CERN Accelerating science

Detector and insertion region layout leading to the $\lstar = \SI{40}{m}$ lattice. The IP is located at $(0,0)$.

Layout of the high luminosity interaction region. The layout is antisymmetric around the IP at $(0,0)$.

Reference orbits (solid lines) and closed orbits with crossing angles (dashed lines) in the interaction region.

Layout of the final focus triplet.

Optics of the high luminosity EIR with $\bstar = \SI{0.3}{m}$.

Overall layout of the insertion region between the IP and Q7. For each beam, the closed orbit, the \SI{2}{$\sigma$} envelope and the \SI{15.5}{$\sigma$} envelope for the ultimate $\bstar$ of \SI{0.3}{m} are shown. The beam sizes include a $\beta$ beating of \SI{10}{\%} and a closed orbit uncertainty of \SI{2}{mm}. Magnet apertures and the detector region beam pipe are illustrated with light gray while absorbers are shown in dark gray. The large aperture triplet magnets leave significant aperture margins.

Beam stay clear of the high luminosity EIR for horizontal crossing and ultimate as well as beyond ultimate optics. For $\bstar = \SI{0.2}{m}$ the beam stay clear is just below the minimum of \SI{15.5}{$\sigma$} in the left Q1, suggesting a slightly larger $\bstar$ can be accommodated.

$\beta$ functions and orbit for EIR optics with alternative triplet and $\beta_{x,y}^*=$0.3~m.

Plot showing BSC for $\beta^* =$ 0.15 m, 0.2 m and 0.3~m for the alternative triplet.

$\beta$ Functions and orbit for $\rm 1.2 \times 0.15~m$ flat EIR collision optics with alternative triplet and $\beta_{x}^*=$1.2~m, $\beta_{y}^*=$0.15~m.

Plot showing BSC in triplet for flat and round optics.

Layout of the low luminosity insertion in point B.

Collision optics (top) and injection optics (bottom) for the low luminosity insertion in point~B.

Aperture in the low luminosity insertion in point~B corresponding to a half crossing angle of~\SI{19.5}{ \micro rad} and for the maximum possible half crossing angle of~\SI{44.5}{ \micro rad}. The minimum allowed beam stay clear of $15.5~\sigma$ is indicated in red.

Collision optics (top) and injection optics (bottom) for the low luminosity insertion in point~L.

Crab orbits for $\bstar = \SI{0.3}{m}$ and orbit leakage into the other high luminosity EIR.

Crab orbits for $\bstar = \SI{0.3}{m}$ and orbit leakage into the other high luminosity EIR.

Crab orbits for $\bstar = \SI{0.3}{m}$ and orbit leakage into the other high luminosity EIR.

Crab orbits for $\bstar = \SI{0.3}{m}$ and orbit leakage into the other high luminosity EIR.

Minimum DA over 60 seeds versus $\beta^*$ with and without non-linear correctors.

Minimum Dynamic Aperture in the presence of beam-beam interactions as a function of the crossing angle at the interaction points A and G for the Ultimate collisions optics with $\bstar = \SI{0.3}{m}$ and $\lstar = \SI{40}{m}$~\cite{barrancoFCCweek2018}.

Orbit bump for a \SI{200}{\micro rad} crossing angle required at $\bstar = \SI{0.3}{m}$ in the horizontal plane for IPA and in the vertical plane for IPG.

Orbit bump for a \SI{200}{\micro rad} crossing angle required at $\bstar = \SI{0.3}{m}$ in the horizontal plane for IPA and in the vertical plane for IPG.

Beam-beam long range separations in units of the transverse beam size in the IR for the Ultimate scenario with $\bstar = \SI{0.3}{m}$ with a crossing angle $\theta =\SI{200}{\micro rad}$ and the nominal normalized emittance $\epsilon_n=\SI{2.2}{\micro m}$ (blue dots) and for a reduced normalized emittance of $\epsilon_n=\SI{1.5}{\micro m}$ (light blue dots). The beam-beam long range for the Baseline scenario for $\bstar = \SI{1.1}{m}$ are also plotted with a crossing angle $\theta=\SI{200}{\micro rad}$ (red dots) and with a reduced crossing angle $\theta=\SI{100}{\micro rad}$ (green dots). For this last cases the nominal normalized emittance of $\epsilon_n=\SI{2.2}{\micro m}$ has been considered.

Minimum Dynamic Aperture, evaluated over $10^6$ turns, as a function of the crossing angle in IPA and IPG for H-V alternating crossing scheme for Nominal bunches (the red line) and for PACMAN bunches in the head of a train (the green line) and in the tail of a train (the blue line)~\cite{garciaIpac}.

Two-dimensional tune footprints for particles up to 6 $\rm{\sigma}$ amplitude at the end of the beta squeeze including long-range beam-beam interactions and Landau octupoles powered with negative polarity, for the Ultimate scenario (the green color) and for the Baseline scenario (the red color). For comparison the case with only Landau octupoles powered with negative polarity (maximum strength) is also shown (the blue color). Note that the blue footprint does not depend on $\beta^*$ as Landau octupoles are placed in the arc.

Minimum Dynamic Aperture, evaluated over $10^6$ turns, as a function of the half crossing angle at IPB and IPL, including beam-beam long range interactions in IPB only (the green line), in IPL only (the blue line) and in both IPB and IPL (the red line)~\cite{garciaIpac}.

Two-dimensional tune footprints with head-on collisions in IPA and IPG for the Baseline scenario with $\bstar = \SI{1.1}{m}$ (green color) and for the Ultimate scenario $\bstar = \SI{0.3}{m}$ with a reduced normalized emittance of $\epsilon_n=\SI{1.5}{\micro m}$ rad (blue color).

Collision debris from a single \SI{100}{TeV} c.m. proton-proton inelastic reaction at 5 mm from the interaction point (black) and at the exit of the TAS (red) at \SI{35}{m} from the IP.

3D rendering of the FLUKA geometry of the EIR, including $\sim$\SI{700}{m} of beam line. The picture shows the first $\sim$\SI{500}{m} including the TAS, the inner triplet, the TAN, the separation and recombination dipoles D1 and D2.

Absorbed power profile in the elements of the TAS-D2 region at the ultimate instantaneous luminosity of {$30 \times 10^{34} cm^{-2} s^{-1}$}.

Peak power density profile in the triplet quadrupole coils at the ultimate instantaneous luminosity of {$30 \times 10^{34} cm^{-2} s^{-1}$}. Values are averaged over the radial cable thickness, with an azimuthal resolution of \SI{2}{\degree}. Vertical bars indicate the statistical error.

Peak dose profile in the triplet quadrupole coils for the ultimate integrated luminosity target (\SI{30}{ab^{-1}}). Values refer to a radial and azimuthal resolution of \SI{3}{mm} and \SI{2}{\degree}, respectively. Vertical bars indicate the statistical error.

Peak dose profile in the D1 warm separation dipole coils for the ultimate integrated luminosity target (\SI{30}{ab^{-1}}). Values are averaged over a \SI{3}{mm}x\SI{3}{mm} transverse area. Vertical bars indicate the statistical error.

: Peak dose profile for alternative triplet (round optics) for the ultimate integrated luminosity target (\SI{30}{ab^{-1}}).

: Peak dose profile for the alternative triplet (flat optics) for the ultimate integrated luminosity target (\SI{30}{ab^{-1}}).

Low luminosity triplet geometry as modelled in FLUKA.

Peak power density in the innermost cable of the inner triplet magnets as a function of the distance from the IP, for an instantaneous luminosity of 5$\times$10$^{33}$~cm$^{-2}$~s$^{-1}$. The resolution along the z-axis is 10~cm and the resolution on the azimuthal direction is 2~deg. A radial average is considered along the cable thickness (18.6~mm for quadrupoles and 5~mm for correctors) and the maximum over the azimuthal direction is considered.

Dose distribution averaged over the innermost \SI{3}{mm} of the magnet coils, as a function of z and of the azimuthal angle for vertical (top) and horizontal (bottom) crossing, normalised to an integrated luminosity of \SI{500}{fb^{-1}}.

Dose distribution averaged over the innermost \SI{3}{mm} of the magnet coils, as a function of z and of the azimuthal angle for vertical (top) and horizontal (bottom) crossing, normalised to an integrated luminosity of \SI{500}{fb^{-1}}.

FCC-hh interaction region top view as resulting from MDISim, from -700~m to 700~m. The beam pipe is in blue for beam~1 and in red for beam~2. The transverse dimensions have been scaled up 500 times for visualization.

Top view of the beam pipe 3D-model obtained with MDISim. Dipoles are in violet, drifts in light blue, quadrupoles in orange, collimators in yellow.

Histogram of SR photon generation upstream IPA for the ultimate optics, where IPA is at z=0. {\bf Left plot:}~The two peaks at -450 and -200~m are photons produced by 2~T dipoles that reach the two TAS regions (in red), but few of them hit the Be pipe (in blue). In addition, few photons at are generated by quadrupole magnets downstream -200~m, and none of them hit the Be beam pipe. {\bf Right plot:}~With crossing angle, additional radiation comes from quadrupole magnets in the last 100~m. Radiation coming from MQXD.A2LA.H at -77.6~m and MQXC.B1LA.H at -56.3~m hits the Be pipe.

Histogram of SR photon generation upstream IPA for the ultimate optics, where IPA is at z=0. {\bf Left plot:}~The two peaks at -450 and -200~m are photons produced by 2~T dipoles that reach the two TAS regions (in red), but few of them hit the Be pipe (in blue). In addition, few photons at are generated by quadrupole magnets downstream -200~m, and none of them hit the Be beam pipe. {\bf Right plot:}~With crossing angle, additional radiation comes from quadrupole magnets in the last 100~m. Radiation coming from MQXD.A2LA.H at -77.6~m and MQXC.B1LA.H at -56.3~m hits the Be pipe.

{\bf Left:} Photon energy distribution entering the TAS with crossing angle (in red), and without crossing angle (in blue) for the ultimate optics. {\bf Right:} Photons hitting point in the last -8~m to 8~m Be beam pipe around IPA located at z=0. Without crossing angle (in blue) the photons are uniformly distributed, while With crossing angle (in red) they accumulate towards the center.

{\bf Left:} Photon energy distribution entering the TAS with crossing angle (in red), and without crossing angle (in blue) for the ultimate optics. {\bf Right:} Photons hitting point in the last -8~m to 8~m Be beam pipe around IPA located at z=0. Without crossing angle (in blue) the photons are uniformly distributed, while With crossing angle (in red) they accumulate towards the center.

Proton energy distribution \SI{3}{ m} downstream of IPA for $10^6$ $pp$ collision events.

Proton losses in the first 1 km post IPA (S = 0 m, IPB at S = 5400 m). The top plot shows power deposition per element, the bottom plot shows the energy distribution of the losses per element, both with the TCLD collimators included in the lattice.

FLUKA model used for shower simulations in the dispersion suppressor. The green objects are first the TCLD collimator, followed by a \SI{50}{cm} long mask, both made of INERMET180. Following this is the first quadrupole in the DS. The particles are loaded \SI{63}{cm} before the collimator.

Maximum energy deposition per \si{cm^3} in \SI{5}{cm} bins along the first quadrupole in cell 8 after IPA for baseline and ultimate configurations.

Muon energy distribution at intervals downstream of IPA, generated using DPMJET-III in FLUKA, with no detector or accelerator model.

Theoretical range of collision debris muons in rock.

Cross section of the FLUKA FCC-hh tunnel model. The distance from IPA to each point along the tunnel central line, where muons are observed, is indicated. IPB is located \SI{5.4}{km} away from IPA. The lighter grey area is modelled as standard rock. Note that this model was based on an older version of the FCC-hh lattice.

Muon distribution at different positions along the tunnel, as indicated in Fig.~\ref{fig:hr:tunnel_FLUKA}.