Iain Dixon, Jack Toth, & Mark Bird
Florida State University operates the National High Magnetic Field Laboratory which is a premier facility for the creation of high magnetic fields for open scientific research in the areas of physics, biology, chemistry, geochemistry, biochemistry, and materials science, with funds from the National Science Foundation. The lab has several high powered magnets of various technologies including resistive, superconducting, and a hybrid of resistive and superconducting coils. The Magnet Science and Technology group within the NHMFL designs, analyzes, and builds most of the magnets at the lab which are also the highest field magnets in the world. The backbone class of magnets at the lab are the Florida-Bitter resistive magnets that generate up to 35 T. The magnets are constructed of stacked high-conductivity disks with alternating ¾ turn polyimide insulators to form a coil with a helical conductive path. A magnet consists of multiple, concentrically nested coils. A typical magnet operates at a nominal 34,000 A and are cooled by water flowing at 95 l/s (1,500 gal/min).
The magnets experience a finite life, limited by the fatigue of the material. The magnet design continuously evolves to improve the life of the disks and to increase the strength of the magnetic field. The coupled-field features available in ANSYS Multiphysics (University Research) are used extensively in the analysis of these coils. Figures 1 and 2 below show a single disk and a small stacked coil respectively. The elongated holes provide flow channels for the cooling holes. The larger hole is for alignment tie-rods.
Figure 1 (Left): Conductors for Florida-Bitter resistive coils. Elongated cooling holes in staggered grid reduce radial force transmission & stress concentrations.
Figure 2 (Right): A partially stacked inner Florida-Bitter resistive Coil
The procedure for performing a mid-plane analysis is straightforward and utilizes the APDL such that a variety of magnet designs can be analyzed by just adjusting the geometric and physical parameters. The first solution set is the coupled electric-thermal problem in which the distribution of current density, voltage, and temperature is determined. The solution is iterated until the integrated current converges to the design current. Results of temperature and current density are shown in Figures 3 and 4 blow:
Figure 3: Temperature distribution across a Florida-Bitter disk
Figure 4: Current density distribution across a Florida-Bitter disk
The subsequent step computes the Lorentz forces from the current density determined from the coupled filed analysis and magnetic field that is determined from a previous axisymmetric analysis of the entire system of coils. From there the structural analysis is performed which typically includes nonlinear stress-strain properties modeled with the multilinear-kinematic option. Figure 5 blow contains the von Mises stress of a symmetric disk
Figure 5: von Mises Stress over a Florida-Bitter disk
Recently the NHMFL started to develop high field powered magnets with configurations other than simple solenoids; specifically a resistive magnet with a mid-plane split is being developed for its own facility. The corresponding coil geometries require complex 3-D FEA models. Figure 6a shows the volumes of a symmetric model for a particular coil of such a magnet. The different colors illustrate winding sections of axially graded current density. Figure 6b shows the finite element plot of the most critical volume which is adjacent to the mid-plane. The interface is modeled with contact elements to model the possible slip-planes that may occur between selected turns in the winding pack. A half-symmetry model is shown in Figure 7.
Figure 6a (Left): FEA model (volumes) for innermost coil of a resistive split magnet.
Figure 6b (right). Finite element plot of the critical region around the mid-plane.
Figure 7: Radial deformation plot for innermost coil of a resistive split magnet with enlarged scale factor to illustrate slippage between regions of graded current density.