# Machine detector interface for the $\rm e^{+}e^{-}$ future circular collider

M. Boscolo<EMAIL_ADDRESS>O.R. Blanco-Garcia  INFN/LNF  Frascati
Italy
N. Bacchetta1 E. Belli2 M. Benedikt  H. Burkhardt  M. Gil Costa  K. Elsener
E. Leogrande  P. Janot  H. Ten Kate  D. El Khechen  A. Kolano  R. Kersevan
M. Lueckhof  K. Oide  E. Perez  N.A. Teherani  O. Viazlo  Y. Voutsinas and
F. Zimmermann  CERN  Geneva  Switzerland
M. Dam  Niels Bohr Institute  Copenhagen  Denmark
A. Blondel  M. Koratzinos  DPNC/Geneva University  Geneva  Switzerland
A. Novokhatski  M. Sullivan  SLAC  Menlo Park  California  USA
A. V. Bogomyagkov  E. B. Levichev  S. Sinyatkin  BINP SB RAS  Novosibirsk
Russia
F. Collamati  INFN-Rome1  Rome  Italy
1also INFN-Padova  Padova  Italy
2also at University of Rome Sapienza and INFN-Roma1  Rome  Italy

###### Abstract

The international Future Circular Collider (FCC) study [1] aims at a design of
p-p, $\rm e^{+}e^{-}$, e-p colliders to be built in a new 100 km tunnel in the
Geneva region. The $\rm e^{+}e^{-}$ collider (FCC-ee) has a centre of mass
energy range between 90 (Z-pole) and 375 GeV ($t\bar{t}$). To reach such
unprecedented energies and luminosities, the design of the interaction region
is crucial. The crab-waist collision scheme [2] has been chosen for the design
and it will be compatible with all beam energies. In this paper we will
describe the machine detector interface layout including the solenoid
compensation scheme. We will describe how this layout fulfills all the
requirements set by the parameters table and by the physical constraints. We
will summarize the studies of the impact of the synchrotron radiation, the
analysis of trapped modes and of the backgrounds induced by single beam and
luminosity effects giving an estimate of the losses in the interaction region
and in the detector.

##  1 Layout and design criteria

The FCC-ee collider with 100 km circumference and a wide range of beam
energies, from 45.6 to 182.5 GeV, aims at unprecedented levels of energies and
luminosities. The requirements at the collision point for the accelerator and
detector make the interaction region (IR) one of the most challenging parts of
the overall design, this region is named machine detector interface (MDI).
Table 1 summarizes the most relevant beam parameters for the MDI design.

Table 1: FCC-ee beam parameters Most relevant for the IR design. Parameter | Z | $\rm W^{-}W^{+}$ | ZH | $t\bar{t}$
---|---|---|---|---
$\rm E_{beam}$(GeV) | 45.6 | 80 | 120 | 182.5
Luminosity ($10^{34}{\rm cm}^{-2}{\rm s}^{-1}$) | 230 | 28 | 8.5 | 1.55
Beam current (mA) | 1390 | 147 | 29 | 5.4
Particles/bunch ($10^{11}$) | 1.7 | 1.5 | 1.8 | 2.3
Horiz. emittance (nm) | 0.27 | 0.84 | 0.63 | 1.46
Vert. emittance (pm) | 1.0 | 1.7 | 1.3 | 2.9
$\beta^{*}_{x}$ (m) | 0.15 | 0.2 | 0.3 | 1.0
$\beta^{*}_{y}$ (mm) | 0.8 | 1.0 | 1.0 | 1.6
$\sigma^{*}_{x}$ ($\mu$m) | 6.4 | 13 | 13.7 | 38.2
$\sigma^{*}_{y}$ (nm) | 28 | 41 | 36 | 68
SR bunch length (mm) | 3.5 | 3 | 3.15 | 1.97
total bunch length (mm) | 12.1 | 6 | 5.3 | 2.54
RF Acceptance (%) | 1.9 | 2.3 | 2.3 | 3.36
DA energy accept. (%) | 1.3 | 1.3 | 1.7 | -2.8/+2.4
Rad. Bhabha Lifetime (min) | 68 | 59 | 38 | 40
Beamstr. Lifetime (min) | ¿ 200 | ¿ 200 | 18 | 18
|  |  |  |
Figure 1: Schematic layout of the FCC-ee collider rings. The green line
indicates the beamline of the FCC-ee booster and hadron collider FCC-hh. The
plot in the middle shows the two beams trajectories at the IP. Figure 2: IR
layout top view (x-z plane); note the expanded scale for the ordinate ($\pm
200$mm) with respect to the abscissa ($\pm$3m).

To reach the target luminosity of $\rm 2.3\times 10^{36}cm^{-2}s^{-1}$ at the
Z-pole the crab-waist collision scheme is a necessary ingredient together with
pushing the beam current to the limit, obtainable with double rings. The
baseline optics for the FCC-ee double-ring collider is described in Ref. [3].
The main characteristics of the optics design are two interaction points (IPs)
per ring, horizontal crossing angle of 30 mrad at the IP and the crab-waist
scheme with local chromatic correction system. A so-called tapering of the
magnets scales all the magnetic fields with the local beam energy as
determined by the SR. This optics is being improved and modified, for instance
one of the most relevant modification for the IR design is the reduction of
$\beta_{x}^{*}$ to 15 cm at the Z to mitigate the coherent beam-beam
instability [4]. Nominal emittances are very small and especially in the
vertical plane the target value of $\epsilon_{y}=1~{}pm$ at the Z-pole poses
stringent requirements on misalignment tolerances as well as on coupling
correction. The design restricts the total synchrotron radiation (SR) power at
100 MW, thus the stored current per beam varies from 1.4 A at Z to 5.4 mA at
$t\bar{t}$. Following the LEP2 experience where the highest local critical
energy was 72 keV for photons emitted 260 m from the IP [5] the FCC-ee optics
design maintains critical energies from bending magnets below 100 keV starting
from 100 m from the IP; critical energy from the first bend after the IP is
higher, being 691 keV at $t\bar{t}$. An asymmetric optics has been designed to
meet these goals on the critical energy. The asymmetry allows each beam to
come from the inner ring to the IP, to be bent strongly after the IP and to be
merged back close to the opposite ring. Outside the IR, the FCC-ee and FCC-hh
trajectories are on the same footprint while an additional tunnel is necessary
for 1.2 km around the IP in order to allow for the crab-waist collision scheme
with large crossing angle. The collider layout is shown in Figure 1 with the
two beam trajectories.

Figure 2 shows an expanded horizontal view for the region $\pm{3\,{\rm m}}$
from the IP. The free length between the interaction point (IP) and the first
final focus quadrupole (QC1) $\rm L^{*}$ is 2.2 m. The IR is symmetric and the
two beam pipes are merged together at about 1 m from the IP and the distance
between the magnetic centres of the two QC1 for the two beams is only few cm.
In Figure 2 are also shown the main components such as the first focusing
quadrupole named QC1 in yellow. The first element at about 1 m from the IP is
the luminosity counter, magenta in the plot and in red and blue the
instrumentation and cables, followed by the compensating solenoid in light
green and by the screening solenoid starting at about 2 m and out of this
plot. The High Order Mode (HOM) absorber is in dark yellow, the Tungsten
shielding outside the vacuum pipe is in light blue. The detector solenoid, a
cylinder with half-length 4 m and a diameter of around 3.8 m, is outside this
picture. Its peak value is 2 T. To reduce multiple scattering effects in the
luminosity monitor the vacuum chamber from $\pm{0.9\,{\rm m}}$ from the IP
will be made of Beryllium followed by a Copper vacuum chamber throughout the
final focus doublet. Synchrotron radiation mask tips are also shown in the
plot, they are placed in the horizontal plane just in front of QC1 at 2.1 m
from the IP to intercept SR scattered particles. At the mask tips the
horizontal aperture will be reduced from 15 mm to 12 mm. The beam pipe will be
at room temperature and water cooling is foreseen throughout the IR, including
inside the superconducting final focus quadrupoles. The compactness of the MDI
design, as result of the available space to host all the necessary components
is a challenge. An integration study with an assembly concept is in progress,
to study the feasibility of this design. In addition to the elements shown in
Figure 2, also beam position monitors, flanges, bellows, cryostat, vacuum pump
need to be placed.

##  2 Solenoid compensation scheme

The crab-waist collision scheme requires very small vertical beam sizes at the
IP which implies the first final focus quadrupole to be strong and close to
the IP. It needs to be so close to the IP that it is located inside the main
detector solenoid. The additional ingredient for the crab-waist scheme is the
large crossing angle, which brings the two beam trajectories to pass off-axis
from the detector solenoid, inducing also an increase of the vertical
emittance. To handle this unwanted effect, the detector solenoid field maximum
is set at 2 T and, on the other hand, a compensation solenoid is foreseen as
close as possible to the IP. A screening solenoid is also needed to surround
QC1 to avoid transverse beam coupling. A compact design is needed to leave a
large physics detector acceptance; the accelerator components are required to
stay below an angle of 100 mrad from the beam axis. This design gives an
overall emittance blow-up estimate of 0.3 pm for two IPs at the Z-pole.

The stringent requirements of the final focus quadrupoles can be satisfied by
using canted-cosine-theta (CCT) technology. It is an iron-free design with
crosstalk and edge effect compensation, giving a field quality of better than
one unit for all multipoles. Dipole and skew quadrupole correctors can be
incorporated without increasing the length of the magnetic system. The
vertical emittance blow-up due to residual magnetic field has been estimated
with SAD, finding an increase of 0.3 pm. A full mechanical and thermal
engineering analysis has been performed as well. In order to prove
feasibility, a prototype of this design is under construction at CERN.

##  3 IR trapped modes and High Order Mode absorber

The high beam currents produce electromagnetic waves in the IR. The geometry
of the beam pipe in the IR is as constant and smooth as possible to avoid
unwanted electromagnetic trapped modes and heating problems. However, in the
IR the two beams may generate electromagnetic waves where the vacuum chambers
are combined into one near the collision point [6]. This region is shown in
Figure 3.

Figure 3: 3D CAD view of the IR vacuum chamber in the region where two beam
pipes are merged together. Figure 4: HOM absorbers design.

The high order modes (HOM) that interact with a beam particle may cause local
heating in the IR and typically their frequencies are in the range of several
GHz. Other electromagnetic waves, excited by the beam, with a frequency above
the cutoff will travel away from the IR and may cause heating downstream the
ring. 3D calculations have been carried out using CST [7] and HFSS [8] codes.
The numerical simulations show that there is a trapped mode with a frequency
of 3.459 GHz and 2.91 kW power. This effect can be mitigated by HOM absorbers,
with slots oriented perpendicular to the HOM electric field, allowing the mode
field to easily propagate through these slots and, at the same time, the beam
field, will not pass. Water cooled absorbers are above and below the slots.
They will be placed in the region where the two beam pipes are split in two,
and just after the luminosity calorimeter, symmetrically from the IP. Figure 4
shows the HOM absorbers design, which includes a water cooling system to avoid
heating.

##  4 Synchrotron radiation

The large crossing angle together with the high beam energy may induce high SR
in the IR and consequently into the detector. We can state that the SR in the
IR drives the layout design. One of the most significant constraints is the
requirement on the critical energy and power of the synchrotron radiation
generated upstream of the IR that may shine into the detector. An additional
constraint of the FCC-ee layout is the compatibility with FCC-hh, which drives
the infrastructure design. In order to combine the two requests of a large
crossing angle and the need to prevent high energy SR fans from going into the
IP, the IR optics have been designed asymmetrically so that the incoming beam
from both sides comes from the inner ring and the outgoing beam exits to the
outer ring. In this way the outgoing beams are more strongly bent than the
incoming beams thereby lowering the SR energy from the incoming beams.
Independent approaches are used to evaluate the main source of the SR
background in the IR region coming from photons emitted by beam particles
passing through the last bending magnets and by higher amplitude particles in
the final focus quadrupoles.

Table 2: Summary table of the SR coming from the last soft bend upstream the IP. Second column gives the incident number of photons in the central beam pipe per second. $\rm E_{beam}$ | $\rm E_{critical}$ |  $\gamma$ rate on
---|---|---
GeV | keV | central pipe (Hz)
182.5 | 113.4. | $\rm 1.18\times 10^{8}$
175 | 100 | $\rm 1.25\times 10^{8}$
125 | 36.4 | $\rm 1.01\times 10^{7}$
80 | 9.56 | $\rm 7.02\times 10^{5}$
45.6 | 1.77 | $\rm 9.58\times 10^{3}$
Figure 5: Upper plot: MDISim simulation showing the origin of the photons
generated by a beam starting at about -550 m from the IP (see the red arrow);
the IP is at z = 0 m. Lower plot: energy distribution from the SR produced by
the last bend upstream the IP.

MDISim, $\rm SYNC\\_BKG$ and SYNRAD+ are used to evaluate the radiation
critical energy, the SR fans and to design the IR layout including masks,
shieldings and the beam pipe. MDISim [9] is a toolkit that combines existing
standard tools MAD-X [10], ROOT [11] and GEANT4 [12, 13]. It reads the MAD-X
optics files, and uses its twiss output file to generate the geometry and the
magnetic field information in a format which can be directly imported in
GEANT4 to perform full tracking, including the generation of secondaries and
detailed modelling of the relevant processes. $\rm SYNC\\_BKG$ traces beam
macroparticles through sliced magnets and is a modified version of a code
developed at LBNL by Al Clark (see ref. [14] for a detailed description of the
two methods and studies). SYNRAD+ [15] is used to perform a full simulation of
the optical interaction, including reflection as well as absorption, of the
incident radiation with the beam pipe material. It takes as input a geometry
either from CAD or STL format and the magnetic fields and it generates and
tracks SR photons starting from a given beam distribution.

To reduce SR backgrounds to tolerable limits the first criteria was to set a
minimum distance for the bending magnets from the IP and the maximum critical
energy for incoming beam. The synchrotron radiation flux reaching the
detectors can be further reduced by the combination of fixed and movable masks
(collimators), as well as by optimizing surface to reduce X-ray reflection. We
foresee fixed mask tips at 2.1 m upstream of the IP, just in front of the
first final focus defocusing quadrupole, in order to intercept this radiation
fan and prevent the photons from directly striking the central Be beam pipe.
The next level of SR background then comes from photons that strike near the
tip of these masks, forward scatter through the mask and then strike the
central beam pipe. At the top energy, most of these scattered photons will
penetrate the Be beam pipe and then cause backgrounds in the detector. To
reduce the effect of this SR source on the experiment we propose to add a thin
layer (of the order of 5 $\mu m$) of high-Z and high conductivity material
such as gold inside the Be beam pipe. This will also minimize beam pipe
heating from image charge currents. Table 2 is a partial summary of the SR
study with details about the photon rate from the last soft bend upstream the
IP for all the running beam energies of the FCC-ee. In this study the beam has
been considered on-axis. No SR from dipoles or quadrupoles hits directly the
central beam pipe. Figure 5 shows the MDISim simulation for the SR generated
in the last bending magnets before the IP for the t_208_nosol optics for the
top energy.The upper plot shows the origin of these photons in the last
bending magnets, as generated by a beam starting at the red arrow. The lower
plot shows the energy distribution of the SR generated by the last bend before
the IP. These SR photons have been tracked into the CLD and IDEA detectors,
showing good agreement with the $\rm SYNC\\_BKG$ simulation and showing the
effectiveness of the masking system. Figure 6 shows the hits per bunch
crossing with and without the Tungsten shielding.

As a next step more detailed simulations will be performed on the SR, namely
using more realistic optics including the solenoidal field, including
misalignments and realistic beam distributions that may be slightly off-axis
through the final focus quadrupoles. In addition, presently GEANT4 doesn’t
include SR reflection and this effect will be studied as well. SR collimators
to intercept far bends are planned, as from the LEP experience.

Figure 6: Hits per bunch crossing in the different CLD subdetectors (see the
abscissa) due to SR with (blue line) and without (green line) Tungsten
shielding.

##  5 Beam induced and luminosity backgrounds

The deleterious effects of the background is a very important issue in the IR,
detector and Machine Detector Interface designs. Beam induced backgrounds are
scattering processes leading to particles loss; inelastic beam-gas scattering
has been simulated in the MDI region. Scattering of the stored electrons and
positrons with thermal photons responsible for single beam particle losses at
high energies is also presently under study as from [16]. Luminosity
backgrounds are produced at the collision point. Beamstrahlung induced
backgrounds have been studied in full simulation. They generate backgrounds at
the interaction point and are mostly forward directed leaving the IR. Detailed
background studies are in progress to design the MDI region with proper
shieldings and collimators. The impact of machine beam losses in the detector
is being considered with full GEANT4 simulation for all the background
sources. We briefly describe the study performed for these background sources.

###  5.1 Inelastic beam-gas scattering

A precise and effective methodology to perform a detailed study of beam-gas
scattering especially in the IR is provided by MDISim. Beam gas induced
background has been studied in B-factories (PEP-II and KEKB) and in Super-B
factories. SuperKEKB is now starting to benchmark simulation studies with real
data [17].

The MDISim toolkit was used to generate the files needed to perform a full
GEANT4 simulation for the different beam running energies. A constant beam
pipe diameter of 70 mm is considered throughout the ring except for the
section from -10 m to 10 m around the IP, shown in Figure 7. A constant gas
pressure of $10^{-7}~{}Pa$ (or $10^{-9}~{}mbar$) is assumed for our study.

| I | RMDI | RZOOM | RMDI/I
---|---|---|---|---
| [mA] | [MHz] | [MHz] | [MHz/A]
Z | 1390 | $147$ | $29.2$ | $105$
W | 147 | $15.8$ | $3.43$ | $107$
H | 29 | $2.96$ | $0.536$ | $102$
T | 5.4 | $0.526$ | $0.0959$ | $97$
Table 3: Expected particle loss rate both for 1 km of machine section
($R_{MDI}$), and for the $\pm$20 m around the IP ($R_{ZOOM}$), for all the
four energy runs. Figure 7: Loss map in the IR.The loss peaks correspond to
the restriction of the vacuum chamber between the last drift and final focus
quadrupole QC2.

The vacuum chamber in QC2 has a diameter of 40 mm, in QC1 of 30 mm. The
transition is considered in the simulation with conical tapering from 30 mm to
40 mm as well as from 40 mm to 70 mm (from QC2 to the arcs) in about one meter
of longitudinal distance. The beam pipe with magnetic elements was
reconstructed in the simulation from $\pm 850$ m from the IP. Primary
particles were generated starting at -830 m from the IP, with realistic
distributions in transverse phase space, according to the optical parameters
of the beam in that point of the machine, and tracked for about 1000 m.

The simulations were performed for a residual gas consisting of N2 molecules.
This represents a worst case, since the actual residual gas in the beam pipe
is expected to contain only a certain fraction of this molecule. Table 3 gives
the expected particle loss rates both for the whole simulated machine section
and for the $\pm$ 20 m around the IP, for all the four energy runs. We predict
loss rates of roughly 100 MHz per Ampere of beam current around the IR. As
expected, the highest loss rate is found for the Z-pole energy, essentially
due to the high current configuration. IR losses are concentrated in the
regions where the vacuum chamber gets smaller as the beam approaches the
interaction point.

Beam-gas simulation results have been also weighted with a realistic pressure
profile evaluated with MolFlow [18] for the fcc_213 optics at the top energy
for about 600 m upstream the IP. About 40% of increase in the expected losses
has been found.

First estimates of the background induced by these off-energy scattered
particles in the luminosity calorimeter show that the impact is at safe
values, mostly thanks to the high-Z shielding [19].

###  5.2 $e^{+}e^{-}$ pairs and $\gamma\gamma\to$ hadrons

Beamstrahlung induced backgrounds have been simulated with GuineaPig++ [20]
namely coherent and incoherent pair creation (CPC and IPC) and
$\gamma\gamma\to$ hadrons. This effect has been simulated through the detector
with full simulation studies [21]. The Coherent Pair Creation (CPC) is
strongly focused on the forward direction and is negligible at FCC. The
Incoherent Pair Creation (IPC) is expected to be one of the main sources of
backgrounds. The impact of this background source has been evaluated for the
two FCC-ee proposed detectors CLD (Clic Like Detector) and IDEA. The CLD
detector has been derived from CLIC detector model and it has been optimized
for FCC-ee experimental conditions. CLD has a 2 T main solenoid field, with
vertex detector (VXD) with 3 double layers (barrel) and 4 discs (barrel) and a
Silicon tracker. The forward region has a cone of 100 mrad reserved for
accelerator use.

The IDEA detector has a vertex detector (MAPS), an ultra-light draft chamber
PID (DCH) and 2 T field.

The CLD maximum occupancy per bunch crossing for the IPC and SR is low, being
about $\sim 4\cdot 10^{-4}$ in the VXD for the top energy and $\sim 1.6\cdot
10^{-4}$ in the tracker. The drift chamber average occupancy results low as
well, being $\sim$2.9 % for the IPC and $\sim$0.2 % for the SR at the top.

###  5.3 Radiative Bhabha and Beamstrahlung loss map

Radiative Bhaba and Beamstrahlung are luminosity background sources that can
cause beam losses in the IR also due to multiturn effects. GuineaPig++ [20]
and BBBREM [22] are used for the radiative Bhabha scattering generator, then
multiple turns particle tracking is performed with SAD [23] to determine the
IR loss maps. All the beam energies have been considerd, from 45.6 GeV to to
the top energy. At 45.6 GeV, the radiative Bhabhas are all lost up to about 70
m downstream the first IP. At 175 GeV, the radiative Bhabhas are lost mainly
in the first half of the ring, and high energy particles that get eventually
lost reach the second IP. These particles loss distributions are then tracked
into the sub-detectors with a full GEANT4 simulation.

For the Beamstrahlung background, the beam-beam element was inserted at both
IPs and tracking for a thousand turns with full lattice was considered.
Particle losses are mainly concentrated 5 m around the IP in the vertical
plane and losses happen mainly in the first few turns. The impact on detector
performance is still under investigation although we are expecting it not to
be a major issue.

##  6 Conclusions

The FCC-ee Machine Detector Interface baseline conceptual design is ready.
Many details have been studied and work is in progress to develop more and
more realistic simulations. The solenoid compensation scheme foresees a
vertical emittance blow-up of 0.3 pm. Improvements and alternative designs are
on-going.

Beam induced and luminosity backgrounds have been studied. Loss maps have been
evaluated for inelastic beam-gas scattering, and also for radiative Bhabha and
beamstrahlung processes similar study is in progress. Luminosity processes
have been directly simulated in the detectors and incoherent pair creation is
the dominant effect but always at safe values for both detector designs, CLD
and IDEA. At the present level of simulations we find that the SR masking
results are very efficient for protecting the detectors and maximum occupancy
is under control and at safe values.

##  7 Acknowledgments

We thank the FCC-ee team who contributed to discussions related to the
Interaction Region and Machine Detector Interface design.

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