Bernhard Auchmann

We present a predictive multiscale modeling workflow for Nb ₃ Sn Rutherford cables that bridges strand and cable scales to support the design of accelerator magnets in the 14 T range. This experimentally validated framework enables prediction of critical current reduction under load of Nb ₃ Sn Rutherford cables. The workflow is parameterized in strand and cable architecture, allowing it to be applied across cable designs; as done here on two 21-strand cables of different design (CD1 and SMACC-HF), differing most notably in strand diameter and Cu/non-Cu ratio. The workflow integrates a cabling model capturing strand transposition and compaction-induced deformation, a Python tool for generating FEM-ready 2D cross-sections, homogenization of the Nb ₃ Sn interfilamentary region with inter-strand contact modeling, and a linkage connecting simulated strain to critical current reduction. The workflow was mechanically validated against 10-stack Rutherford cable measurements at 77 K, with the simulated macroscopic stress–strain slope matching the measurement to within 6% in virgin loading and 0.1% in reloading. The predicted critical current reduction was validated against the compression BOX experiment. Across the 10–250 MPa transverse-pressure range covered by the experiments, the predicted cable critical current agrees with the measurement to a mean absolute error of ⩽ 3.2% for CD1, where I c was taken from an independent strand measurement and ⩽ 0.9% for SMACC-HF, where the initial I c is taken from the virgin cable measurement. Both measurement and simulation show a correlation between a lower Cu/non-Cu ratio and retaining a higher fraction of the virgin critical current under transverse pressure.

We present a systematic method to tune the turn-to-turn contact resistance $R_{\text{ct}}$ in high-temperature superconducting (HTS) solenoids by applying a polyvinyl butyral (PVB) thermoplastic coating filled with silver-coated copper flakes (SCCF). The filler type and its volume fraction determines the accessible resistance range in the final coil. $R_{\text{ct}}$ strongly affects the charging dynamics and quench resilience of non-insulated (NI) HTS magnets, hence it is important to be able to control this parameter in a reliable and reproducible way. The coating is applied prior to winding in a continuous dip coating process and results in a dry polymeric film on the tape. After winding, the coating layers are fused above $60\,^\circ \text{C}$ and the final $R_{\text{ct}}$ is adjusted through the temperature and the duration of the heat-treatment. This method gives access to a wide range of $R_{\text{ct}}$. Values from about 50 to $10^{6}\,\mu \Omega \cdot \text{cm}^{2}$ can be obtained with the right choice of filler type, concentration and heat-treatment conditions. An 80-turn demonstrator solenoid fabricated using this approach and tested at $\text{77}\,\text{K}$ achieved the targeted $R_{\text{ct}}$ of around $70\,\mu \Omega \cdot \text{cm}^{2}$. A finite-element model, calibrated with the measured field-decay time, was used to extract the average turn-to-turn resistance and validate the tuning method.

In the context of the high-field magnet program, the Swiss Accelerator Research and Technology initiative is dedicated to researching and developing robust, high-field accelerator magnets for the future circular collider. As part of this initiative, the PSI team successfully designed, prototyped, and tested the first subscale stress-managed Nb3Sn common coil dipole magnet with enhanced training behavior. Following this accomplishment, a proposal was made for a stress-managed asymmetric common coil design for improved field quality, compatible with the requirements of accelerator magnets. This work follows the conceptual methodology proposed by PSI and details the electromagnetic and thermal design of a subscale asymmetric common coil magnet, equipped with a ferromagnetic yoke. The influence of the iron yoke on the magnet's field quality is analyzed and optimized according to the specified nominal current. A cooling strategy is proposed that involves cooling the windings using pipes carrying a fluid under forced flow, with the pipes in contact with the conductor. An alternative option, where the yoke is cooled to a higher temperature using a second fluid, is also considered. The magnet protection is analyzed considering an energy extraction system.

This work explores the use of a double-pancake coil for validating electromagnetic numerical models of HTS cables. We present a cost-effective and rapid production method using 3D-printed plastic formers. High-temperature superconducting (HTS) REBCO tapes are a promising solution for high-field magnets, particularly in accelerator applications, due to their ability to maintain superconducting properties in high magnetic field and high critical current density. One of the most effective ways to utilize HTS tapes is through straight soldered stack cables, which offer excellent packing efficiency in racetrack coil geometries-ideal for Block and Common-coil dipole magnet configurations. Measurements were performed in self-field conditions in liquid nitrogen, with AC current applied at frequencies up to 20 Hz. The current was increased in steps of 5 A of peak current, reaching a maximal of 100 A-below the critical current of the tested samples. For each frequency, the AC loss dependence on peak current showed a smooth trend, while AC losses per cycle remained independent of frequency. The validation process involved finite element method (FEM) modeling, using Jc(B) interpolation from experimental data, ensuring high accuracy. Both single REBCO tapes and soldered face-to-face cables were analyzed and compared to models of different modelling depth. The computational model matched the measured results with an accuracy within 10%. These findings provide a foundation for further research on the practical application of HTS straight soldered stack cables in high-field accelerator magnets.

REBCO coated conductor tapes are a promising technology for developing high-field accelerator magnets since their increased current carrying capacity and operational temperature allows achieving higher-fields and current levels with higher thermal margin. Superconducting materials still present challenges associated with their non-negligible losses in transient conditions, hence, finite element analyses become essential to design feasible superconducting systems. The H formulation is known in literature for its accuracy, while the T-A formulation offers computational efficiency. Nonetheless, both methods remain computationally demanding, especially when the superconducting tapes are modelled considering the extreme aspect ratios of different materials in the layered tapes. Homogenized models have been proposed to reduce computational requirements, however, modelling all layers as a single domain can impose the current to flow through all conducting layers rather than only the REBCO layer, even when its resistivity is very low. This study presents a comparative analysis using the H and the T-A formulations for a partially homogenized model, where the superconducting layer is modelled independently from the remaining conducting layers, and a fully homogenized model. The models' accuracy for transport loss estimation in transient conditions is discussed and compared with experimental loss measurements for a REBCO tape powered with AC currents.

The Paul Scherrer Institute (PSI) is developing an integrated system for cooling and protection of high-field superconducting magnets. Increasing the overall current density of superconducting cables reduces the conductor volume required for high fields but also decreases magnet protectability. To mitigate this, a strategy combining auxiliary coils and electrical discharge has been proposed to generate fast transients in the superconducting coils and enhance protection. For effective coupling, the auxiliary conductor must be located close to the magnet coils; however, in multi-layer configurations, this can reduce magnetic efficiency. Another key challenge in high-field magnets is cryogenic efficiency—both in steady-state cooling and in handling transient losses. To avoid the high costs of helium-bath systems in large magnets, PSI is investigating a conduction-cooling approach using forced-flow pipes embedded between coil layers. Yet, this integration can also impact magnetic performance. To address both protection and cooling challenges simultaneously, PSI proposes a dual-function concept using a hollow electrical conductor that serves as both the protection circuit and the cooling channel. The auxiliary coils are wound from this hollow conductor, which offers suitable electrical properties and enhanced thermal performance through forced-flow cooling. This work applies the proposed strategy to the subscale stress-managed asymmetric common-coil magnet under development at PSI. The study includes multi-physics transient analyses to assess system performance and validate the concept as a compact and efficient approach for superconducting accelerator magnets

High-temperature superconducting (HTS) cables of fer a promising opportunity for high-field magnet applications. However, the exact technology stack that would lead to accelerator-quality magnets is as yet not consolidated. A vigorous design-build-test cycle is required to evaluate the potential of different approaches. To implement such program at PSI, in the framework of the CHART initiative, we propose using the same magnet geometry previously tested with an LTS stress-managed magnet while replacing the rectangular Nb3Sn Rutherford cables with HTS straight soldered stack cables– a design that seamlessly integrates into the existing structure. Currently, we are in the design and process-development stage, with testing planned for later in 2025. This study presents magnetic field-quality estimation and AC loss computations for the HTS common coils magnet, based on finite element method (FEM) modeling of the final magnet design. The study includes an estimation of the required stabilizer content for protection with dump resistor at a maximum applied current of 10 kA, as well as the design of internal and external joints. Additionally, a novel coil winding technique enables simultaneous winding, insulation, and soldering of the cable, thus, overcoming the tape-stack cable's low minimal bending radius and offering scalability for larger magnet applications. This work represents a possible way for the practical application of HTS cables in accelerator magnets. A direct benchmark against LTS cables in identical geometry provides valuable insights and a faster path-way to experimental results and model validation.

The Magnet Development (MagDev) laboratory at the Paul Scherrer Institute (PSI) has designed and successfully manufactured the first subscale stress-managed common coil magnet. The magnet was tested at CERN and reached 98% of its short sample current at 4.5 K. Following the high-field magnet roadmap of the Swiss Accelerator Research and Technology initiative (CHART), a new magnet was assembled after replacing two of the four Nb₃Sn coils and manufacturing and integrating four copper-based coils, which are part of the Energy Shift with Coupling (ESC) quench protection method. The ESC system uses normal-conducting auxiliary coils that are strongly magnetically coupled with the magnet’s Nb₃Sn coils for protection. When a quench is detected, a current is discharged through the auxiliary coils, leading to a rapid transfer of the magnet’s energy from the Nb₃Sn coils to the copper-based coils. This process results in transient losses and quick transition to the normal state of the Nb₃Sn conductor, which facilitates quick energy extraction. This work presents the manufacturing of the copper-based coils, magnet assembly, and test results of the subscale SMCC2.

This paper presents the design of a non-insulated (NI) high-temperature superconductor (HTS) 15 T solenoid with a 72 mm diameter warm bore, intended for use in the Paul Scherrer Institute positron production (P³) experiment. The P³ experiment, scheduled to start in Q3 2026, aims to demonstrate a high-yield positron source that is relevant in the context of FCC-ee. The coils will be solder-impregnated using techniques developed with a small-bore HTS NI coil stack. This magnet produced a magnetic field of 18 T at 12 K and 2 kA, in a cryogen-free, conduction-cooled setup. Similarly, the P³ magnet will be conduction-cooled by two cryocoolers. This larger-bore magnet is designed to operate at 15 K with a nominal operating current of 1.2 kA. To ensure the protection of the NI magnet, quench prevention is the preferred strategy. Several potential failure modes are analyzed, including thermal runaway in the event of failures in the current leads, power supply, or cryocoolers. By enhancing the cold mass’ heat capacity through the addition of a large lead mass, the stored magnetic energy can be safely dissipated in the cold mass through the electrical path formed by the superconductor and the solder. Mechanical analysis indicates that the hoop, radial and axial stresses are kept below allowable limits.