Deduction of Steady-State Cable Quench Limits for Various Electrical Insulation Schemes with Application to LHC and HL-LHC Magnets

Undesired quenches of superconducting magnets can be a limiting factor for the operation of the LHC accelerator, both for its forthcoming exploitation at full energy as well as for its future upgrades. An accurate knowledge of the quench limit, the maximum amount of heat deposit the magnets can withstand, is required to be able to prevent beam induced quenches. In this paper we provide an overview of the heat extraction through the multitude of cable insulation schemes used in particle accelerators in the past 20 years and foreseen for the coming years. Based on the relevant heat transfer measurements, we deduce steady-state cable quench limits both for the LHC Nb-Ti magnets and for the future HL-LHC Nb$_{3}$Sn ones. We provide them for different operating conditions and different locations within the coil.