Dynamic aperture of the CERN large hadron collider with injection optics

In a hadron collider, the stability of the particle motion is basically determined by the field‐shape imperfections of the superconducting dipoles, especially during the injection flat bottom, when the effect of the persistent currents is maximum and the transverse size of the beam is large. Some precautions can make the motion of the particles less sensitive to the nonlinear components of the guiding fields. Correcting multipoles can be foreseen in the regular cells, to reduce the non‐linear tune‐shift caused by the systematic components of the field errors. The variations of the orbit functions can be limited along the insertions. The closed orbit and the linear coupling can be corrected sufficiently well. Finally the ripple of the power supplies can be reduced as much as possible. Most of these concepts have been embedded in the design of the LHC and their beneficial effects on the dynamic aperture have been extensively evaluated by computer simulations. Cost optimization implies that the dynamic aperture of the LHC has to be mainly limited by the field‐shape imperfections in the dipoles rather than by the errors in the quadrupoles or by the mechanical limitation represented by the primary collimator, inserted to collect the halo particles before they hit the cold bore.