^2^ cross-section. Good field area of the dipole is 185 x 20
mm^2^, which is slightly larger than it is necessary for this dipole
location. This allows using the dipole in the utility straight section
where larger beam separation is required.

Besides the separation/recombination dipoles, each of the two IR
sections requires a set of focusing quadrupoles similar to described in
section 5.1.5.1. Required strength of these quadrupoles can be found in
Table 5.9. The total length of 70 T/m quadrupoles for use in each of the
two FNAL-site IR section is 445.1 m. Quadrupoles with lengths longer
than 6.1 m will be composed using two quadrupoles.

#### 5.1.5.4 Utility Section Conventional Magnets {#utility-section-conventional-magnets .unnumbered}

Utility straight section is introduced into the ring lattice to provide
needed space for various accelerator systems like RF accelerating
station, injection, extraction, and abort system. In the utility
sections, where RF sections are installed, required beam separation is
460 mm. To manipulate the beams, separation dipoles are used similar to
that used in the IR sections. At the input and the output to the
section, these dipoles have air gap width that accommodates both beams.
In the middle of the section, individual separation dipoles are
installed in both rings back-to-back. Cross-section of the dipole can be
found above (Figure 5.19-Figure 5.20). Length of the dipoles in the
utility section is 25 m, which allows shifting of each beam by 155 mm
within the 242-m space as is shown in Figure 5.22 below.

Two types of quadrupoles are used in the Utility section. Most of the
quadrupoles have nominal gradient of 70 T/m and do not differ from the
straight section quadrupoles described earlier. Total length of this
type of quadrupoles used in each of the two FNAL-site utility sections
is 208,675 m. Quadrupole triplet installed between the abort system
kicker and Lambertson requires more radial space to accommodate beam
deflected by the kicker. In each of the two FNAL-site utility section,
58.9 meters of these quadrupoles, described below, are to be fabricated.

Because it provides needed interface with Tevatron, used as an injector,
and with beam dump facility, it is relevant at this point to refresh
injection/extraction scheme of the machine. As it was described in
section 2, the Tevatron run bipolar is used to inject protons into the
collider rings. Beams for both collider rings are extracted using two
sets of equipment installed at B0 area. Two identical injection transfer
lines end at the corresponding collider downstream utility section where
injection lambertsons and kickers are installed (see Figure 5.21. ).

![](media/image22.wmf){width="3.8506944444444446in"
height="1.7013888888888888in"}

Figure 5.21. Injection and beam abort system scheme

At the end of the transfer channel, Lambertson and dipole magnets bring
proton beam into position close to an appropriate ring where it moves
almost parallel to the equilibrium orbit crossing it in the horizontal
plane. At the location of the crossing, a kicker magnet adjusts injected
beam propagation direction, so that it follows as close to the
equilibrium orbit as reasonably possible. All these magnets belong to
the injection system described below. The layout of the utility section
that includes injection line elements is shown in Figure 5.22.

![](media/image23.wmf){width="3.926388888888889in"
height="2.439583333333333in"}

Figure 5.22. Utility straight section

##### 5.1.5.4.1 Injection System {#injection-system .unnumbered}

Thirty meters of pulsed kicker magnets with magnetic field 0.05 T
provide the horizontal angular kick of 0.5 mrad to the injected beam.
Horizontal beam displacement in the beginning of the kicker magnet
string is 7.5 mm. The nearest lambertson with the 25-mm horizontal
separation of the injected beam from the orbit is installed 35 meters
before the kicker. With the magnetic field level of 0.8 T in the
lambertsons, 20 m of magnets is required to achieve vertical beam
separation of 53 mm. At this point, horizontal beam separation is 35 mm.
Vertical angular kick provided by the lambertsons is 5.33 mrad. Beam
displacement inside the lambertsons is 10 mm in the horizontal plane and
53 mm in the vertical plan. This displacement can be dealt using two
types of an asymmetric lambertson configurations. Fifteen meters
upstream of the lambertsons, vertical beam separation is 133 mm; this
allows placing a set of dipoles with magnetic field of 0.8 T and total
effective length of 36.26 m. These magnets bring beam angular kick up to
15 mrad with vertical separation 550 mm and horizontal separation 60 mm.
This beam separation insures proper spacing for equipment installation.
The total longitudinal space required to place injection magnets is
about 135 m, that fits comfortably into the available space in the
utility section. An additional set of dipoles with gap field of 0.8 T
and total effective length of 56.25 m is installed to bring angular kick
to the required 30 mrad value \[3\].

The duration of the kick provided to the injected beam is about 20 μsec
and is defined by the length of the extracted from the Tevatron beam.
Kicker magnetic field rise time is about 150 nsec; this defines time
separation between the next two (of 72) injected batches. To allow a
reasonable amount of time for the abort kicker current rise, a
three-microsecond gap is arranged between the first and the last
injected batches. This gap also sets requirement for the current decay
time in the injection kicker. Because the kicker magnet must be rather
fast, working in the MHz frequency range, it is difficult to use high
magnetic field in this device. As a reliable reference field value, 0.05
T field strength is used for this study, close to that used for SSC
injection system with similar pulse shape requirements \[2\]. The system
is composed of 30 separate modules, each 1 m long. Each module is fed by
an individual pulse forming network (PFN). A C-shaped magnet is made
from ferrite blocks and with additional capacitors forms a twelve-cell
lumped delay line with a characteristic impedance of 16.6 Ohm. The
ceramic beam pipe has thin resistive coating on the inside surface, and
conductive strips for image current on the outside. Table 5.11 lists the
injection kicker system parameters. Equivalent PFN/kicker circuit does
not differ much from the SSC \[2\].

Table 5.11. Injection kicker system parameters

  ---------------------------------------------- ------------------------
  Impedance (Ohm)                                16.6

  Maximum field (T)                              0.05

  Maximum current (kA)                           2.1

  Maximum voltage (kV)                           70

  Total length (m)                               30

  Number of modules                              30

  Rise time (0 to 100%) (nsec)                   150

  Fall time (μsec)                               3
  ---------------------------------------------- ------------------------

**Injection system lambertson** provides needed bending strength to
steer the injected beam in the vicinity of the circulating beam. Two
types of the magnets are used that differ by location of field free
regions. Cross-section of one of them is shown in Figure 5.23. The
magnet pole with the field free region is made of a solid piece of
annealed, low carbon steel to reduce magnetic field in the field free
region. To simplify vacuum problems, the pole is enclosed in a thin-wall
stainless steel shell. The pole gap is fixed with the use of stainless
steel spacers. For magnet excitation, conventional copper wire coils are
used. Because injection cycle can be repeated not more often than about
once a minute, water cooling can be omitted if injection channel magnets
are on only for a short period of time. Five second cycle is accepted
for this study. The main parameters of the Lambertson are summarized in
Table 5.12 below.

![](media/image24.wmf){width="3.6951388888888888in"
height="3.120138888888889in"}

Figure 5.23. Injection Lambertson magnet

Table 5.12. Parameter list of an injection lambertson magnet

  --------------------------------------------------------- -------------
  Magnetic field, T                                         0.8

  Pole spacing, mm                                          25

  Length, m                                                 4

  Width, mm                                                 288

  Height, mm                                                260

  Number of coils per winding                               2

  Number of turns per coil                                  42

  Conductor cross section area, mm^2^                       42

  Resistance of the winding, Ohm                            0.32

  Rated current, A                                          208

  Voltage drop, V                                           70

  Maximal power consumption, kW                             15

  Average power consumption, kW                             1.25

  Magnet surface temperature rise, °C                       20
  --------------------------------------------------------- -------------

Transfer channel dipole magnets, that do not have field free region,
have been designed using the same coil cross-section. Because pole width
can be made significantly smaller, and because no vacuum shell is
required for this magnet, it is even more compact, 180 x 180 mm^2^ in
cross-section, with pole gap of 25 mm and magnetic field reaching 0.8 T.
The rest of the magnet parameters are very close to those shown in Table
5.12.

Besides vertically bending magnets, horizontal bending with total angle
of 80 mrad (not completely justified at the moment) is required in the
transfer channel. This bend can also be made using the magnets of the
same type. Total magnet string length required for this bend in both
transfer lines is about 300 m.

For this study, conventional magnets have been chosen to establish a
reference point for a future research work with the goal of building the
transfer channel using only permanent magnet based equipment. Although
this technique is well studied during fabrication of the Fermilab
Recycler Ring, requirement of having adjusted bending and focusing
strength makes it difficult to use the system cost scaling without
making first a thorough design study of this approach. An encouraging
approach to this study has been undertaken in \[3\].

There are 86 quadrupoles installed in the transfer channels, most of
them having integrated gradient of 40 T. With quadrupole gradient of 40
T/m, length of the quadrupoles is 1 m. Using design similar to described
in chapter 5.1.5.1, and intermittent powering with only about 0.8 kW of
maximal power per a lens, we can employ air cooling that results in
about 10 °C of magnet surface temperature rise.

##### 5.1.5.4.2 Beam Abort System {#beam-abort-system .unnumbered}

The abort magnet system consists of a kicker magnet, lambertson, and a
beam sweeper. Beam normally goes through the field free area of the
lambertson magnet. Whenever it is necessary to dump the beam, kicker
magnet provides needed radial kick to beam, and the beam is bent by the
lambertson in vertical direction into a beam dump channel equipped with
a beam sweeper. At each moment, magnetic field of the kicker, lambertson
and sweep-magnet must be related to the beam energy. On its way from the
kicker to the Lambertson, the beam that must pass through the set of
quadrupoles as shown in Figure 5.22, acquires a radial displacement of
17 mm, making it impossible to use a regular focusing quadrupole
described earlier in section 5.1.5.1. Special quadrupole with enlarged
horizontal aperture has been designed for this area. For this
quadrupole, lower field gradient (of about 45 T/m) can be achieved, and
longer quadrupole lengths are required for beam focusing. A longer
quadrupole results in higher power consumption and cooling water
temperature rise. Using two 5-meter quadrupoles instead of one 10-meter,
it is possible to have a lower water temperature rise at the expense of
higher total water flux. Table 5.13 summarizes the major abort
quadrupole parameters.

Table 5.13. Main Parameters of the special quadrupole

  --------------------------------------------------- -------------------
  Gradient, T/m                                       45

  Aperture radius, mm                                 20

  Quadrupole width, mm                                260

  Quadrupole height, mm                               260

  Length, m                                           5

  Number of coils per winding                         4

  Number of turns per coil                            12

  Conductor size, mm                                  11.7x11.7

  Conductor cross section area, mm^2^                 104

  Resistance of the winding, ohms                     0.091

  Rated current, A                                    625

  Voltage drop, V                                     61

  Power consumption, kW                               38

  Hole diameter, mm                                   6.35

  Water pressure drop, MPa                            1

  Cooling circuits per winding                        8

  Water temperature rise (deg. C)                     16

  Water flow per magnet (l/min)                       35
  --------------------------------------------------- -------------------

Eight 5-meter quadrupoles are then to be installed in each of the two
abort sections.

**Kicker magnet** switches the beam between the ring orbit and the abort
channel; its strength is chosen to provide needed beam separation of 17
mm at the entrance to the abort lambertson located 300 m downstream.
Assuming kicker field strength of 0.2 T, required length of a kicker is
30 m. Cross-section of the kicker is shown in Figure 5.24.

![](media/image25.wmf){width="3.7125in" height="2.0208333333333335in"}

Figure 5.24. Abort System Kicker Magnet

Current rise time of injection kicker is about 3 μsec, so a beam abort
gap in the ring beam of about 3 μsec is needed. This requirement results
in using a high frequency magnetic material for magnet core fabrication.
Mn-Zn MN8CX (Ceramic Magnetics) ferrite was chosen for this study. The
core is made of ferrite blocks and assembled using epoxy bonding after
windings and ceramic vacuum pipe are installed inside. At nominal field
of 0.2 T, windings current is 2410 A. Maximal field in the core is about
0.45 T, which is below the material saturation level. Pole width was
optimized using pole profiling by attaching 1-mm ferrite stripes near
the pole wedges. With this shaping, field uniformity in the entire
vacuum pipe region is within 0.1 %, which is good enough for this
device. In the configuration shown, magnet inductance is 2.5 μH/m. Ten
3-m sections are used, installed one following another, with each
section having 7.5 μH inductance and 2.5 ohm resistance. Each section is
fed independently by its own pulser.

The abort kicker pulser uses a two-stage scheme. The first stage
delivers high voltage for a fast current rise time. Capacitor discharge
is used at this stage. Then, in the second stage, a long SCR-regulated
pulse with much lower voltage is used to support needed flat top level.
For the three-meter section, discharge capacitor with C = 0.5 μF insures
needed current rise rate. This results in the maximal voltage at the
first stage of 9600 V. Energy stored in the capacitor bank or in the
magnetic field is about 25 J. Flat top length for the abort kicker
magnet is defined by the ring circumference and is about 800 μsec. To
have this long pulse shape, a separate power source must be switched on
when current in the primary circuit starts to decay. Because this is a
typical long-pulse pulser implementation (see, for example, \[2\]), we
will not go into further details.

**Lambertson magnet** uses superconducting transmission line as an
excitation winding. This ensures that at each moment magnetic field is
proportional to the beam energy. The magnet cross-section is shown in
Figure 5.25. The magnet part that includes field free beam channels is
placed inside a stainless steel vacuum box. Only one field free channel
is used in this device; another channel has been added to obtain needed
symmetry. Magnetic field in the field free area limits the maximum field
in Lambertson magnet. The deflecting gap field value of 0.8 T was chosen
to have field in the field free region on the level of 20 Gauss. The 67
m total length of the Lambertson gives the beam a kick of 0.8 mrad that
results in at least 200 mm of beam separation at the location of the RF
cavities. Force applied to the transmission line is about 25 kg/m for
this magnet.

![](media/image26.wmf){width="4.3in" height="3.0097222222222224in"}

Figure 5.25. Lambertson magnet

Main parameters of the Lambertson are summarized in Table 5.14 below.

Table 5.14. Main Parameters of abort system Lambertson Magnet

  ------------------------------------------- ---------------------------
  Maximum field, T                            0.8

  Total length, m                             67

  Air gap, mm                                 20

  Field homogeneity, %                        0.1

  Maximum field in the hole, Gauss            20

  Maximum current, kA                         100

  Weight, kg/m                                330
  ------------------------------------------- ---------------------------

**Sweeping system** is introduced to reduce heating of the dump block by
distribution of beam energy through a larger dump surface area. Although
reliability of this sweeping system must be high, the field quality
requirements for sweeping magnets can be quite modest, allowing about
10% of field uniformity in the sweeping magnets. Sweeping magnets
deflect beam in X and Y direction with amplitude that corresponds to
beam striking the dump block at a location close to its radial
dimension. If phase difference between X and Y oscillations is 90°, beam
projection on the dump surface will move along a circular path. The
velocity of this movement must be high enough to allow beam circling
around the block at least twice during the extraction time, \~800 μsec.
This requires about 2 kHz of beam oscillation frequency. Required
magnetic strength of the sweeping magnets must be about 12 T⋅m in each
direction. 0.3 T of field strength was chosen for this device, resulting
in 40 m magnet. Taking into account possible steering mistakes due to
kicker malfunction and larger beam size in cases of emergency
extraction, required aperure must be about 50 mm. To make the system
simple and reliable, the two steering systems are combined in a single
unit, as shown in Figure 5.26. Field uniformity in this magnet is at an
acceptable level of about 5% at reference radius of 15 mm. Positive
sextupole component in the whole aperture results in additional beam
defocusing on the target. Magnet yoke is made of standard toroidal iron
powder cores T520-40D by Micrometals. Core effective permeability is 60
to 150 in the frequency range up to 100 kHz and in the flux density
range up to 1 T.

![](media/image27.wmf){width="3.9722222222222223in" height="2.8875in"}

Figure 5.26. Sweeping magnet cross-section.

Main parameters of the magnet are summarized in Table 5.15.

Table 5.15. Sweeping Magnet Parameters

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

  Magnetic field                             T             0.3

  Magnet length                              m             40

  Maximum field in the core                  T             0.45

  Stored energy / meter                      J/m           160

  Number of turns                                          2 x 8

  Wire diameter                              mm            5

  Maximum current                            A             2000

  Inductance                                 μH            2 x 80
  ------------------------------------------ ------------- ---------------

For safety reason, sweeping magnet is made of 10 separate 4-m sections
powered by independent pulsers. Simultaneous failure of two sections,
which is a very low probability event, does not compromize safety of the
unit. For each section, current in the magnet windings is supplied by a
simple pulser that utilizes capacitor bank discharge onto the windings.
For each 4-meter section, capacitance required to have oscillation
frequency of 2000 Hz is about 20 μF. With circuit impedance of 4 Ohm and
resistance of windings at 2000 Hz of about 0.1 Ohm, one can expect
periodic discharge with a rather low rate of current decay. Adding some
resistance to the circuit, it is possible to adjust decay rate to a
desirable value to ensure a better beam current distribution through the
dump block surface. Maximal voltage is about 8000 V, requiring about
12000 V of windings and capacitor bank insulation rating because high
reliability of the system is required. This voltage and current level,
and also relatively low frequency, allow using very reliable
semiconducting switching devices like SCRs, and besides can allow a
reserve.

Depending on the final dump block position, certain amount of vertically
and horizontally bending dipoles located between the lambertson and the
sweeping magnet may be wanted. Because the magnetic field of these
magnets must follow particle energy, conventional dipoles must be
considered for this purpose with maximal gap field of about 1.5 T. For
each 1 mrad of bending, 45 meters of dipoles are required then. That\'s
why nominal position of the dump must be chosed to avoid an additional
beam stearing, after the beam is out of the lambertson magnet string.

Summary.

-   Lattice arrangements in straight sections allow placement of sets of
    magnets for beam injection, abort, IR, and cross-over systems;

-   Feasible design solutions have been found for major systems;

-   Magnets located in straight sections can be made using conventional
    magnet fabrication technology.

#### References: *{ note---for Sec. 5.1.5 }* {#references-notefor-sec.-5.1.5 .Reference-heading .unnumbered}

\[1\] V.V. Kashikhin, I. Terechkine. \"Superconducting straight section
quadrupole magnet for low-field VLHC\", FNAL, TD-01-008, Feb. 2001.

\[2\] Conceptual design of the Superconducting Super Collider.
SSC-SR-2020, DE93 007234.

\[3\] J. Volk, Injection transfer line magnets. TD note \# TD-01-027,
FNAL, 2001

### 5.1.6 Magnet Production {#magnet-production .unnumbered}

Construction of the VLHC Stage 1 accelerator will require the
fabrication of several thousand magnets. The largest and most numerous
of these are the combined function arc magnets. They, along with the
dispersion suppressor dipoles, represent the majority of magnet costs.
They are also the most technically challenging as they are a significant
departure from existing magnet technology and, because of their extreme
length, require unique assembly procedures and facilities. All of the
other required magnets are variations of magnets previously produced for
other accelerators. They do not present any significant technical
challenge, as fabrication methods are well understood and a broad
experience base exists at various facilities within the labs and in
private industry. A breakdown of magnet type and quantities is shown in
Table 5.16.

Table 5.16. Magnets required for the VLHC Stage 1.

  ---------------------------- ------------------- -----------------------
  **Magnet Type**              **Physical Length,  **Quantity Required**
                               m**                 

  Main Arc Dipole              67.75               3136

  Dispersion Suppressor Dipole 48.8                160

  Straight Section Quadrupole  6.0                 464

  Quadrupole, Large Aperture   10.0                10

  Low Beta Quadrupole          10.0                8

  Special Magnets              Various             Various

  Dipole Corrector             0.7                 3296

  Quadrupole Corrector         0.7                 3296

  Sextupole Corrector          1.0                 3296
  ---------------------------- ------------------- -----------------------

The extreme length of the combined function and dispersion suppressor
dipole magnets makes the fabrication process unique. The obvious
problems associated with the transport of these long devices make it
necessary to assemble the magnets on site at assembly facilities
strategically located to facilitate delivery of the completed and tested
magnets directly to the accelerator tunnel. Two production facilities
are envisioned. One facility will be located adjacent to the injection
transfer line with the other remotely located on the opposite side of
the ring.

The facilities are considered assembly centers rather than manufacturing
sites. The magnet components will be fabricated off site at
subcontractor facilities to the highest level of completeness (value
added) possible, considering that the components will need to be
transported to the final assembly site. Constraints have been applied to
the maximum length of component parts and subassemblies so as not to
prohibit fabrication at remote locations around the country or overseas.
Twelve meters was chosen, as it is the standard for shipboard containers
and can easily be trucked over roadways without the need for special
permits and vehicles. The on site assembly facilities will do only that
work that cannot be done off site given the above constraints. Magnet
fabrication is projected to take place over approximately six-years.

In any large-scale production program, a thorough quality assurance
program must be carried out during all stages of manufacture. Inspection
of parts upon receipt, testing of components where needed, and
statistical sampling techniques will be employed to ensure that
specifications are met. Warm magnetic measurements will be performed on
all magnets as part of the QA program. Cold tests will be performed on
all of the initial, low rate arc dipole production magnets and will
continue during full production at rates determined by the test
capacity. A discussion of magnet measurement and testing can be found in
section 5.1.7.

In this section we will concentrate on fabrication of the arc dipoles:
they are a cost driver and present some unique requirements, including
the superconducting transmission line. The facilities design, dominated
by the 65m length of the final magnet assemblies, is discussed first.
Factory throughput, labor required, and fabrication details associated
with the arc dipole magnet are then proposed. Fabrication of the iron
and structural assembly is discussed as well. Costs and schedules are
covered elsewhere.

#### 5.1.6.1 Production Facilities {#production-facilities .unnumbered}

The fabrication of the transmission line magnets (combined function and
dispersion suppressor dipole) takes place in two separate custom
facilities each with an approximate size of 210 meters by 140 meters. A
floor plan of the building is shown in Figure 5.27. Each facility has
three distinct areas; 1) component storage, 2) assembly and test, 3)
storage and staging into tunnel.

Component storage: The facility will be used as the terminus for
components fabricated off site. These components range from 12-meter
long iron core subassemblies to individual small parts. The space is
sufficient to house stock for at least three months of production. In
addition to bulk storage, space is allocated for staging (kitting)
components at the various assembly area stations.

Assembly and test area: The bulk of the facility is dedicated to magnet
assembly. There are fourteen "areas", each devoted to a specific step in
the fabrication process. Each fabrication area includes one or more
stations needed to achieve the required throughput for specific
operation. Each area will work autonomously and have the capability of
locally storing one week's production. The facility will be manned 24
hours per day (three shifts) five days per week. Two shifts (shifts 2
and 3) will do production at the assembly stations. One shift (shift 1)
will be used exclusively to move product between the various stations,
stage components at the stations and provide routine maintenance. The
output of each facility is one magnet per day. Table 5.17 lists each
area, its function, number of stations required, and a list of the
tooling necessary to accomplish the stated function. A more detailed
description of the tooling necessary is included in reference \[1\].

The factory will have special handling requirements. Since the magnets
and their subassemblies are 65 meters long, and will need to be
transported laterally between areas, no columns can be located within
the primary assembly area. A custom hoist system is required to lift and
transport the long subassemblies between the various assembly area
stations. Storage areas, associated with each assembly area, will be
needed to house finished subassemblies before moving to the next
higher-level assembly area. Most stations will require a staging area
where the various component parts for the day's production are
marshaled. Figure 5.28 shows, schematically, an elevation of a section
of the plant, showing the workstations in nine areas.

![](media/image28.wmf){width="5.986805555555556in"
height="4.492361111111111in"}

Figure 5.27. Transmission Line Magnet Assembly Factory Floor Plan

Storing and staging into tunnel: the completed and tested magnets will
be stored until they need to be transported into the tunnel. Magnet
installation in the tunnel is expected to take place at a peak rate of 4
magnets per day, significantly faster rate than the production rate.
Consequently, space has been allocated to allow a sufficient number of
completed magnets to be stored in preparation for installation. Support
stands will allow the magnets to be stacked vertically. A custom hoist
system (described previously under assembly and test area) will move the
magnets from the test stand to the storage space. An area is provided to
allow transfer from the storage area to a specially built transporter
rig (see section 5.1.8).

Table 5.17. Assembly area and tooling summary

![](media/image29.wmf){width="5.997916666666667in"
height="6.229166666666667in"}

![](media/image30.wmf){width="6.498611111111111in"
height="1.448611111111111in"}

Figure 5.28. Transmission Line Magnet Assembly Factory Elevation

####  5.1.6.2 Factory Throughput {#factory-throughput .unnumbered}

Each magnet construction factory is designed to produce one magnet per
day, accomplished in approximately 2 shifts. As with any normal
production scenario, initial throughput would be much lower than one
magnet per day, with the schedule eventually increasing to reach the
peak production levels.

Table 5.18 lists, for each area, the number of technicians and times
necessary to accomplish each operation, the number of technician-hours
required per day to manufacture one magnet, and the number of stations
needed in each area to complete the required tasks. All activities shown
in Table 5.18 are accomplished in two, 8 hour shifts per day.

Reference \[2\] shows detailed schedules for each sub-assembly
manufactured for the transmission line magnet, with a breakdown of times
elapsed for each individual operation described in section 5.1.6.3.
"Throughput" schedules for each work area are also shown.

Table 5.18. Technician resources required to produce one magnet per day.

![](media/image31.wmf){width="5.990972222222222in"
height="3.533333333333333in"}

At the end of each day, enough components or subassemblies are completed
in each area to produce one magnet. The subassemblies are stored on a
rack near each station after they are completed. A third shift is used
to move the components to the appropriate area of operation for the next
day's work. Maintenance of tooling is also done on the third shift or
weekends. Table 5.18 does not include these third shift activities.

#### 5.1.6.3 Magnet Assembly {#magnet-assembly .unnumbered}

Assembly of the arc dipole magnet for the VLHC Stage 1 accelerator is
summarized in this section. It is described in more detail in reference
\[1\].

###### A. Assembly of Drive Transmission Line for Stage 1. VLHC {#a.-assembly-of-drive-transmission-line-for-stage-1.-vlhc .unnumbered}

The transmission line consists of four components made by outside
vendors: inner tube sections, a superconducting braid, a copper braid,
and outer tube sections.

Mount 6, 12-meter long invar pipes together into one continuous section
at Area #1. Weld using automatic rotary welding heads, and inspect
mechanically. Tooling pulls the copper and superconducting braids over
the invar tube at Area #2. The outer tube is fed, in 12-meter sections,
over the assembly, then returned to Area #1 to be welded, then leak
checked at Area #5. The welded transmission line is moved to Area #3 for
ball swaging. 3 carbide balls, each of increasing diameter, are pulled
through the inner tube, swaging out the diameter and compressing the
braid between the two tubes. The line is moved to Area #4 for the
cryostat assembly. Support rings and aluminum thermal shield sections
are automatically fed onto the transmission line from the end. Trace
tubes for 60K helium are installed on the sides. 30 layers of
superinsulation are individually spiral wrapped onto the shield, while
the cryostat rotates on the assembly table. Tooling punches holes in the
insulation as it is being wrapped, to accept the penetrations from the
support rings. The extruded aluminum vacuum jacket is then fed over the
insulated assembly in 12-meter sections, returned to Area #1 and welded,
then leak checked at Area #5. The end of the drive conductor is bent
into a dogleg shape at Area #6. It is then moved to storage to wait for
installation into the iron at Area #11.

Assembly of the transmission line will require somewhat complex tooling,
which must perform seven types of automatic processes; automatic rotary
welding, feeding parts longitudinally onto pipes, pulling copper and
superconducting braid onto pipes, installing trace tubes, pulling
carbide balls through the assembly to swage the inside diameter, and
bending the line into the dogleg shape. Pictorial representations of
each of these processes are shown in reference \[1\].

###### B. Assembly of the Return Transmission Line  {#b.-assembly-of-the-return-transmission-line .unnumbered}

The return transmission line design is similar to the drive transmission
line, except a slightly larger size. The return transmission line is not
surrounded by an individual cryostat, as was the drive line. Instead, it
is included in the cryopipe assembly. Fabrication scenario is identical
to that given for the drive assembly, excluding the cryostat.

###### C. Fabrication of Cryopipe Assembly {#c.-fabrication-of-cryopipe-assembly .unnumbered}

Weld the 6.5K flow return pipes, the 40K shield supply header, and the
70K shield return header pipes together longitudinally in Area #1, and
leak check in Area #5. Transport the three pipes, together with the
Return Transmission line, to the assembly station Area #7 \[1\]. Mount
and align the four pipes. Feed 34 spiders over the pipes, spaced every
two meters. Attach shield sections. They are each two meters long, and
will clip on between each spider. Attach braids to intercepts from 4.5K
with connection to 6.5K. Apply superinsulation. Inspect, and transport
to storage area.

###### D. Installation of iron and structural support over the cryopipe assembly and transmission lines. {#d.-installation-of-iron-and-structural-support-over-the-cryopipe-assembly-and-transmission-lines. .unnumbered}

At Area #11 the Transport Drive Transmission Line and Cryopipe Assembly
are positioned in space using special tooling. The 12 meter long Iron
and Structural support subassemblies slide over the prepositioned drive
line and cryopipe assemblies, are positioned and attached.

When installed, the transmission line, complete with cryostat, needs to
be positioned with an accuracy of +/- ½ mm with respect to the iron
laminations. This will be accomplished by using a series of steel balls,
which will contact the outside surface of the transmission line cryostat
and fit into pockets stamped into the iron laminations. The balls,
cryostat, and iron laminations can easily be manufactured to a tolerance
acceptable to accomplish the accuracy necessary between the transmission
line and the iron. The specific tooling and procedure still need to be
developed, since this process was not used on the initial prototype.

Welds are then made at each junction between the magnet support tubes
(vacuum vessel). The vacuum vessel is leak checked, and the entire
assembly is inspected.

It is presumed that the iron and structural support subassembly,
including vacuum vessel, will be prefabricated in industry and supplied
to the final assembly site for assembly in the 65M long magnet. As the
accuracy of lamination profile and stackup are paramount in achieving
the design parameters some discussion is warranted.

The pole tip profile is required to be reproducible to within 20
microns. This tolerance is certainly not achievable for all features of
the stamped laminations. Manufacturing experience indicates, however,
that it is possible for the limited range over which the pole is
defined. The laminations are to be stacked directly on the base datum
feature for the profile. This minimizes the tolerance buildup due to the
stacking operation. The design of the core assembly tie bars and welding
of the spacer bars to the laminations draw the laminations toward the
reference datum from which the profile is defined, assuring that the
basic dimension is maintained accurately.

The internal welding of the spacer bars to the laminations poses some
unique problems associated with physically fitting the required
automated welding equipment within the small space. Equipment will need
to be designed that fits within the limited space. A properly designed
apparatus will produce very repeatable results.

E. End Assembly

Still at Area #11, connect drive transmission line shield cooling line
to 70K header. Assemble end components. Fit up and weld end vacuum
vessel. Leak check completed vacuum vessel.

F. Assembly of the beam tube and vacuum pumping chamber

Start at Area #8. Beam Tube sections are received in 12-meter long
extrusions. Two pieces must be seam welded together to make the final
assembly \[1\]. Inner and outer pieces are butt welded together into
68-meter long sections. Welds and interior surface quality is inspected,
while the assembly is still in two pieces. Getter pumps are installed
into outer piece. Then beam tube halves are connected and seam welded
longitudinally at Area #9. Leak check and beam tube bake out takes place
at Area #10.

###### G. Measurement of the magnetic field of the assembly. {#g.-measurement-of-the-magnetic-field-of-the-assembly. .unnumbered}

All magnets are measured magnetically: warm measurements will be
performed on all magnets while cold testing will be limited to a
fraction of the total production. Measurements must be done before the
beam tube and vacuum pumping chamber is installed, because the test
probe must be placed in the area occupied by the beam tube. Separate
stations are used for warm and cold testing and appropriate space has
been allocated in the facilities layout. A key concern is isolation of
the measurement area from sources of electrical noise which are
typically welding, electric motors, etc. The testing operation takes
approximately 30 hours for a warm test and 70-80 hours for a cold test.
More details on measurements and testing follow in Section 5.1.7.

###### H. Installation of the beam tube and vacuum pumping chamber {#h.-installation-of-the-beam-tube-and-vacuum-pumping-chamber .unnumbered}

Beam Tube Assemblies are mounted onto Structural Support and installed
from the sides at Area #14. On half the assemblies, the beam tube must
be "sprung" into position, but then will stay in position after being
installed. On the other half, they will slide into position easily, but
will need to be secured afterward. The completed magnet is then
transported to the storage area to await installation into the tunnel.

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

\[1\] J. Carson, R. Bossert, \"A Proposed Production Procedure for Stage
1 Transmission Line Magnets\", TD-01-028, 2001.

\[2\] J. Carson, R. Bossert, \"Throughput for Stage 1 Transmission Line
Factory\", TD-01-029, 2001.

### 5.1.7 Magnetic Measurements and Testing {#magnetic-measurements-and-testing .unnumbered}

In this section, we focus discussion on testing of the combined function
magnets during production since these magnets are the dominant element
of the Stage 1 machine. No doubt measurement and testing of other
magnetic elements in the ring are necessary, but most of these are of
more conventional design which can be accommodated by existing equipment
and approaches. Also because of their length and small bore, the
combined function magnets are the most difficult to measure.

Unlike 'conventional' superconducting magnets, the conductor of the
combined function magnets (transmission line) is not in a high field
region and quench 'training' is not a significant issue for magnet
performance. Thus magnetic field measurements dominate the magnet
testing process, both as a quality control measure and as
characterization necessary for machine operation.

Field measurements will be performed on all magnets. This must be done
before the beam tube and vacuum pumping chamber is installed, because
the test probe must be placed in the area occupied by the beam tube.
Roughly 10% of magnets will be measured with the transmission line
cooled to cryogenic temperatures allowing characterization of the field
to full current. The remainder will be measured with the transmission
line at room temperature. During initial stages of production when the
fabrication rate is lower, we will cold test all magnets. As rates
approach one magnet per day, the fraction of total magnets cold tested
will be determined by test facility capacity and test needs as indicated
by initial results.

We first discuss a conceptual design for a measurement system to be used
for the combined function magnets. We then follow with a brief overview
of the approach to cold testing and conclude with a few remarks on other
test and measurement considerations.

#### 5.1.7.1 Measurement System {#measurement-system .unnumbered}

As described above, magnetic measurements are the primary concern of the
test program. While one would also expect to perform an extensive series
of measurements, possibly using several measurement techniques, during
the R&D phase of magnet development, here we have chosen to present one
concept for measurements of production magnets. This concept utilizes a
rotating coil. We try to define the most important issues related to
this concept and examine the consequences. A brief discussion of other
approaches follows.

The main parameters of the arc dipole magnets are \~2 T field, ≤12%
horizontal gradient, 65 m length, and 20 mm gap. Measurement of the
integrated dipole field is needed with an accuracy of a few parts in
10^4^. Desired measurement accuracy for the higher order harmonics is
0.1 units.[^1] We begin by examining the implications of requirements
for field strength measurements. Based on this discussion we present a
concept for a measurement system. Given this system we then address the
issue of measurement of field harmonics.

With respect to measurement of the integrated field strength, there are
two issues. The fractional accuracy of the measured field goes as ∆*R/R*
where *R* is the radius of the rotating coil \[1\]. This requires that
the radius of the probe be known with high accuracy. Typical
manufacturing and measurement uncertainty for magnetic measurement
apparatus is \~0.001 inch (25 μm) which translates into a field error of
3e-3 for a probe of 10 mm maximum radius. At least an order of magnitude
greater precision (3e-4 strength error) is required. This level of
precision can only be achieved using a calibration magnet in which the
strength is known at least as well as one need know it in the subject
magnets.[^2] The second issue is unique to measurement of combined
function magnets. Due to the horizontal field gradient, an error in the
horizontal position of the probe translates into an error in measured
field strength. In a magnet with 10% gradient, measurement of the
strength to 1 part in 10^4^ requires positioning the probe with 0.1 mm
accuracy. Although difficult, this can be achieved using mechanical
fixtures referencing to the magnet laminations. Vertical placement of
the probe is not as critical.

The main conclusions from the preceding discussion are that (1) a
rotating coil of the size we are considering can be calibrated with
sufficient precision, and (2) that the horizontal position of the probe
can be set with mechanical fixtures. For reasons we list below, we
choose to insert the rotating probe into the aperture from the side
rather than from the end. The probe is supported on a frame attached to
the magnet as shown in Figure 5.29. Principle elements of the design are
the following:

-   The probe body is clamped to a precisely machined fixture
    ('strong-back') on an edge which describes the magnet sagitta.

-   The strong-back slides horizontally in a series of guide brackets
    ('jaws ') attached to the vertical member of the frame. The
    strong-back is spring loaded so that it and the probe are forced
    against the magnet laminations at the edge of the magnet gap,
    referencing the horizontal probe position with respect to the
    laminations.

-   The vertical position of the probe is defined by the precision with
    which the frame is attached to the magnet and the precision of the
    jaws relative to the vertical member of the frame and the horizontal
    surfaces of the strong-back. A tilt sensor is mounted on the
    strong-back to monitor its alignment.

-   The motor for rotation and encoder for probe angle readout are
    mounted on the frame and connected to the probe by a mechanism such
    as a toothed belt or right angle drive. Other drive components could
    also be mounted outside the magnet bore (e.g. gearboxes).

-   Development of slip rings small enough to fit the probe bore is
    assumed although one might choose to digitize and transmit the
    signals from inside the bore. A pre-amplifier circuit sized to fit
    the bore is also assumed allowing a boost in signal size.

![](media/image32.jpeg){width="3.201388888888889in"
height="2.2319444444444443in"}

Figure 5.29. Measurement Fixture. Note that the magnet sagitta is highly
exaggerated.

A consequence of insertion from the side is that one loses a few extra
mm of probe radius due to the reduction in gap at the magnet edge of the
focusing magnet. One also needs to allow space for the clamps holding
the probe to the strong-back and for clearance during insertion.

Given a probe radius, we need to examine the accuracy of the measurement
of field harmonics. From \[1\] we see that probe calibration matters
little in measuring harmonics. Accuracy of 10% or so is adequate. This
requires knowing the probe radius to 10e-3. What is of greater interest
is the evaluation of the interplay of signal size with harmonic
measurement. This has implications for the required level of excitation
current during test. For a reasonable set of probe parameters,
pre-amplifier gain of 100, measurement accuracy of 0.1 unit through n=9
requires at least 200 A excitation current \[1\]. This should be
possible for room temperature measurements. We would no doubt increase
the gain and run at the highest tolerable current for increased
accuracy.

A probe length of 6.5 m was assumed above. Ten measurements are then
required to construct the integral field. The time required for
measurement is estimated as 2.5 hours with 2 crews of 3 technicians
using 4 sets of measurement apparatus \[1\]. This certainly allows for
the required production throughput. Automation and optimization of
procedures will reduce the time required. We also note that the
apparatus described could be used for either warm or cold measurements.
The only special consideration for cold measurements would be to
construct the strong-back of a nonmetallic material to prevent the
formation of eddy currents during ramping.

We have chosen a probe inserted in the magnet bore from the side and
supported by an external frame. An alternative approach would be a
\"mole\", such as have been developed for measurements of SSC \[2\] and
LHC magnets \[3\] which are probes with drive and angular alignment
systems built in. The obvious advantage of this approach is that the
probe can be larger by as much as 25% as insertion is from the magnet
end rather than the side. A larger probe produces larger signals.
However, development of drive apparatus operating in a strong magnetic
field is neither trivial nor cheap. We have no doubt that this could be
done; however, we have chosen a simpler approach that removes elements
of the measurement system other than slip rings and pre-amplifiers from
the bore accepting as a consequence somewhat smaller signals.

#### 5.1.7.2 Cold Testing {#cold-testing .unnumbered}

As a quality control measure and to characterize the magnetic field of a
sample of the magnets to full current, we plan to cold test at least 10%
of produced magnets. The peak rate of 2 magnets built per day requires 1
magnet cold test per week. As discussed in the introduction, quench
training is not a significant issue for the superferric design employed.
However, it is important to have a full set of field measurements of
magnets produced early in the program to check the overall design, iron
saturation, yoke fabrication, and related effects on the field quality
and transfer function. This increased testing also produces a
statistically significant warm-cold correlation for the field harmonics.
As the production rate rises, measurements check mechanical properties
of the magnets as well as properties of the materials used to build
them; and the set of measurements can be reduced to those necessary for
quality assurance.

The cold parts of the magnet are the transmission line and return bus
and their relatively small cryostat. Refrigeration requirements are
modest; cool down and warm up times, short. The associated test
equipment -- cryogenic end boxes, transfer lines, pumps, and
refrigerators -- is simple and inexpensive when compared to facilities
developed for testing 'conventional' superconducting magnets. Cold
testing can be done in a small area in the production facility in
conjunction with warm measurements rather than in a large, separate cold
test laboratory. The actual time spent in hooking up, cooling down,
testing, warming up, and disconnecting the magnet is small when compared
with conventional superconducting magnets. A peak production cold test
cycle occupying the test stand for one five day week would allocate a
two shift day to each of these tasks: installation and connection of the
magnet on the stand, cool down, testing, warm up, removal.

#### 5.1.7.3 Other Testing Considerations {#other-testing-considerations .unnumbered}

One of the difficult issues in design and construction of a magnet
system of the scale proposed is the understanding of its overall
reliability. Failure rates for the magnets must be very small if
collider availability is to be kept at the level necessary to carry out
the physics program. Determining failure rate is itself a difficult task
as it is unrealistic to plan for the number of tests necessary to
'prove' that the magnets as constructed will meet the lifetime
reliability requirements for the collider (even assuming that we could
agree on a 'proof'.) However, since the iron yoke design and peak fields
are similar to conventional magnet designs in use for decades, we do not
envision reliability problems here. Key components will be subjected to
'lifetime' testing -- equivalent magnetic and thermal cycles (if
appropriate) --to verify that they meet requirements. While it is
impossible to argue the statistical validity of a small sample of test
magnets, accelerated life testing of a few early magnets will be used to
validate design and provide feedback early in production should any
degradation in performance be detected.

####  {#section .Reference-heading .unnumbered}

#### References *{note -- for sec. 5.1.7}* {#references-note-for-sec.-5.1.7 .Reference-heading .unnumbered}

\[1\] P. Schlabach, \"Magnetic Measurements during Production of VLHC
Low Field Combined Function Magnets\" TD-01-007, 2001.

\[2\] G. Ganetis, et al., \"Field Measuring Probe for SSC Magnets\",
Particle Accelerator Conference, 1987.

\[3\] L. Walkiers, \"Measurements for the Acceptance Tests of the LHC
Superconducting Magnets\', Eleventh International Magnet Measurement
Workshop, 1999.

### 5.1.8 Magnet Installation {#magnet-installation .unnumbered}

More than three thousand 67.75-m super-ferric magnets must be installed
in the arcs of the two 240-km accelerator rings. Besides, about 1000
conventional magnets are to be installed in the 10 straight sections and
in the two transfer channels (see part 5.1.5) The scale of this work
will require technique that ensures high quality of the installation
resulting in high reliability of the accelerators\' magnetic system. The
next baseline scenario was accepted for the magnet installation:

-   transmission line and vacuum pipe are embedded into each magnet at
    the fabrication stage;

-   magnets are transported into the accelerator tunnel one-by-one and
    installed onto aligned adjustable support stands;

-   needed interconnections are made for transmission line, cryo-pipes,
    and for the beam pipes;

-   electric network cross-check, high-pot test, and vacuum leak check
    are performed after each half-cell is assembled;

-   cryo-check and current load test is performed after each 20-km
    magnet string is assembled;

-   corrector magnets are installed and needed beam pipe
    interconnections are made;

-   final magnet alignment is performed.

![](media/image33.wmf){width="2.714583333333333in"
height="2.7111111111111112in"}Tunnel (or tunnel section) construction is
considered completed when no mud removal traffic is going through the
tunnel section, when finished, dry and ventilated tunnel allows
transport vehicles traffic, when escape egresses are available, and when
light, environmental safety monitor, and power lines for transport
vehicles are mounted. Because at the second stage High Field Ring will
modify tunnel layout, while planning all of the mentioned above works,
we must consider this future collider upgrade so that installed
equipment wouldn\'t make this upgrade too complicated. Tunnel cross
section with both Low Field and High Field accelerators installed is
shown in Figure 5.30.

Figure 5.30. Tunnel cross-section after the stage-2 upgrade.

Before magnet installation, cable and LCW racks must be mounted, and
needed cabling completed. For magnet installation, horizontal and
vertical survey monuments must be embedded into the tunnel wall and
concrete floor to the predetermined accuracy, and magnet support stands
installed and aligned to the accuracy of ± 1 mm in vertical direction
and in horizontal plane.

Magnet installation schedule, number of working crews and number of
members in each crew will be defined to accomplish the job during the
3-4 year term. At least two access points at the opposite sides of the
ring are required. The simplest magnet delivery scenario can be realized
when assembly starts from the middles of the half-arcs connecting
Fermilab site and Far End site and goes to four direction
simultaneously. If magnet replacement is required after the magnet
string is installed, more complicated scheme must be used. In this case
magnet traffic will go down the tunnel with already installed magnets,
and additional measures must be taken to allow parallel work of an
assembly crew. The magnet installation procedure in this case also is
more complicated because it requires magnet movement across the tunnel.

During installation, the magnet is bent in the horizontal plane to the
radial position predefined by the pre-aligned support stands. It is
assumed that support stand rough alignment is done with the help of a
semi-automated surveying system using available survey monuments in the
tunnel.

Because of an unprecedented magnet length and relative weakness, strong
attention must be devoted to their transportation to the place of
installation in the tunnel. Magnets will be delivered using specially
designed tooling to prevent any undesirable events from happening. Even
using this kind of fixture, magnet transportation speed will be quite
moderate, about 5 km/h to reduce dynamic loading of the magnet and
prevent any plastic deformations. Because of a high average magnet
transportation length inside the tunnel (about 30 km!), only one magnet
per day can be installed by each installation crew. Several crews must
work simultaneously to make installation time acceptable. Connection of
the installed magnets in a string can be made simultaneously for several
magnets. Automatic welding machines will produce high quality vacuum
tight connections of all helium pipes. Appropriate fixture for the
100-kA conductor splicing between the magnets must be designed and
thoroughly tested to guaranty 100% reliability for these connections.
Magnet interconnection appears to be the most time consuming procedure
in the process of magnet installation, so some R&D must be devoted to
making this procedure simple. High voltage test (5kV) to ground is to be
made for each magnet before final closing of the external vacuum jackets
of the interconnecting boxes.

Cryogenic and power test must be done after interconnection procedure is
completed for any 20-km string of magnets. Connection to the cryogenic
system and to a current supply will be required at this point. Any
possible vacuum leaks could be detected at this point. If any
malfunction can be taken care of after warming up of the magnets string.

Beam pipe is interconnected after the cryo-test shows an acceptable
magnet string quality and correction magnet block is installed. After
the beam pipe interconnections are made, it will be checked for vacuum
separately for each half-cell.

**Magnet transportation** is one of the most critical issues in magnet
installation procedure. Table 5.19 below gives an idea of what is an
allowable range of magnet displacement during handling. In all the three
cases in the table, it was considered that magnet position was fixed in
the two cross-sections separated by 12 m and force (or force couple) is
applied between these two sections. It corresponds to the distance of
about six meters between the magnet support stands.

Table 5.19. Limits of relative displacement of magnet parts

  ------------- ------------- --------------------------------------------
  Mode          Allowable     Limitation type
                range         

  Horizontal    ± 3 mm        Relative displacement of upper and power
                              magnet halves is more than 100 μm

  Vertical      ± 4 mm        Stress in magnet structural elements exceeds
                              yield limit

  Twist         ± 16 mrad     Stress in magnet structural elements exceeds
                              yield limit
  ------------- ------------- --------------------------------------------

The magnet structure is quite flexible taking into account its length.
Just due to its own weight, vertical sag can exceed the limits from the
table if one of the supports is removed. During transportation and
installation, it is necessary to monitor and correct relative
displacement of magnet parts to the limits well below those shown in the
table. To significantly reduce a risk of magnet damage during
transportation, a 60m long aluminum frame is used at this stage. The
frame increases assembly rigidity and preserves magnet from the vertical
bending damage. Picture in Figure 5.31 shows the frame moving inside the
tunnel.

![](media/image34.wmf){width="5.988888888888889in"
height="0.375in"}Figure 5.31. Magnet transportation frame.

During transportation, dynamic loading effects increase stress level in
magnet structural elements, especially when the transportation vehicle
leaves an entrance ramp having the inclination of about 4° and goes into
the horizontal collider tunnel. To significantly reduce the undesirable
and potentially dangerous relative movement of the frame (and magnet)
parts and to eliminate a possibility of any magnet damage during
transportation, an active shock absorber system is used. Several
four-wheel carts installed along the frame use position controlled
hydraulic cylinders to support the frame with the magnet inside during
transportation. Inclinometers installed on the carts provide needed
information to a feedback system about relative position of the
neighboring carts. Accelerometers installed near critical points on the
magnet detect any mechanical oscillations and slow down or stop
transportation if any danger to magnet is suspected. Through the
coordinated action of the cylinders it is possible to lower the magnet
to its final destination in a controlled manner.

Two motorized vehicles on both sides of the frame, each with engine
power of 60 kW, pull the frame during transportation from production
facility to the designated location in the tunnel. As a major power
supply, a 480 V bus protected against easy human access is to be
installed in the tunnel. Besides, the vehicles will have sufficient
battery power to move to a nearest egress without being hooked to the
power bus as it is needed in a case of a major power failure.

To insure smooth automated movement of a magnet delivery train, a
positioning system must be used. This system can use the bus as a
reference base, or other solution can be used. For example, parallel
slots in the floor can define distinct pathway(s) for the transport
traffic. As another option, it is possible to use magnetic field of a
wire placed in a groove in the floor and carrying current to define a
direction for all vehicles to follow.

**Installation scheme** shown by the cartoon in Figure 5.32 corresponds
to the case when magnet installation starts from the middle of the arcs.
A guide groove in the floor under the beam line or other technique can
be used to guide transportation vehicle (Figure 5.32a). Magnets are
delivered to their location and put on the support blocks without any
transverse movement (b). Unloaded frames are then moved back along a
parallel pathway (c). In this case, each next magnet can start its
movement to the assembly place without waiting for the unloaded frame
and the transport vehicles. Two magnet transport vehicles and an escape
or a crew delivery vehicle can move in the tunnel simultaneously and
independently. This scenario suggests a lot of flexibility for
organizing optimal delivery traffic.

Figure 5.![](media/image35.wmf){width="5.988888888888889in"
height="1.2625in"}. First installation scheme

![](media/image36.wmf){width="5.988888888888889in"
height="1.2673611111111112in"}A need to replace a magnet after it is
installed will require another magnet installation scenario. In this
case the magnet will be transported along the magnets that have already
been installed (Figure 5.33a; installed magnets are not shown). Using
hydraulic and control system of transportation trailers, the magnet will
be lowered down to temporary support stands installed beneath the carts
(Figure 5.33b). After the frame is removed (Figure 5.33c), the magnet is
to be shifted horizontally and placed on the permanent stands with the
use of a specially designed hydraulic pulling system based on the
permanent support blocks (Figure 5.33d, e). Control equipment similar to
used during transportation will synchronize the system during this
operation.

Figure 5.33. Magnet replacement scheme

**Interconnections** of several different types are to be made after
magnets are installed. First, the two magnets in each half-cell must be
connected to form common electrical, cryogenic and vacuum system. There
is a 1-m space available for this interconnection. Second, between
half-cells active superconducting transmission line must be moved into
the return line enclosure to clear a 3.5-m space for conventional
correction magnets. Finally, in the straight sections where special
magnets are installed there is need for several modes of transmission
line positioning. The interconnection scheme does not differ much for
all these cases; it is thoroughly described in section 5.1.2.3.4. The
basic steps of this procedure are listed below:

-   connection of the transmission line inner invar pipes for both
    active and return lines;

-   splicing of superconducting cables;

-   installation of electrical insulation and performing a high-pot
    test;

-   connection of cryogenic piping;

-   installation of a 50 K screen;

-   installation of a super-insulation and closing the area of the high
    pressure pipe;

-   checking for a vacuum leak and repairing if needed;

The described procedure will ensure interconnections of a high quality;
nevertheless, after each 20-km magnet string assembly is completed, a
cryo-test must be performed. This cryo-test will involve pressure test,
relieve valve setting tests, magnet string cooling down, heat leakage
test, and transmission line current test. The cryogenic plant
performance and magnet string quench test will be also conducted.

If there is a need to replace a magnet, the following **replacement
procedure** can be used that utilizes the magnet repair magnet delivery
scenario described above:

-   cut off beam pipes of the replaced magnet;

-   open the connection space;

-   remove super-insulation;

-   cut all the cryo-pipes and transmission lines of a the magnet to
    replace;

-   remove replaced magnet moving it horizontally out of the magnet
    string;

-   install new magnet following the repair scenario of magnet
    installation;

-   make interconnections as described above;

The goal for a replacement procedure is to complete it during one 8-hour
shift of multi-crew work.

**Corrector magnets** can be installed after the cryo-test is
successfully completed. Six air-cooled correctors occupy the 3.5-m gap
between arc half-cells. All these magnets are factory assembled on
common support structure, with beam pipes installed in magnet gaps.
Description of the correctors can be found in 5.1.3. Totally 1568
corrector blocks will be transported and installed. A two-ton load
capacity crane or hydraulic fixture will be used to install the
corrector magnet blocks on their support stands. All corrector coils
will be electrically tested and connected to the power supply leads.
Then beam pipe interconnections can be made following by a vacuum leak
test.

Arc magnets are ready for **final alignment** after correction magnets
are installed and vacuum pipe interconnections are made. Each magnet
must be installed so that magnet reference center is within **± 0.25
mm** from the nominal orbit position. For each magnet, an acceptable
roll angles are less than 1 mrad. Conventional optical techniques
(theodolites and laser trackers) for alignment will have angular errors
in the range of 10 microns per meter, corresponding to ± 300 microns at
the magnet ends from a setup at the center of the magnet. This would be
marginally adequate to meet the magnet alignment specification of 250
microns RMS over the length of the magnet. However this accuracy can be
exceeded using the hydrostatic leveling and stretched wire techniques
described below.

For each magnet there will be a support every 6 meters with horizontal,
vertical and roll adjustment capability. The magnets will be built
"laser straight" in the factory. The magnets will be installed in the
tunnel with a 15.57-mm sagitta over the 65-meter length. The stiffness
of the magnet will allow an independent range of motion of
approximately\
± 2mm horizontally or vertically at each adjuster. Motions outside this
range will require coordinated movements of nearby adjusters. The magnet
position will be roughed in using optical techniques along the beam line
relative to the internal tunnel network. At each of the support stands
there will be a **hydrostatic leveling pot** for vertical alignment,
**capacitive stretched wire pick up** for horizontal alignment, and an
**electronic gravity sensor** for roll. As the adjustment screws are
turned there will be real time readout of both systems to allow for the
positioning of each segment of the magnet. A ± 3cm range of the
adjusting screws will be sufficient to put in the sagitta and to
compensate for installation errors in the magnet stands as well as drift
and settling of the tunnel (± 1cm maximum) over a 20-year lifetime.

**Vertical alignment** can be made using a hydrostatic leveling
technique, that make use of fluid-filled containers with capacitive
readouts. This technique allows vertical alignment within ± 100 μm for
each magnet. For larger scale, corrections taking into the account
non-uniformity in Earth gravitation field must be made. This will
require careful study of the Geoid and the change in the density of the
earth in the region of the machine. Corrections to the vertical can then
be imposed on each magnet.

**Magnet roll** can be adjusted using the technique similar to used
during leveling of the magnets. It can help to establish a real time
display of the roll of the magnet at each adjustment station. Given a
base support of 500 mm and a resolution of 2 microns for the hydrostatic
levels a roll angle of ±4 micro-radians is achievable. This exceeds the
1 mrad requirement for acceptable vertical closed-orbit distortion.

**Horizontal alignment** is done using the stretched wire technique. A
small diameter (less than 1 mm) copper beryllium wire mechanically
attached to both ends of the magnet forms the reference base. Two wires
separated vertically can be used to increase the signal to noise ratio.
Using capacitive pickup electrodes at each support stand, it will be
possible to adjust horizontal position of each magnet to a needed
accuracy. Alignment of the entire 66-meter magnet to within ±100 microns
should be possible. To set the sagitta of 15.6 mm for the magnet all the
adjustments must be made at the same time. Starting with optical tooling
the rough sagitta can be set to an accuracy of ±300 microns. Once this
is done the stretched wire system can be installed. Each capacitive pick
up will have a different offset from the magnet to account for the
saggita. The final adjustment will involve moving all adjusters at the
same time.

A varying degree of automation is possible. The simplest approach is for
the person at the central display of magnet alignment data to give
directions to one or more workers with wrenches. A more sophisticated
alternative is to manually place motorized wrenches at each of the
adjusters, then run automated software procedures to bring the entire
magnet into alignment. If these systems were permanently installed and
coupled with motorized adjustment stands they could be used as an active
alignment that continually aligns the magnets as the machine runs. Beam
position monitor information could also be used.

**Special magnets** of several types are to be installed in the ten
straight sections and two beam injection lines (see 5.1.5). Straight
section focusing quadrupoles and injection line dipole and lambertson
magnets are conventional magnets. Maximal weight of these magnets does
not exceed 5 tons and their length is less than 6 meters, so they are
installed on their support stands using conventional technique.

Separation/recombination dipoles and abort lambertson use transmission
line for excitation. Installation technique for theses magnets is
similar to that used for the arc dipole magnets except they are made of
pieces with length that do not exceed 6 meters and weight less than 5
ton. To avoid time spending related to interconnections, these magnets
are assembled around preinstalled transmission line and vacuum pipes.
Because none of the straight section dipole magnets is of combined
function, alignment procedure for these magnets is straightforward.

The third type of magnets is pulsed injection and abort kicker magnets
and abort sweep-magnet. These magnets are of dipole type, so
installation and alignment procedures for these magnets are
straightforward.

Finally there are eight 10-meter, superconducting, high gradient,
low-beta IR quadrupoles described in 5.1.4. Each quadrupoles will weigh
about 25 ton and is rigid enough to be transported to the place of
installation using two high load trailers and two transport vehicles of
the type used for the arc magnet transportation. Alignment requirement
for these quadrupoles installation is ±100 μm, so two adjustable support
stands will be used, and alignment procedure is going to be similar to
described above for arc dipoles.

Because sections that use special magnets are located closer to the
Fermilab and Far End sites than accelerator\'s arcs, installation of
these magnet can be done quite independently of the installation of arc
magnets, even allowing injection line testing while arc magnet
installation is still in process.

## 5.2 Accelerator Systems {#accelerator-systems .unnumbered}

The systems are distributed around the ring circumference include
cryogenics, arc instrumentation, corrector power supplies, and beam
vacuum systems. The "once per turn" systems are located primarily in the
straight sections on the Fermilab site. These include RF, injection and
extraction, and once-per-turn instrumentation.

A completely conventional approach is taken to the standard utilities in
the straight sections. Warm iron/copper magnets use LCW cooling and
standard power supplies. Electronics and major power supplies are
located in underground shielded instrumentation rooms that are
accessible with beam on. A larger tunnel, conventional power systems,
and generous cable trays provide the infrastructure for RF systems,
injection and extraction kickers and Lambertsons, beam crossovers, beam
halo scraping, beam current and beam profile monitoring, etc.
Concentration of these major subsystems at the Fermilab site makes
maintenance and accessibility requirements similar to other Fermilab
accelerators. These systems are modeled on existing designs from recent
projects for which the specifications and costs are well known.

Four systems contain notable new features which will be described in
some detail: the cryogenic system which is smaller and simpler than
comparable systems, the beam stop which must deal with the large kinetic
energy in the beam, the arc instrumentation which is distributed as
electronics modules in "holes in the wall" at each quad location, and
the beam damper system which is distributed around the ring
circumference.

### 5.2.1 Cryogenic System {#cryogenic-system .unnumbered}

#### 5.2.1.1 Cryogenic System Description {#cryogenic-system-description .unnumbered}

The magnet's super conducting transmission line is cooled by pressurized
supercritical helium at 4.5-6.0 K. The heat load of the magnet system is
removed by the sensible heat of the supercritical helium stream. The
fluid operates just outside the critical region expanding the helium
stream as it passes through the transmission line producing a large
effective heat capacity.

![](media/image37.png)

Figure 5.34. VLHC transmission line temperature profile.

Cryogens are fed from six (6) refrigerator plants spaced at 38 km
intervals around the ring. For efficiency reasons, refrigeration is
provided at two (2) temperature levels. Refrigeration at a higher
temperature (40K) provides cooling for a heat shield that is used to
intercept much of the heat that would otherwise be absorbed by the lower
temperature superconductor. Each plant provides refrigeration for
upstream and downstream magnet streams. Each string is sub-divided into
two (2) loops, referred to as "near" and "far" loops.

##### 5.2.1.1.1 Helium Distribution System {#helium-distribution-system .unnumbered}

The helium distribution system is designed to distribute refrigeration
to the magnet system with a minimal temperature variation. The
distribution system consists of cryogenic valve boxes, transfer lines,
and warm helium header.

###### (a) Cryogenic Valve Boxes {#a-cryogenic-valve-boxes .unnumbered}

Cryogenic valve boxes are used to redistribute the helium between the
conductor loops for steady-state operation and perform various transient
state operations. These boxes are located every 9.5 km and house the
control valves and instrumentation required for each circuit. Boxes vary
in configuration dependent upon location in the magnet string. These
boxes are relatively simple devices mainly providing a transition for
flow redistribution.

###### (b) Transfer Lines {#b-transfer-lines .unnumbered}

Transfer lines are a part of the magnet assembly. A line contains five
(5) circuits: 4.5 K superconductor supply line (near loop only), 6.0 K
superconductor return line, 40 K shield supply line, 70 K shield return
line, and a vacuum circuit. Each section of transfer line is equal in
length to a magnet (67.5 meters) and is attached to the magnet assembly
via a structural anchor at the midpoint of the magnet.

-   The 70 K return line is 0.102 m OD stainless steel pipe is connected
    to an extruded aluminum shield that surrounds all the inner lines.
    The shield is wrapped with a double-sided aluminized mylar (dimpled
    and perforated). The longitudinal contraction of the line is
    compensated with guided formed bellows in the inner connect. During
    this shrinkage, the G10 support structure is allowed to move within
    the vacuum space.

-   The 40 K shield supply line is a 0.089 m OD stainless steel pipe
    supported on the G10 spiders from the aluminum shield. Bellows are
    used at the end of each 67.5 m module to compensate for thermal
    contraction and expansion.

-   The 4.5 K supply -- near loop only -- and 6.0K super conductor
    return line is Invar tubes which are also anchored at the midpoint
    of the module. These lines are of concentric design. The 6.0K helium
    flows between two (2) concentric Invar tubes

-   The 4.5K supply line is suspended via G10 spiders from a 6.0K inner
    line.

##### 5.2.1.1.2 Helium Pressure Relief and Venting System {#helium-pressure-relief-and-venting-system .unnumbered}

Relief valves for each of the five (5) circuits are located every 540
meters. These valves will vent into the warm helium header that is
itself protected every 1 km at 3 MPa (30 bar) from over pressurizing.
Each relief is conventional in nature and set to the MAWP of its given
circuit. The primary need for these reliefs are for trapped volume and
loss of insulating vacuum scenarios. The warm header is further
protected at the refrigerator (above ground) at a set pressure of 0.2
MPa (2 bar), venting to atmosphere.

![](media/image38.png)

Figure 5.35. Helium pressure relief valves.

Quench protection of the transmission line is discussed in \[Koepke et.
al. & DR doc\]. The 100kA transmission line conductor contains enough
copper that it can be safely shut down with a 1 second time constant
following a quench. A number of detailed quench simulations have been
performed \[N. Shatil final report\]. The peak temperature is \~250K.
The worst-case peak pressure comes from a situation in which a
mis-steered beam (kicker misfire) causes the beam to oscillate
side-to-side in the beam pipe and scrape heavily in a series of
locations separated by a half-betatron wavelength. In this case the peak
temperature is unaffected, but a worst-case pressure occurs when the
hydrodynamic shock waves from two adjacent quenches collide at the
midpoint between quenches. The peak pressure is below the 4 MPa (40 Bar)
pressure rating of the transmission line. Thus no helium needs be vented
anywhere, even for a long period following the quench. The pressure
burst from the hydrodynamic shock wave, as registered on pressure
sensors along the transmission line could provide a convenient method of
identifying where the quench occurred.

##### 5.2.1.1.3 Heat Shield Cooling System {#heat-shield-cooling-system .unnumbered}

Pressurized 40K helium is used to intercept the radiation and conduction
heat leak to the transmission line. Helium is supplied from the
refrigerator at 1.7 MPa (17 bar) and returns at less then 70K and 1.3
MPa (13 bar). Flow is supplied via a 0.089 m O.D. tube and distributed
via a pair of 6E-3 m OD lines every 270 meters carrying 2.0 g/sec. This
scheme provides shield cooling for every two magnets. Control valves and
temperature sensors are included every 270 meters for heat shield flow
control based on temperature requirements.

##### 5.2.1.1.4 Transmission Line Heat Load Estimates {#transmission-line-heat-load-estimates .unnumbered}

Transmission line heat load estimates are divided into two (2)
components: the primary heat load on the 4.5K system and the heat load
to the 40K shield system. The calculated heat loads are presented in
Table 5.20.

Table 5.20. VLHC Design Study Calculated Transmission Line Heat Loads

![](media/image39.wmf)

##### 5.2.1.1.5 Power Lead Cooling {#power-lead-cooling .unnumbered}

Due to its low inductance (3uH/m) and low stored energy (15kJ/m), the
transmission line magnets require only a single 50V power supply and a
single set of 100kA current leads for the entire machine. The helium
consumption for these leads is estimated to be 5g/s for each lead. If
desired, this power requirement can be reduced by a factor of 4\~5 with
the use of High Temperature Superconductor (HTS) current leads.

##### 5.2.1.1.6 Refrigeration System {#refrigeration-system .unnumbered}

The refrigeration system is composed of six (6), 4.5kW @ 4.5K capacity
facilities equally spaced around the ring. Each plant will also provide
100kW of 40K refrigeration used in the shielding of the magnet system.

![](media/image40.png)

Figure 5.36. need figure caption.

This provides approximately a 50% margin above predicted steady state
requirements. This margin is required to ensure continued operation when
the heat load increases either due to events such as a magnet quench or
vacuum leak, or because refrigeration capacity falls below its intended
design value (i.e. decreasing machine efficiency or inefficient heat
transfer due to contamination). With this scheme, all six refrigerators
must be operational for the accelerator to function. No plant redundancy
is built into this design.

Table 5.21. Predicted power requirements

![](media/image41.wmf)

The process helium is compressed from suction pressure of 0.101 MPa
(1.01 bar) up to an intermediate pressure of 0.4 MPa (4.0 bar) by means
of first stage compressor discharging into a second stage, which
compresses the helium to 1.85 MPa (18.5 bar). Turbo machinery is used
for the refrigeration plants while reciprocating machines comprise the
compressor system. There are two cold boxes: the upper and lower cold
boxes. Each cold box contains five (5) plate-and-fin type heat
exchangers and three expanders. To avoid return helium gas instabilities
due to the elevation change from the tunnel to the surface, the lower
cold box will be located at the tunnel level. This requires a dedicated
space of 432 m^3^ (6 m along the beam by 6 m transverse by 12 m high)
located near the accelerator tunnel.

![](media/image42.png)

Figure 5.37. need figure caption

Discussed plants are well within the existing commercial vendor
capabilities. These plants contain no nitrogen pre-cooling. The cold box
configuration is a horizontal carbon steel shell enclosure housing all
heat exchangers, piping, valves, cold end of turbo expanders and vessels
operating at cryogenic temperatures. The equipment within the cold box
and the inner face of the vacuum jacket are covered by multi layer
aluminized Mylar. The cold boxes are designed to withstand the outside
atmospheric pressure while they are evacuated and are also protected
against overpressure by safety valves. All internal valves, filters,
turbo expanders, bayonets and major pipe connections are fixed at the
top plate and are accessible from a structural steel platform along the
length of the cold box. The turbo expanders are self activated gas
bearing superior in their performance to oil bearing turbines. Each
turbo expander is a small single-stage centrifugal turbine braked by a
direct-coupled, single stage centrifugal compressor. The turbine housing
is vertically mounted to a plate at the cold box top, projecting into
its vacuum space. Within the cold box are brazed aluminum heat
exchangers, pressure vessels containing and adsorbent to remove
impurities and the cold end of gas bearing turbo expanders. Part of the
outer shell cover is flanged and has an O ring seal, and is removable,
for complete access to all cold box internal components and piping. Two
panels will be mounted on the structural steel platform next to the cold
box. One containing all instrument terminations and transmitters, and
the other an assembly of purge and defrost valves. Provisions for
purification of the process helium is provided at each plant as well as
oil removal systems. A commercial control system package will permit the
unattended operation of these plants.

##### 5.2.1.1.7 Helium Compressor System {#helium-compressor-system .unnumbered}

The compression package will consist of three oil flooded rotating screw
compressors. One compressor will compress from 0.11 MPa (1.1 bar) to 0.4
MPa (4.0 bar), and the two other will compress in parallel from 0.4 MPa
(4.0 bar) to 1.85 MPa (18.5 bar). The first stage compressor is smaller
than the two (2) second stage machines. Each compressor skid contains
the compressor, main drive motor, oil reservoir/separator vessel, and
lubrication system mounted on a common rigid skid base. The base plate
provided is suitable for installation on a flat pad without grouting.
The helium enters the compressor and is compressed through the rotating
screw compressor, also flooded with oil. The oil seals the rotor and
absorbs some heat of compression. The compressed warm helium passes
through a water-cooled heat exchanger and then into a bulk oil
separator. The oil is also passed through a separate water-cooled heat
exchanger. Each compressor is direct driven by an electric induction
electric motor. The compressor assemblies are equipped with automatic
inlet and outlet block valves and automatic recycle valves.

The high-pressure helium from the compressors passes through a skid
mounted oil removal system. The oil removal system consists of three
stages of coalescing filter housings followed by a vessel containing
activated carbon. All entrained oil is filtered out of the gas stream by
the three stages of filters. The small amount of oil in the vapor phase
is removed by the activated carbon. The total amount of oil contained in
the helium leaving the oil removal assembly is less than 10 ppb .

##### 5.2.1.1.8 Helium Liquid and Gas Storage and Inventory Management {#helium-liquid-and-gas-storage-and-inventory-management .unnumbered}

The inventory for the entire cryogenic system is estimated to be 75 tons
of liquid helium, which is twenty (20) times the Tevatron inventory.
Each cryogenic plant will have three (3) 37.8 \[m3\] liquid helium
storage dewars, and fifteen (15) gas tanks capacity of 113.6 \[m3\].
This will provide 143 percent of the total helium inventory. The gas
storage serves as make-up/kick back during normal operations, and as a
buffer/storage during quenches and warm up of a single loop. The liquid
storage station will have pumps and heat exchangers necessary to
liquefy/warm up cold gas during upset conditions. During the planned
warm-up of the entire ring, the inventory will be liquefied into the
dewars. In case of one sector warm, the inventory can be distributed
between five sectors gas/liquid storages via the cooldown header. The
tunnel transfer line and the cooldown header can be used to hold up to
40% of inventory at pressure below MAWP of any component in the system

##### 5.2.1.1.9 Cryogenic Control System {#cryogenic-control-system .unnumbered}

A well-proven process control system will be used. The cryogenic system
in each sector will be controlled by a commercially available
distributed control system (DCS). Commercial program logic controllers
will be used for a local control of the cryogenic hardware in the event
that high-speed network connection is unavailable. The cryogenic control
system will provide full automation of any operation mode, including
transient modes. The accelerator high-speed network will be used for
communication and data exchange between sectors.

#### 5.2.1.2 Design Operating Conditions {#design-operating-conditions .unnumbered}

##### 5.2.1.2.1 Steady State {#steady-state .unnumbered}

Helium is supplied from a refrigerator at 4.5 K, 0.4 MPa (4 bar) and
returned at 5.8 K, 0.19 MPa (1.9 bar). Supercritical supply helium is
fed from the helium plant to four parallel loops. Each loop is comprised
of 9.5 km of magnet and transmission line. There are cryogenic
connecting boxes at the beginning and end of each 9.5 km section. At the
exit of the refrigerator the helium process is split into four (4)
paths. There are upstream and downstream magnet strings that are mirror
images of each other. The typical flow schematic of a magnet string is
shown in Figure 5.38.

![](media/image43.png)

Figure 5.38. need figure caption

As helium enters the upstream or downstream magnet strings the flow is
split into two parts: half enters the 4.5 K transmission line circuit
(for the near loop) and half enters the 4.5 K current return circuit
contained in the magnet (for the far loop). There is expected to be an
approximately 1 K gradient across each loop. These loop flows are then
re-distributed at valve boxes and become the return 6.0 K shield flow.

The cooling scheme relies on a balance between heat leak and pressure
drop. Any scenario causing an upset in the heat load (i.e. vacuum
degradation) can be compensated by increasing the helium flow rate and
supply pressure for the proper loop. The refrigerator has been oversized
by 50% to compensate for these types of upset conditions.

##### 5.2.1.2.2 System-Wide Purification {#system-wide-purification .unnumbered}

Purification of this machine will be done in two (2) steps. First each
sector will be pumped and backfilled five (5) times to 25 inches of
mercury via pump outs on every helium circuit at each valve box located
every 10 km. This method has been proven to work in the Tevatron. Levels
of contamination less than 100 ppmv are achieved with this first step by
using roughing pumps. The second step is dilution purification. A
purifier with a nitrogen cooled charcoal bed will be located at each
refrigeration plant. The discharge gas of the compressor system will be
circulated through this purifier and then will be distributed to the
magnet/transmission line system. Contamination instrumentation, such as
arc cells used on the Tevatron, will be used to monitor the ppmv levels
in each sector. The system will be ready for cool down when
contamination levels are \< 5ppm. It is estimated that the purification
for a sector in the VLHC will be 72 hours.

##### 5.2.1.2.3 System-Wide Cool down {#system-wide-cool-down .unnumbered}

Cool down of the VLHC will be done in three (3) stages. The first stage
involves the cool down of the helium plants. The second stage is the
cool down of the transmission line to 40K. Finally the transmission line
will be cooled done to operating temperatures.

In the first stage, cooling is provided by turbines and should not take
more than 24 hours per plant. In the second stage, the plant is setup in
the liquefaction mode and 40K gas at 0.4 MPa (4 bar) is sent via cool
down valves located at each valve box back to the compressor suction
warm gas header located in the tunnel. Gas flows from the refrigerator
into the warm header through the near loop transmission line, the 6.5K
return, and the current return circuits. When the temperature at the end
of the "near" loop (measured at the valve box) is 70K the flow is then
re-directed to the "far" loop and into the return header. As the "far"
loop temperature reaches 70K the second cooldown stage can be started.

During the second cool down stage the plant is re-tuned for an outlet
temperature of 4.5K. The flow pattern for the second stage is the same
as the first stage. As the temperature for each loop is at 7K the cool
down valves can be closed and the flow will be looped back in
refrigerator mode. Total cool down time is expected to be on the order
of 10 days.

### 5.2.2 Magnet Power Supplies, Current Leads, and Quench Protection {#magnet-power-supplies-current-leads-and-quench-protection .unnumbered}

Stage 1 power supplies are summarized in Table 5.22 below. The major
item is the single 100kA supply for the transmission line magnets. The
Interaction Region power supplies, current leads and quench protection
are discussed in sect 5.1.4. Total Stage 1 power supply requirements
(both ramping and steady state) are about a third of the Fermilab Main
Injector.

Table 5.22. Power Supply, Current Leads and Quench Protection Summary
for Stage 1 Machine

+----------------+------------+-------------+------------+------------+
|                | Tr         | IR          | Straight   | Corrector  |
|                | ansmission | Quadrupole  | section    | Magnets    |
|                | Line Power | Power       | Warm       | (warm      |
|                | Supply     | Supplies    | Magnet     | copper)    |
|                |            | (sect       | Power      |            |
|                |            | 5.1.4)      | Supplies   |            |
+----------------+------------+-------------+------------+------------+
| Number         | 1          | 2           | 16 approx. | 12,000     |
+----------------+------------+-------------+------------+------------+
| Location       | FNAL       | at          | Straights  | Quad       |
|                |            | Experiments |            | locations  |
+----------------+------------+-------------+------------+------------+
| Voltage per    | 62         | 10V typ.    | 1000V typ. | 100 Typ    |
| supply         |            |             |            |            |
+----------------+------------+-------------+------------+------------+
| Current per    | 100kA      | 25kA        | 200A typ   | 2A typ     |
| supply         |            |             |            |            |
+----------------+------------+-------------+------------+------------+
| Ramping MVA    | 6.2 MVA    | 1 MVA       | \-         | \-         |
| (tot)          |            |             |            |            |
+----------------+------------+-------------+------------+------------+
| DC Power       | 0.4 MW     | 0.6 MW      | 7.4 MW     | 2.1 MW     |
| (total)        |            |             |            |            |
+----------------+------------+-------------+------------+------------+
| LCW            | \-         | \-          | 150        | *(air      |
| Consumption    |            |             | liters/sec | cooled)*   |
+----------------+------------+-------------+------------+------------+
| Quench         | 1 Circuit  | 2           | \-         | \-         |
| Detection      | at PS      | ci          |            |            |
|                |            | rcuits/quad |            |            |
+----------------+------------+-------------+------------+------------+
| Quench         | Dumps @    | 4           | \-         | \-         |
| Protection     | 20km       | h           |            |            |
|                |            | eaters/quad |            |            |
+----------------+------------+-------------+------------+------------+
| SC Current     | 100kA-pair | 60kA-pair   | \-         | \-         |
| leads          |            |             |            |            |
+----------------+------------+-------------+------------+------------+
| **Peak Ramping | **17.7     |             |            |            |
| Supply Power** | MW**       |             |            |            |
+----------------+------------+-------------+------------+------------+
| **Total Power  | **10.5     |             |            |            |
| Supply**       | MW**       |             |            |            |
|                |            |             |            |            |
| **Power in     |            |             |            |            |
| Collision**    |            |             |            |            |
+----------------+------------+-------------+------------+------------+

#### 5.2.2.1 Main Transmission Line Power Supply {#main-transmission-line-power-supply .unnumbered}

The low inductance (3uH/m, 0.6H ring total) and low stored energy
(10kJ/m, 3GJ total) of the single-turn transmission line magnet allow
the entire ring to be powered from a single supply \[1\]. See Figure
5.39. A voltage of ±62V ramps the machine up or down in 1000 seconds.
The design current of 100kA at flattop exceeds the 90kA required for the
transmission line magnet to reach its design field. The supply will be
located on site at Fermilab in a shielded underground room approximately
25' x 50' TBD in size. The ramping power and footprint of the power
supply is comparable to one of the six Main Injector power supply
buildings. Superconducting current leads will be located immediately
adjacent to the supply to minimize power loss in warm buswork.
Superconducting buswork will carry the current through a short
connecting conduit to the transmission line magnets in a manner
identical to the MS6 test string \[2\].

![](media/image44.png){width="5.54375in" height="3.7958333333333334in"}

Figure 5.39. 100kA Power Supply and Quench Protection For Transmission
Line Magnets

The power supply is actually two supplies in series. The main ramping
supply generates the positive or negative voltage to transfers the
inductive energy into and out of the magnets. It is not used when the
magnet is at constant current. The second "holding" supply maintains the
current during long periods at flat top and injection, and provides only
the voltage necessary to overcome resistive losses in the current leads,
warm busswork, superconducting splices, and the shorting SCR switch
across the ramping supply. This approach minimizes the cost of the
ramping supply, simplifies the power distribution system, and moves the
tightest regulation and ripple requirements to the precision holding
supply.

The Main Ramping Supply design (Figure 5.40) is based on paralleling
8500A modules of design similar to Main Injector supplies. This approach
permits spare modules to be taken off line for repair, and allows the
use of commercially available 10kA DCCTs for current regulation. A
2-quadrant 12-phase SCR bridge returns inductive power to FNAL as the
magnets ramp down. Ramping systems are designed to have RMS power sized
to be halfway between the peak (6.2MVA) and the RMS (3.1 MVA). This has
proven to be a reliable design methodology for similar supplies at
Fermilab. The RMS feeder load of 4,800KVA is less than one feeder cable
for the source.

![](media/image45.wmf){width="6.5in" height="1.9520833333333334in"}

Figure 5.40. 100kA Ramping Supply Schematic (one 2 x 8.5kA module shown)

The +2.5V holding supply is essentially a copy of the 100kA switching
converter \[3\] constructed for the R&D magnet test. The device consists
of a 450VDC 500kW bulk supply followed by ten 10kA DC-DC converter
modules in parallel. This two-stage regulation scheme provides immunity
to variations in input line voltage. The modules use tape-wound cores
and Schottky power diodes. The switching frequency is \~2 kHz. To
minimize output ripple the 10 modules will be phased to switch
sequentially. This pushes the fundamental ripple frequency up to 10x the
switching frequency or \~20kHz. The switching will be phase locked to
the revolution frequency so that beam emittance growth due to power
supply ripple will be negligible. The control system for this switcher
will be integrated into that of the main ramping supply to simplify
regulation and load hand-off.

#### 5.2.2.2 Current Leads {#current-leads .unnumbered}

Superconducting current leads are required for both the main
Transmission Line and for the IR quadrupoles. IR quadrupoles can use
commercially available High-Temperature Superconductor (HTS) leads
similar to the LHC. The total current leads requirement for the Stage 1
machine is about 150kA-pair, or about 1/10 of the leads required by the
LHC \[3.5MA from Lynn Evans' stump speech\].

A single pair of 100kA current leads is required for powering the
transmission line. These could either be conventional copper leads
identical to the leads developed for the MS6 transmission line test
facility \[2\], or could be a specially built HTS version using the 50K
transmission line shield flow as the inter-stage temperature. The
cryogenic wall power associated with the conventional 100kA leads is
approximately 300kW. This could be reduced by a factor of 4 with HTS
leads \[4\]. Payback time for the electrical cost savings from HTS leads
is approximately 3 years.

![](media/image46.png){width="3.979861111111111in"
height="2.4305555555555554in"}

Figure 5.41. 100kA Superconducting Current Leads and switching
converters developed for the MS6 test string. A more compact arrangement
of the leads and power converter will be small enough to be placed in
the tunnel to be used for partial-ring commissioning.

#### 5.2.2.3 Quench Protection {#quench-protection .unnumbered}

The only superconducting magnets of the Phase I collider are the
transmission line magnets and the IR Quadrupoles. Protection of the IR
quads with heaters is described in section 5.1.4.

The low inductance and low stored energy of the transmission line magnet
allows a simple and inexpensive quench protection system. The magnets
themselves require no internal quench detection or protection circuitry.
Ring-wide quench detection is performed by a single circuit located at
the power supply terminals (Figure 5.42). Quenches are detected by a
voltage imbalance at the power supply (Figure 5.39). When a quench is
detected, magnetic energy is extracted with a 1-second L/R time constant
by cryogenic "dump resistors" spaced at 20km intervals around the ring.
This keeps the peak temperature and pressure in the quenched section of
the conductor at acceptable levels as described in section 5.1 Quench
protection system parameters are given in Table 5.23. The theory of
operation is explained \[5\] and a detailed write-up is given in \[6\].

![](media/image47.wmf){width="5.75in" height="1.8743055555555554in"}

Figure 5.42. Quench Protection Cell of the Transmission Line Magnet

The "dump switches" are deliberately quenched sections of transmission
line conductor built with Cu-Ni stabilized NbTi "switch wire"\[7\] which
is designed to have a high normal state resistance. Current is
transferred to a thick-walled Invar pipe which provides thermal mass.
These dumps are efficiently recooled using helium from the cryogenic
shield flows and transmission line flows, with the warm gas vented into
the return header.

The protection circuit for the 100kA current leads and power supply is
integrated into the quench protection system. When an overtemperature or
overvoltage is detected in the current leads, nearby copper buswork, or
power supply components, the power supplies are shut off and a ring wide
dump is forced. The required response time is equal to the thermal time
constant of the leads or approximately 100 seconds.

Table 5.23. Stage 1 Quench Detection and Protection Parameters

  ----------------------------------- -----------------------------------
  Transmission Line Current           100 kA

  Magnetic Stored Energy \@100kA      10 kJ/meter, 2100 MJ/ring

  Magnet Inductance at low field      3uH/m 600mH/ring

  Energy Dump Time Constant           1 second

  Peak Voltage To Ground during Dump  ± 3 kV

  I^2^t during dump                   5 x 10^9^ Amp^2^Seconds

  Peak Temperature of Conductor       250K
  During Quench                       

  Peak Pressure of Helium During      35 Bar
  Quench                              

  Pressure relief during quench       Every 2 cells (500m)

  Effective Copper Cross Section of   3cm^2^
  Conductor                           

  Quench Detection Threshold          1 Volt

  Quench Detection Method (primary)   Analog bucking with midpoint of
                                      current return bus

  Quench Detection Method (backup)    Deviation from V=LdI/dt at power
                                      supply terminals

  Energy Dump Resistance              60 mΩ per location,

  Dump Switch Locations               at cryoplants and midpoint of arc
                                      (20km spacing)

  Dump Switches                       Quenched superconducting cables 65m
                                      long

  Superconducting Dump Switch         1:1 CuNi:NbTi "Switch Wire"
  Conductor                           

  Cryogenic Dump Resistor Thermal     65m long x 20cm2 Thick Wall Invar
  Mass                                pipe

  Final Dump Temperature after Dump   325K
  from 100kA                          

  LHe Required for recovery after     1600 liters (less if shield flow
  Dump from 100kA                     used for pre-cooling)
  ----------------------------------- -----------------------------------

It is instructive to compare this quench protection system to those of
other accelerators. The LHC for example \[8\] requires a crate of quench
detection electronics in the tunnel underneath each dipole in the
tunnel. Each LHC magnet has more than 10 voltage taps and
instrumentation feed-throughs. The LHC also requires a much larger array
of energy dump resistors, dump switches, and current leads around the
circumference of the ring. Despite the larger machine circumference, the
quench protection system of the Stage 1 magnet is far simpler and should
be more reliable.

#### 5.2.2.4 Straight Section (Warm Magnet) Power Supplies {#straight-section-warm-magnet-power-supplies .unnumbered}

The straight sections use warm iron/copper quadrupoles and a small
number of other magnets. In each straight section all F and D
quadrupoles are powered in series by a single supply. The IR straight
sections have a larger number of independently programmable "tuning
quads" but the total power and LCW usage is approximately the same as a
normal straight section. The power supplies are located in shielded
rooms (one per straight section) which contain \~500kW of power supplies
and are accessible with beam on. These are single quadrant supplies.
Given the limited scope of these supplies it is desirable to make them
fully redundant, especially those at the far side of the ring from FNAL.
A detailed breakdown is given in \[Terechkine note\].

Dipoles and quad correctors magnets identical to the arcs are provided
at each quad location. Dipole magnets used to separate and cross over
the beams are powered by the 100 kA transmission line and require no
separate supplies.

Table 5.24. LCW and Power Dissipation Summary for Stage 1

+-------+-------------------+-----------+------------+---------------+
|       | **Heat Load**     | **Total   | **Total    | **LCW Flow    |
|       |                   | Loads**   | kW**       | (l/min)**     |
+-------+-------------------+-----------+------------+---------------+
| On    | Resistive Magnets | 188       | 4480       | 3200          |
| -Site |                   |           |            |               |
|       |                   |           |            |               |
| Str   |                   |           |            |               |
| aight |                   |           |            |               |
|       |                   |           |            |               |
| Sec   |                   |           |            |               |
| tions |                   |           |            |               |
+-------+-------------------+-----------+------------+---------------+
|       | Power Supply      | 22        | 500        | 600           |
|       | Cooling           |           |            |               |
+-------+-------------------+-----------+------------+---------------+
|       | RF Klystrons      | 16        | 3760       | 6400          |
+-------+-------------------+-----------+------------+---------------+
|       | RF Loads &        | 16        | 5600       | 4500          |
|       | Recirculators     |           |            |               |
+-------+-------------------+-----------+------------+---------------+
|       | Beam Stop         | 1         | 500        | 600           |
+-------+-------------------+-----------+------------+---------------+
|       | Total (on-site)   | 227       | 14840      | 15300         |
+-------+-------------------+-----------+------------+---------------+
| Far   | Resistive Magnets | 176       | 3320       | 3500          |
| Side  |                   |           |            |               |
|       |                   |           |            |               |
| Str   |                   |           |            |               |
| aight |                   |           |            |               |
|       |                   |           |            |               |
| Sec   |                   |           |            |               |
| tions |                   |           |            |               |
+-------+-------------------+-----------+------------+---------------+
|       | Power Supply      | 9         | 550        | 600           |
|       | Cooling           |           |            |               |
+-------+-------------------+-----------+------------+---------------+
|       | Beam Collimation  | \-        | 40         | 50            |
+-------+-------------------+-----------+------------+---------------+
|       | Total (far side)  | 185       | 3910       | 4150          |
+-------+-------------------+-----------+------------+---------------+
|       | **LCW Systems     | **412**   | **18750**  | **19150**     |
|       | Total**           |           |            |               |
+-------+-------------------+-----------+------------+---------------+

#### 5.2.2.5 Water Cooling (LCW) System {#water-cooling-lcw-system .unnumbered}

The "on-site" and "far side" straight sections require LCW systems. No
LCW system exists in the arcs. Major heat loads are the resistive
magnets, power supplies, and the RF klystrons. Loads are are detailed in
\[Terechkine note\] and summarized in Table 5.24. The overall scope of
the onsite LCW system is comparable to the MI-60 LCW system of the
Fermilab Main Injector. The far site LCW system is about half that size.

The layout of the LCW system is sketched in Figure 5.43. The on-site
straight section is connected to the Main Ring LCW system and can use
the FNAL infrastrucure for filling and makeup. Existing (unused) Main
Ring ponds exceed requirements for power dissipation. New ponds and
purification systems are required at the far side sites. The vertical
drop generates a 150 PSI pressure head which is overcome by locating the
circulation pumps at tunnel elevation and pumping the return flow
upwards. The beam stop and beam collimation cooling systems require
separate pumped loops for radioactive water (RAW) which will be heat
exchanged with the main cooling water flow to maintain isolation.

![](media/image48.wmf)

Figure 5.43. LCW System Layout for on-site Straight Section. The far
side LCW system is similar except that the RF loads are absent, the Beam
Dump load is replaced by the smaller load from the Beam Collimation
System, and an independent system of ponds and makeup water is needed.

#### References *{ed note---for sec. 5.2.2}* {#references-ed-notefor-sec.-5.2.2 .Reference-heading .unnumbered}

\[1\] Steve Hays, "*100kA Power Supply Options for the VLHC*", internal
note (unpublished).

\[2\] H. Piekarz et. al., "*Summary of Transmission Line Magnet R&D
Activities at MS-6*"

\[3\] G.W. Foster, S. Hays, H. Pfeffer, "*Design of a Compact 100kA
Switching Power Supply for Superconducting Magnet Tests*"

\[4\] J. G. Weisand (ed.), *Handbook of Cryogenic Engineering*, P.411

\[5\] Koepke/Mazur/Zlobin Snowmass '96

\[6\] GWF/Piekarz "Quench Protection of the Transmission Line Magnet",
VLHC note (unpublished)

\[7\] Switch wire is uses on persistent-current MRI magnets. Multiple
commercial sources include Oxford Instruments and Supercon.

\[8\] See the LHC PAC '99 papers. See also the proceeding of the
workshop on powering the LHC,
<http://lhcp.web.cern.ch/lhcp/TCC/PLANNING/TCC/Power2000/welcome.htm>

### 5.2.3 Arc Instrumentation and Power Distribution {#arc-instrumentation-and-power-distribution .unnumbered}

#### 5.2.3.1 Reliability and Maintenance Considerations in the Arcs {#reliability-and-maintenance-considerations-in-the-arcs .unnumbered}

The long arcs of bending magnets the have specialized and limited
requirements. The once-per-turn subsystems and their cabling, power and
cooling requirements are absent. No LCW system is required. Only the
repetitive instrumentation and corrector power supplies at each of the
1760 "quad locations" (every 135m around the ring at the location of
beta-max in each half-cell) are required. Infrastructure for power and
communications occurs at alcoves at 10 km intervals.

Reliability is at a premium for the arc instrumentation due to the large
size of the machine. Repair technicians at a centrally located facility
require a 20 mile drive to reach the surface facility and begin the
access into the tunnel. Travel time will not be small compared to the
1.5 hour time needed to refill the machine and reaccelerate the beams.
For this reason fully redundant capability is provided for all
mission-critical subsystems in the arcs. Power distribution is provided
to each module by two independent loop feeders with auto-resetting
circuit breakers and remote disconnects. Two independent power supplies
are provided for each corrector magnet and control function. Redundant
network connections to each module are provided. The critical function
of beam loss monitoring is provided by redundant sensors read out from
alternate quadrupoles modules. The system design is such that even the
death of a handful of quad electronics modules will not require
immediate maintenance.

![](media/image49.wmf){width="3.047222222222222in" height="2.275in"}
![](media/image50.png){width="3.1840277777777777in"
height="2.283333333333333in"}

Figure 5.44. Electronics module at each quad location (every 135m)
contains beam instrumentation and DC-DC Power Converters for corrector
supplies. Modules are in a radiation-shielded "hole in the wall" and
dissipate their power in the ambient tunnel air via a heat
pipe/thermosiphon and heat sink.

These electronics are located in a radiation-shielded modules buried in
"holes-in-the-wall" at each quad location. All cables for
instrumentation and corrector magnets are pre-assembled on the magnet
and factory tested before installation. Every other quad location (270m)
cryogenic thermometry and a valve controller are used to regulate the
50K shield flow. Every 10km there is a walk-in alcove associated with a
tunnel egress point that contains conventional electronics racks and
provides network connection, tunnel safety systems, bulk DC power for
the instrumentation modules, and cryogenic instrumentation for the
cooldown valve box. Average power dissipation is approximately 15 W per
meter of tunnel, which can be air cooled.

#### 5.2.3.2 Cabling in the Arcs {#cabling-in-the-arcs .unnumbered}

At the Fermilab Main Injector the cable tray to each service building
contains 316 cables with a total cable cross sectional area of 180cm^2^
\[1\]. Over 95% of these cables service Beam Position Monitors (BPMs),
Beam Loss Monitors (BLMs), ion pumps, corrector magnets, and temperature
and vacuum monitoring. The superconducting Tevatron also has a large
cable plant associated with quench protection and cryogenic monitoring
and controls. The installation, termination, and testing of these cables
are a significant cost and schedule item.

The Stage 1 design eliminates most cabling costs by multiplexing the
signals to a local electronics module (Figure 5.44) at each halfcell
boundary or "quad location". Signals are digitized locally and sent to
the control room via network fiberoptics. Instrumentation and corrector
magnets are clustered at the quad location and cable runs are typically
5 meters. Cable harnesses are prefabricated by outside vendors and
mounted on the magnets and tested in the factory.

![](media/image51.wmf){width="6.104166666666667in"
height="3.2305555555555556in"}

Figure 5.45. Cabling Layout on the Transmission Line Magnet. Cables and
instrumentation are preinstalled and factory-tested on the 65m magnets.
Each magnet has a 5m "extension cord" which jumpers to an electronics
module located in a hole in the wall at each quad location (135m
spacing).

#### 5.2.3.3 Corrector Power Supplies {#corrector-power-supplies .unnumbered}

The warm (air-cooled copper) correction magnets \[sect 5.1.3\] dominate
the power consumption in the arcs. The electronics module at each quad
location has 6-8 corrector magnet loads with a maximum installed power
of approximately 1400W. Average corrector power is \< 1000W in a
realistic operating scenario. At maximum current approximately 90% of
the power is dissipated in the magnets themselves with the remaining 10%
(\~150W) in the power supply converters. Instrumentation and control
power at each quad location is estimated to be \~100W for a total of
250W dissipated in the module. Power at this level can be passively
carried away from the electronics (Figure 5.44) via a heat pipe \[2\]
and removed by the tunnel airflow of \~1m/sec.

#### 5.2.3.4 Power Distribution in the Arcs {#power-distribution-in-the-arcs .unnumbered}

Redundant DC-DC power converters are provided both for module control
power and for each trim magnet. Power can be drawn from either of two
redundant 1kVDC feeders that loop the ring (see Figure 5.46). Power
supplies are connected in parallel at each load. Under normal
circumstances the load is shared and each power supply operates at \<
50% of rated load, encouraging long lifetimes. Under failure conditions
the load is taken over by a single supply which operates near its design
rating (or less, if the corrector magnet setting is below 100%).

![](media/image52.wmf)

Figure 5.46. DC Power Distribution Scheme in Arcs. Redundant Bulk DC
supplies in walk-in alcoves every 10km supply a redundant Loop Feeder.
Each local electronics module contains two DC-DC converters for each
load. Under normal conditions all supplies share loads and run at less
than 50% of rated capacity. By means of auto-resetting circuit breakers
(not shown), the system can tolerate short or open circuits on the loop
feeders, a failure of one or both bulk supplies at any alcove, a failure
of the AC surface feed to any single alcove, and individual failures on
many corrector supplies.

Medium-voltage 1kV DC is chosen for power distribution to the
electronics modules at each quad location. The DC is provided by 100A
bulk supplies every 10km located in racks of electronics in walk-in
alcoves. Two redundant bulk supplies are provided at each location, and
two independent distribution loops are provided to route the power to
the modules. Under normal conditions 25A is sourced in either direction
onto each of the 500 MCM loop feeders, and less than 3% of the power is
lost in the distribution cabling. Under fault conditions one or both of
the bulk supplies at one of the 10km locations can fail, with the slack
being taken up by adjacent supplies in the loop feeders. A short-circuit
fault in one segment of the loop feeders can be tolerated by letting its
circuit breaker trip and relying on the remaining loop feeder. Each
module is protected with fault current limiting via automatically
resetting "solid-state fuses"\[3\] .

The advantages of DC power in this application are as follows. The main
power consumption is due to corrector power supplies that naturally
operate as DC-DC converters. These are more compact than
line-transformer based supplies, an important consideration for the quad
electronics modules. Modern DC-DC converters \[4\] have the following
parameters: power density 200W/in^3^, efficiency \~90%, cost
\~\$0.35/watt. In fact, essentially all modern AC devices (fluorescent
light ballasts, computers, high current welders, motor controllers...)
rectify the AC line power then chop the signal using DC-DC techniques.
Rectification requires bulky capacitors and produces current spikes with
power factor and noise problems that complicate AC distribution. DC
power distribution makes the most efficient use of the copper in
distribution cables, which is a major cost component in power
distribution. DC power also simplifies the design of loop feeders, which
may be powered from separate segments of the power grid without regard
to the relative phase of the incoming AC power. Finally, by
phase-locking the switching frequencies of the DC-DC converters to a
frequency near the revolution frequency of the machine, noise effects on
emittance growth can be essentially eliminated as discussed in section
5.2.xxx.

#### 5.2.3.5 Beam Position Monitors (BPMs) {#beam-position-monitors-bpms .unnumbered}

Both X and Y BPMs (Figure 5.47) will be provided at each "quad location"
at half-cell boundaries between corrector magnets. This is twice the
number used in the Main Injector where it was determined that
measurement of the second coordinate only improved the closed-orbit
distortion by 10% \[5\] and only a single coordinate readout per quad
location was provided. However the added redundancy obtained by an
independent readout of both coordinates every half-cell will be
beneficial given the small aperture and the travel distance to repair
failed BPMs.

Button style beam pickups similar to those used on electron machines and
the LHC are adequate. These devices are nonlinear outside the central
30% of their aperture. Given anticipated closed orbit distortions \<1mm
this is not a problem. In a few special locations near beam transfers
where multiple off-axis orbits must be measured, split-plate BPMs with
better linearity will be used.

BPM readouts using either AM/PM or Log Amp electronics are acceptable.
In the case of Log-Amp readout both log(A/B) and log(A)+log(B) would be
digitized to provide both position and intensity readout. In the case of
AM/PM conversion a separate channel (possibly a log amp) is required to
provide intensity information. In either case an in-situ calibration is
desirable. The calibration circuit injects equal signals of adjustable
amplitude into both channels to accurately determine the zero-offset
response at different input strengths. A recent example of log-amp
readout made for the SLAC B-factory fit on a 2.7" x 4.7" board which
also included calibration circuitry \[6\].

Digitization bandwidth is determined by the first turn and transient
response desired. A digitization rate \>25MHz can be supported by the
DMA channels of today's DSPs, with no external components other than the
flash ADC. A 10-bit digitization of log(A/B) would provide 20μm least
count resolution. Power dissipation for 4 channels of 10-bit 40 MHz
digitization would be 300mW total \[6\].

The cable run from the BPM to the quad electronics module is about 5m.
This is long enough that the signal must be terminated but short enough
that normal RG-58 can be used. The cable runs are short enough that no
cable trimming for phase matching is required if AM/PM electronics are
selected.

![](media/image53.wmf)
![](media/image54.png){width="2.7958333333333334in"
height="3.203472222222222in"}

Figure 5.47. Beam Position Monitor (BPM) and Beam Loss Monitor(BLM) for
Stage 1 magnets. The BPM is a capacitive "button" style typically found
on small aperture beam pipes. The X&Y pickups are rotated by 45-degrees
to avoid the synchrotron radiation (this is common at light sources).
The BLM is a permanently sealed Argon filled cable-style ionization
chamber. Two redundant BLMs run the full length of the magnet. It
features all metal and ceramic construction similar to the Tevatron BLMs
to allow the device to operate unattended for years (no gas bottle to
change).

#### 5.2.3.6 Beam Loss Monitors (BLMs) {#beam-loss-monitors-blms .unnumbered}

The BLM function in the arcs is mission-critical in that no blind spots
may exist which might allow chronic beam loss to go undetected. We
therefore choose a cable style BLM which is essentially a long
ionization chamber that can provide complete coverage along the length
of the magnet. The cable will be all metal/ceramic construction (Figure
5.47) so that no gas-bottle changing will be required. For redundancy,
two independent cable BLMs are provided. Each runs the full length of
the magnet but they are read out at alternate quad locations. These
provide complete coverage even when the electronics module at a single
location goes *incommunicado*. Separate BLMs on each side of the magnet
provide some differential sensitivity to beam losses in each bore.
Electronics required include a 2kV/100μA Cockroft-Walton DC-DC converter
module, an op‑amp integrator, and a medium bandwidth \~100kHz 14-bit
ADC. Power dissipation should be \<2W.

#### 5.2.3.7 Ion Pump Power Supplies & Vacuum Gauges {#ion-pump-power-supplies-vacuum-gauges .unnumbered}

The electronics module for each 135m half-cell requires 12 ion pumps
(22.5m pump spacing in each bore). These are powered from the
electronics module. Each pump requires a 5kV supply with a starting
current of up to 30mA but an operating current less than 0.1mA. The
power for all 12 pumps is provided by single transformerless bulk supply
(a 5-stage Cockroft-Walton converter operating from the 1kVDC feeder).
High voltage DC relays (Cotto 5501) isolate each pump and give the
capability of providing the full starting current sequentially to each
supply. Individual current readback on each pump is provided via an
array of V/F converters operating at HV with an optically isolated data
link to the DSP.

Failure of the bulk supply shuts down all ion pumps in a 135m half-cell.
Pumping from the NEG strip remains intact. This results in a 50x rise in
the pressure of a single gas species (CH4) over the length of one half
cell, equivalent to a 3% rise in the average pressure of CH4 in the
ring. Redundancy in the ion pump power supplies is therefore
unnecessary.

#### 5.2.3.8 Network & Clock Connections {#network-clock-connections .unnumbered}

The electronics module at each quad location contains a Digital Signal
Processor (DSP) computer with an optical fiber connection running a
network protocol stack. This CPU can store, average, spectrum analyze,
and data-compress all digitized information before transmitting over a
conventional fiber network. A separate dedicated fiber handles the
FNAL-specific real time signals such as clock, event triggers, and beam
abort heartbeat signals. This will be handled in hardware logic by a PLD
in the electronics module.

A minimal set of fiber connection to each module consists of one network
connection plus one dedicated fiber for delivering Fermilab-specific
clock, event, and safety system signals. For cost estimation purpose we
have assumed four direct point-to-point fiber connections between each
quad location and redundant network hubs at located in the 10km alcoves.
The fiber cable will be a pre-assembled harness 5km long with 4-fiber
breakouts at quad locations every 135m. Installation will consist of
laying the fiber harness in the cable tray immediately below the
electronics modules (Figure 5.48) and plugging the breakout into each
electronics module.

![](media/image55.wmf)

Figure 5.48. Fiberoptic Clock and Network Connections in the tunnel
including redundant hubs & clock fanouts at 10km alcoves.

The long-haul fiber backbone interconnecting the 10km alcoves around the
ring will be buried with the power duct in the invert. This provides
additional radiation shielding to compensate for the longer distance of
the backbone fiber runs.

#### 5.2.3.9 Quad Electronics Module Miscellaneous Functions {#quad-electronics-module-miscellaneous-functions .unnumbered}

The networked DSP at each quad location provides the infrastructure for
additional features to be added at relatively low cost. In many cases
this requires adding only an interface IC, transducer and software to
the quad electronics module. The engineering effort for this is not
unreasonable given the large quantity of quad electronics modules. Some
possibilites:

-   Tunnel temperature, humidity, and airflow transducers.

-   Integrated radiation dose monitor for the electronics module (FET +
    resistor).

-   RF modules to communicate with the cell phones and PDAs of tunnel
    crews.

-   Microphones for detecting quenches, tunnel dripping, and goofing-off
    crews.

-   Speakers to communicate with the above.

-   Cryogenic sensors and valve controls (presently estimated as a
    separate system)

-   Vacuum valve controls (presently estimated as a separate system)

#### References *{ed note---for sec. 5.2.3}* {#references-ed-notefor-sec.-5.2.3 .Reference-heading .unnumbered}

\[1\] Fermilab Main Injector Technical Design Report, table 3.9.1.

\[2\] Your *{mine? I don't have one}* laptop computer probably has a
heat pipe in it. See <http://www.thermacore.com/papers.htm>

\[3\] Auto-resetting fuses are sold (for example) by:
[http://www.circuitprotection.com](http://www.circuitprotection.com/)

\[4\] Specifications quoted are single-quadrant DC-DC converters from
Vicor inc. [www.Vicr.com](../www.Vicr.com)

\[5\] Fermilab Main Injector Note #MI-75

\[6\] Medvenko & Smith, Beam Instrumentation Workshop 2000, p.503

\[7\] Specifications quoted are from
<http://products.analog.com/products/info.asp?product=AD9203>

### 5.2.4 Beam Vacuum System {#beam-vacuum-system .unnumbered}

The beam vacuum system is divided into two sections. In the 225km of
transmission line magnets an extruded-aluminum warm vacuum system
similar to LEP and electron storage rings is used. In the 8km of
straight sections synchrotron radiation is absent and the vacuum system
will be a conventional stainless steel system similar to those commonly
used at Fermilab.

![](media/image56.png){width="6.145833333333333in"
height="4.128472222222222in"}

Figure 5.49. Extruded Aluminum beam vacuum system in the transmission
line magnets.

#### 5.2.4.1 Arc Magnet Vacuum System {#arc-magnet-vacuum-system .unnumbered}

An extruded aluminum vacuum system (Figure 5.49) is used for the 225 km
of arc magnets (450 km of beam pipe) . The design of this system is
driven by vacuum desorption from synchrotron radiation, the small
aperture of the magnet gap, beam impedance and cost. Aluminum is chosen
for reasons of economy and beam impedance. The system is pumped by a
non-evaporable getter (NEG) strip located in an antechamber of the
extrusion. Methane and noble gasses are pumped by 10 l/s sputter-ion
pumps spaced every 22.5m. The antechamber dimensions are chosen to
provide adequate vacuum conductance to transport synchrotron-desorbed
methane to the ion pumps. Pump power and vacuum gauges are discussed in
5.2.3.7.

The parameters and performance of this system have been analyzed by
\[1,2\]. Inputs to the calculation included: 1) the measured
synchrotron-induced desorbtion of major gas species from aluminum \[3\]
as a function of the integrated dose of E~CRIT~ = 86 MeV photons, 2) the
measured pumping speeds for NEG strip as a function of absorbed gas
\[4\], 3) calculated conductances of the extrusion antechamber, 4) ion
pump speeds for methane, and 5) scattering cross sections for the
relevant gas species. This approach has given good agreement with the
measured performace of LEP \[5\]. The result of the calculation (Figure
5.50) is that a beam lifetime greater than 200 hours will be achieved
after approximately one week of operation. During the "beam cleaning"
period the beam current will be increased from an initial 50 mA to the
design value of 190 mA in five successive fills. The beam power
scattered into the cryogenic system (sect 5.3.3) will not be a limiting
factor during this time period.

![](media/image57.wmf){width="4.261805555555555in"
height="3.3645833333333335in"}

Figure 5.50. Beam Scrubbing Scenario for Stage 1 Aluminum Vacuum
Chamber. During the first 5 fills the beam current is increased from
50mA to the design value of 190mA. As synchrotron radiation desorbtion
cleans the walls of the beam chamber the vacuum lifetime increases to
\>200 hours.

Production of the aluminum vacuum system will be integrated into the
magnet factory. Tunnel labor is minimized by pre-assembling 65m lengths
of extruded pipe which are installed in the magnets, cabled, and tested
at the factory. Beam pipe extrusions 12m in length will be received,
inspected, and cleaned using an enviromentally safe alkaline cleaning
procedure developed at the APS and used on the Fermilab Recycler \[6\].
The sections will be welded together to form 65m lengths which includes
the Ion Pumps, NEG strips and feedthroughs, and end transition sections.
The assembly will be selaed, pumped and baked at 200°C for 12 hours in a
65m long vacuum oven similar to the one built for the Recycler beam
pipes.

The vacuum pipe assembly is then snapped into the C-magnet gap (Figure
5.51) in such a way that the beam chamber is pre-loaded against the
magnet laminations. The preload prevents any possible loss of vertical
aperture inside the magnet. The beam pipe has to be deformed slightly to
get it inside of the horizontally focussing gradient magnet. This has
been analyzed \[7\] in ANSYS and stresses are acceptable even for
annealed aluminum.

![](media/image58.wmf){width="4.95in" height="3.359027777777778in"}

Figure 5.51. Cross section of beam pipe extrusion inserted into the
magnet. During insertion the beam pipe is elastically deformed to fit it
into the gradient magnet.

The design does not provide for an in-situ bakeout. After factory
bakeout the magnets will be stored and transported with the beam pipes
capped off and under vaccum, and the beam pipes will be let up to dry
nitrogen and the caps cut off to make the field joints in the tunnel.
Under these circumstances an in-situ bakeout gains about a factor of 2
in initial dynamic outgassing \[8\], and gains very little after the
beam scrubbing has completed \[9\]. A similar conclusion has been
reached at the ELETRA light source \[10\]. Our R&D program should verify
this.

#### 5.2.4.2 Straight Section Vacuum System {#straight-section-vacuum-system .unnumbered}

Synchrotron radiation is absent or reduced in most of the 8km of
straight sections and the vacuum system will be a conventional baked
stainless steel / ion pump system similar to those commonly used at
Fermilab. The 10 cm aperture of the 135 m stainless steel pipes between
quadrupole locations is large enough that the beam impedance and vacuum
conductance are not a problem. The reduced apertures at the the
quadrupoles and corrector locations will be handled with 30 cm funnel
transitions which may be copper-plated stainless or aluminum.

#### References *{ed note---for sec. 5.2.4}* {#references-ed-notefor-sec.-5.2.4 .Reference-heading .unnumbered}

\[1\] W. Turner "*Beam Tube Vacuum in Low Field and High Field Very
Large Hadron Collider*", LBNL-39482, UC414, presented at the Snowmass
Conference, CO, October 1996.

\[2\] M. Pivi and W.C. Turner , "*Beam Tube Vacuum in a Very Large
Hadron Collider Stage 1*", Version 2.1, 12 Aprill 2001

\[3\] J. Gomez-Goni, O. Gröbner and A.G. Mathewson *"Exposure of a baked
Al lined stainless steel chamber to photons",* CERN, Vacuum Technical
Note 94-10 pg. 9, AT-VA/JGG.

\[4\] C. Benvenuti, *"Molecular Surface pumping: the getter pumps",* CAS
CERN Accelerator School - Vacuum Technology, CERN Yellow book, pg. 48.

\[5\] J.C. Billy, J.P. Bojon, O. Gröbner, N. Hilleret, M. Jimenez, I.
Laugier, P. Strubin, "*The LEP Vacuum System: a summary of 10 Years of
Successful Operation",* Proc. EPAC 2000.

\[6\] G.P.Jackson, "*The Fermilab Recycler Technical Design Report*",
FNAL-TM-1991

\[7\] Tsvetkov VLHC note note on vacuum pipe stresses.

\[8\] A. Chao and Tigner*, "Handbook of Accelerator Physics and
Engineering",* pg.225

\[9\] Oswald Grobner pvt. comm.

\[10\] A. Gambitta and et.,"*Experience with Aluminum Vacuum Chambers at
ELETTRA*",EPAC 2000, Vienna, Austria, and J. Miertusova et. al. "*How to
Save Money Designing a Vacuum System for a Third Genertion Synchrotron
Light Source*", EPAC 1996.

### 5.2.5 Once-per-Turn Instrumentation {#once-per-turn-instrumentation .unnumbered}

A number of standard instrumentation systems occur only once per ring.
In general these can be copied from existing systems in the Tevatron
and/or Main Injector. The 53 MHz bunch structure and modest beam
currents (\~1/3 of Tevatron fixed target) provide no special challenges.
Readout electronics for these systems is located in shielded rooms at
the Utility Straight Sections. A warm beam pipe is used everywhere
except the IR triplet and superconducting RF cavities, so the
instrumentation interface is simple. Physical layout of these systems is
not heavily constrained since quadrupole spacing is typically 150m, the
beam pipes are separated by \~45cm for much of the utility straight
sections, and the transmission line and current return have been moved
away from the beam to reduce fringe field.

Table 5.25. Once-per-Turn Instrumentation Parameters

  ------------------------ ------------- --------------- --------------------------
  **FUNCTIONOccurances**   **Readout     **Comments**    
                           Frequency**                   

  Tune Measurement         a few/ring    10 Hz           Use Arc Module DSP's for
                                                         FFT?

  Beam Current Toroids     1/ring                        Also on injection lines

  Sampled Bunch Display    1/ring        1 Hz             

  Fast Bunch Integrator    1/ring        1 Hz             

  Synchrotron Light        1/ring        1 Hz             
  Monitor                                                

  Ion Profile Monitor      2/ring        .1 Hz            Small beam size may be
                                                         challenging

  Flying Wires             1/ring         \~few per       
                                         store           
  ------------------------ ------------- --------------- --------------------------

These are discussed more fully in:
<http://www-linac.fnal.gov/~mccrory/papers/VLHC_Controls>.

### 5.2.6 Radiofrequency Systems  {#radiofrequency-systems .unnumbered}

Either superconducting or warm copper cavities produce workable RF
acceleration systems for the stage 1 machine \[1\]. During the design
study acceptable parameters and costs based on the B-factory RF systems
were developed \[2\]. The system described here is based on
superconducting RF (SCRF). The advantages of SCRF are a higher energy
efficiency during the long periods at storage flattop, and more
flexibility to produce RF overvoltage to control beam instabilities if
this proves to be an advantage.

The RF system parameters and some RF relevant machine parameters are
summarized in Table 5.26. The RF frequency is 371.7 MHz, the seventh
harmonic of 53.1 MHz. Overall the VLHC RF system is similar to the LHC
RF \[3,4\], but with somewhat relaxed requirements to higher-order mode
damping due to lower total beam current. The superconducting cavities
are manufactured using niobium on copper technology developed at CERN.
As in the case of LHC, there will be separate RF systems for
counter-rotating beams. The beam separation in LHC is 420 mm. If we just
scale cryomodule dimensions with RF frequency, we get beam separation of
453 mm.

To minimize the effect of the transient beam loading, cavities with high
stored energy are preferred. The LEPII RF system experience \[5\] and
tests of LHC \[4\] and SOLEIL \[6\] cavities show that it is reasonable
to expect operating gradients as high as 8 MV/m. For VLHC we chose
gradient of 7.75 MV/m (3.125 MV per cell). Sixteen single-cell
superconducting cavities are needed for each beam in Stage 1 machine and
64 cavities are needed for each beam in Stage 2 machine. The low *R/Q*
of the LHC cavity helps to increase its stored energy. Still the large
(10%) beam gap will produce very strong periodic modulation of RF phase
of 27° for stage 1 and 10° for stage 2. This modulation is bigger than
at LHC. Special RF feedback loop around the amplifier-cavity system
assisted by the programmed phase modulation *a la* LHC \[7\] will be
necessary to suppress this effect.

Each cryomodule will accommodate four single-cell cavities with
cell-to-cell distance of 3λ/2. The overall length of the cryomodule is
approximately 5.6 m. Static heat leak of cryomodule is 60 W, RF cavity
wall losses is 55 W, which give us total cryogenic load of 280 per
cryomodule. Overall cryogenic heat load (without losses in cryogen
distribution system) is 2.24 kW for stage 1 and 8.96 kW for stage 2.

Due to rather small RF power per cavity we propose to use 500 kW
klystrons with 2 cavities per klystron in stage 1 and 8 cavities per
klystron in stage 2. The number of klystrons required is 16 for each
stage. A 500 kW CW klystron was developed and constructed recently
jointly by CERN and SLAC for testing LHC cavities \[8\]. The klystron
has high efficiency of 68% and thus required AC power is 735 kW to
generate RF output power of 500 kW. Then the maximum total wall-plug AC
power for klystrons is 11.76 MW per ring.

The klystron collector cooling water flow of ≥ 400 l/min gives us the
total amount of cooling water required to cool klystrons is 6400 l/min.
RF water loads will need additional 4000 l/min (during beam
deceleration) and ferrite circulators will consume 480 l/min. Thus the
total amount of de-ionized water required for RF system is 10,880 l/min
per ring.

To estimate cost of stage 1 cryomodules we will use formula \[9\]

$$C = k \cdot \left( 0\text{.}8 \right)^{\text{log}(L)}\sqrt{\frac{\text{1300}\text{MHz}}{f\left\lbrack \text{MHz} \right\rbrack}} \cdot L$$

Here *L* is the active length of accelerating structure, *k* = 200 k\$/m
is the cost factor. As one can see, the cryomodule cost scales
approximately linearly with total length of the RF structure. The total
cost of cryomodules for stage 1 is then equal to 4.2M\$. The RF chain
cost (including klystrons, high voltage power supplies, low level
electronics, and RF distribution) is \$1/W and totals to 8M\$.

VLHC RF system would greatly benefit from R&D on improving technology of
sputtering niobium on copper with the goal to decrease if not completely
eliminate phenomenon of the *Q* slope. Special efforts should be devoted
to understanding the nature of this effect. Success of this R&D would
allow increase of accelerating gradient without taking serious
punishment in the cryogenic heat load. Also, R&D program is required to
develop RF controls for heavy beam loading. Careful analysis of
transients during injection, acceleration and beam storing is necessary
and may necessitate having an individual klystron for each cavity \[4\].

Table 5.26. Summary of RF System Parameters

+----------------------+-----------+---+---------+-----------+----------+
|                      | **Stage   |   |         | **Stage   |          |
|                      | 1**       |   |         | 2**       |          |
+----------------------+-----------+---+---------+-----------+----------+
|                      | Acc       | S |         | Acc       | Storage  |
|                      | eleration | t |         | eleration |          |
|                      |           | o |         |           |          |
|                      |           | r |         |           |          |
|                      |           | a |         |           |          |
|                      |           | g |         |           |          |
|                      |           | e |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Beam current         | 190 mA    |   |         | 68.9 mA   |          |
+----------------------+-----------+---+---------+-----------+----------+
| Beam energy          | 0.9 -- 20 |   | 20 TeV  | 10 --     | 87.5 TeV |
|                      | TeV       |   |         | 87.5 TeV  |          |
+----------------------+-----------+---+---------+-----------+----------+
| Acceleration time    | 1000 sec  |   |         | 2000 sec  |          |
+----------------------+-----------+---+---------+-----------+----------+
| Acceleration per     | 14.8 MV   |   |         | 39.4 --   |          |
| turn                 |           |   |         | 18.15 MV  |          |
|                      |           |   |         |           |          |
|                      |           |   |         | (30.0 MV  |          |
|                      |           |   |         | av.)      |          |
+----------------------+-----------+---+---------+-----------+----------+
| Acceleration power   | 5.62 MW   |   |         | 4.134 MW  |          |
| (2 beams)            |           |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Synch. rad. loss per |           |   | 0.03    |           | 12.37    |
| turn                 |           |   | MeV     |           | MeV      |
+----------------------+-----------+---+---------+-----------+----------+
| Total s.r. power (2  |           |   | 13 kW   |           | 2.1 MW   |
| beams)               |           |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Revolution frequency | 1286.5 Hz |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Bunch length, rms    | 142 mm    |   | 66 mm   | 81.9 mm   | 33.7 mm  |
+----------------------+-----------+---+---------+-----------+----------+
| Synchrotron tune     | 0.00845   |   | 0.00179 | .00280    | .00189   |
+----------------------+-----------+---+---------+-----------+----------+
| Synchrotron          | 10.87 Hz  |   | 2.30 Hz | 3.60 Hz   | 2.43 Hz  |
| frequency            |           |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Bunch frequency      | 53.1 MHz  |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Number of buckets    | 41280     |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Bunch spacing        | 5.646 m,  |   |         |           |          |
|                      | 18.8 ns   |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| RF harmonic number   | 288960    |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| RF frequency         | 371.7 MHz |   |         |           |          |
| (7×53.1)             |           |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| RF wavelength        | 80.65 cm  |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| RF voltage           | 50 MV     |   | 50 MV   | 50 MV     | 200 MV   |
+----------------------+-----------+---+---------+-----------+----------+
| Accelerating         | 7.75 MV/m |   |         |           |          |
| gradient             |           |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Voltage per cavity   | 3.125 MV  |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| *R/Q*                | 89 Ohm    |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| *Q* factor at 8 MV/m | 2×10^9^   |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Number of cavities   | 32        |   |         | 128       |          |
|                      | (16+16)   |   |         | (64+64)   |          |
+----------------------+-----------+---+---------+-----------+----------+
| Cavities per         | 4         |   |         |           |          |
| cryostat             |           |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| RF cavity wall       | 55 W      |   |         |           |          |
| losses               |           |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Cryostat static heat | 60 W      |   |         |           |          |
| leak                 |           |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Total cryogenic heat | 2.24 kW   |   |         | 8.96 kW   |          |
| load                 |           |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Beam power per       | 176 kW    |   | 0.406   | 42.4 kW   | 16.4 kW  |
| cavity               |           |   | kW      | peak      |          |
+----------------------+-----------+---+---------+-----------+----------+
| Number of 500 kW     | 16 (8+8)  |   |         | 16 (8+8)  |          |
| klystrons            |           |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+
| Number of cavities   | 2         |   |         | 8         |          |
| per klystron         |           |   |         |           |          |
+----------------------+-----------+---+---------+-----------+----------+

#### References *{ed note---for sec. 5.2.6}* {#references-ed-notefor-sec.-5.2.6 .Reference-heading .unnumbered}

1.  V. Shiltsev, "*Summary of the Working Group II \\RF, Instabilities
    and Feedback Systems",* VLHC Accelerator Technology Workshop, TJNAF,
    Feb.1999. <http://www.vlhc.org/tjef/wg2_summary.pdf>

2.  A. Jackson, contribution to the VLHC Design Study, unpublished.

3.  The LHC Study Group, "The Large Hadron Collider -- Conceptual Design
    Report", CERN/AC/95-05 (LHC) (1995).

4.  D. Boussard and T. Linnecar, "The LHC Superconducting RF System,"
    *Proceedings of the 1999 Cryogenic Engineering and International
    Cryogenic Material Conference (CEC-ICM'99),* 12-16 July 1999,
    Montreal, Canada.

5.  P. Brown, et al., "Performance of the LEP200 Superconducting RF
    System," *Proceedings of the 9th Workshop on RF Superconductivity,*
    1-5 November 1999, Santa Fe, NM, USA.

6.  P. Bosland, et al., Completion of the SOLEIL Cryomodule,"
    *Proceedings of the 9th Workshop on RF Superconductivity,* 1-5
    November 1999, Santa Fe, NM, USA.

7.  D. Boussard, "RF Power Requirements for a High Intensity Proton
    Collider," *Proceedings of the 1991 Particle Accelerator
    Conference,* pp. 2447-2449.

8.  H. Frischholz, W.R. Fowkes and C. Pearson, "Design and Construction
    of a 500 kW CW, 400 MHz Klystron to be Used as RF Power Source for
    LHC/RF Component Tests," *Proceedings of the 1997 Particle
    Accelerator Conference,* pp. 2911-2913.

9.  H. Padamsee, "SRF for Muon Colliders," *Proceedings of the 9th
    Workshop on RF Superconductivity,* 1-5 November 1999, Santa Fe, NM,
    USA.

### 5.2.7 Beam Dampers  {#beam-dampers .unnumbered}

In the last 30 years high intensity storage rings have become absolutely
dependent on beam damper circuits. The Tevatron in fixed-target mode,
the Booster, and the LHC will not operate anywhere near design intensity
without them. At synchrotron light sources and B-factories the beams are
lost within milliseconds without dampers. It is thus not surprising that
the VLHC requires damper circuits to reach design luminosity for both
Stage 1 and Stage 2 operation. Fortunately this technology is well
developed. One new element which does occur in the Stage 1 VLHC is the
necessity to distribute the dampers for one type of instability (the
coupled-bunch resistive-wall instability) around the large circumference
of the ring. While this provides some level of redundancy (since the
beam is stable even if one of the distributed circuits fails) it is a
new element which will be described below. Other dampers are
conventional.

#### 5.2.7.1 Distributed Transverse Dampers for Resistive-Wall Stability {#distributed-transverse-dampers-for-resistive-wall-stability .unnumbered}

Growth of transverse motions of bunches in the LF ring will be
suppressed with active feedback systems. The strongest beam impedance
arises from resistive-wall. At the frequency of the first lower-sideband
coupled-bunch mode, which is (1-0.235)*f~0~* = 0.99 kHz, the transverse
beam impedance is (7.84+1.27j)10^10^ ohm/meter. This causes an
exponential growth rate of 2.53 x 10^3^ per second for a fully filled
machine. Prompt cancellation of this growth is provided by six localized
feedback stations spaced around the ring circumference. At each station,
radial and axial damping are the same and for each there are two
feedback systems displaced azimuthally by 270 degrees in betatron phase
to address both 'sine' and 'cosine' phases of the oscillation; this
makes the damping tolerant of changes of tune that might be desired.

![](media/image59.wmf)

Figure 5.52. Layout of Pickup and Kicker positions for the horizontal
coordinate at one station. Incoming beams with sine-like or cosine-like
oscillations have their positions sensed by pickups at cell boundaries
(F- locations) and are kicked back towards the design orbit after
one-quarter betatron oscillation. An identical set of vertical pickups
and kickers operates at D-locations. Six identical stations are
distributed around the ring, one at each stage 1 cryoplant location.

In localized feedback, a kicker is located downstream from the pickup by
90 degrees in betatron phase (one lattice cell) and the signal is
transmitted promptly from pickup to kicker through foam-insulated coax
to minimize delay. Delay in the 271 meters of cable is 180 nanosec. to
which one adds about 50 ns. for electronic processing and amplification.
Although with this delay the signal from one bunch is delivered to the
12^th^ following bunch, the phase delay at 1 kHz is a negligible 1.5
milliradian. For higher-frequency sidebands the phase delay increases,
becoming a significant 1/8-oscillation at 550 kHz. The localized
feedback systems will be used up to 500 kHz; at that frequency the
impedance has become small enough to be controlled by a conventional
one-turn bunch-by-bunch system that extends up to the needed 26.5 MHz
bandwidth of coupled-bunch modes.

![](media/image60.wmf)

Figure 5.53. Electronic Elements of the Coupled-Bunch Feedback System.

The hardware in a local feedback system consists of (1) a pair of
capacitive pickup plates, (2) electronics and cable to the kicker, and
(3) a 4-meter long stripline-pair kicker. The pickup strips are 25 cm
long and connect to high-impedance amplifiers. The signals are then
differenced and the unipolar pulses are stretched to half the interval
between bunches to give a baseband signal for the kicker. At the lowest,
strongest mode, the required feedback loop-gain is *G* = 0.287 and to
damp injection errors of 0.1 mm calls for a transverse kick of 83.3 kV.
The kicker delivers this with a power input of 1.10 kW. Injection in
bunch trains separated by 2 seconds produces unwanted transients,
especially if there is closed-orbit offset. Bunch signals will be
recorded and analyzed to generate a correction for the local
closed--orbit corrector; this will zero the closed-orbit well before the
second train of bunches is injected. After the ring is filled,
additional rejection of very low frequency excursions will be made by
the low-frequency cutoff of the feedback electronics; this is possible
with baseband operation as we have here. For damping both radial and
axial motions at 6 stations, 24 systems are required for each
circulating beam.

Pickup and kicker are located at points of maximum betatron amplitude in
slightly modified standard arc cells. The modifications \[1\] involve
removing 5m of magnet iron at the boundaries of 8 successive half-cells.
An additional quadrupole corrector is used at each location to repair
damage to the β-functions caused by the missing focusing. The \~10%
dispersion wave generated by the missing bend automatically cancels
outside the insertion by virtue of the 360° phase advance across the 8
half-cells. The damper system uses at most 6 of the 8 available free
spaces. Placing the damper pickups and kickers where the dispersion is
nonzero is not believed to cause difficulties although this is will be
the subject of continuing study.

At the coupled-bunch mode frequency of 500 kHz, the growth rate has
reduced to 57 per second or 0.044 per turn. This and all higher
coupled-bunch modes are suppressed by the one-turn bunch-by-bunch
feedback system that operates over the range 53.1±26.5 MHz. The kicker
is a quarter-wavelength long at this frequency, 1.41 meter. The required
kick for 0.1 mm excursion is 26.4 kV and power is 513 watt. Power
amplifiers for this application are commercially available. The pickup
is the same length as the kicker and feedback gain is 0.108. Radial and
axial systems are similar.

One can ask if electronic noise in these dampers will add emittance
during a long collision time. Fortunately, although the loop gains are
high, the small aperture and peak bunch current of 8.4 ampere make the
pickup signal strong and large electronic gain is not needed. The peak
current gives a pickup sensitivity
$\text{IZ}_{L}\frac{g}{b}\sqrt{2} = 2\text{.}6´\text{10}^{4}$
volt/meter. Input thermal power with an amplifier noise figure of 1 dB
is 1.2*kTB* =5.2x10^-21^*B* where *B* is the bandwidth. Equating this to
the pickup signal power with equivalent rms noise amplitude *X~N~* gives
$X_{N^{2}}\text{>=}3\text{.}7´\text{10}^{- \text{28}}B$. The higher
energy at collision reduces the gain to G =0.013. The 12 feedback
systems would then cause an emittance growth rate, without allowing for
damping, of

$\frac{de}{\text{dt}} = \text{12}\frac{f_{0}g}{2\beta} < G^{2}X_{N^{2}}\text{>=}2\text{.}1´\text{10}^{- \text{17}}$
m/sec

Nominal emittance is 1.7x10^-6^, thus this dilution rate is of no
concern and would actually be smaller because of damping by the
feedback. The broadband system produces a similarly negligible emittance
growth.

#### References *{ed note---for sec. 5.2.7}* {#references-ed-notefor-sec.-5.2.7 .Reference-heading .unnumbered}

\[1\] J. Johnstone, Presentation to VLHC workshop in Lake Geneva, WI Jan
2001.

### 5.2.8 Injection {#injection .unnumbered}

The magnets and optics needed for 900 GeV beam injection are described
in section 5.1.5.4. An important design specification (not often taken
at Fermilab) is that the injection and extraction devices not present
any aperture limitaton smaller than the arc magnets. This requires
full-aperture kickers and special large aperture copper/iron quadrupoles
in the vicinity of the Lambertsons. A high beta insertion minimizes the
strength of standard kickers required. The large aperture quadrupole is
described in section The magnet designs and layout in section 5.1.5.4
(for both injection and abort) meet that goal.

Transfer line magnet parameters based on both air-cooled copper and
permanet magnets have been developed. Either solution will require one
corrector magnet per quad location, with the power supply and
instrumentation in local modules similar to the arcs.

Beam is injected near the midpoint of the Utility straight section.
Downstream of this it will be convenient to have an internal beam
absorber for transfer line commisioning and tests independent of the arc
magnets. The injected beam, after passing through two quad locations to
maesure position and steering errors, will be deflected 5-10 cm onto the
absorber by a standard corrector magnet. The scope of absorber will be
comparable to the Tevatron collider-mode abort. With reasonable
administrative intensity limits air-cooling should be sufficient. A few
bunches of 10^9^ protons are sufficient for a good BPM measurement.

## 5.3 Radiation, Machine Protection, and Beam Abort {#radiation-machine-protection-and-beam-abort .unnumbered}

### 5.3.1 Overview {#overview .unnumbered}

The 2.8 GJ of kinetic beam energy in the Stage 1 machine is
approximately eight times that of the LHC. Under normal circumstances
roughly 50% of this energy is gradually dissipated in beam-beam
collisions at the IRs and 5-10% is lost diffusely due to beam--gas
collisions around the circumference of the ring. Another 5-10% may be
intercepted at beam collimation inserts which scrape away beam halo
particles. The rest of the energy is disssipated in the RF loads as the
beam is decelerated and deposited in the beam absorber when the
decelerated beam is ejected.

A very small fraction of the machine circumference exceeds the limit (\~
1 W/m of beam losses) for normal "hands-on" maintenance \[1\]. These
regions include the small-angle regions of the IR's, the beam
collimation system, and a small region or arc magnets downstream of the
beam collimation system. The average radiation load in these components
is a few times higher than the LHC, and the shielding and handling
requirements comparable. LHC experience will be useful in optimizing
these designs.

Under accidental conditions there is enough energy to cause severe
damage to the magnet and surrounding environment. This is not a new
situation for high energy colliders. The ISR beams had enough energy to
repeatedly burn holes in the machine \[2\]. The magnitude of the problem
has increased however. The beams of the Stage 1 machine carry enough
energy that in principle they could liquefy 400 liters of stainless
steel (whereas the LHC beams can only liquefy 50 liters).

Under worst-case accident assumptions the beam will leave the machine
and strike the tunnel wall. We have begun to study the mechanical and
radiological consequences. See section 5.3.3. A single shot beam
accident releases beam energy equivalent to losing the Main Injector
beam at one place for about an hour. This is not outside the scope of
existing shielding requirements at Fermilab, and should not be major
problem for a tunnel in deep bedrock.

Tunnel groundwater activation from single-pulse accidents appears not to
be a concern. A preliminary calculation indicates that it would be
possible to lose the beam in a single spot, immediately transfer the
activation into the tunnel water sump pit, and pump out the activated
water without violating applicable federal guidelines. Another way of
saying this is that you could dump the beam into the tunnel sump cistern
and the water would still be safe to drink. (This is of course an
absurdly pessimistic scenario, since it will take days or weeks for the
groundwater to collect in the sump, by which time most of the
radioactivity will have vanished).

Effective strategies have evolved to deal with machine protection issues
culminating with the Tevatron, SSC, and LHC. These issues have been
revisted for VLHC energies \[3,4\] and the results are summarized here.

Firstly, a robust and redundant extraction system removes the beam
whenever the position becomes unstable or anomalous losses are detected.
This protects the machine from anything which happens "slowly" (in
miliseconds to seconds) such as magnet quenches, RF or power supply
failures, vacuum failures or corrector magnet trips. Such a system has
prevented the Tevatron (so far) from having a hole burned through it.
This is a standard feature which continues to be essential at VLHC
energies.

The one credible accident which occurs on a rapid time scale involves an
abort kicker module misfire. The incompletely extracted beam will rattle
around the machine and hit various well-defined limiting apertures such
as extraction septa, IR quadrupoles, beam collimators, and (god willing)
the silicon detectors. The probablity of this will be reduced in the LHC
by replacing Thyratrons with solid-state kicker power supplies, and
appropriate fail-safe logic which in principle prevents a single module
misfiring ("a partial-beam abortion"?). Since the probability of this
cannot be reduced to zero, a set of "sacrificial collimators" are placed
upstream of the vulnerable components. These are replaceable graphite
structures which absorb and diffuse the beam energy at great personal
cost. This strategy is essential at the SSC/LHC and will be necessary
and sufficient for the VLHC.

Three qualitiatively new features emerged while reviewing the machine
protection situation at VLHC energies. First, the graphite core of the
beam absorber may be damaged by a single pulse in the case of a sweeper
magnet failure. The core must be protected (sect 5.2.7.1) with a
replaceable sacrificial collimator immediately upstream. Secondly, in
the case of a sweeper magnet failure the beam window in the extraction
channel will have a hole melted in it. This is not a safety issue, but
in this accident scenario the beam vacuum must protected with an
automatically closing gate valve and the window must be replaced.
Finally, the beam collimation system (sect 5.2.7.2) will require water
cooling for the jaws of the secondary collimators.

### 5.3.2 Beam Abort System {#beam-abort-system-1 .unnumbered}

#### 5.3.1.1 Extraction {#extraction .unnumbered}

It turns out to be quite straight forward to kick the beams out of the
machine towards absorbers. The magnet parameters and layout are
discussed in section 5.1.5.4.2. Like the Tevatron, SSC and LHC abort
systems, we use fast kicker magnets to switch the circulating beam into
the other aperture of Lambertson magnets. The circulating beam goes
through the field-free hole in the Lambertson magnets, and the extracted
beam is bent upward in the Lambertson magnets so as to clear the first
quadrupole in the downstream half of the straight section. A full
aperture extraction kick is used and the separation of the circulating
and extracted beams is 25 mm at the entrance to the Lambertson magnets.
Thus any beam which is circulating anywhere in the physical aperture
will be extracted. Special large-aperture warm-iron-and-copper
quadrupoles are used near the Lambertsons so that no aperture
restriction is presented to the circulating beam.

Normally the beam extraction is synchronized with an "abort gap" in the
beam which is equal to the rise time of the extraction kicker. During
certain control system failures it may be necessary to unconditionally
extract the beam. This sweeps the beam across the extraction septum
which must survive without damage. For the VLHC the stress on the
extraction septum is roughly equal to the LHC (since the beam energy per
unit time is similar) and does no damage.

The requirements for the reliability of a one-turn extraction mechanism
are comparable to the SSC \[5\] and LHC \[6\]. The extraction kicker is
broken into 10 independent modules, with any 7 out of 10 sufficient for
a safe abort. Solid-state pulsers (as opposed to Thyratrons) will be
used to minimize accidental prefires. Three Musketeer logic
("All-for-one, and one-for-all!") guarantees that any single module
firing will automatically trigger the rest of the modules.

Figure 5.54. Schematic layout of Beam Abort channel including kickers,
Lambertson septa, extraction beam sweeping, beam defocussing, beam
window, sacrificial rod, and 4-in-1 Beam Absorber. Under normal
circumstances the extracted beam is swept in a spiral pattern to spread
the energy across the graphite dump. If the sweeper magnet fails, the
beam travels straight ahead into a sacrificial graphite rod which takes
the damage and must be replaced.

#### 5.3.2.2 Beam Absorber {#beam-absorber .unnumbered}

For TeV beams, the natural choice for the absorber is graphite, as at
the Tevatron, SSC and LHC. The major difficulty lies in making the beams
big enough that they will not crack a graphite absorber. A standard
absorber consists of a graphite core, contained in an aluminum jacket
with water cooling, followed by adequate steel and cement to protect
ground water. The graphite core is rectangular, with dimensions 10 ×1.2
×1.2 m. The thickness of steel shielding around the aluminum container
is about 1.3 m on each side and extends about 3 m downstream. At present
we consider a "4-in-1" design where extracted beams from both directions
hit absorber cores in a common sarcophagus. The Stage 1 and Stage 2
machines share a common absorber for each direction.

Activation and cooling water considerations are driven by the average
beam power on the target. The 500kW average power (corresponding to one
full-energy abort of both beams every 12 hours) is comparable to the
300kW design value for the Main Injector beam absorber. The overall
design is patterned on the Main Injector absorber which has proven
satisfactory and meets ES&H requirements for this power level.

The graphite dimensions and beam size necessary to contain the showers
without cracking the graphite were found by detailed simulations with
the MARS14 code. The design goal was to keep the maximum temperature
rise at the axis of the graphite core per spill below 1300-1500°C (from
successful Tevatron dump experience and theoretical shockwave
considerations). For a purely Gaussian beam with a spill that is
stationary in transverse position, the beam sigma would need to be 19 cm
in both x and y for the maximum temperature rise in the core of 1330°C.
Expanding the beams to this size with defocussing quadrupoles is out of
the question.

##### 5.3.2.3 Beam Sweeping System {#beam-sweeping-system .unnumbered}

A spiral beam sweeping scheme similar to the SSC and LHC is adopted to
spread the beam energy across the absorber core. Magnets are described
in 5.1.5.4.2. A horizontal and a vertical sweeper, 90° out of phase,
both oscillate with decaying amplitudes. Ideally the frequency should
increase as the radius of the spiral decreases in order to keep the
temperature rise constant. Since this is electrically difficult a
suitable compromise is to limit the inner radius of the spiral to half
that of the outer radius and accept a factor two higher temperature rise
at the inner radius. An estimation indicates that an outer radius of 30
cm would be adequate to keep the temperature below 1500°C. If the beam
sigma was 0.5 cm in both planes, the frequency of these sweepers would
be 9.7 kHz.

In the case of a failure of both coordinates of the sweeper system the
beam would damage the graphite absorber core \[7\]. To prevent this a
sacrificial graphite rod 5 cm in diameter and 4 m long is positioned on
the beam axis immediately upstream of the main absorber. See Figure
5.54. Normally the extracted beams will spiral around this rod without
hitting it. If the beam is extracted with all sweeping magnets off, the
beam damage will be confined to the sacrificial rod. The rod will be
housed in a metal box to prevent the spread of radioactive debris.

A beam window will not be protected in case of sweeping system (or
defocussing quadrupole) failure, if the effective beam sigma on the
window is less than 0.5 cm. The ring vacuum can be preserved by
rapid-acting gate valves and/or multiple windows in series. Each window
gets a small hole drilled in it when the sweepers fail, and pumping
between the windows isolates ring vacuum until a slow gate valve closes.
Alternatively, differential pumping with several wire meshes would do
the same job.

![](media/image61.png){width="3.0416666666666665in"
height="1.2777777777777777in"}

![](media/image62.png){width="3.140972222222222in"
height="0.6583333333333333in"}

![](media/image63.png){width="2.8006944444444444in"
height="1.1631944444444444in"}

![](media/image64.png){width="2.536111111111111in" height="1.15in"}

Figure 5.55. Beam sweeping system optics. Left: 3-sigma beam half-size
at 1 TeV injection (beam size at 20 TeV is 4.5x smaller), and beam line
layout. Right: beam displacement with respect to the direction of
extraction straight section and maximum sweeping kick in the horizontal
or vertical plane.

### 5.3.3 Radiation and Beam Loss {#radiation-and-beam-loss .unnumbered}

#### 5.3.3.1 Quenches from Beam Loss in Transmission Line Magnets {#quenches-from-beam-loss-in-transmission-line-magnets .unnumbered}

The warm-iron design of the Transmission line magnet is less sensitive
to radiation-induced quenches than ordinary superonducting magnets. To
determine tolerable beam loss in the arcs, MARS14 simulations are done
in the lattice both at injection (1 TeV, σx,y = 1.4 mm, α*~inc~* = 0.7
mrad) and top energy (20 TeV, σx,y = 0.3 mm, α*~inc~* =0.15 mrad).
Corresponding materials and magnetic field distributions have been
implemented into a 3-D model. Inward and outward beam losses were
considered both for inner and outer beam pipes (see Figure 5.56).

![](media/image65.png){width="3.0805555555555557in"
height="2.5861111111111112in"} ![](media/image66.wmf){width="2.2125in"
height="2.5597222222222222in"}

Figure 5.56. Beam loss geometries simulated in the Stage 1 VLHC magnets.

Simulations show that the superconductor in the transmission line
magnets is rather well protected radially by warm iron. The distance
from the hottest spots in showers started by protons hitting the beam
pipe, peak energy deposition density is relatively low. Therefore, the
tolerable beam loss is significantly higher than in a conventional
cosine-theta type magnets. Table 5.27 shows fast (1 msec) and slow (0.1
sec) beam loss rates needed to initiate a SC magnet quench---assuming
the same quench limits as in the Tevatron SC dipoles --- at injection
and top energy in the Stage I ring. For comparison, the values for the
Tevatron at 0.9 TeV are shown. The assumption that the temperature
needed to incite a quench in both magnets is identical is probably
pessimistic since the braided cable of the VLHC can re-route the current
around a quenched region on the magnet midplane and a cosine-theta
magnet cannot.

Table 5.27. Quench-Inducing Loss Thresholds for the VLHC Stage 1 and
Tevatron

  ------------------------ ------------------------ ----------------------
                           Fast Loss Protons/pulse  Slow Loss Protons/sec

  0.9 TeV                  9 ×10 ^8^                3 ×10 ^9^

  20 TeV                   2.5 ×10 ^7^              7.5 ×10 ^7^

  Tevatron                 4 ×10 ^7^                3 ×10 ^8^
  ------------------------ ------------------------ ----------------------

#### 5.3.3.2 Cryogenic Heat Load from Beam Losses {#cryogenic-heat-load-from-beam-losses .unnumbered}

Heat load from beam-beam interaction debris in the IR quads is included
explicitly in the discussion in section 5.2. The cryogenic heat load
from beam loses in the arcs is also a potential concern. At 20 TeV
roughly 5% of the energy from beam losses is estimated to be absorbed in
the cryogenic transmission line. If 1% per hour of the (3+3) GJ of beam
energy were lost uniformly in the arcs, this amounts to a total heat
load of 800 W (3.5mW/m average) which is a 5% perturbation on the 5K
heat load. The collimation system (section 5.3.4) is expected to
localize essentially all beam halo losses into collimators in warm
sections, thereby eliminating that heat load from the cryo system.

The collimation system will be ineffective against losses from inelastic
beam-gas scattering. With the expected vacuum lifetime (sect 5.2.4.1) of
\>200 hours, the cryogeninc heat load will be \< 2mW/m, less than 3% of
the 4.5K heat load. If continued R&D reduces the 4.5K heat leak this
will become an increasingly important part of the total.

#### 5.3.3.2 Radiation Damage to Tunnel Electronics {#radiation-damage-to-tunnel-electronics .unnumbered}

The Section 5.2.3 describes electronics housed in small enclosures
("holes in the wall") at each quad location. This approach was studies
at UNK \[8\] and the electronics was found to survive under rather
conservative assumptions about their radiation hardness. A recent
interesting development \[9\] is that modern CMOS is found to be
intrinsically rad-hard due to the absence of long-term charge trapping
at the gate oxide layer in sub-micron devices. The LHC is apparently
contemplating placing unshielded electronics under each dipole, and is
initiating a study of the radiation hardness of commercially available
electronics \[10\]. Depending on LHC operational experience, the rather
modest costs of the module enclosures might be saved by eliminating the
enclosures. Or not.

Radiation damage to fiber optics placed in the tunnel is was studied at
the SSC \[11\]. It was found that placing the fibers into the trough in
the invert guaranteed their survival even for upgrades to 10x the SSC
luminosity. We have followed this approach (section 5.2.3.8).

### 5.3.4 Beam Collimation System  {#beam-collimation-system .unnumbered}

Even in good operational conditions, a finite fraction of the beam will
leave the stable central area of accelerator because of beam-gas
interactions everywhere along the accelerator, intra-beam scattering,
collisions in the IPs, RF noise, ground motion and resonances excited by
the accelerator imperfections continuously produce a beam halo. As a
result of beam halo interactions with limiting apertures, hadronic and
electromagnetic showers are induced in accelerator and detector
components will cause accelerator related background in the detectors,
magnet heating and accelerator and environmental irradiation. The design
strategy of the VLHC is that the beam losses are controlled as much as
possible by localizing them in a dedicated beam collimation system. This
minimizes losses in cryogenic parts of the accelerator, and drastically
reduces the source term for radiation hazard analysis in the rest of the
lattice. The technology for these systems has been well developed for
the Tevatron, SSC, and LHC.

For the VLHC a complete beam cleaning system which provides for both
betatron and momentum scraping has been designed and simulated
\[11,12\]. The three-stage beam collimation system consists of 5 mm
thick primary tungsten collimators placed at 7σ~x,y~ and 3 m long copper
secondary collimators located in an optimal phase advance at 9.2σ~x,y~
and aligned parallel to the circulating beam envelope. Two more
supplementary collimators are placed in the next long straight section
to decrease particle losses in the low-β quadrupoles and in the
accelerator arc. They are located at 14σ ~x,y~ to intercept only
particles scattered out from the secondary collimators.

![](media/image67.png){width="2.654861111111111in"
height="3.5868055555555554in"}

Figure 5.57. Beam loss distribution along the accelerator at injection
(top) and at collisions (bottom).

![](media/image68.png){width="2.638888888888889in"
height="3.5395833333333333in"}

Figure 5.58. Beam loss distributions in the collimation section at
injection (top) and at collisions (bottom).

The simulated performance of the system meets the goal of essentially
eliminating losses away from the cleaning insert. A main reason for this
excellent performance is that the system uses a purpose-built lattice
insert rather than a something which has been retrofit into an existing
machine such as the Tevatron. The maximum beam loss in the arc section
behind the collimation region () is 1 W/m in two 21.5 m long dipoles and
one 6 m long quadrupole, and 0 .2 W/m in two 21.9 m long gradient
magnets.

The effect of beam cleaning system operation on the particle loss
distribution in the entire machine was design and calculated with
emphasis on reducing losses and detector backgrounds near the high
luminosity insertions. But in our calculations, with 6 ·10^4^ particles
lost in the collimators, we did not see any loses in the vicinity of
interaction point. Farther investigations should be done to determine
particle backgrounds in the IP from the collimation system.

The primary collimation insert will be located in a far side straight
sections conjugate to the on-site Utility Straight Sections. Secondary
collimators will be located in this section as well as in special
locations near the IR's. The secondary collimator will absorb
approximately 20kW of beam power and will require water cooling,
probably thorough an isolated RAW (radiaoactive water) loop heat
exchanged with the LCW flow. Shielding of the collimators will require
approximately 1m of radial iron followed by 50cm of radial concrete over
a length along the beam line of \~15m to allow free passage of
rad-trained personnel. This will require locally enlarging the tunnel
cross section but should not require a bypass tunnel.

#### References *{ed note---for sec. 5.3.4}* {#references-ed-notefor-sec.-5.3.4 .Reference-heading .unnumbered}

\[1\] proc. Beam Halo workshop

\[2\] Bryant & Johnsen, "Circular Accelerators and Storage Rings", p.308

\[3\] A.I. Drozhdin and N.V. Mokhov, "Energy Deposition Issues in the
Very Large Hadron Collider", Workshop on VLHC, Fontana, Wisconsin,
February 22-25, 1999.

\[4\] A.I. Drozhdin , N.V. Mokhov, C.T. Murphy, S. Pruss, "*Beam Abort
For a 50X50 TEV Hadron Collider",*
<http://fnalpubs.fnal.gov/archive/vlhc/VLHCPub-51.ps>

\[5\] Baishev, I.S., Drozhdin, A.I., Mokhov, N.V., Parker, B.,
Richardson, R.D., Zhou, J. *"Dealing with Abort Kicker Prefire in the
Superconducting Super Collider",*PAC 93, Washington, DC, May 1993

\[6\] The Large Hadron Collider, Conceptual Design, CERN/AC/95-05(LHC)
October 20, 1995..1.5

\[7\] A legendary SSC video contains a visualization of the extracted
SSC beam drilling a hole in the absorber block when the sweeping magnet
system fails. We should put this online.

\[8\] N. Mokhov, pvt. comm.

\[9\] R. Yarema, pvt comm.

\[10\] LHC Talk at Beam Instrumentation Workshop '00

\[11\] SSC Note \#

\[11\] Drozhdin et. al., "*The VLHC Beam Collimation System*",VLHC
design study note

\[12\] A.I. Drozhdin, N.V. Mokhov and A.A. Sery, "The Very Large Hadron
Collider Beam Collimation System", Workshop on VLHC, Fontana, Wisconsin,
February 22-25, 1999.

### 5.3.5 IR Protection {#ir-protection .unnumbered}

A sophisticated system must be designed to protect the IR SC magnets,
particularly from kicker misfires. As in the LHC, it will consist of a
front collimator, inner and intermediate absorbers in the inner triplet,
and of a neutral beam dump and several collimators in the outer triplet.
The similarity of the Stage 1 IR layout to the LHC makes it likely that
a similar protection layout would be workable. The length of these
sacrificial collimators will likely have to be increased reflecting the
increased energy and decreased beam spot size of the VLHC beams.

### 5.3.5 Worst-Case Beam Acccidents {#worst-case-beam-acccidents .unnumbered}

Work has begun on understanding the implications of a "worst-case" beam
accident in the VLHC. The assumption is that some unspecified agent
causes the beam to be kicked out of the machine with a rise time fast
compared to the revolution frequency, so that the normal beam abort does
not have time to act. This agent is also assumed to possess a "kicker
flat top" accurate enough (\<1%) that then beam is effectively held in
one place for the duration of the accident. Under these assumptions the
beam will rapidly melt a hole in the magnet and impact the tunnel wall
at near grazing incidence (3-5mrad).

A preliminary observation is that the nearby cryogenic piping would
explode due to the instantaneous temperature rise. This would also be
true of the Tevatron, HERA, and the LHC so it is important to keep this
mysterious agent out of these machines as well. The cryo piping is
contained inside carbon-steel structures (vacuum jackets and magnet
iron) which would limit collateral damage. It would probably not even be
noticed from the outside of the magnet. This is not our biggest problem.

A second observation is that the "beam drilling" scenario (in which a
stable beam vaporizes a small channel deep into the target) is
impossible at grazing incidence, even if the beam were perfectly
extracted on a single trajectory. This beam drilling scenario is
expected when the beam is normally incident onto a semi-infinite slab of
material such as a beam absorber block. However at grazing incidence,
the imbalance of the mechanical forces near the beam impact point (due
to local heating of the rock) will cause a rock chip to "spall"out from
the tunnel wall. This spalling behavior has been observed during rock
excavation tests with electron beams \[ \] and follows this simple
mechanical model. This spalling effectively sweeps the beam and
guarantees that fresh (i.e. non-vaporized) material will be available to
initiate the shower even if the beam is extracted perfectly. So the
pattern of energy deposition can be calculated accurately enough that
the shower intiates at a more-or-less fixed position near the point of
grazing incidence.

A MARS calculation has been performed (Figure 5.59) to evaluate the
energy depostition under the assumption that both the rock and beam
position remain fixed. The simulation indicates that a region 8 metres
long and about 15cm in radius are heated to the melting point of
Dolomite. Obviously the lava will splatter to the floor. The next step
in the calculation (in progress) is to use ANSYS to evaluate the thermal
stresses in the surrounding rock and estimate the amount of rock which
breaks off from thermal stress. The rise time of the heat pulse (1
machine revolution or about 0.8 msec) allow the mechanical stresses to
relieve themselves on the scale of a couple of meters, so a static
mechanical analysis is approximately valid.

![](media/image69.png){width="2.748611111111111in" height="2.7125in"}
![](media/image70.png){width="2.5in" height="2.7131944444444445in"}

Figure 5.60. VLHC Stage 1 beam at 6.5mrad grazing incidence on tunnel
wall.

A more realistic situation in which angle of the beam angle sweeps by
even a few milliradians during extraction the changes the situation
signficantly. In this case the heating is distributed into a large
enough rock mass that the only a very small region (of order a
centimeter wide) is taken near the melting point. The picture becomes
that of a destroyed magnet, a centimeter-wide scar on the tunnel wall,
and an amount or residual radiation comparble to that of a 1-hour
continuous beam loss of the Fermilab Main Injector.

### 5.3.6 General ES&H Considerations {#general-esh-considerations .unnumbered}

*{ed. note: this section will be derived from the following material
provided by Don Cossairt}*

**Potential Environmental, Safety, and Health Issues**

**Environment, Safety, and Health Considerations for a New Accelerator
Facility**

**I. Introduction**

All of the possible future accelerators under study present a number of
considerations in the general area of environment, safety, and health.
It is the intent of this chapter to identify the character of these
challenges in a general way. The environment, safety, and health issues
peculiar to a particular possible accelerator are discussed in the
chapters related to that technology. Some of the considerations which
much be taken into account are very similar to those that have been
encountered and solved during the construction and operation of other
facilities at Fermilab and at similar laboratories elsewhere in the
United States and worldwide. Other considerations have not been
encountered on the same scale previously in connection with the
construction and operation of accelerator laboratories. These novel
issues will require particular attention as such a project proceeds to
assure their timely resolution in a manner that is cost-effective and
that meets the approval of the public. In this chapter, both the
conventional and the novel issues are discussed, with perhaps more
emphasis devoted to the latter. It is concluded here that with adequate
planning in the conceptual design stages, these problems can be
adequately addressed in a manner that merits the support of the
Laboratory, the Department of Energy, and the public.

**II. Procedural/Regulatory Matters**

The actual design, construction, and operation of any future accelerator
will have to meet a number of procedural/regulatory milestones in the
area of environment, safety, and health to assure timely and continued
support of this project by the public and by the Department of Energy.
The devotion of early attention to these issues is likely the best way
to enhance public support of any chosen accelerator technology.
Requirements in environment, safety and health are currently set forth
as a part of Fermilab\'s Work Smart Standards in Environment, Safety,
and Health that are incorporated in the current version of the contract
between Universities Research Association and DOE. Currently, the Work
Smart Standards are reviewed annually to assure that they adequately
address the hazards of the laboratory, including those of any new
facility. If changes are necessary they are negotiated with the DOE-FRMI
Group and the URA-DOE contract is revised accordingly. These standards
include listings of applicable Federal and State Regulations as well as
internally developed policies and national standards (WSS 99). Of
course, the contract under which Fermilab or a future accelerator might
operate in the future is likely to change in ways that could modify the
applicable requirements.

**A. [Environmental Protection Procedural/Regulatory
Matters]{.underline}**

All DOE activities are subject to the requirements of DOE\'s regulations
for implementing the National Environmental Policy Act (NEPA) (CFR 97).
First, any new project of the magnitude of those under consideration in
this report will be the subject of an Environmental Assessment (EA). A
review will be done of all possible impacts of this project on the
environment and the public. The required analysis is broad in scope and
includes societal impacts along with those topics that are more
generally associated with environmental protection such as the
discharges of pollutants, effects upon wetlands and floodplains, and
exposures of people to chemicals and radioactive materials. It will
include a review of the alternatives of carrying out the project
elsewhere or not at all. This process is centered on the production of a
comprehensive document but also includes the participation of the public
by methods that will be chosen by DOE. As a result of the environmental
assessment process DOE will either issue a Finding of No Significant
Impact (FONSI) or conclude that that the preparation of an Environmental
Impact Statement (EIS) is necessary. An EIS may well be required due to
the size, scope, cost, or impact on the human environment of the
project. For example, it is likely that an EIS will be required for any
new facility that extends beyond the present boundary of the Fermilab
site. The completion of the EIS process results in the issue of a formal
public notice called a Record of Decision (ROD). The EIS process is
generally considered to be an arduous one, but one that can be followed
to a successful conclusion stated in the ROD. The preparation of an EIS
is certain to be a large task having significant cost, customarily
accomplished using external resources. Regardless of the eventual path
of the NEPA process, project funds cannot be issued to support such a
Congressional \"line item\" project beyond the early conceptual stage
prior to the successful completion of the NEPA process. It is thus
crucial that this process be conducted in a manner that is honest and
which comprehensively addresses the potential concerns of members of the
public. A good working relationship with the Department of Energy is
also a necessity to a successful result.

Other procedural requirements apply in the area of environmental
protection. These will be more certainly identified as a part of the
NEPA process but early planning may well serve to avert problems later.
DOE facilities are generally subject to Federal and State environmental
protection regulations promulgated chiefly by the U. S. Environmental
Protection Agency (USEPA) and the Illinois Environmental Protection
Agency (IEPA), respectively. There are environmental permits to obtain
from both state and federal authorities that are likely to be found to
apply to any of the possible facilities. Some of these apply during the
construction stages, others apply during operations, and some apply
during both stages. Permits are likely to be required to cover such
topics as storm water discharges, discharges of cooling water, wetlands
mitigation, releases of air pollutants for both non-radioactive
pollutants and for radionuclides, and construction in any floodplains.
Archaeological sites are also located in the region that might need
further investigation and study prior to the commencement of
construction. The preparation of the applications for these permits and
approvals is generally straightforward, but must be accomplished with
the long lead times, typically 180 days, required by the issuing
agencies. Early coordination with the project design team should greatly
facilitate completion of the associated milestones. Any chose
accelerator is likely to be initially viewed by the public and by
Federal and State regulators as a poorly understood, esoteric
technology. In recognition this and also of the fact that any of the
chosen accelerators will involve some sort of impact beyond the
geographical boundaries of the present Fermilab site, early coordination
with the Federal and State regulatory agencies is recommended as a
vehicle to promote enhanced understanding of the nature and impact of
the chosen facility.

**B. [Safety and Health Procedural/Regulatory Matters]{.underline}**

In accordance with the Fermilab\'s Work Smart Standards, the Laboratory
will be required to prepare an assessment of the environment, safety,
and health issues associated with this project in the form of a Safety
Assessment Document (SAD). Given the size, scope, cost, and novelty of
any of the candidate facilities, the preparation of a first stage
document called a Preliminary Safety Assessment Document (PSAD) is
needed. The purpose of the PSAD is to identify the relevant
environmental, safety, and health issues at an early stage and propose
how they might be mitigated. A final Safety Assessment Document (SAD),
then, documents the resolution of all the pertinent issues raised by the
PSAD. Environmental issues are customarily integrated into the PSAD/SAD
process to promote program cohesiveness. Given the scope of any of the
candidate projects discussed elsewhere in this report, it is nearly
certain that DOE will choose to review these safety documents by
utilizing an external review team composed of both DOE staff and
representatives from other DOE facilities. Just prior to facility
operation, a readiness review will be conducted in similar fashion using
an external review team. DOE has specified a somewhat more rigorous
procedure for the conduct of this safety review process in its Orders.
The details of the procedures to be followed in the safety review
process will be determined by the terms of the contract under which the
Laboratory is operated at the time the project might proceed. Unlike
NEPA assessment activities, PSAD/SAD activities generally begin after
funds are issued. Nevertheless, careful consideration of PSAD/SAD in the
design can only result in beneficial results. Efforts should be taken at
early stages to promote consistency between the conclusions of the NEPA
assessment and the safety and health documentation.

DOE is presently \"self-regulating\" in the areas of industrial safety
and occupational radiation protection. There is a possibility that
during the development of the next accelerator facility, DOE activities
might become subject to \"external\" regulation in these areas, as well
as in occupational radiation protection. It is difficult at this time to
anticipate the form such external regulation might take or which
agencies might be involved. Fermilab staff and DOE continue to monitor
the status of DOE self-regulation in order to identify new requirements
or procedures that might apply to Laboratory activities.

**III. Occupational Safety During Construction**

Any of the accelerators under consideration will involve a great deal of
construction. In regions where the standard \"cut and fill\" method used
elsewhere successfully at Fermilab for many years, the standard
practices embodied in the Occupational Safety and Health
Administration\'s (OSHA\'s) regulations on the safety of construction
activities will be followed (see WSS 99). Particular requirements that
address excavations, the provision of applicable personnel protective
equipment, coordination of emergency response measures, fire safety,
chemical safety, and electrical safety would apply as they have for many
years to other civil construction projects on the Fermilab site.
Adequate means of egress of construction workers would need to be
provided. Given the nature of the candidate facilities, somewhat unlike
present facilities, significant slopes may be involved in some
locations. Well-thought means of prevent of accidents due to heavy
objects moving downhill should be included in the design.

The candidate facilities all involve a considerable amount of tunneling
in bedrock units, some of it horizontal and others with slopes. In
addition to the safety requirements pertaining to construction
activities, Federal regulations pertaining to underground operations
(e.g., \"mining\" activities) come into play. Solutions to these issues
are being developed to address challenges of this type encountered in
the excavation for the NuMI project. These include the standard concerns
about tunneling safety and material movement as the tunneling proceeds.
The choice of construction methods between the use of Tunnel Boring
Machines (TBMs) or the employment of drilling and blasting methods will
most likely be one of economics or availability. However, either
alternative has associated occupational safety considerations.
Provisions for emergency response including underground rescues will be
needed. Again, egress issues relevant to protection of the construction
workers will be of paramount importance.

Given the location within several major aquifers, and the existence for
some facilities of downward slopes at certain locations, it is clear
that stringent measures must be taken to prevent flooding both during
the construction period and thereafter. This problem must be addressed
in harmony with the related environmental protection concerns (see
Section IV). Likewise, any downward slopes in the bedrock units will
require the same attention to the prevention of uncontrolled movements
of heavy objects downhill as in the \"cut and fill\" zone. While such
control measures are well within those encountered in mining operations
elsewhere, they are novel at accelerator laboratories. The existence of
any steep slopes also needs to be carefully considered in planning for
emergency rescue operations that conceivably could be needed during
construction.

During project construction, industrial radiography, a tool commonly
used in general industry, is likely to be employed to assure the quality
if pipe welds, etc. Such radiographic operations, which typically use
radioactive sources of high activity and relatively hazardous compared
with the sources commonly used in particle physics experiments, would
need to be conducted in compliance with the pertinent requirements of
the State of Illinois in order to control the hazard to personnel of
these intense radioactive sources. In the course of construction, other
radiation-generating devices such as soil density gauges and media
water-content probes might also need to be used. Standard procedures
pertaining to such activities should be applied.

**IV. Environmental Protection During the Construction**

All of the candidate facilities will be placed in whole or in part
underground. Some portions will be located near the surface, in the
glacial till, while others will be located underground in the various
rock strata. For the portions near the surface, construction may proceed
by cut and fill techniques similar to those employed to build most of
the present facilities at Fermilab. Erosion control measures similar to
those in practice for a number of years will be employed in accordance
with good engineering practice and Federal and State regulations. Dust
from any spoil piles must be kept under control. Likewise, a storm water
management plan will need to be developed. If 5 acres (2.0 hectares) or
more of land surface are impacted by the construction, a National
Pollutant Discharge Elimination System (NPDES) Stormwater Permit for
construction will be needed which will include specific actions which
must be followed during the construction period. The usual precautions
to prevent pollution from spills of regulated chemicals from the
construction equipment will need to be taken. Noise from construction
activities is not expected to be significantly larger than that
associated with normal civil construction activities in the vicinity of
Fermilab.

The NEPA process described in Section II.A should result in a
determination of the impact of the project on wetlands and or
floodplains. A general description of how any identified effects will be
mitigated will have been developed. For example, if more than 3 acres of
wetlands are identified, it may be necessary for compensatory man-made
wetlands to be created. Rearrangement/enlargement of the Fermilab pond
system might prove to be necessary to compensate for possible
interference with floodplains. It may be especially important to
demonstrate adequate care for floodplains due to significant local
public concerns about flood prevention.

Tunneling in the bedrock units will result in the removal of a
considerable volume of rock, dependent upon project details. The
management of the spoil is a major issue that must be addressed and
provisions for its proper stockpiling provided. In particular, concerns
about dust may be more severe for this material, largely pulverized
rock. The duration of this storage may be temporary for the spoil that
is of marketable quality and longer for that requires reuse at Fermilab
or disposal. This should be carefully planned in accordance with
Fermilab\'s longstanding tradition of placing high importance on
aesthetic issues. The management of spoil materials will need especially
vigorous attention if its removal at any off site locations is needed.
The placement of such a project in any aquifers results in the need to
protect drinking water resources from contamination during construction.
Also, the \"dewatering\" of tunnels as the construction proceeds will
require measure to be developed to prevent the depletion of wells and
also to manage effectively any additional water discharges from this
source.

The storm water management plan will need to take into account any
releases of groundwater generated in the course of \"dewatering\" the
tunnel. Careful hydrogeologic studies need to be performed to understand
the interplay of the construction of the project with the various
aquifers. This must be done to establish with certainty that the
construction activities will not cause significant perturbations of the
local individual and municipal water supplies, either in quality or in
quantity. It should be mentioned that the exact depth of the various
aquifers are not known in detail at all locations involved in the
proposals discussed in this report. Accurate measurements will be
needed, through geological investigations over the entirety of the
affected region. The results can be used to plan a strategy for
preventing the tunnel from serving as a possible path of
cross-contamination from one aquifer to another. During construction
activities, precautions are needed to guarantee that spills of
chemicals, including lubricants and fuels from the construction
equipment, are captured before they enter the groundwater. The presence
of any downward slopes presents special considerations in this regard
that should be addressed.

Tunneling activities can generate considerable noise and vibration.
Should blasting techniques be used, quantitative standards apply to the
amplitude of the vibrations that are allowable at the surface. Noise
exposure, both occupational and to the public at the site boundary and
at off site locations will be an issue that needs to be addressed.

**V. Occupational Safety During the Operations**

**A. [\"Ordinary\" Occupational Safety Hazards]{.underline}**

The occupational safety hazards encountered at all other large particle
accelerator facilities will be found in all of the candidate facilities.
In this section, the focus is on the issues that have been successfully
addressed before, at Fermilab and elsewhere. These have been
successfully addressed by well-known techniques and are simply listed
here, along with the corresponding safety and health needs, for
completeness:

-   The facility will use high current electrical circuits on a large
    scale. Present techniques in managing power distribution and
    providing means to effectively lock out supplies should be adequate
    to address the electrical hazard.

-   Radiofrequency (RF) generation and distribution equipment will be
    used extensively. Present techniques for controlling possible
    exposures to non-ionizing radiation should be sufficient.

-   Large amounts of cables in cable trays will be installed. Current
    methods for addressing fire protection concerns should be adequate.

-   Long tunnels will be present. There is a need to adequately address
    Life Safety Code/fire protection issues to assure adequate
    provisions for egress and adequate means of prevention of and
    response to fires.

-   There will be movements and alignment of large, heavy components.
    There is a need to include considerations in the design related to
    ease of movement of equipment to facilitate the prevention of
    injuries.

All of these issues can be readily addressed by applying the present
collective experience to the design at an early stage.

**B. [Novel Occupational Safety Hazards]{.underline}**

This section is directed to those occupational safety hazards that are
not generally encountered at accelerator facilities. These will all
require consideration in the early planning stages in order to be
addressed in an efficient manner.

*i. Large Scale Use of Cryogens*

This facility requires the extensive use of superconducting materials
and cryogenics in both magnets and RF structures. While these
technologies are relatively new, a number of accelerators world-wide
have developed techniques adequate for addressing them. Provisions will
need to be made for the safe release of cryogens to the surface both
during normal operations and in the event of quenches. Current
accelerator facilities have developed mechanisms for using skilled
engineers to independently review such systems for safety during the
design and commissioning stages. The result has been the development of
a number of standard engineering practices to mitigate both direct
cryogenic hazards and the accompanying oxygen deficiency hazards (ODH).
This general approach, if taken, should adequately address these.

*ii. Ionization Cooling Technology*

Some concepts involve the use ionization cooling, a choice that presents
some novel hazards. The use of liquid hydrogen (LH~2~) is being
considered as a possibility preferable to hazardous or toxic materials.
While this choice may be preferred from environmental protection and
industrial hygiene standpoints due to the lack of the potential for
spills or exposures to hazardous or toxic materials, the fire/explosion
hazard represents an important consideration. In an ionization cooling
system, the LH~2~ cells will be interleaved with RF structures and
magnets that apply a great deal of electrical energy. The impact of the
absorption of energy from the particle beams is also a consideration. In
view of these considerations, a recommended approach would be to convene
a review committee of qualified individuals at the earliest reasonable
state in the design of any facility chosen which incorporates this
technology to assure adequate, cost-effective solutions.

*iii. Life Safety-Egress Considerations*

As during construction, the strong desire to minimize the number of exit
points will render adequate design and engineering with respect to the
Life Safety Code imperative. It is likely that special means of
communication underground will need to be provided, \"refuge\" locations
incorporated into the design, and adequate means of transport of
personnel, both healthy and injured, to the surface established. These
provisions will need to incorporate recommendations of a qualified fire
protection professional at the time of the development of the conceptual
design in order to assure adequate allowances for their costs. Later
involvement of fire protection engineering will also be needed as the
detailed design proceeds.

**VI. Ionizing Radiation Safety During Operations**

**A. [Prompt Radiation Shielding]{.underline}**

All of the possible choices of the future accelerator will likely
require significant amounts of passive shielding to attenuate prompt
radiation to levels acceptable to the members of the public. Indeed,
this fact is implicitly recognized by the proposed siting of these
facilities deep underground. The shielding demands of proton
accelerators are generally recognized to greatly exceed those of
electron machines especially with regard to attenuating the neutrons
produced at large angles. At the forward angles, given the copious
production of muons, and the increased importance of range-energy
straggling at high energies (Va87), the shielding requirements of any of
the new machines increase rapidly with energy and must be
well-understand at the earliest possible stage in the design and in the
NEPA process.

Some detailed understanding of the pertinent requirements must preface
further discussion. Current Department of Energy requirements are not
well-matched to discussions of radiation fields that exist beyond the
boundaries of DOE sites. DOE has specified the annual limits on the
radiation dose equivalent that can be received by occupational workers
and members of the public (see Regulation 10 CFR 835 in WSS 99 and DOE
93). These limits, in all situations expressed to date, pertain to the
dose equivalent delivered to people or to locations where people could
reasonably be. For individual members of the public, the primary limit
is 100 mrem (1 mSv) in a year, not including man-made, medical, or
enhanced natural radioactivity. This limit is intended to apply to all
sources of radiation exposure that a person might receive, even from
non-DOE manmade sources. Special reporting requirements apply when the
annual dose equivalent received by an individual exceeds 10 mrem (0.1
mSv) in a year. DOE has expressed the view that nonoccupational annual
doses to real members of the public are not expected to exceed a few
mrem in a year. In light of public concerns about radiation exposures,
any new facility should be designed to keep the dose that could be
reasonably received by actual members of the public to as small a value
as possible. Higher annual dose equivalents at underground locations
inaccessible to people but beyond the control of host laboratory might
well be allowable. These criteria should be selected early in the NEPA
process with the support of DOE secured. As a convenient reference
point, the average annual radiation dose equivalent received by
individuals living in the United States is about 360 mrem (3600
microSv). Of this exposure, about 300 mrem (3000 microSv) is due to
natural sources, including exposure to radon indoors (NCRP 87).

While the proper shielding against hadrons (mostly neutrons) and
electrons at high energy accelerators is quite well understood, several
new problems must be successfully solved for most of the facilities
under consideration. The likely large dimensions of the facility coupled
with the long ionization ranges and the increased importance of the
range-straggling phenomenon of muons in any new regime of higher energy
will require that the curvature and profile of the earth\'s surface be
taken into account to assure valid shielding calculations. Also, for
some facilities prompt radiation dose due to neutrinos may arise as a
significant consideration for the first time (Mo 99). Both of these
problems have considerable impact upon the selection of the
\"footprint\" of controlled, and uncontrolled property that is needed
for or impacted by the facility.

**B. [Residual Radioactivity of Components]{.underline}**

Several of the accelerators under study will have portions that must
handle beam powers of unprecedented magnitude. As is well known, in the
high energy region, most, but not all, of the radiation effects scale
roughly with the beam power for either accelerated electrons or protons.
In particular the effects of high residual activity levels should be
carefully taken into count at early stages of design of collimation
systems, targets, ionization cooling apparatus and other locations of
possible high losses of beam. The usage of materials in the target
stations of high atomic number and which might not be solids at their
operational temperature merit significant, early attention as plans
proceed and choices are made. Doses that might be received by workers
are an important subject that must be assessed as a part of the NEPA
process. The need to minimize the generation of radioactive wastes and
to eliminate the creation of wastes that contain materials that are both
toxic or hazardous and which contain radioactive is an important concern
at all points during the design effort.

**C. [Airborne Radioactivity]{.underline}**

The production of airborne radioactivity at a future accelerator needs
careful consideration. Federal Regulations promulgated by the U. S.
Environmental Protection Agency (EPA) have established an annual limit
on dose equivalent of 10 mrem (100 microSv) to any member of the public
that can be received as a result of operations of DOE facilities such as
accelerators (CFR 89). Further, the same regulations impose stringent
continuous monitoring requirements if the annual dose equivalent to any
member of the public is to exceed 0.1 mrem (1 microSv) in one year. In
addition, if the level of 0.1 mrem in one year is to be exceeded, then
an application for approval to construct and a notification of startup
must both, in proper sequence, be submitted to the U. S. Environmental
Protection Agency. Given the nature of the proposed facilities and their
extent beyond the present boundaries of the Fermilab site, careful
attention must be paid to the production of airborne radioactivity. The
high beam power of any of the possible machines can lead to the
production of airborne radionuclides that, while generally of short
half-life, have the potential to deliver annual doses above allowable
levels in areas accessible to the public. Care in design should be able
to mitigate these releases.

**D. [Radioactivity in Soil and Groundwater]{.underline}**

The placement of any of the future facilities in both the glacial till
and the underlying bedrock requires that the production of radioactivity
in these hydrogeologic units be given careful attention. Again the
anticipated beam powers require careful consideration of such
radioactivity. Before the exact footprint of any chosen facility is
irrevocably determined, detailed hydrogeologic studies should be
conducted to determine the relevant parameters precisely, as they are
known to vary significant in the vicinity of the Fermilab site. It is
clear that protection of groundwater against contamination with
radioactivity merits early, detailed attention in project design to
assure satisfaction of likely public concerns. It may well be that the
most prudent choice of design objectives might be far below present
regulatory standards for drinking water.

**VII. Non-Radiological Environmental Protection Issues During
Operations**

Operations of the facility should be planned in a way that incorporates
proper measures to control the generation of non-radioactive wastes.
Further, there is a need to address potential spills of hazardous or
toxic materials in a way that fully protects members of the public and
of environmental resources. The detailed attention to these issues will
be required as part of the NEPA process and the designs should provide
information of the quality needed to support all required permit
applications to State and Federal environmental regulatory agencies. For
the operational facility, in any enclosures located deep underground the
cross-contamination of the various aquifers must be prevented and any
dewatering operations must assure that local community or individual
drinking water supplies are not perturbed.

**VIII. Summary**

All of the candidate facilities result in a number of challenges in the
area of environment, safety, and health. Many of these have been
encountered, and effectively addressed, at other accelerator facilities.
Some of the problems are common to other recent projects undertaken at
Fermilab and elsewhere that have resulted in the need to develop new
methods to address them. Given the new scale of any of the candidates,
and their nature, some of these issues may have a greater importance
than found in the present experience. It is concluded here that with
adequate planning in the design stages, these problems can be adequately
addressed in a manner that merits the support of the Laboratory, the
Department of Energy, and the public.

**References**

CFR 89 United States Code of Federal Regulations, Title 40, Part 61,
Subpart H, \"National Emissions Standard for Hazardous Air Pollutants
(NESHAP) for the Emission of Radionuclides other than Radon from
Department of Energy Facilities\", 1989.

CFR 97 United States Code of Federal Regulations, Title 10, Part 1021,
\"\[Department of Energy} National Environmental Policy Act
Implementation Procedures\", 1997.

DOE 93 U. S. Department of Energy, \"Radiation Protection of the Public
and the Environment\", DOE Order 5400.5, January 7, 1993.

Mo 99 N. V. Mokhov and A. Van Ginneken, \"Neutrino Induced Radiation at
Muon Colliders\", presented at the 1999 Particle Accelerator Conference,
New York, New York, Marcy 19-April 2, 1999, FERMILAB-Conf-99/067.

NCRP 87 National Council on Radiation Protection and Measurements,
*Ionizing radiation Exposure of the Population of the United State and
Canada from Natural Background Radiation,* NCRP Report No. 94, December
1987.

Va 87 A. Van Ginneken, P. Yurista, and C. Yamaguchi, \"Shielding
calculations for multi-TeV hadron colliders\", Fermilab Report FN-447
(1987).

WSS 99 \"Fermilab Work Smart Standards Set\", Fermi National Accelerator
Laboratory, http://www-lib.fnal.gov/library/protect/worksmart.html,
November 15, 1999.

[^1]: One unit is 10^4^ • the harmonic normalized to the main field.

[^2]: Calibration in both a dipole and quadrupole magnet are required
    due to the large gradient which we want to measure with high
    accuracy.