### 6.2.3 Vacuum System 

#### 6.2.3.1 Synchrotron Radiation

With a proton energy of 87.5 TeV and a bending radius of 29.9 km, the
critical energy of the synchrotron radiation emitted by the protons is 8
keV, which corresponds to a wave-length of \~1.6 Å. At a peak current of
57.4 mA each beam releases 4.7 W/m and 1.2⋅10^16^ photons/sec/m in the
bending magnets. The total synchrotron radiation power emitted by the
two beams is 9.4 W/m. This, combined with additional heat load
contributions such as resistive wall power loss and emittance growth
related loss due to multipactoring electrons and ion-induced desorption
-- estimated to \<1 W/m/beam all together, would be an excessive heat
load for the cold mass. Thus, a beam screen, maintained at a higher
temperature by a flow of gaseous helium, is inserted inside the magnet
cold bore to intercept this power.

The synchrotron radiation photons impinging on the beam screen desorb
gas molecules from the near surface layer and convert them into a
steadily increasing surface density of loosely bound (physisorbed)
states. These physisorbed surface molecules are easily redesorbed by the
photons, deteriorating the quality of the vacuum in the beam chamber.
Therefore, the beam screen will be perforated over a few percent of its
surface, to allow cryopumping to the 5 K cold bore surface, where the
vapor pressure of all gases (except H~2~ and He) is negligible and the
condensed gas is shielded from synchrotron radiation and ion
bombardment.

#### 6.2.3.2 Beam Screen Cooling

##### 6.2.3.2.1 Optimum Beam Screen Temperature

The cooling of the beam screen is a key issue in the VLHC -- the beam
screen refrigeration power requirement is the leading contributor to the
total cryo-budget. The beam screen refrigeration power requirement is a
strongly varying function of the beam screen operational temperature.
The optimum beam screen temperature balances between the heat load
absorbed by the beam screen refrigeration system and the heat load
absorbed by the cold mass. At low beam screen temperature the heat load
is absorbed mainly by the beam screen, at low thermodynamic efficiency
and thus at high cost. For a high beam screen temperature the cost of
beam screen refrigeration is reduced, but a significant part of the heat
load is transferred from the beam screen by conduction and radiation to
the cold mass, where it is extracted with low thermodynamic efficiency.
The thermodynamic optimum beam screen temperature in the VLHC-2 was
calculated to be 86 K \[1\] for the case of 5 W/m/beam. The base-line
VLHC-2 cryo-concept \[Section 6.2.2\] foresees that the beam screens are
cooled in series with the cold-mass thermal shield by the same high
pressure helium gas. Although both systems have different optimum
operational temperatures when separated, the optimum (average) operating
temperature of the cold mass thermal shield in the combined system is 84
K, and the ensuing average beam screen temperature is 100 K. At this
temperature the beam screen refrigeration system requires a total plug
power of 14.1 MW (both beams). In these conditions the heat load
transferred from two beam screens to the cold mass is 0.26 W/m
(conduction) and 0.07 W/m (radiation). At a cold mass temperature of 5 K
the evacuation of the heat load transferred from both beam screens to
the cold mass represents a plug power requirement of 12 MW for the
complete ring.

##### 6.2.3.2.2 Concept for a Beam Screen Cooling System

Following a calculation procedure outlined in \[1\], the beam screen
cooling system requires 12% of the area enclosed by the cold bore (ID=34
mm), or 110 mm^2^ in cross-sectional area, to be taken up by the coolant
at an average temperature of 100 K, The coolant is high pressure gaseous
helium, entering the beam screen cooling system at 89.3 K, 19.2 bar and
exiting at 108.4 K, 18.1 bar. The beam screen cooling system length is
assumed to be the length of a half-cell (135 m). The total flow rate per
beam screen is 6.6 g/s. In the calculations the stainless steel cooling
duct wall thickness was assumed to be 0.5 mm.

#### 6.2.3.3 Vacuum

##### 6.2.3.3.1 Synchrotron Radiation

The high photon flux is the dominant source of gas -- on the other hand
it is very effective in cleaning the exposed surfaces via photo induced
desorption. The use of superconducting magnet technology results in the
amenity of a low cold bore temperature of \~5 K, at which most gases
have a very low saturation vapor pressure. Therefore most gases get
trapped at the cold bore walls and remain there until the magnets are
warmed up again to room temperature. The pumping capacity of such a
cryo-pump is very large and compatible with the accelerator lifetime. In
addition, the high beam screen temperature decreases the rate of
re-adsorption of gas on the beam screen and thus facilitates the
cleaning process. The higher saturation vapor pressure of H~2~ at 5 K on
the other hand results in the limitation that H~2~ cannot be cryo-pumped
beyond one monolayer. Therefore the cold bore will have to be warmed up
to room temperature at regular intervals (some years) to allow
regeneration of the cryo-pumping surfaces.

##### 6.2.3.3.2 Residual Gas Pressure

The residual beam-tube pressure must be low enough to limit beam-gas
scattering to a level at which the luminosity lifetime of the beam is
not significantly affected, and at which the radiation into the magnet
cold mass remains below a stipulated limit. Estimations of the bounds on
the beam tube gas pressure for the most common UHV gases are listed in
Table 6.1. The beam lifetime limiting pressure is calculated,
stipulating that the beam-gas scattering lifetime be five times larger
than the luminosity lifetime (13 hours). The beam lifetime reduction
stemming from beam-gas scattering related emittance growth is neglected
because of strong radiation damping. The limiting pressure to restrict
the power radiated into the magnet cold mass due to beam-gas scattering
is calculated, stipulating that the beam-gas scattering power be less
than 0.1 W/m/beam.

Table 6.1. Numerical bounds on the beam tube gas pressure for the most
common UHV gases in the VLHC2 -- calculated for each gas "alone" for
ambient room temperature equivalent pressure.

  -------------- ------------ --------------------------- ------------ ----------------------------
  Gas            Max pressure                             Max pressure 
                 for a beam                               for a Beam   
                 gas                                      gas          
                 scattering                               scattering   
                 lifetime of                              power of 0.1 
                 5⋅13 hours                               W/m/beam     
                 (nTorr)                                  (nTorr)      

  H~2~                        35                                       50.3

  CH~4~                       6.6                                      9.3

  H~2~O                       6,2                                      8.7

  CO                          4.2                                      6

  CO~2~                       2.7                                      3.8
  -------------- ------------ --------------------------- ------------ ----------------------------

According to the table, the limiting pressure in the VLHC has to be in
the nTorr range for the most common UHV gases.

##### 6.2.3.3.3 Photo Desorption and Pumping Speed

Photo-induced desorption due to synchrotron radiation with a critical
energy of 8 keV is the most important source of vacuum contamination in
the VLHC. Calculations, based on procedures formerly developed in \[3\],
have recently \[2\] been performed to estimate the quantity of gas
desorbed by synchrotron radiation from a copper coated beam screen.
Copper can be prepared (baked) to have a small initial photo-desorption
coefficient η~0~ (e.g. \~0.0035 H~2~ molecules per photon) and offers
the advantage of a low secondary electron emission coefficient (reducing
the electron cloud effect). It is believed that the initial
photo-desorption coefficient does not increase further with the critical
energy of the photons, above some keV, a range for which reliable
measurements exist \[4\]. The photo-desorbed gas load has to be matched
by a pumping speed to remain within the specified pressure. The CO
equivalent pumping speed required to keep the heat dissipation in the
magnet below 0.1 W/m after one third of an operational year (I⋅t=48
A-hours) is 5.6 lit/sec-m. For H~2~ this pumping speed is 21 lit/sec-m.
During the commissioning phase of the machine the photo-desorption rate
is larger, requiring a larger pumping speed and/or a smaller beam
current. A possible commissioning beam- current profile (for a CO
equivalent pumping speed of 61 l/sec-m) was proposed \[2\]. The current
in the profile is calculated for the condition that the beam-gas
scattering power always remains below 0.1 W/m. It consists of 3 15 hour
cycles with initial currents of 30 mA, 38 mA and 54 mA. The total
conditioning time is thus 45 hours.

##### 6.2.3.3.4 Cryo-pumping

Due to its low saturation vapor pressure, H~2~ cannot be cryo-sorbed on
a 5 K surface beyond one monolayer (\~3⋅10^15^ H~2~/cm^2^). Pumping
speeds of 61 lit/sec-m, as required for conditioning, can be achieved
through cryo-pumping the gas onto the cold (**5** K) magnet bore. The
beam screen surface fraction occupied by pumping slots to obtain 60
lit/sec-m is \~1.5 %. The integrated gas-load set free by the
synchrotron photons during a 20 year accelerator operation is
\~1.1⋅10^19^ H~2~ molecules/m. This represents 3.3 mono-layers of H2.
This gas-load can be managed by periodic warm-up of the machine to allow
regeneration of the cryo-pumping surfaces.

#### 6.2.3.4 Conceptual Beam Screen Design

We propose a vacuum system design (Figure 6.1), similar to the LHC
design \[6\], using a perforated liner, operating at \~100 K. The beam
screen is a 1 mm thick non-magnetic stainless steel (µ~r~\<1.005) tube
with a round cross-section, flattened top and bottom. The space between
it and the surrounding cold bore contains the cooling pipes carrying the
forced flow supercritical helium. The pipes, e.g. made of stainless
steel, are laser welded to the beam screen. The beam screen is centered
within the cold bore by steel/bronze rings, every 0.5 m. The assumed
magnet bore ID is 40 mm. A 1.5-mm gap is needed to allow the insertion
of the cold bore into the

![](media/image1.jpeg){width="2.5458333333333334in"
height="2.357638888888889in"}

Figure 6.1. A schematic view of the beam screen showing supports,
cooling pipes and pumping slots.

magnet. Then, to withstand the quench-pressure, the cold bore tube needs
a wall thickness of 1.5 mm, hence the cold bore inner diameter becomes
34 mm. The supports require an additional 0.75-mm gap between the cold
bore and the beam screen. The remaining aperture for the beam screen
becomes 32.5 mm. The inner dimensions of the beam screen are 30.5 mm in
width and 20 mm in height. To minimize resistive wall heating and
longitudinal beam impedance the interior surface of the screen is
covered by a thin co-laminated layer of high purity copper. The pumping
slots are rounded (1.5 mm wide, 8 mm long)) and randomly distributed to
reduce beam-coupling impedance and resonance effects.

To obtain a pumping speed of 60 lit/sec-m 120 holes are required per
meter of beam screen (e.g. 4 rows of 30 holes, one hole every 5 cm). As
in the case of LHC \[6\] the beam-screen is fabricated from sheet metal
with stamped cooling slots and cold rolled with the copper foil and cold
pressed into the shape of a half tube, which are then welded together.
To eliminate the effects of heat load variations between the apertures
the cooling tubes should cross-over to the other aperture at every half
cell (as proposed in Section 6.2.2).

#### 6.2.3.5 Photon Stops

##### 6.2.3.5.1 Justification

The strong synchrotron radiation in the VLHC 2 results in a
refrigeration power requirement of \~25 MW. Intercepted at room
temperature, the synchrotron radiation heat load would represent a
reduced power at the plug of \~1.9 MW. Motivated by the considerable
cost saving potential the use of room temperature operated photon stops,
which are commonly used in synchrotron light sources \[7\], is under
evaluation. Photon stops are devices that protrude into the beam tube at
the end of each bending magnet and scrape off the synchrotron light beam
emitted in the second magnet up-stream from their location. A
preliminary feasibility study was recently performed \[8\], showing
that, given the arc bending radius in the VLHC of 29.9 km, it is
possible to place photon stops between the magnets with a length and
aperture compatible with the current VLHC design. We believe that
synchrotron radiation in the VLHC is a sufficiently serious issue to
justify even the use of both a traditional beam screen system and photon
stops together. In the case that the photon stops are retractable, the
synchrotron heat load could be shared in a controlled way between both
systems which would allow operation of the accelerator at energies and
luminosities above nominal.

##### 6.2.3.5.2 Geometrical Issues

A geometrical model, based on the assumptions 1) that the bending
magnets are straight and positioned such that the average distance
between the ideal particle orbit and the magnet center is minimal and 2)
that all particles are moving very close to the ideal orbit, allows to
estimate the maximum permissible magnet length and the minimum distance
between the photon stop and the beam. Given that the photon stops are
placed at the beginning of the 3 m long straight section between the
magnets and a 30 mm diameter beam screen aperture, the maximum
permissible bending magnet length is 14 m, which is compatible with the
maximum magnet length imposed by quench protection and transportation
constraints. In this condition the synchrotron radiation emitted from
the beginning of the second up-stream magnet will heat the photon stop
at its base (where it enters the beam tube) and the radiation emitted
from the end of the same magnet will hit its tip. The emission angle of
the SR is 1/γ\~10 µrad. The total radial extension of the photon stop is
1 cm, such that its (minimum) distance from the particle orbit becomes 5
mm.

##### 6.2.3.5.3 Engineering Design

Assuming that a single photon stop intercepts the synchrotron radiation
heat load emanating from one magnet, the thermal load is given with
**\~**5 W/m times the magnet-length, which is 70 W. The required \[9\]
heat exchange surface is \~1 cm^2^ at a coolant flux of 0.2 liter/sec,
given a cooling tube wall thickness of 1 mm and a cooling tube diameter
of 10 mm. The coolant assumed in this calculation is water at room
temperature, the coolant temperature rise is 5 K. The peak heat flux of
0.6 MW/m^2^ remains safely below the critical heat flux of \~2 MW/m^2^.
The largest SR power fraction is transported by photons with a
wave-length of 0.5 Å. The radiation length of steel, which was used as
reference material in the thermal calculation, is \~0.04 g/cm^2^ or
0.05 mm. The synchrotron radiation hits the absorber in a \~0.5 mm (rms)
thin strip. The absorber surface material needs sufficient thermal
conductivity to distribute the heat load over a larger area to dilute
the surface heat flux density to the coolant. Heaters, wrapped around
the cooling tubes, are required to prevent the cooling liquid from
freezing when no synchrotron radiation heat load is present. An
engineering design that satisfies the above mentioned thermal
stipulations was presented \[9\].

![](media/image2.jpeg){width="2.5034722222222223in"
height="2.5729166666666665in"}

Figure 6.2. Photon-stop sketch according to the engineering design
proposal.

According to this design, the photon stop is a T-shaped piece,
consisting of a \~6 cm short copper tube shaped like the beam screen
(but without holes) with flanges at the ends, to which a \~0.5 m long
warm finger, the photon-stop, is attached perpendicularly. The
photon-stop enters the beam screen from the side, where it is hit by the
synchrotron radiation (Figure 6.2). The warm finger consists of an outer
hull with flanges on top and bottom to fix it to the cryostat hull and
the short beam screen piece with vacuum tight seals. Into this hull the
core of the photon-stop is inserted. The core piece consists of the
cooling tubes with the radiation absorber at the end. The short beam
screen piece is inserted into a specially prepared gap in the
beam-screen / cold-bore assembly and welded at each end.

The cold-bore tube is discontinued over the \~10 cm of the photon-stop
to reduce the heat influx from the 100 K beam screen / photon stop
system. The bellows, required to allow the beam tubes contract during
magnet cool-down, are placed in sections further away from the photon
stop. The beam-screen cooling tubes have to be guided out of the beam
screen to bypass the bellows, usually in the form of flexible tubes. In
the case of the photon-stop we propose that the cooling tubes bypass as
well the photon stop system. Furthermore it is assumed that the photon
stop will be placed close to the magnet anchoring point. This offers the
advantage of not having to cope with longitudinal thermal contraction
effects. At the heart of the photon-stop is the radiation absorber, a
hollow cylinder, machined at one end to a special shape. The inside of
the end piece is hollow to allow the cooling liquid to extract the heat
deposited by the synchrotron radiation on its outer surface. The wall
thickness of the absorber is \~ 2 mm. It is made from copper to obtain a
low initial photo-desorption coefficient and a high thermal
conductivity. To reduce the thermal emissivity and the photo-desorption
coefficient the outer surface of the end piece requires a high grade
polishing. The shape of the absorber was optimized to yield low
impedance. It has the shape of a prism () with axial / radial /
azimuthal (with respect to the beam tube) extensions 35 x 10 x 10 mm and
rounded edges. The impedance calculations are discussed next.

##### 6.2.3.5.4 Photon Stop Impedance

The longitudinal impedance of the photon-stop has to be small to 1)
reduce the impedance related power loss per turn and 2) to avoid beam
instabilities, such as for example the microwave instability. The
transverse impedance has to remain below beam instability thresholds,
such as for example for the transverse mode coupling instability (TMCI).
A major issue is whether the photon stops can be treated as independent
-- in the coupled case the sum of the impedances of all coupled devices
would be the relevant parameter, and thus the impedance limitations
would be more stringent. A first estimation of the coupling strength can
be obtained from the damping length of the first order mode. The damping
length was calculated \[10\] to be 4.2 cm, which is sufficiently smaller
than the projected distance between the photon stops of \~14 m, such
that coupling is suppressed.

The beam tube impedance of a copper coated, round beam tube (ID=30 mm)
is of the order of some Ω. The cut-off frequency of a similar pipe is
2π⋅7.6 GHz, which is larger than the largest characteristic beam
frequency in the VLHC, the intra-bunch frequency at collision of 2π·5.8
GHz. A simple, analytical model to calculate the impedance of a "half
ellipsoidal" protrusion in the beam pipe \[11\] predicts , for a total
number of 14500 photon stops and a longitudinal extension of the
protrusion of 3.5 cm and a radial/azimuthal extension of 1 cm, the
longitudinal impedance Z~II~/n becomes 25 mΩ. The transverse impedance
for all photon-stops together becomes Z~⊥~=8 MΩ/m.

An estimate \[10\] of the micro-wave instability threshold bunch
population is 3⋅10^12^, two orders of magnitude larger than the VLHC-2
bunch population. Numerical wake calculations \[10\] indicate a
Transverse Mode Coupling Instability threshold bunch-population of
4.5⋅10^11^, still larger than the design peak number of protons per
bunch. We believe that the photon stops will not cause TMCI. Trapped
modes are of concern in cavity like structures, e.g. holes in the beam
pipe, sharp edges, ..etc. We believe that photon stops, with the
appropriate design, will not be a major cause of trapped modes.

The impedance calculations were performed assuming that the photon stops
are made of e.g. copper. The preliminary calculations have indicated the
viability of this concept. Another possible approach to the design of
this device would be the use of dielectric materials with low electrical
permittivity and high thermal conductivity, such as sapphire or diamond.
Although this approach would be advantageous from an impedance
standpoint, complications are expected to arise in conjunction with the
removal of surface charge and the lack of knowledge on the
photo-desorption coefficients. In addition these solutions could be more
expensive.

##### 6.2.3.5.5 Photon Stop --Vacuum Issues

The strong synchrotron radiation flux impinging on the photon stop
results in a fast clean-up of the photon stop surface. However, it is
necessary to pump the desorbed gas load. According to the engineering
design proposed the beam screen in the photon stop system has no pumping
holes. The desorbed gas load has to diffuse \~5 cm to each side into the
beam tube to reach sections where active pumping to the cold-bore
removes the gas from the beam area. The high temperature of the photon
stop (\~300 K) and the beam screen (\~100 K) certainly prevents
re-adsorption of the desorbed gases and thus the pumping task is
simplified. The high surface temperatures result as well in a high
molecular speed, accelerating the gas diffusion into the adjacent beam
screen regions, where the pumping occurs. On the other hand the high
temperature of the photon stop raises the thermal desorption rate.
Vacuum simulations are required to determine if the longitudinal
diffusion is sufficient to ensure a proper vacuum at the photon stop
locations. Another issue, still to be investigated in further detail,
pertains to the thermal desorption at 300 K, the surface temperature of
the photon stop. It will certainly be necessary to perform a high
temperature heat treatment (bake-out) of the photon stop insert before
installation.

#### References: *{ed. note---for Sec. 6.2.3}* {#references-ed.-notefor-sec.-6.2.3 .Reference-heading}

\[1\] C. Darve et al., "VLHC Beam Screen Cooling", Fermilab Technical
Division Note TD-01-005, 02/01.

\[2\] P. Bauer et al., "Vacuum Calculations for the VLHC - stage 2",
Fermilab, Technical Division Note, TD-01-011, 04/01.

\[3\] W.C. Turner, "Beam Tube Vacuum in Low Field and High Field Very
Large Hadron Colliders", LBNL- 39482, UC 414, presented at the Snowmass
Conference, Oct. 1996.

\[4\] A. Mathewson, O. Groebner, P. Strubin, R, Marin, R. Souchet, AIP
Conf. Proc., 236, 313, 1990.

\[5\] C. Benvenuti, R.S. Calder, G. Passardi, J. Vac. Sci. Techn.,
13,6,1976, p. 1172.

\[6\] O. Groebner, "The LHC Vacuum System", Proceedings of the Particle
Accelerator Conference1997.

\[7\] D. Cheng et al., "Status of the PEP II Low Energy Ring Vacuum
System" Proceedings of the Particle Accelerator Conference1997.

\[8\] I. Terechkine, "Synchrotron Radiation in the VLHC", Fermilab,
Technical Division Note, unpublished note, 01/01.

\[9\] P. Bauer et al., "A Photon Stop for VLHC-2 -- Engineering Design
-- Part 1", Fermilab, Technical Division Note, TD-01-023, 04/01.

\[10\] P. Bauer, N. Solyak, "A Photon Stop for the VLHC-2 -- Impedance
Calculations", Fermilab Technical Division Note TD-01-014, 04/01.

\[11\] S. Kurennoy in M. Tigner, A. Chao, "Handbook of Accelerator
Physics and Engineering", p. 207, World Scientific, 1998.