Conceptual design of 20 T dipoles for high-energy LHC

Availability of 20 T operational field dipole magnets would open the way for a 16.5 TeV beam energy accelerator in the LHC tunnel. Here we discuss the main issues related to the magnet design of this extremely challenging dipole: main constraints, superconductor choice, coil lay-out, iron, forces and stresses, and field quality. A tentative cost estimate is also given. The present technology, based on Nb-Ti and now near to be extended to Nb$_{3}$Sn superconductor, would allow reaching 15 T operational field. To reach 20 T, HTS conductors capable to carry 400 A/mm2 at 15-20 T under transverse stress of 150-200 MPa are an essential element.