Transient heat transfer in superfluid helium cooled Nb$_3$Sn superconducting coil samples

An experimental setup is operational at the Central Cryogenics Laboratory of the European Organization for Nuclear Research to measure the cooling mechanisms of superfluid $^4$He (He II) from prepared Rutherford-type superconducting cable stacks to a stagnant He II bath. For novel magnets designed for the so-called high-luminosity large hadron collider upgrade, a segment of a fully impregnated Nb$_3$Sn 11T dipole magnet was measured. A dataset on the thermal behavior is presented, with homogeneous heat inputs of up to approximately 4.8 mW cm$^{-3}$ corresponding to an average steady-state temperature of 3.1 K for the inner layer and 4.0 K for the outer layer when cooled via a 1.9 K He II bath. We discuss the steady state as well as transient behavior observed.