Beam Dynamics Challenges for FCC-ee

The goals of FCC-ee include reaching luminosities of up to a few 1036 cm-2s-1 per interaction point at the Z pole or some 1034 cm-2s-1 at the ZH production peak, and pushing the beam energy up to ≥175 GeV, in a ring of 100 km circumference, with a total synchrotron-radiation power not exceeding 100 MW. A parameter baseline as well as high-luminosity crab-waist options were described in [1] and [2], respectively. The extremely high luminosity and resulting short beam lifetime (due to radiative Bhabha scattering) are sustained by top-up injection. The FCC-ee design status and typical beam parameters for different modes of operation are reported in [3]. One distinct feature of the FCC-ee design is its conception as a double ring, with separate beam pipes for the two counter-rotating (electron and positron) beams, resembling, in this aspect, the high-luminosity B factories PEP-II, KEKB and SuperKEKB as well as the LHC. The two separate rings do not only permit operation with a large number of bunches, up to a few 10,000’s at the Z pole, but also allow for a well-centered orbit all around the ring as well as for a nearly perfect mitigation of the energy sawtooth, e.g. by tapering the strength of all magnets according to the local beam energy, and for an independent optics control for the two beams. A side benefit at low energies is a reduction of the machine impedance by a factor of twos. A long list of optics and beam dynamics challenges for FCC-ee includes the following: (1) final focus optics design with a target vertical IP beta function of 1 or 2 mm, 50 or 25 times smaller than for LEP2, incorporating sextupoles for crab-waist; (2) synchrotron radiation in the final focus systems and the arcs, with effects on the detector (background, component lifetime) and on the beam (vertical emittance blow up and dynamic aperture); (3) beam-beam effects, including single-turn and multi-turn beamstrahlung; (4) design of the interaction region with a strong detector solenoid with possible compensation solenoids, a large crossing angle and a pair of final-focusing quadrupoles; (5) compatibility of the layout with the design of the hadron collider sharing the same tunnel; (6) RF acceleration system for high voltage (ZH, tt) and high current (Z, WW) with possible staging scenario; (7) impedance, HOM losses and instabilities, especially for high-current “low-energy” operation at the Z pole; (8) the top-up injection scheme; (9) achieving the dynamic aperture required for adequate beam lifetime and for the top-up injection, comprising the optimization of the arc optics; (10) vertical emittance control, including alignment and field errors, lattice nonlinearities, as well as beam-beam effects; (11) energy calibration and transverse polarization; (12) adapting to a non-planar tunnel; and (13) the development of a mono-chromatization for direct H production in the s channel. In the following we consider some of these challenges.