Analytical calculation of field error due to radial coil distortions of the LHC low-beta quadrupole magnets

The magnetic field of superconducting accelerator magnets is mainly determined by the current distribution. A distortion of current distribution induces unexpected multipole fields. A simple analytical field calculation with radial distortions, which are described by Fourier series, is developed. Analytical equations which give the correlation between the deformation patterns and the multipole field components are found. The equations are applied to the measurement results for the LHC-MQXA magnets developed by KEK. The radial distortions which introduces normal octupole and twelvepole fields are estimated. The direction of distortions follows the magnet mechanical tendency. The amplitude of those is within the construction errors. A numerical computation applying the distortions to the real cross section is performed. The computation results prove that the analytical equations give the good approximation.