Random Errors induced by the Superconducting Windings in the LHC Dipoles

The problem of estimating the random errors in the LHC dipole is considered. The main contributions to random errors are due to random displacements of the coil position with respect to nominal design and to the variation of the magnetization of the superconducting cable. Coil displacements can be induced either by mechanical tolerances or by the manufacturing process. Analytical and numerical scaling laws that provide the dependence of the random errors due to random displacements on the multipolar order are worked out. Both simplified and more realistic models of the coil structure are analysed. The obtained scaling laws are used to extract from experimental field shape data the amplitude of the coil displacements in the magnet prototypes. Finally, random errors due to interstrand resistance variation during the ramp are estimated