Superconducting Magnet Coil Stresses

Superconducting magnets need to be designed to withstand very large conductor forces, arising from the interaction of large counductor current densities, and magnetic fields. Stress distributions in the coils themselves, and the stresses and deflections of the coil suporting structures need to be considered. These can be predicted using finite element modelling techniques, although the modelling techniques can be quite complex.

The coil can be represented by an appropriate set of orthotropic material properties. These can be established by analytical methods, or by detailed 2d sub-modelling, or a combination of both. Ansys software also allows the creation of super-elements which can be used to model entire coils yet resolve stresses at conductor level. The magnetic loads can be transferred to the coil stress problem after having been modelled either using Ansys EMAG or other software packages, for example Vector Fields Opera 3d.

Intra-coil forces and inter-layer behaviour could be modelled using the non-linear contact capabilities in Ansys, although an approach based on sophisticated use of nodal constraint equations offers big advantages in terms of run times, since the problem is linear. In order to implement this, the Ansys Parametric Design Language offers almost unlimited possibilites for the manipulation of nodal and element coordinate systems and the efficient definition of large nubers of constraint equations. APDL is especially powerful for this application if the coil geometries are not simple, for example, saddle or bedstead shaped coils.

For consideration of the coil supporting structures, both static and transient finite element models are often used. A static model can be used to predict the loads that the supporting structure must bear under normal conditions. Structure stiffness must be sufficient to ensure low deflections and mechanically stable coils. During a quench, the rapid collapse of magnetic field induces eddy currents in any surrounding metalwork. The co-existance of induced currents and magnetic field give rise to a force distribution on any metalwork which can be substantial. Large enough to lead to the self-destruction of the magnet, if the quench loads are not taken into account. The affected metalwork could be the supporting structure for the magnet coils, or the helium can or vacuum chamber.