Chapter 2 Machine Layouts

**2.1 The Staged Approach and Footprint Description**

The staged approach to the VLHC described in this feasibility study
requires placing two collider rings in a common tunnel. This requirement
imposes constraints on the lattices of the rings as well as on the civil
construction parameters. In this report we describe the design,
construction, installation and maintenance of these two proton-proton
colliders. The first of these, called Stage 1, with a nominal 40 TeV cm
energy uses relatively low-field superferric magnets and use NbTi
conductor. The Stage 1 ring has as its injector the currently operating
\~ 1 TeV Tevatron. The Stage 1 VLHC will operate at an initial
luminosity of 1 × 10^34^ cm^--2^sec^--1^.

![](media/image1.png){width="3.8854166666666665in" height="5.5in"}

After Stage 1 has been in operation for several years carrying out a
frontier physics program the Stage 2 ring will be added and a bypass for
the Stage 1 ring constructed. Stage 2 will have a nominal cm energy of
175 TeV and use the Stage 1 ring operating at 10 TeV as its injector.
The Stage 2 magnets will have an operating field of \~10 T and use
Nb~3~Sn superconductor. The Stage 2 VLHC will have a peak luminosity of
2 × 10^34^ cm^--2^sec^--1^.

One anticipates that the multi-billion dollar investment in the
conventional facility described will serve the world high-energy physics
program over many decades. Therefore the tunnel should be designed to
allow adding as yet unspecified other future collider rings to the
complex.

**2.2 Geometry**

The circumference of the collider is 232 km. The protons take \~78 msec
to circle the ring and their revolution frequency is 1290 Hz. A ring of
this size with arbitrary orientation is shown in Figure 2.1. The overall
footprint is a racetrack. An approximate description is two half circles
of radius = 35 km joined by two long straight sections, each 6 km long.
A more precise description of the proposed footprint is the major arcs
bend the beams 174^o^ and the remaining 6^o^ of bending occurs in the 6
km, which is a cluster of 5 straight sections separated by four bends.
These clustered straight sections are for injection, abort, rf cavities,
interaction regions for two experiments, and for the transfers between
Stage 1 and Stage 2.

Several possible orientations allowing injection from the Tevatron are
discussed in Chapter 4 and several possible geographical sitings based
on geological considerations are shown in Chapter 7. Fermilab is an
excellent site for constructing this frontier physics facility due to
the existence of an injector chain having the required beam
characteristics and the excellent geology of the region. An important
design goal is to put as much as possible on the site especially the
beam dumps for ES&H and public relations reasons.

Grouped below or nearly below the existing Fermilab site are the
underground injection and extraction (abort) beam lines, the abort beam
dump, and the rf acceleration stations. In the long "on-site" straight
section is room for two detectors, separated sufficiently to avoid muon
background from one detector to the other. In this study, it is assumed
that the long straight opposite the Fermilab site is "passive" although
a "far" campus could be developed there.

The depth below surface depends on the specific orientation of the
collider tunnel. The relative merits of three configurations are
discussed in Chapter 5: These are

-   ![](media/image2.png)South Ring with 0.08% incline and depth at
    Fermilab of 235 feet

-   North Ring, no incline and depth at Fermilab of 330 feet

-   North Ring with 0.20% incline and depth at Fermilab of 501 feet

The size of most of the tunnel is 12-foot clear diameter with a 10-foot
wide invert (floor) as shown in Figure 2.2. The Stage 1 collider ring is
placed directly over the high-field ring.

This diameter should be regarded as a minimum. A larger tunnel might be
preferred for reasons of economy, i.e. it might be cheaper to build. A
larger tunnel eases the alignment tolerance and provides more room for
multiple activities during installation. The Civil Construction required
to accommodate the technical components that make up the Stage 1
collider, in addition to the main tunnel will have many wider portions
for special purposes, injection and extraction beam line tunnels, access
shafts, and a large number of caverns of varying sizes. These caverns
will accommodate the beam stop, rf klystrons, kicker magnet power
supplies, groundwater collection caverns and pumping stations, ac power
distribution alcoves, cryo valve alcoves, quench resistor caverns, cryo
systems caverns, and a large number of electronics drawers. These latter
are 5-foot deep by 1-foot in diameter bored into the aisle side of the
tunnel wall to house a variety of power supplies, instrumentation and
controls.

When Stage 2 is implemented additional civil construction will be
required for the bypass around the near side cluster only.

Spaced around the circumference are twelve surface facilities that
during civil construction are used for spoils removal and then serve to
house cryogenics plants and other required machine functions.

***Paragraph:** Describe footprint of a "typical" surface facility. A
few sentences about utilities, how many MW installed, water pumping ...
etc**. Figure**.*

Both low field and high field ring lattices are constructed from optical
modules placed end to end like Lego blocks. Each optical module --- an
arc, dispersion suppressor, or interaction region straight --- has an
overall length which is an integer multiple of L~hc~, the arc half-cell
length. Low and high field modules with the same function are quite
different in implementation. The low field modules use combined function
magnets, while high field modules always use separated function magnets.
For example, the low-field arc half-cell contains two combined function
bending magnets, while the high field arc half cell contains seven
"pure" dipoles. Nonetheless, optical modules in both low-field and
high-field rings always have the same overall length and the same net
bending angle. Another example is the dispersion suppressor modules. In
both low and high field rings a Dispersion Suppressor module is
3 × L~hc~ long, constructed from 4 dispersions suppressor half cells of
length 3/4 × L~hc~ each with 2/3 of the bending of a regular arc half
cell.

Table 2.1 lists the fundamental parameters of the VLHC footprint that
are common to both low and high field rings. Table 2.2 lists the
sequence of optical modules for half the ring --- one arc and the
utility region on the Fermilab site ---in mnemonic form. IR stands for
Interaction Region modules; DM for Dispersion Suppressor modules, and IA
for the Injection/Abort straight section. The footprint geometry for the
far off-site utility region, half way around the VLHC, is identical. The
two utility regions are separated by identical arcs. Table 2.3 lists the
sequence of optical modules in the on-site utility region in greater
detail, including the key for the mnemonics.

**Table 2.1**. Fundamental lattice parameters common to both low and
high field rings

![](media/image3.png){width="3.470138888888889in"
height="2.8381944444444445in"}

**Table 2.2**. Sequence of optical modules around half of the VLHC

![](media/image4.png){width="5.992361111111111in"
height="0.4548611111111111in"}

![](media/image5.png){width="3.9902777777777776in"
height="2.9097222222222223in"}**Table 2.3**. Sequence of optical modules
in the on-site utility region of the VLHC

Figure 2.3 shows a scale layout of the optical modules in the on-site
utility region, including two interaction points (IPs). Injection from
the Tevatron is naturally away from the two IPs, since the VLHC is about
100 meters below the ground at Fermilab. One of the two abort lines per
ring is shown, missing the neighboring IP by about 40 meters. A common
abort dump area is possible for the four beams, approximately 100 meters
from the horizontal crossing point "X" of the low-field ring.

![](media/image6.png){width="3.9902777777777776in"
height="3.321527777777778in"}

**Figure 2.3.** Layout of the on-site utility region of the VLHC,
showing the clearance of the abort lines and muon plumes from the
experiments.

***Comment:** I suggest that here the muon plume is dropped from the
figure but a similar figure with the muon plume is shown in section 2.5
Experimental Areas.*

This arrangement suggests the possibility of a common abort dump area as
shown in Figure 2.4. Also shown are the beam crossovers. An even number
of crossovers are required to keep the circumference of the two counter
rotating beams equal. Since the near and far utility straight sections
have the same lattice structure there are six crossovers around the
circumference.

![](media/image7.wmf)**Figure 2.4**. Single On-site Beam Stop Beam Stop
(not to scale)

***Comment:** I'd like a version of Figure 2.3 without the Stage 2
bypass.*

One advantage of modular construction is that low and high field
lattices are guaranteed to have almost identical footprints, and
therefore to fit in the same tunnel, so long as corresponding low and
high field modules are placed on top of each other. The maximum
transverse offset of the high field ring relative to the low field ring
is only about 6 mm, easily allowing one ring to be placed on top of the
other at all locations in the VLHC tunnel.

Another advantage of modular construction is the ability to
independently modify one particular module --- for example, to increase
a module length in units of L~hc~ --- without adjusting any other
modules. This is only possible if the arc half cell length is an integer
times the bunch spacing, because only then is the total circumference
guaranteed to correspond to an integer number of evenly spaced bunches.

***Paragraph:** magnet counts, lengths, dipole, and for Stage 2, quad
strengths, packing (or filling?) factors (or fractions?).*

***Paragraph:** what's in the gaps; descriptive. **Figure** showing a
straight section with joints, pumps, correction elements.*

The (minimum) bunch spacing is taken to be one 53.1 MHz rf wavelength in
the Tevatron. This guarantees a relatively simple filling scheme from
the Tevatron, with a bunch time spacing of 18.8 ns, a value not
unreasonably challenging to the experiments. Thus the half cell length
is 135.486 m. The value chosen is to make the half cell length to be as
long as possible, without leaving both rings too vulnerable to
systematic field harmonic errors, and without increasing too much the
equilibrium emittance in the high field ring due to synchrotron
radiation. It is quite probable that the current value of L~hc~ is not
optimal, since we do not yet fully understand what are realistic values
systematic magnet harmonics.

***Paragraph:** general discussion of rf parameters and rf systems.
Choice of f~rf~ = 477.938 MHz, superconducting cavities. Flat beams in
Stage 2.*

Synchrotron radiation is a major issue in Stage 2. It limits E and L and
damps the beam. There is a tradeoff between E and L imposed by a total
power limit. The optimum choice will not be determined until the physics
case is developed.

***Add to above paragraph:** numbers of L at 150, 175, 200 TeV, maximum
magnetic field in Stage 2; also synchrotron power.*

***Question:** should this chapter also describe vacuum systems and beam
screen?*

**2.3 Injection Lines**

![](media/image7.wmf)

**Figure 2.5.** Injection Lines. (***redo figure***)

Various suggestions for transporting the 900 GeV protons from the
Tevatron to the Stage 1 ring are described in Chapter 4. In one of these
schemes, shown in Figure 2.5, with the Tevatron operating as a bipolar
proton accelerator, two 3.2 km long beam lines transfer the 900 GeV
extracted beams from the Tevatron to the VLHC ring. The lines drop 120 m
in vertical height at a 4% grade, permitting their use for equipment
transport during magnet installation and tunnel construction. Since the
beam lines are long and the magnets sparse, permanent magnets are used
wherever possible to eliminate cable, cooling water, power supply, and
safety system costs associated with conventional magnets. Focusing and
optical matching is performed with adjustable strength (± 20%) permanent
magnet quadrupoles similar to those developed for NLC work at Fermilab.
The beam vacuum is a conventional stainless steel/ion pump system.

![](media/image8.wmf){width="5.135416666666667in" height="4.05625in"}

**Figure 2.6.** Transfer Line Tunnel

Most of the transfer line is a sparse quadrupole channel as shown in
Figure 2.6. The beam line is placed near the ceiling to keep the tunnel
clear for installation and access. Figure 2.7 shows a possible transfer
line module. Stepping-motor controlled stands are used to eliminate
orbit correctors, power supplies, and corrector magnet cables.
Multiplexed electronics in modules similar to the arcs provide
instrumentation and ion pump power and control functions without a
significant cable plant. Dog-leg bellows provide flexibility for a 1 cm
range of motion. Figure 2.8 shows permanent magnet dipole (0.8 Tesla)
and Quadrupole (60 T/m) beam line elements.

![](media/image9.png){width="5.99375in" height="1.476388888888889in"}

**Figure 2.7.** Girder with Permanent Magnet Quad, X-Y stage, Ion Pump,
and BPMs

![](media/image10.png){width="1.979861111111111in"
height="2.201388888888889in"}
![](media/image11.png){width="1.7048611111111112in"
height="1.895138888888889in"}

**Figure 2.8.** Permanent Magnet elements used for transfer line

### The exact design of the transfer line optics depends on VLHC ring orientation and site considerations. The example beamline shown in Figure 2.9 and described below has most of the essential characteristics of a workable solution.

![](media/image12.wmf){width="6.052083333333333in"
height="4.144444444444445in"}

**Figure 2.9** Example of possible optics for Tevatron-to-VLHC transfer
line

The Lambertson magnets totaling 45 m length and operating at 1.1 Tesla
bend the extracted beam downward at 17 mrad. The remaining 23 mrad of
down bend is completed in the next 200 m using 0.8 T permanent magnet
dipoles with trim dipoles. The length of the down bend is not set by
magnet bend strength but by the requirement of generating sufficient
phase advance to cancel the vertical dispersion caused by the
Lambertson. Site-specific transverse bending may also be required.

The 2.8 km main body of each line is a FODO channel consisting of
permanent magnet quads. The small horizontal bends which may be needed
can be provided by permanent magnet dipoles. The bends are configured to
maintain zero horizontal dispersion in the straight sections between
bends. In the example lattice shown above, a single non-dispersive
horizontal bend of 80 mrad is placed at the center of the transport
line.

At the VLHC end of the line an up bend is required. This section is
mirror image of the down bend. Permanent magnets provide 23 mrad of
vertical bend and the injection Lambertson completes the bend and kills
the vertical dispersion at the injection point. Matching (adjustable)
quadrupoles in the last few cells adjust the transfer line lattice
functions to match the \~250 m cells of the main collider.

## 

## Steering trims are desirable not only to establish an initial orbit centered on each quadrupole, but also for aperture scans to verify a clear aperture in the vicinity of the design orbit. This is accomplished with mechanical quad movers (a step motor/lead screw stage in both the X or Y direction) for each permanent magnet quad. In a FODO channel with 60-degree phase advance, there is a 2:1 ratio between the downstream orbit deflection and the quad motion necessary to produce that deflection. Thus quad movers with a 1 cm range of motion will be able to produce a 2 cm "two-bump" (or a 4 cm "four-bump"), sufficient to probe the full aperture of the beam line.

It is desirable to have some degree of momentum adjustability in the
transport line. Depending on operational experience and cryogenic
upgrades, it may be best to inject at the highest possible energy (up to
1 TeV). Conversely, performance may prove optimal to cycle the Tevatron
as rapidly as possible at a lower energy of 800 GeV to minimize dwell
time at injection. This is an issue for permanent magnets.

The quadrupole FODO channel will operate over a range of energy. The
phase advance per cell is \~65/60/55 degrees at 800/900/1000 GeV. As
discussed previously, adjustable permanent magnet matching quadrupoles
will be placed at each end of the line. The Lambertson will be powered
in series with the Tevatron bus so their bend scales automatically with
energy. The required energy adjustability to the dipole bends can be
accomplished with either a limited number of electromagnets, or
mechanically adjustable permanent magnet dipoles similar to those
described in ref. \[1\].

The extracted beam size in the transfer line is a couple of mm, so that
the aperture requirements will be set by estimates of misalignments and
vacuum considerations. In the long straight FODO channels we propose a
4-inch beam pipe between quadrupoles to maximize vacuum conductance and
minimize pipe alignment requirements. The integrated gradient of the
quads in the FODO channel is 40 T-m/m. This can be attained with
rare-earth permanent magnets. The weight (and approximate cost) of
permanent magnet quadrupoles scale as the cube of the aperture. At
present we consider a 33 mm elliptical beam pipe (corresponding to
25.4 mm pole tip diameter).

4.  **Extraction (abort system)**

**2.5 Stage 1 to Stage 2 transfer and bypass**

***Add:** description of the Stage 1 to Stage 2 transfer.*

![](media/image13.png){width="5.992361111111111in"
height="1.4951388888888888in"}In the transition from Stage 1 to Stage 2
operation, the experiments will remain centered on the same interaction
points. At the same time it is envisaged that they will be upgraded to
take up more space along the beam line, increasing the distance from the
IP to the first magnet, L\*, from 20 m to 30 m. It is therefore
necessary to add a bypass to keep the low field ring beams well clear of
the experiments. This must be done without changing the total low-field
ring circumference. Figure 2.10 is a cartoon of a "proof-of-principle'
by pass which will work, but which has not been design in detail. The
total length of the bypass is approximately 8 km.

**Figure 2.10**. Cartoon of a bypass to transport low-field ring beams
past the experiments in Stage 2 operation

6.  **Experimental Area(s)**

***Discussion of Experimental caverns. Brief summary of what is in
chapters 7 and 8. Figure?***

![](media/image14.png){width="3.9916666666666667in"
height="3.3222222222222224in"}**Figure 2.11** Shows that the muon plume
emanating from one IP misses the other experiment by approximately 70
meters

![](media/image7.wmf)

**Figure 2.12**. Shows Bonnie and Clyde**. *Another version of Bill's
drawing.***

***Paragraph:** Stage 1 operating scenario, time line for injection,
acceleration*

***Paragraph:** Stage 2 operating scenario, time line for injection,
acceleration; mention a few of the basic parameters, proton burnoff
time, IBS time, damping time.*

**References**

\[1\] KEK paper