FCC-ee and alignment issues E. Gianfelice (Fermilab) Content: - Introduction over FCC - Some accelerator concepts - Results of preliminary studies of effect of misalignments on: • vertical emittance • polarization - Conclusions CERN, March 2017, Final PACMAN Workshop 1/35 < > ≪ ≫ � � ⊖ ? i P �
FCC: an introduction CERN is planning its future at the energy frontier after the completion of the LHC program. Following 2013 recommendations of the Council on European Strat- egy for Particle Physics, CERN has launched a 5 years interna- tional design study for a Future Circular Collider (FCC). 2/35 < > ≪ ≫ � � ⊖ ? i P �
A pp circular collider with a center of mass energy of about 100 TeV is believed to have the necessary discovery potential. (N. Arkani-Hamed, Geneva 2014 Kick-off meeting) The c.m. energy reachable by re-placing LHC dipoles with 20 T dipoles is 33 TeV. • For 100 TeV a new tunnel is needed. • It could first host a e ± collider. • Further options: ions, ep collider. • Site: Geneva, it would use existing accelerators as injectors and exploit existing technical and ad- ministrative infrastructures. 3/35 < > ≪ ≫ � � ⊖ ? i P �
The Standard Model has successfully described the observed phenomena for over 40 years. However it does not have space for some phenomena as neutrinos mass or for dark matter and dark energy which existence has been postulated for explaining recent observations. The physics case for a e ± : • Energy Upgrade: from 45 GeV to 175 GeV beam energy • Large luminosity • Precise energy knowledge of the c.m. energy through resonant depolarization allow for precise measurements and thus for discovery of new physics. Complimentary and synergetic to the pp -collider. 4/35 < > ≪ ≫ � � ⊖ ? i P �
The timetable First milestone: Conceptual Design Report by end 2018! 5/35 < > ≪ ≫ � � ⊖ ? i P �
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Schematic FCC layout K. Oide et al, PRAB 19, 111005 (2016) 7/35 < > ≪ ≫ � � ⊖ ? i P �
Civil engineering • Cooperation with Swiss and French geolog- ical national institutions to set up a 3D model of the Geneva ground. • Cooperation with commercial providers to develop a unique Building Information Mod- eling (BIM) Tunnel Optimisation Tool (TOT), to be used for optimizing depth and site of the tunnel. J. Osborne FCC Infr.&Operation Meet. – First spin-off: ILC tunnel optimisation in Oct 1, 2014 KEK (Japan) • Lifts and cranes for up to 400 m deep shaft... • Removal of 10 000 000 m 3 of debris... Plenty of technical challenges but no show stoppers so far! 8/35 < > ≪ ≫ � � ⊖ ? i P �
The Reference System From B. Goddard et al., LHC Project Report 719 The coordinates { x, y } used by accelerator physicists are the beam position wrt the design orbit at a given longitudinal position, s , along that orbit. 9/35 < > ≪ ≫ � � ⊖ ? i P �
Collider Luminosity Luminosity is one measure of the potential of a collider. It is defined as the counting rate for a process of unit cross section. The rate of events for any other process is therefore R = L × σ For gaussian beams colliding head-on it is L = N 1 N 2 [t] − 1 [ ℓ ] − 2 4 A n b f rev with N 1 , 2 ≡ # of particles/bunch in beam 1 and 2 n b ≡ # of colliding bunches ✎ ☞ ✍ ✌ f rev ≡ revolution frequency A ≡ π σ x σ y 10/35 < > ≪ ≫ � � ⊖ ? i P �
Beam Emittance The size of a beam in a given point of an accelerator depends on the beam emittance, ǫ , and on the value of the β and dispersion functions at that point � � ∆ p � 2 � � σ z = ǫ z β z + D z z ≡ x, y p rms The emittance is the area in 6D phase space occupied by the beam. This area is preserved in a system described by a Hamiltonian. If the 3 degrees of freedom are uncoupled, the invariance applies to each of the 3 planes separately. The emittance may depend on the “beam history”. 11/35 < > ≪ ≫ � � ⊖ ? i P �
The dispersion, D z ( s ) , describes the dependence of the particle orbit upon its energy. It originates from the bending magnets. 30 p 0 p>p 0 20 10 0 y -10 -20 -30 0 5 10 15 20 25 30 x 12/35 < > ≪ ≫ � � ⊖ ? i P �
In a ring where particles radiate in the bending magnets, as it is for relativistic e ± , the beam has no memory and the equilibrium emittance is the result of two counteracting processes: excitation, due to photon emission, and RF damping. Horizontal equilibrium emittance ǫ x = C q γ 2 I 5 J x I 2 with ds β x D ′ 2 x + 2 α x D x D ′ x + γ x D 2 ds 1 � � x I 2 ≡ I 5 ≡ ρ 2 | ρ | 3 In a “flat” designed machine dipoles are lying on a plane, namely the horizontal one, where the design orbit lyes. In such a machine nominally it is D y ( s ) =0: vertical emittance originates only from the cone of photon emission, which sets the lower limit for ǫ y , negligibly small, especially for large rings. 13/35 < > ≪ ≫ � � ⊖ ? i P �
In a real machine however vertical emittance originates from • magnet misalignments – vertical displacement of quadrupoles – roll of horizontal bending magnets – roll of quadrupoles ∗ through D y if D x � = 0 at the quadrupole ∗ through betatron motion coupling – vertical misalignment of sextupoles (used for correcting chromatic effects) 14/35 < > ≪ ≫ � � ⊖ ? i P �
FCC- e ± design relies on ultra-flat beams (from http://tlep.web.cern.ch/) t ¯ Z W W H t Beam energy [GeV] 45.6 80 120 175 ǫ x [nm] 0.2 0.09 0.26 0.61 1.3 ǫ y [pm] 1 1 1 1.2 2.5 β ∗ x [m] 0.5 1 1 1 1 β ∗ y [mm] 1.0 2 2 2 2 σ ∗ x [ µ m] 10 9.5 16 25 36 σ ∗ y [nm] 32 45 45 49 70 15/35 < > ≪ ≫ � � ⊖ ? i P �
β -function in a “drift” (magnet free) region β z ( s ) = β z (0) − 2 α z (0) s + γ z (0) s 2 with γ z ≡ 1 + α 2 α z ≡ − 1 dβ z z 2 ds β z β (s) with α 0 =0 10 β 0 = 1 m 9 β 0 = 0.001 m 8 7 6 5 β β (s) [m] 4 3 2 β (s) [km] 1 0 0 0.5 1 1.5 2 2.5 3 s[m] 16/35 < > ≪ ≫ � � ⊖ ? i P �
FCC-ee IP ( β ∗ y =2 mm) K. Oide et al, PRAB 19, 111005 (2016) A ± 2.2 m long drift is provided for the experiment solenoid and anti-solenoids. 17/35 < > ≪ ≫ � � ⊖ ? i P �
Effect of quadrupoles mis-alignment on closed orbit Orbit sensitivity to quadrupole misalignments < z rms > = F δz Q z = x, y rms with 1 � Σ NQ � i =1 β z,i ( kℓ ) 2 F ≡ √ < β z > i 2 2 | sin πQ z | and Q z ≡ f β /f rev ( betatron tune ) 12000 β x (m) β y (m) 10000 8000 6000 β [m] β ∗ y = 1 mm 4000 QC2L QC2R 2000 � ˆ β y ≃ 9.8 km at QC1R QC1L QC1R 0 -2000 49.982 49.984 49.986 49.988 49.99 49.992 49.994 49.996 49.998 50 s [km] 18/35 < > ≪ ≫ � � ⊖ ? i P �
With frac( Q y )=0.2 for FCC-ee it is a F < y rms > (mm) for δy Q rms =200 µ m all quads 613 123 w/o IPs doublets(*) 141 28 (*) QC1R, QC2R, QC1L,QC2L Huge effect of vertical misalignments on orbit due to • large number of quadrupoles • large contribution of doublet quadrupoles a In the following the focus will be on vertical mis-alignments which are the most important 19/35 < > ≪ ≫ � � ⊖ ? i P �
Effect of quadrupoles mis-alignment on dispersion Non vanishing vertical closed orbit at quadrupoles introduces radial magnetic fields, B x = Ky co , and thus vertical dispersion d 2 D y + K ( s ) D y = e pB x ds 2 � β y ( s ) � y ( Kℓ ) cos ( πQ y − | µ y ( s ) − µ q y | ) y q β q D y ( s ) = co 2 sin πQ y The vertical emittance may become no more negligible! 20/35 < > ≪ ≫ � � ⊖ ? i P �
The FCC-ee orbit problem “Tricks” needed for introducing misalignments errors in the simulation (!): • Move tunes away from integer (“ injection” tunes) – q x : 0.1 → 0.2 – q y : 0.2 → 0.3 • Switch sextupoles off • Add errors to “arc” quads in steps of 5-10 µ m (!) and correct by each step with large number (some hundreds) correctors • Add errors to each doublet quadrupole in steps of 1 µ m (!!) and correct with close by correctors In the process for each quadrupole the misalignment increment ∆ δ Q i is kept constant so that at the end it is δy Q rms =200 µ m (or whatever realistic number). A lengthy procedure not feasible in a real machine. In practice: use “relaxed” optics and one-turn steering through correction dipoles for establishing a closed orbit. 21/35 < > ≪ ≫ � � ⊖ ? i P �
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