Comparative Study of Heat Transfer from Nb-Ti and Nb$_3$Sn coils to He II

In superconducting magnets, the energy deposited or generated in the coil must be evacuated to prevent temperature rise and consequent transition of the superconductor to the resistive state. The main barrier to heat extraction is represented by the electric insulation wrapped around superconducting cables. In the LHC, insulation improvement is a key point in the development of interaction region magnets and injector chain fast-pulsed magnets for luminosity upgrade; the high heat load of these magnets, in fact, is not compatible with the use of current insulation schemes. We review the standard insulation schemes for Nb-Ti and Nb$_{3}$Sn technology from the thermal point of view. We implement, in an analytical model, the strongly nonlinear thermal resistances of the different coil components including the permeability to superfluid helium of Nb-Ti insulations, measured during the LHC main dipole development. We use such a model to compare Nb-Ti and Nb$_{3}$Sn technologies by taking into account their specific operating margin in different working conditions. Finally, we propose an insulation scheme to enhance the heat transfer capability of Nb-Ti coils.