Figure 3

Top left: The maximum value of the β and dispersion function over the periodic cell are shown as a function of the cell length. The horizontal dashed lines represent the corresponding value of the maximum β and dispersion function for the nominal FODO cell of the FCC–hh ring. Top right: The maximum of the beam size over the periodic cell and available aperture are shown as a function of the cell length. The horizontal dashed lines represent the corresponding value of the maximum of beam size and the available aperture for the nominal FODO cell of the FCC–hh ring. The target value for the aperture is also shown (dotted-dashed line). Bottom left: The quadrupolar and sextupolar gradients are shown as a function of the cell length. The horizontal dashed line represents the corresponding value of the sextupolar gradient for the nominal FODO cell of the FCC–hh ring. Bottom right: The longitudinal parameters \((\gamma _{\mathrm{tr}}, \eta )\) are shown as a function of the cell length. The horizontal dashed lines represent the corresponding value of \(\gamma _{\mathrm{tr}}\) and η for the nominal FODO cell of the FCC–hh ring. In all plots, the number of CF magnets is also reported (the nominal FODO cell of the FCC–hh ring is based on twelve dipoles)