Lattice and optics options for possible energy upgrades of the Large Hadron Collider

Studies of possible energy upgrades of the Large Hadron Collider (LHC) aim at increasing the current nominal beam energy of 7 TeV in view of expanding the discovery potential and physics reach of the LHC. Some critical aspects of the feasibility of partial or full energy upgrades are studied here, together with novel mitigation measures. Higher beam energies can be realized by pushing the installed main dipoles to their limits or by replacing different fractions of installed magnets. Moreover, a revised lattice design for a full energy upgrade, also known as the high-energy LHC (HE-LHC), is presented. The studies reported focus on the linear optics design and on the lattice layout. In particular, an optics with 60\ifmmode^\circ\else\textdegree\fi{} transverse phase advance in the regular arc cells, meant to alleviate the strength requirements for the main quadrupoles, has been designed in view of possible beam tests during the next LHC run 3. The methods developed in this article, for matching the ring geometry to a reference tunnel, for improving the beam aperture, and for minimizing the required field strengths for new high-energy LHC-like machines, will also be applicable to other future circular collider projects.