Magnetothermal study of a superconducting coil in a carbon therapy cyclotron magnet

Abstract

The C400 is the first compact superconducting cyclotron used for carbon therapy in the world. During the ramp-up procedure from zero to nominal current, the changing magnetic field leads to heat dissipation within the superconducting coil. The aim of this thesis is to predict the magnetothermal behaviour of the superconducting coil during ramp-up. To this end, a finite element model of the C400 has been developed using the GetDP open-source software. Based on a detailed theoretical background, the magnetic and thermal models are first described individually as their numerical parameters are fine-tuned for optimal efficiency. The magnetothermal results are then studied in detail. The hysteresis losses, occurring in superconducting filaments, play a central role in the magnetothermal behaviour of the coil, as the inter-filament coupling losses are found to be negligible. Due to the efficiency of the liquid helium cooling system, the maximal temperature rise in the coil is less than 0.01K. The results are compared with expectations from dimensional analysis and several parametric studies are carried out. Among other results, the ramp-up procedure cannot be performed in less than 20 minutes and an optimized current profile allows the maximal temperature rise to be reduced by 14%. In the second part of this work, a filament model is introduced to compute the hysteresis loss at the superconducting filament scale. The results are compared with analytical approximations, highlighting the complexity of the physical phenomena involved. Among other observations, the critical current density dependence on flux density and the effect of transport current on flux penetration cannot be neglected. Finally, a multi-scale approach, based on the filament model, is proposed and implemented for computing the hysteresis loss within the coil, together with the corresponding temperature distribution. Its robustness significantly improves the accuracy of the results, since analytical approximations underestimate the losses in the intermediate field regime. The observed temperature rise in the coil is small and the filaments should remain in the superconducting state during a regular ramp-up procedure.