Heat transfer through cable insulation of Nb-Ti superconducting magnets operating in He II

The operation of Nb–Ti superconducting magnets in He II relies on superfluidity to overcome the severe thermal barrier represented by the cable electrical insulation. In wrapped cable insulations, like those used for the main magnets of the Large Hadron Collider (LHC) particle accelerator, the micro-channels network created by the insulation wrappings allows to efficiently transfer the heat deposited or generated in the cable to the He bath. In this paper, available experimental data of heat transfer through polyimide electrical insulation schemes are analyzed. A steady-state thermal model is developed to describe the insulation of the LHC main dipole magnets and the Enhanced Insulation proposed for the High Luminosity LHC upgrade (HLLHC), according to the relevant geometric parameters. The model is based on the coupled mechanisms of heat transfer through the bulk of the dielectric insulation and through micro-channels between the insulation tapes. A good agreement is found between calculations and tests performed at different applied pressures and heating configurations. The model allows identifying the heat fluxes in the cable cross-section as well as the dimensions of the micro-channels. These dimensions are confirmed by microscope images of the two insulations schemes.