A Method to Evaluate the Field-Shape Multipoles Induced by Coil Deformations

A semi-analytical method to evaluate the effect of coil de-formations 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 mm. The decom-position in modes of the truncated series permits identification of displacements which are dangerous for the multi-polar content and how they could be cured. An application to compare two designs of the LHC dipole is given

Modeling of Coil Pre-stress Loss During Cool-down in the Main Dipoles of the Large Hadron Collider

We describe a finite element mechanical model of the main LHC dipole, based on the geometry and on the properties of its components; coil characteristics are derived from measurements on stacks of conductors. We show how to define equivalent properties of cable blocks that take into account the collaring procedure when it is not explicitly modelled. Numerical results are then compared to experimental measurements of loads and deformations in dipole prototypes. At cryogenic temperature, equivalent properties are used to implement in the model a pressure- dependent thermal contraction factor observed in stack measurements. This allows to forecast the large pre-stress loss during the cool-down observed in the LHC dipole prototypes

Modelization of the Thermo-Mechanical Structure of the LHC Main Dipole and Influence on Field Quality

The mechanical structure of the main LHC dipole is analysed. A finite element model is used to estimate the loads and the deformations at cryogenic temperature. The correct setting of the model parameters is crucial to obtain a reliable model to forecast the influence of design and tolerances on field quality. We discuss how the prestress loss from room to cryogenic temperature experimentally observed in the prototypes can be predicted using the finite element model. An estimate of the influence on field quality of deformations and tolerances due to manufacturing is given

Analysis of Conductor Displacements in the Coil of the LHC Main Dipole by Speckle Interferometry

Magnetic field quality in superconducting magnets mostly depends on conductor position in operational conditions (under pressure, at 1.9 K). For the case of the LHC main magnets, the conductor layout must agree with the nominal design within less than 0.05 mm to met the field quality specifications. Finite element models are a numerical tool to forecast loads and deformations of mechanical structures, and can be used to evaluate conductor displacements. To verify the FEM response at room temperature, we made displacement measurements using speckle interferometer on a short sample of the dipole coils. Experimental results are compared with the numerical calculations, allowing a stringent test of the most critical features of the FEM (interfaces between different materials and coil properties)

Field-shape imperfections of the CERN-LHC dipole arising from mechanical deformations and component tolerances

The stability of the geometry of the superconducting coils is essential to the field homogeneity of the LHC dipole magnets. Mechanical stresses during coil assembly, thermal stresses during cool-down and electromagnetic stresses during operation are the source of deformations of the coil geometry. Additional sources of field-shape errors are the dimensional tolerances of the magnet components and of the manufacturing and assembly tooling. To provide a realistic evaluation of the field-shape imperfections of the LHC dipoles arising from the above effects, appropriate finite-element computations were carried out to model the dipole cross-section in presence of stresses and a first statistical simulation of the effect of the manufacturing tolerances was performed as well

Modeling of random geometric errors in superconducting magnets with applications to the CERN Large Hadron Collider

Estimates of random field-shape errors induced by cable mispositioning in superconducting magnets are presented and specific applications to the Large Hadron Collider (LHC) main dipoles and quadrupoles are extensively discussed. Numerical simulations obtained with Monte Carlo methods are compared to analytic estimates and are used to interpret the experimental data for the LHC dipole and quadrupole prototypes. The proposed approach can predict the effect of magnet tolerances on geometric components of random field-shape errors, and it is a useful tool to monitor the obtained tolerances during magnet production

Thermomechanical properties of the coil of the superconducting magnets for the Large Hadron Collider

The correct definition and measurement of the thermomechanical properties of the superconducting cable used in high-field magnets is crucial to study and model the behavior of the magnet coil from assembly to the operational conditions. In this paper, the authors analyze the superconducting coil of the main dipoles for the Large Hadron Collider. They describe an experimental setup for measuring the elastic modulus at room and at liquid nitrogen temperature and for evaluating the thermal contraction coefficient. The coils exhibit strong nonlinear stress-strain behavior characterized by hysteresis phenomena, which decreases from warm to cold temperature, and a thermal contraction coefficient, which depends on the stress applied to the cable during cooldown. (35 refs)