SPS efficiency for physics [%]

Fig. 2.46. CERN SPS availability for physics, including the pre-accelerator chain [276].

was typically 80% since the 1990s [276], as is illustrated through the “physics efficiency” in Figure 2.46; this figure includes the PS chain.

Efficiency

In the case of FCC-ee, no time is lost for acceleration and the efficiency only reflects the relative downtime due to technical problems and associated re-filling and recov-ery time. Therefore, the efficiency will be roughly equal to the hardware availability, taken to be at least 80%, minus ∼5% reduction for beam recovery after a failure.

For example, after a hardware failure in the collider rings proper, it will take less than 20 min (1.4% of a day) to refill the collider from zero to nominal beam current.

The assumed efficiency of 75% with respect to the daily peak luminosity is lower than achieved with top-up injection at KEKB and PEP-II. Figure 2.47 presents example evolutions over 24 h of beam currents and luminosity, during PEP-II oper-ation with on-energy top-up injection in 2006 and in 2008, respectively. Beam currents and luminosity are constant, except for a few short interruptions due to hardware failures. The performance of KEKB looked quite similar, as is illustrated in Figure2.48, with examples from 2005 and 2009.

Comparing this performance model with LEP operation, the main difference lies in the on-energy top-up injection scheme, without any luminosity decay, and in the implied absence of ramp-down and acceleration.

Fig. 2.47. Example evolution of PEP-II beam currents and luminosity in 2006 [277] (top) and 2008 [272] (bottom). Stored beam current of the high energy ring (red curve), the low energy ring (green curve), and luminosity (blue curve) of PEP-II over 24 h.

Fig. 2.48. Example evolution of KEKB beam currents and luminosity in 2005 [278] (top) and in 2009 [279] (bottom). Stored beam current of the high energy ring (red line in the top figure), the low energy ring (red line in the middle figure), and luminosity (yellow line in the bottom figure) of KEKB over 24 h.

In summary, the assumed annual physics run time of 185 days, a hardware avail-ability of at least 80%, a corresponding physics efficiency of 75%, and the projected annual luminosities of FCC-ee are supported by the experience from several circu-lar lepton colliders operated over the past 30 years. The FCC-ee design parameters leave sufficient margins to eventually exceedi the design values of both peak and integrated luminosity.

2.10 Running at other energies

The FCC-ee can produce further important physics results by running at additional centre-of-mass energies. Worth mentioning are the possibility of direct H production at 125 GeV using a monochromatisation scheme and the implications of pushing the energy well beyond the t¯t threshold.

2.10.1 s-channel H Production

Direct s-channel H production in e⁺e⁻ collisions, with a collision energy around 125 GeV, allows the measurement of the Hee Yukawa coupling, provided that the centre-of-mass energy spread, σ_ecm, can be reduced to about 6–10 MeV to be compa-rable to the width of the standard model Higgs boson. The natural collision-energy spread at 125 GeV due to synchrotron radiation is about 46 MeV. Its reduction to the desired level can be accomplished by means of monochromatisation [280], which is most efficiently achieved by introducing non-zero horizontal dispersion of opposite sign at the IP for two beams in collisions without a crossing angle. This requires either a change of beam-line geometry in the interaction region or the use of crab cavities to compensate for the existing angle. However, monochromatisation is pos-sible even in the presence of a crossing angle and without crabbing.

The decrease in σ_ecm is described by the monochromatisation factor Λ:

Λ²= 1 + λ²_m

1 + φ²(1 + λ²_m), (2.15) where λ_m = D^∗_xσ_δ/σ_xβ is the ratio between synchrotron and betatron horizontal beam sizes at the IP, and φ is the Piwinski angle. The dependence of the Higgs event rate on luminosity and σecm can be expressed by the function fH:

N˙H ∝ fH= L

pΓ²_H+ σ_ecm² , (2.16)

where σ_ecm =√

2E₀σ_δ/Λ, σ_δ= 5.2 × 10⁻⁴, E₀= 62.5 GeV, Γ_H ≈ 4.2 MeV.

The main parameters for the monochromatisation scheme can be obtained from the following considerations. The experiment needs an energy calibration using resonant depolarisation, which imposes a requirement on the synchrotron tune:

Q_s ≥ 0.05. To get this value, a 60^◦/60^◦ lattice is required with an RF voltage VRF> 0.5 GV. The lattice determines the natural emittance εx≈ 510 pm and the RF voltage constrains σz≤ 2.4 mm. The optimum εy≈ 1.1 pm can be derived from the condition εy≥ 0.002 × εx+ 0.05 pm, where the last term is the contribution from the detector solenoids. β_y^∗should be equal or slightly less than σzto avoid hav-ing a strong hour-glass effect, so 2 mm was chosen. Another possibility is to increase VRF, which makes the bunches shorter so that β_y^∗ can be reduced. On the other hand, beamstrahlung is amplified for short bunches and its negative consequences exceed the advantage of decreasing β_y^∗, so this is not a good choice.

Fig. 2.49. σecm (left) and fH (right) as functions of the bunch population. The colors correspond to head-on collision with D^∗x= 15 cm (red), and collision without crabbing and D^∗x= 50 cm (blue).

The target value of σecm only determines the D_x^∗2/β^∗_x ratio, but there are two reasons why it would be better to reduce them both: firstly, obtaining a large D^∗_x will be difficult with the current design of the interaction region. Secondly, smaller σ_xallows the same luminosity to be achieved with less populated bunches:

this is important because the bunches are rather short. Therefore, β_x^∗ should be about 20 cm, which is a reasonable minimum at this energy. Then the necessary D^∗_x can be found from equation (2.15), so for head-on collisions (i.e. crab cross-ing), a value of about 15 cm is found and for a collision without any crabbing 50 cm is obtained. It is worth noting that the corresponding lattices have not yet been developed and these numbers are used simply to estimate the possible gain from monochromatisation.

The next step is to optimise the bunch population. Here it is necessary to take into account beamstrahlung, which has a very different impact in the crab waist and monochromatisation schemes. In the first case, it can lead to a sig-nificant increase in the energy spread, but does not affect the horizontal emit-tance. By contrast, in the second case εx increases due to dispersion at the IP, which has two consequences: a decrease of Λ, which affects σecm, and an increase in ε_y (due to the betatron coupling), which affects the luminosity. Optimisation should aim at increasing f_H whilst σ_ecm is kept within the range of 6–10 MeV.

The corresponding dependencies are shown in Figure 2.49. It can be seen that, after Np reaches a certain threshold (which is the optimum), fH decreases due to beamstrahlung.

In the crab waist collision without monochromatisation one can obtain f_H ≈ 0.72 with N_p= 3 × 10¹⁰and σ_ecm = 54 MeV. As can be seen from Figure2.49, the Higgs event rate in the monochromatisation scheme without crab crossing will be even smaller and a higher bunch population, which can cause problems, is required to achieve maximum performance. The only advantage of this scheme is a decrease in σ_ecm to the desired level. In collisions with crab crossings, the production rate can be almost doubled with a moderate Np= 3 × 10¹⁰, but this scheme is more com-plicated because it requires crab cavities; nevertheless it is considered as the main option. The corresponding luminosity per IP is about 1.3 × 10³⁵cm⁻²s⁻¹ [281].

This translates into an integrated luminosity of almost 2 ab⁻¹ per IP per year. For a c.m. energy spread commensurate with the natural width of the Higgs boson, the cross section of e⁺e⁻ → H is about 290 ab [282]. Assuming this value, the monochro-matised FCC-ee would produce approximately 500 s-channel H bosons per IP per year.

2.10.2 Higher collision energy

For tt running at a c.m. energy of 365 GeV, the RF system (common for both beams) occupies a total length of about 2 km and provides a voltage of ∼10 GV. In principle, the FCC-ee collision energy could be pushed beyond 365 GeV by installing additional RF systems as was done in LEP-2 or by raising the RF gradient of the existing cavities, provided the other accelerator subsystems, such as the magnets and vacuum chambers, can also handle the higher energy. For example, running at a centre-of-mass energy of 475 GeV would imply a total RF voltage around 30 GV and, at constant RF power, the beam current would drop to about 2 mA at 475 GeV.

Also taking into account the increase of the transverse emittance with beam energy, the luminosity per IP could be about 5 × 10³³cm⁻²s⁻¹ at this collision energy.