### 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 total \<1 W/m/beam, 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 83 K, and the ensuing average
beam-screen temperature is 98 K. At this temperature the beam-screen
refrigeration system requires a total plug power of 15 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 14.4 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 87 K, 19 bar
and exiting at 106 K, 18 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-desorption. 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 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
Error! No text of specified style in document..1. The beam lifetime
limiting pressure is calculated, stipulating that the beam-gas
scattering lifetime be five times larger than the luminosity lifetime
(7.5 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 **Error! No text of specified style in document.**.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⋅7.5 hours                              W/m/beam     
                 (nTorr)                                  (nTorr)      

  H~2~                        31.8                                     50.3

  CH~4~                       5.9                                      9.3

  H~2~O                       5.5                                      8.7

  CO                          3.8                                      6

  CO~2~                       2.4                                      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 stage 2 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) which 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 bounds. 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 three 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 (see above), 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 H~2~.
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 Error! No text of specified
style in document..1), similar to the LHC design \[6\], using a
perforated liner, operating at \~100 K. Beam-stability issues related to
the "higher" temperature of the beam-screen are being investigated. 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 **Error! No text of specified style in document.**.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. It is cold-rolled with the copper foil and
cold-pressed into the shape of a half tube, which is 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 the use of both a traditional beam-screen as well as
photon-stops. In the case that the photon-stops are retractable, the
synchrotron heat load can 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 always 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 horizontal 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
SR emitted by the magnet up-stream from the photon-stop passes through
the gap between the photon-stop tip and the beam. The emission angle of
the SR is approximately 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 emitted by one beam over the length of one magnet, the thermal
load is given with **\~**5 W/m times the magnet-length, which is 70 W.
The required 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 \[9\]. 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
forced flow water (\~5 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 (and thickness) 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. A preliminary engineering
design that satisfies the above mentioned thermal stipulations was
presented \[9\].

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

Figure **Error! No text of specified style in document.**.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 pumping slots) 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 Error! No text of specified style in
document..2). The photon-stop assembly 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 to 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 also 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 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. Another
major issue regarding the absorber is scattering of the low energy (long
wave-length) spectrum of the SR. Measures, aiming at the reduction of
the scattered photon-fraction, have to be pursued. One possibility, for
example, is to make the absorber piece hollow, with an entry slot for
the photons. For such a photon-catcher to be efficient, a more detailed
knowledge of the geometrical characteristics of the photon-beam is
required.

##### 6.2.3.5.4 Photon-stop Impedance

The longitudinal impedance of the photon-stop has to be small 1) to
reduce the impedance related power loss per turn and 2) to avoid beam
instabilities, such as the microwave instability. The transverse
impedance has to remain below beam instability thresholds, such as 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 such a pipe is
2π⋅7.6 GHz, which is larger than the largest characteristic beam
frequency in the VLHC, the bunch-length 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, using MAFIA^^ \[10\],
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 of 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 (\~350 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 in the photon-stop
sections. It will certainly be necessary to perform a high temperature
heat treatment (bake-out) of the photon-stop insert before installation.

##### 6.2.3.5.6 Photon-stop --R&D Issues

A R&D plan has been presented, that lists the most important tasks on
the path toward the realization of a photon-stop for stage 2 VLHC
\[12\]. These tasks include 1) in detail investigation of the
characteristics of the stage-2 VLHC SR to allow for an optimization of
the absorber shape, 2) continued impedance calculations to improve the
understanding of the effects of the photon-stop on beam stability
(especially with the use of improved absorber shapes aiming at a
reduction of the photon scattering rate), 3) vacuum simulations to
investigate the magnitude of the pressure bump in the photon-stop
sections and to calculate a suitable conditioning profile, 4) (warm)
testing of prototypes in a synchrotron source photon beam, 5)
cryo-testing of the prototypes and finally 5) full blown vacuum tests in
a VLHC-2 vacuum system mock-up exposed to SR, as they have been
performed in the past for the SSC and LHC projects.

#### 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.

\[7\] S. Sharma et al., "High Heat-Load Absorbers for the APS Storage
Ring" Proceedings of the 1^st^ International Workshop on Mechanical
Engineering Design of Synchrotron Radiation Equipment and
Instrumentation, PSI-Wurenlingen, Switzerland, July 2000.

\[8\] 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.

\[12\] P. Bauer et al., "Photon-Stop R&D Plan", Fermilab Technical
Division Note TD-01-030, 05/01.