A Simplified Structural Model for the Analysis of Shape Deformations of the LHC Superconducting Dipole Cold Mass

In superconducting magnets for particle accelerators the mechanical accuracy along the length of the Cold Mass is one of the crucial parameters to guarantee the field quality needed by beam dynamics. This issue is made even more challenging in the twin-aperture LHC superconducting dipole where tolerances in the 0.3-1 mm range shall be obtained over a length of 15 m, for a Cold Mass of about 30 tonnes which, to minimize thermal losses, is supported in three points only. To reach this goal a number of geometrical checks and analyses are carried out at all stages of magnet assembly, handling, installation and operation. In this paper we present the structural model of the dipole based on which the checks and the analysis are performed, the nature of the geometrical imperfections identified and the temporary or permanent shape modifications predicted.