Challenges of the FCC-ee machine
The FCC e+e- collider with target luminosities in the range of 1034 to 1036 cm-2s-1 in 4 interaction points (IPs) has a number of challenges related to the high performance that is required.
With a limit on the synchrotron radiation emitted by one beam of 50 MW, the total beam current is fixed for a given bending radius (currently 11 km for a 100 km tunnel). The total beam current and the associated peak luminosity (for the current parameter set) are shown below.
While at and above 120 GeV the performance can probably be achieved with a single ring and a maximum of 50-100 bunches per beam (both beams share the same vacuum chamber all along the ring) using Pretzel schemes to separate the beams in the arc regions, the high current and large number of bunches required for Z pole and WW threshold operation makes two rings mandatory. In that case a scheme with large crossing angle at the IP (~30-100 mrad full crossing angle) and a crab-waist optics may be the best solution. Such a scheme also has the advantage that the bunch length can be rather long (5-6 mm) as compared to head-on collision where the bunch length must be of the same order than the vertical ß*, i,e. ~ 1-2 mm.
As a consequence of the high luminosity and the strong beamstrahlung (at higher energies) the beam lifetimes are low, down to 15-20 minutes. To ensure efficient operation the beams must be topped up continously from a full energy booster ring.
Optics and emittance challenges
- Such high luminosities can only be achieved with very strong focusing at the IP. While most e+e- colliders so far operated with vertical ß* in the range of 6-15 mm, FCC-ee must operate with ß* of 1 mm (SuperKEKB target is 0.3 mm). Such low ß* requires local chromaticity correction. The IR optics must have a large momentum aperture of 1.5% to 2% and a sufficient dynamic aperture over the enture momentum range. The large momentum aperture is required for beamstrahlung lifetime. It currently seems that 1.5% momentum aperture should be achievable (SuperKEKB), but the last 0.5% will be a challenge. With the latest parameters of FCC-ee 1.5% is sufficient up to the H operation point.
- IR design issues:
- The local chromaticity correction schemes required bending magnets close to the IR to generate a local horizontal dispersion bump. Sextupoles installed at strategic positions provide a chromaticity correction while maintaining a sufficiently large dynamic aperture.
- A side effect of relatively large crossing angles (10-30 mrad full angle) and of the local chromaticity correction schemes are the required bending magnets that generate significant synchrotron radiation. The current estimates imply 1-2 MW of additional SR from those bends in each IR. For 4 IRs, this implies a 10-20% reduction of the beam current (and luminosity) with respect to the reference parameter table.
- The geometry must remain compatible with the FCC-hh layout (which is a copy of the LHC - for the moment).
- The FCC-ee arc lattice must be flexible to provide a range of horizontal emittances for the different energy points.
- The vertical emittance as small as ~1 pm must be achieved. This corresponds to a coupling ratio of the order of 0.1% which is challenging to obtain in such a larger machine where the vertical emittance may be driven by vertical dispersion (itself driven by the alignment and the quality of the corrections). It must be noted that 1 pm corresponds to the best performance achieved in synchrotron light sources.
Beam-beam and beamstrahlung challenges
- The luminosity performance is limited by the beam-beam effect (beam-beam limit, increasing with energy). The working point and lattice must also be optimized for a large beam-beam tune shift. The assumed beam-beam limit as a function of energy is shown n the figure below. The limits have been scaled from the LEP machine.
- The beam-beam tune shift limit may be increased by a factor 2-5 with a crab waist scheme embedded within the local chromaticity correction. It must be noted that for such a scheme a large crossing angle is required (2 rings) and the bunch length must be increased. This scheme favors a 400 MHz RF system which is currently also the baseline for FCC-hh. The parameters for a crab waist scheme a significantly different from the reference table values.
- For the highest energies (H and top) beamstrahlung at the IP may affect the lifetime. The beam parameters must be adapted to optimize lifetime and luminosity. A large momentum acceptance is required, ideally around 2% (see above).
RF system challenges
- At the highest energy the RF system must provide a large total voltage of around 10 GV for a modest beam current of a few mA. The energy loss per turn is shown in the figure below.
- At the Z pole the RF system must be able to cope with very high beam loading from the 1.5 A beam current (each beam).
Polarization of the beams is of interest for energy calibration (resonant depolarization with target accuracy ~ 0.1 MeV on the beam energy) and for physics with longitudinal polarization.
- For such a large ring the sources of energy changes are numerous, for example tides, geological deformation, the present of the booster ring etc. To achieve sub-Mev accuracies the energy must be monitored continuously. Fortunately for energy calibration only a modest amount of transverse polarization is required (few %, sufficient to observe a depolarization). Despite the fact that the Sokolov-Ternov polarization risetime is around 200 hours for FCC-ee at the Z pole, a few percent of polarization should be achievable on a reasonable time scale of ~30 minutes or so. A few non-colliding bunches may be reserved in each beam for regular depolarization scans. At the WW threshold the polarization times are more comfortable and it should be possible to achieve transverse polarization since the energy spread of the beam is still reasonable as compared to the 440 MeV spacing of the spin integer resonances.
- For a meaningful physics program the longitudinal polarization must be at least 40% for each beam. Since this may be difficult to achieve with natural polarization, a dedicated polarizing ring may be considered. The polarized beams would be injected directly into the ring. Spin rotators must be installed on either side of the interaction points to rotate the polarization direction from the vertical plane to the longitudinal plane and back.