FEM modeling of multilayer Canted Cosine Theta (CCT) magnets with orthotropic material properties

CCT magnets are becoming more popular, especially as they provide support for each separate turn of a coils,thus significantly lowering the coil stresses and deformations. A four layer nested CCT dipole was designed atCERN as an R&D; effort to study the possibility of using the CCT technology for such a complex magnet. Two pairsof layers produce dipole magnetic fields at 90° angles, allowing a 360° control over the resulting dipole fieldvector. In order to validate the design in terms of the mechanical strength and the allowed deformations, me-chanical FEM models were needed. Three models, having different levels of geometrical details have been de-veloped in the APDL language in the ANSYS software: a 3D model with periodic symmetry and two 2D models,one assuming very simplified geometry of the coils and the formers and the second one with real geometry of thecoils and the formers. Realistic coils properties were accounted for via homogenization technique used to obtainaverage properties of the Nb-Ti strands and the cured resin. Orthotropic behavior of the coil was accounted forvia rotations of the element coordinate systems in the 3D periodic model, and via anisotropic material propertiesfor the detailed 2D model.The electromagnetic (EM) analysis was done for the full 3D model of 1.4 m long nested CCT dipole. The EMforces were mapped to the 3D periodic models and the 2D models. The mechanical analysis consisted of the cool-down to 1.9 K in the first step and subsequent application of the nominal Lorentz forces. In addition, behavior at1.9 K without thermal strains but only EM forces was studied to compute the maximum coil deformations –important to be kept low for good field quality.All three FEM models have been successfully solved providing three estimations of the resulting deformationsand stresses. The most loaded part was the interlayer insulation – due to the thermal strains and large torquebetween the layers, shear stresses above the safe level of 10 MPa were found. Another design was proposed toremove the possibility of the failure of the interlayer insulations via castellations in the formers. Further studieswill include the full 3D model and a comparison to the periodic model, in order to find the most suitableboundary conditions for the periodic model. The detailed 2D model requires further developments in terms ofelectromagnetic force import. As the 2D model requires much less computational power w.r.t. the periodic 3Dmodel, it shows a potential for more realistic geometrical modeling including the Nb-Ti strands and their Kaptoninsulation, to study the behavior of the interface between the strands, the cured resin, and the formers.