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The major advantage of reduced magnetic vector potential formulations (RMVPs) is that complicated coil structures do not need to be resolved by a computational mesh. Instead, they are modeled by thin wires, whose source field is included into the simulation model along Biot-Savart's law. Such an approach has already been successfully employed in ROXIE for the simulation of superconducting Large Hadron Collider magnets at CERN. This work presents an updated RMVP approach, which significantly outperforms the original method. The updated formulation is postulated, implemented, verified, compared to the original formulation, and applied for the simulation of a quadrupole magnet. The promising results of this work encourage further investigation towards an updated simulation framework for next-generation accelerator magnets., Comment: 9 pages, 13 figures, to be published in IEEE Transactions on Magnetics

The European Laboratory Directors Group (LDG) was mandated by CERN Council in 2021 to oversee the development of an Accelerator R&D Roadmap. To this end, a set of expert panels was convened, covering the five broad areas of accelerator R&D highlighted in the ESPPU. The High Field Magnet (HFM) Panel is proposing a programme to demonstrate Nb3Sn magnet technology for large-scale deployment and to investigate the suitability of high temperature superconductors (HTS) for accelerator magnet applications. A summary of this programme is presented here., Comment: contribution to Snowmass 2021. arXiv admin note: substantial text overlap with arXiv:2201.07895

We explore transient heat transfer, on the millisecond time-scale, from a narrow, rectangular stainless steel heater cooled from one side by He II confined to a channel of 120 $\mu$m depth. The helium is isolated from the external bath with the exception of two pin-holes of cross section about 10% that of the channel. We measure the temperatures of both the heater strip and the channel helium during slow-pulse heating that reaches peak power after 9 ms, fast-pulse heating that reaches peak power after 100 $\mu$s, and step heating that reaches steady power after 100 $\mu$s. Using the steady state Kapitza heat transfer expression at the interface between heater and helium, and the Gorter-Mellink heat transfer regime in the helium channel, we obtain excellent agreement between simulation and measurement during the first 5 ms of slow-pulse tests. Using instead the measured helium temperature in the Kapitza expression, we obtain excellent agreement between the simulated and measured heater response during the first 150 ms of slow-pulse tests. The same model fails to explain the fast-pulse transient response of the heater and helium, while it can explain the helium response to a step in applied power but not the heater response. The steady state Kapitza expression may therefore not be applicable to heating events that are over within a single millisecond.

We explore steady state and transient heat transfer from a narrow, rectangular stainless steel heater strip cooled from one side by an open bath of He~II. Setup validation is done by fitting the Kapitza heat transfer expression $Q = a_\mathrm{K} \left( {T_\mathrm{s}}^{n_\mathrm{K}} - {T_\mathrm{b}}^{n_\mathrm{K}} \right)$ to steady state measurements, finding fit parameters within the expected range; $a_\mathrm{K}$ = 1316.8$\pm10\%$ $\mathrm{W}\mathrm{m}^{-2}\mathrm{K}^{-1}$, $n_\mathrm{K}$ = 2.528$\pm10\%$. We find critical heat flux in line with estimates from literature, and the time between a step in heating and the onset of film boiling follows the expected $\propto Q^{-4}$ dependence. During the first millisecond after a step in applied heating power density our measurements show a slower thermal rise time than that found by a time-dependent one-dimensional model of our setup using the steady state Kapitza heat transfer expression as the cooling boundary condition. However, the results compare favourably with transient measurements in literature. After the first millisecond, agreement between measurement and model is excellent. We do not find conclusive evidence of an orientation dependence of the Kapitza heat transfer mechanism, nor heat transfer differences that can be attributed to local surface variations along the same heater.

The application of high-temperature superconductors to accelerator magnets for future particle colliders is under study. Numerical methods are crucial for an accurate evaluation of the complex dynamical behavior of the magnets, especially concerning the magnetic field quality and thermal behavior. We present a coupled $\textbf{A}$-$\textbf{H}$ field formulation for the analysis of magneto-thermal transients in accelerator magnets. The magnetic field strength $\textbf{H}$ accounts for the eddy current problem in the source regions containing the superconducting domains, while the magnetic vector potential $\textbf{A}$ represents the magnetoquasistatic problem in the normal and non-conducting domains. Furthermore, we include a slab approximation for the source regions, making the formulation suitable for large scale models composed of thousands of tapes. In this work, the relevant equations are derived and discussed, with emphasis on the coupling conditions. The weak formulation is derived, and numerical results are provided in order to both, verify the formulation and scale it to the size of an accelerator magnet., Comment: 10 pages, 11 figures

Simulating the transient effects occurring in superconducting accelerator magnet circuits requires including the mutual electro-thermo-dynamic interaction among the circuit elements, such as power converters, magnets, and protection systems. Nevertheless, the numerical analysis is traditionally done separately for each element in the circuit, leading to possible non-consistent results. We present STEAM, a hierarchical co-simulation framework featuring the waveform relaxation method. The framework simulates a complex system as a composition of simpler, independent models that exchange information. The convergence of the coupling algorithm ensures the consistency of the solution. The modularity of the framework allows integrating models developed with both proprietary and in-house tools. The framework implements a user-customizable hierarchical algorithm to schedule how models participate to the co-simulation, for the purpose of using computational resources efficiently. As a case study, a quench scenario is co-simulated for the inner triplet circuit for the High Luminosity upgrade of the LHC at CERN., Comment: 7 pages, 14 figures

In this paper we present an algorithm for the coupling of magneto-thermal and mechanical finite element models representing superconducting accelerator magnets. The mechanical models are used during the design of the mechanical structure as well as the optimization of the magnetic field quality under nominal conditions. The magneto-thermal models allow for the analysis of transient phenomena occurring during quench initiation, propagation, and protection. Mechanical analysis of quenching magnets is of high importance considering the design of new protection systems and the study of new superconductor types. We use field/circuit coupling to determine temperature and electromagnetic force evolution during the magnet discharge. These quantities are provided as a load to existing mechanical models. The models are discretized with different meshes and, therefore, we employ a mesh-based interpolation method to exchange coupled quantities. The coupling algorithm is illustrated with a simulation of a mechanical response of a standalone high-field dipole magnet protected with CLIQ (Coupling-Loss Induced Quench) technology., Comment: 5 pages, 6 figures

This contributions discusses the simulation of magnetothermal effects in superconducting magnets as used in particle accelerators. An iterative coupling scheme using reduced order models between a magnetothermal partial differential model and an electrical lumped-element circuit is demonstrated. The multiphysics, multirate and multiscale problem requires a consistent formulation and framework to tackle the challenging transient effects occurring at both system and device level.

Superconducting accelerator magnets require sophisticated monitoring and means of protection due to the large energy stored in the magnetic field. Numerical simulations play a crucial role in understanding transient phenomena occurring within the magnet, and can, therefore, help to prevent disruptive consequences. We present a 2-D FEM model for the simulation of electro-thermal transients occurring in superconducting accelerator magnets. The magnetoquasistatic problem is solved with a modified magnetic vector potential formulation, where the cable eddy currents are resolved in terms of their equivalent magnetization. The heat balance equation is then investigated, and the relevant heat sources are discussed. The model implements a two-port component interface and is resolved, as part of an electrical circuit, in a cooperative simulation scheme with a lumped-parameter network., Comment: 4 pages, 12 figures, approved for publication, IEEE Transactions on Magnetics, 2017

In this paper we present the co-simulation of a PID class power converter controller and an electrical circuit by means of the waveform relaxation technique. The simulation of the controller model is characterized by a fixed-time stepping scheme reflecting its digital implementation, whereas a circuit simulation usually employs an adaptive time stepping scheme in order to account for a wide range of time constants within the circuit model. In order to maintain the characteristic of both models as well as to facilitate model replacement, we treat them separately by means of input/output relations and propose an application of a waveform relaxation algorithm. Furthermore, the maximum and minimum number of iterations of the proposed algorithm are mathematically analyzed. The concept of controller/circuit coupling is illustrated by an example of the co-simulation of a PI power converter controller and a model of the main dipole circuit of the Large Hadron Collider.

In this paper, we propose an optimized field/circuit coupling approach for the simulation of magnetothermal transients in superconducting magnets. The approach improves the convergence of the iterative coupling scheme between a magnetothermal partial differential model and an electrical lumped-element circuit. Such a multi-physics, multi-rate and multi-scale problem requires a consistent formulation and a dedicated framework to tackle the challenging transient effects occurring at both circuit and magnet level during normal operation and in case of faults. We derive an equivalent magnet model at the circuit side for the linear and the non-linear settings and discuss the convergence of the overall scheme in the framework of optimized Schwarz methods. The efficiency of the developed approach is illustrated by a numerical example of an accelerator dipole magnet with accompanying protection system., Comment: 8 pages, 7 figures

We present boundary-integral equations for Maxwell-type problems in a differential-form setting. Maxwell-type problems are governed by the differential equation $(\delta\mathrm{d}-k^2)\omega = 0$, where $k\in\mathbb{C}$ holds, subject to some restrictions. This problem class generalizes $\textbf{curl}\,\textbf{curl}$- and $\mathrm{div}\,\textbf{grad}$-types of problems in three dimensions. The goal of the paper is threefold: 1) Establish the Sobolev-space framework in the full generality of differential-form calculus on a smooth manifold of arbitrary dimension and with Lipschitz boundary. 2) Introduce integral transformations and fundamental solutions, and derive a representation formula for Maxwell-type problems. 3) Leverage the power of differential-form calculus to gain insight into properties and inherent symmetries of boundary-integral equations of Maxwell-type., Comment: 69 pages

We introduce a relativistic splitting structure as a means to map fields and equations of electromagnetism from curved four-dimensional space-time to three-dimensional observer's space. We focus on a minimal set of mathematical structures that are directly motivated by the language of the physical theory. Space-time, world-lines, time translation, space platforms, and time synchronization all find their mathematical counterparts. The splitting structure is defined without recourse to coordinates or frames. This is noteworthy since, in much of the prevalent literature, observers are identified with adapted coordinates and frames. Among the benefits of the approach is a concise and insightful classification of splitting structures that is juxtaposed to a classification of observers. The application of the framework to the Ehrenfest paradox and Schiff's "Question in General Relativity" further illustrates the advantages of the framework, enabling a compact, yet profound analysis of the problems at hand., Comment: 93 pages. This is an author-created, un-copyedited version of an article published in J. Phys. A: Math. Theor. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://iopscience.iop.org/1751-8121/47/43/435202/