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PhD Defence Thomas Nes | Towards a cloverleaf type accelerator magnet

Towards a cloverleaf type accelerator magnet

The PhD defence of Thomas Nes will take place in the Waaier building of the University of Twente and can be followed by a live stream.
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Thomas Nes is a PhD student in the department Energy, Materials and Systems. (Co)Promotors are prof.dr.ir. H.H.J. ten Kate and dr.ir. A.U. Kario from the faculty of Science & Technology and dr. G. de Rijk from CERN.

The thesis delves into the development of a cloverleaf geometry based accelerator magnet made with high-temperature superconductor ReBCO tape. To this, various aspects are researched.

Two tapes are used in this work: tape from Shanghai Superconducting Technology (SST) for the pancake coils, and tape from SuperPower for a demonstrator cloverleaf coil. For predicting the performance of a superconducting magnet, detailed knowledge of the critical surface of the ReBCO tape used is of paramount importance. To this, the first part of the thesis revolves around the development of a fitting process for the critical surface of SST tape using publicly available measurement data. This approach of fitting, rather than simple interpolation, is essential for extrapolating to parameters beyond the established, measured, data range. The critical surface fit of the SST tape is subsequently compared with the critical current values provided by the manufacturer at 77 K, along with the nominal reported critical current density at 4.2 K and 20 T. Additionally, an interpolation method is employed for the SuperPower tape, based on measurement outcomes of a similar tape utilized in the EUCARD2 project. The critical current of the SST tape is measured at 77 K in self-field, aligning with the reported manufacturer's critical current of 400 A.

Among the various strategies aimed at enhancing the quench stability of ReBCO tape-based coils, the implementation of no-insulation technology stands out as a promising avenue. In-depth investigations are undertaken through a comparative study involving four single pancake coils, all identical in size. These coils, featuring inner and outer diameters of 52 mm and 102 mm respectively, are  wound with 10 mm wide tape obtained from Shanghai Superconducting Technology. Two variations of no-insulation coils were fabricated: dry-wound with no interstitial material between the coil-windings, and the other solder-filled, where solder paste is added between the turns. Two different winding techniques were utilized: one employing a single tape, while the other adopts a twin-tape cable configuration with the superconducting layers facing each other. Crucial parameters such as time constants, inter-turn resistances, dynamic voltage behaviour, current distributions, magnetic field behaviour during charging and discharging processes, critical currents, and quench currents are meticulously derived and comprehensively analysed. These findings offer valuable insights into the quench behaviour and stability of no-insulation coils, serving as a basis for potential advancements in accelerator magnet applications and other high-field devices.

An essential aspect of the research pertains to the estimation of the effective time constant for non-insulated windings in accelerator type of magnets. The effective time constant plays a critical role in determining the magnet's responsiveness, which needs to be closely correlated to the increasing momentum of particle bunches in an accelerator. To accurately estimate the effective time constant, an expanded model is proposed that accounts for mutual inductances between coil turns. This refined model provides a more precise estimation, enhancing the understanding of the temporal behaviour of non-insulated coils. Moreover, the study employs spectral analysis to unveil a set of eigenmodes, each characterized by a corresponding characteristic time constant. Among these eigenmodes, the most significant one dictates the overall decay time, which is crucial for the magnet's performance. This comprehensive analysis sheds light on the reasons why certain strategies, such as partial insulation or overcurrent, to reduce the effective time constant are more effective than others, opening up new avenues for optimization and improved performance of accelerator magnets.

A new innovative design approach is proposed for three-dimensional coil layouts and coil-end geometries, considering the geometrical constraints imposed by the large aspect ratio of ReBCO tape (width exceeding thickness). Through a systematic investigation, the research leads to novel design strategies that address various deformation modes of ReBCO tape and meet the requirements for effective coil-end design. The thin strip model, based on classical differential geometry, plays a pivotal role in modelling the large aspect ratio of ReBCO tape as a thin strip surface, yielding valuable insights for design optimization. To ensure the prevention of conductor degradation, new optimization criteria valid for three-dimensional geometries are introduced, emphasizing prevention of conductor creasing, minimization of overall bending energy, and avoidance of over-straining the conductor. These criteria guide the design process for two distinct 3D coil configurations: the helix, well-suited for ReBCO cables and solenoidal magnets, and the canted-cosine-theta, tailored for creating magnets with multipoles of any order. Moreover, a novel design method is proposed, employing Bézier splines for coil-end geometries, which substantially enhances design flexibility compared to conventional methods. Two examples of coil-end geometries generated with Bézier splines, namely the cloverleaf and the cosine-theta coil-end geometry, highlight the efficacy of this innovative design approach.

In a significant practical application, the design of a demonstrator cloverleaf-racetrack magnet is presented, exemplifying a candidate configuration for 20 T accelerator dipole magnets. This design synthesizes valuable insights gained from previous chapters, ensuring a coherent and optimized magnet system. The utilization of non-insulated coils for quench protection allows for transverse redistribution of coil current during quenching, enhancing operational safety and performance. A modelling-based comparison between dry-wound and soldered non-insulated coils is carried out, evaluating mechanical performance and time constant management. The findings indicate that the dry-wound coil exhibits a lower time constant and better mechanical stability, making it a more suitable choice for the cloverleaf-racetrack configuration, if no-insulation technology were to be utilized.

With the prospect of passing over the beam-pipe while minimizing hard-way bending, the cloverleaf configuration presents a practical solution. However, the thesis delves into addressing challenges associated with coil-end design and coil winding, cooling, and operational considerations. Through a detailed examination, an eight-turn cloverleaf coil has been wound using two 12 mm SuperPower tape conductors in parallel, with the ReBCO layers facing each other. 

The presence of 20 turns of 0.1 mm thick copper on both the inside and outside of the coil serves as a stabilizer and facilitates current entry and exit points. Mechanically supporting the coil, the copper is fully soldered on the inside. The coil underwent rigorous testing, including cooling to 77 K and current supply at this temperature. Key parameters, such as critical current, n-value, effective time constants, current distribution, and magnetic field response, are thoroughly examined, providing valuable insights for future coil designs. Finally, a conceptual design of a 10 m long 20 T dipole magnet is presented.