Dimensional Changes of Nb$_{3}$Sn Rutherford Cables During Heat Treatment

In high field magnet applications, Nb$_{3}$Sn coils undergo a heat treatment step after winding. During this stage, coils radially expand and longitudinally contract due to the Nb$_{3}$Sn phase change. In order to prevent residual strain from altering superconducting performances, the tooling must provide the adequate space for these dimensional changes. The aim of this paper is to understand the behavior of cable dimensions during heat treatment and to provide estimates of the space to be accommodated in the tooling for coil expansion and contraction. This paper summarizes measurements of dimensional changes on strands, single Rutherford cables, cable stacks, and coils performed between 2013 and 2015. These samples and coils have been performed within a collaboration between CERN and the U.S. LHC Accelerator Research Program to develop Nb$_{3}$Sn quadrupole magnets for the HiLumi LHC. The results are also compared with other high field magnet projects.