Analysis of Temperature Uniformity During Heat Treatment of Nb$_{3}$Sn Coils for the High-Luminosity LHC Superconducting Magnets

The High-Luminosity upgrade of the Large Hadron Collider at CERN comprises the implementation of a new generation of high-field superconducting quadrupole and dipole magnets. The dipole fields of up to 12.1 T at nominal current require the use of high-critical-current Nb_3Sn strand for the fabrication of the coils. These coils will be up to 8 m long and represent the longest Nb_3Sn coils so far fabricated for operation accelerator magnets. This brittle A15 phase material requires coil winding prior formation of the superconducting material. The development program at CERN includes the construction of 2-m-long models and full-length prototypes by the wind-and-react technique. The process time and temperature uniformity are stringent during heat treatment and performed inside an EN 1.4841 (AISI Type 314) stainless-steel retort furnace with turbulent flow of Ar atmosphere. During the process, the coil is supported inside a reaction fixture made from 316LN. This paper presents temperature uniformity measurements and results from numerical simulations. The goal is to further improve the heat transfer in combination with turbulent flow generated by a ventilation system. This allows optimizing control parameters for improved heat performance during both the ramping and the dwell time.