Simulation of Transient Effects in High-Temperature Superconducting Magnets

Particle colliders for high-energy physics are important tools for investigating the fundamental structure of matter. In circular accelerators, the collision energy of particles is proportional to the bending magnetic field and the radius of the machine. As a consequence, circular accelerators such as the Large Hadron Collider at CERN have traditionally relied on high-field magnets made of low-temperature superconductors, confining the particle beams within a complex of acceptable dimensions. This class of superconductors shows a practical limit in the achievable magnetic field in the magnet aperture of about 8T for a Nb-Ti alloy, and 16T for a Nb3Sn compound. Overcoming these limits requires the use of high-temperature superconductors (HTS) in accelerator magnets, in particular rare-earth barium copper oxide (ReBCO) tapes. With respect to the low-temperature counterpart, accelerator magnets based on ReBCO tapes are known to behave differently in terms of magnetic field quality and protection from quench events. The tapes are equivalent to wide and anisotropic mono-filaments, resulting in screening currents detrimentally affecting the magnetic field quality, in particular at low currents. At the same time, quenches are less likely to occur due to the enhanced thermal stability of the tapes, but are more difficult to detect and mitigate. Moreover, the dynamic behavior of accelerator magnets is also affected by the surrounding circuitry which must be taken into account, leading to multiphysics, multirate and multiscale problems. Numerical methods play a crucial role for overcoming the challenges related to magnetic field quality and quench protection. In this work, the magnetothermal dynamics in high-temperature superconducting magnets is modeled by means of an eddy-current problem in the time domain. A mixed field formulation is developed to cope with the nonlinear resistivity law of superconducting materials. The formulation is complemented with distribution functions for the coupling of external voltage and/or current source quantities. Further simplifications are discussed in case of tapes with high aspect ratio, and multifilamentary conductors. Moreover, a field-circuit coupling interface is derived as an optimized Schwarz transmission condition, such that the formulation can be used in field-circuit coupled problems by means of co-simulation methods. The implementation of the formulation in the finite element method is verified against analytical and reference solutions available in literature, and validated against measurements on the HTS-based dipole magnet Feather-M2. As a case-study, the formulation is applied to proof-of-concept ReBCO screens for the passive field-error cancellation in accelerator magnets. The proposed design is called HALO (harmonics-absorbing layered object) as it is made of stacks of tapes arranged in layers which are fully scalable and expandable. The screens are positioned such that their persistent magnetization shapes the magnetic field in the magnet aperture, canceling the undesired field imperfections. Experimental measurements at 77K in liquid nitrogen show a significant reduction of the field error, up to a factor of four. Moreover, numerical extrapolation for accelerator-like conditions shows that a careful design of the superconducting screens allows matching the typical field quality requirements for accelerator magnets.