Numerical Assessment of the Inhomogeneous Temperature Field and the Quality of Heat Extraction of Nb₃Sn Impregnated Magnets for the High Luminosity Upgrade of the LHC

The High Luminosity upgrade of the Large Hadron Collider (HL-LHC) at CERN foresees the installation of Nb ₃ Sn-based quadrupole magnets at selected interaction points of the accelerator. The precise knowledge of each magnet's thermal characteristics and heat extraction performance in response to power depositions during both nominal and ultimate conditions is essential in determining safe operating margins. A 2D numerical framework has been developed to systematically assess the temperature distribution in the combined magnet structure-superfluid He system of each magnet and enveloping cold mass using open-source software. Here a full cross-section of a magnet cold mass is modelled, under the power density distribution expected at the most exposed longitudinal position during accelerator operation at an instantaneous luminosity of 5.0 × 10 ³⁴ cm ⁻² s ⁻¹ , corresponding to the nominal conditions for HL-LHC. Temperature maps and margins are presented for the inner triplet magnets (MQXF) for both horizontal and vertical beam crossing conditions, along with the validation of the design of cold mass cooling channels for heat extraction.