A method to evaluate the field-shape multipoles induced by coil deformations

A semi-analytical method to evaluate the effect of coil deformations on the field-shape imperfections of the LHC dipole is presented. The deformation induced by the collaring procedure and by the thermal stresses is evaluated numerically with a finite element code. The vector field of mechanical displacements is approximated with truncated Taylor and Fourier series. The fitting function agrees with the numerical data to within less that 10 μm. The decomposition in modes of the truncated series permits identification of displacements which are dangerous for the multipolar content and how they could be cured. An application to compare two designs of the LHC dipole is given