Ground-up circular Higgs Factory ring design and cell length optimization

A “ground-up” Higgs Factory design methodology is described. For concreteness, numerical parameter choices are drawn primarily from CEPC, the Circular Electron Positron Collider. The goals are to find: (i) optimal parameters, (ii) improved understanding , (iii) a tentative lattice design. As illustration of the method, six chromaticity-corrected lattices, with cell lengths ranging from 45 m to 280 m, all with identical ${\beta }_y=2$ mm or ${\beta }_y=10$ mm intersection region optics, are designed and their properties compared. For simplicity only a single “toy ring,” circumference (76 km), with one interaction point, and a single beam energy (120 GeV) is considered. For the cell-length optimization a figure of merit FOM (essentially integrated luminosity) is maximized consistent with a dimensionless “fine tuning penalty function” or figure of demerit FOD not being allowed to exceed a conservatively chosen upper limit. The tentative recommendation from this investigation is that the optimal CEPC route is (except for obvious changes) to simply copy LEP: 80 m cell length and two-in-one single-ring operation. The main luminosity-increasing improvements are increased radius and power, top-off-full-energy-injection, noninterleaved sextupoles, more than 100 beam bunch operation, and improved intersection region design. Local chromaticity compensation (with its inevitable intense hard X-rays incident on the detectors) is found to be unnecessary. With these changes luminosity in excess of $10^{34}{\mathrm{\text{cm}}}^{-2}{\mathrm{\text{s}}}^{-1}$ is projected to be achievable.