Lorenzo Bortot

A Consistent Simulation of Electrothermal Transients in Accelerator Circuits

Transient effects occurring in a superconducting accelerator circuit can be correctly simulated only if the models consistently account for the electrothermodynamic coupling between the magnets, the protection systems, and the remaining network. We present a framework based on the idea of cosimulation. The core component is a coupling interface exchanging information between the independent models. Within the framework, we simulate selected parts of a magnet and the electrical network, combining appropriately different commercial tools. This modularity gives the possibility of integrating new tools in the framework, to provide further insights on different physical domains as mechanics or fluid dynamics. The workflow is applied to the field-circuit coupling of an LHC main dipole magnet.

Coupling of Magnetothermal and Mechanical Superconducting Magnet Models by Means of Mesh-Based Interpolation

In this paper, we present an algorithm for the coupling of magnetothermal 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 magnetothermal 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 Coupling-Loss Induced Quench Technology.

STEAM: A Hierarchical Cosimulation Framework for Superconducting Accelerator Magnet Circuits

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 inconsistent results. We present STEAM, a hierarchical cosimulation 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 cosimulation, for the purpose of using computational resources efficiently. As a case study, a quench scenario is cosimulated for the inner triplet circuit for the high luminosity upgrade of the Large Hadron Collider at CERN.

Application of the waveform relaxation technique to the co-simulation of power converter controller and electrical circuit models

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.

A 2-D Finite-Element Model for Electro-Thermal Transients in Accelerator Magnets

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 electrothermal 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.

submitter : Simulation of a quench event in the upgraded High-Luminosity LHC Main dipole circuit including the 11 T Nb

To achieve the goal of increased luminosity, two out of eight main dipole circuits of the accelerator will be reconfigured in the coming LHC upgrade by replacing one standard 14.3-m long, Nb-Ti-based, 8.3 T dipole magnet by two 5.3-m long, Nb3Sn-based, 11.2 T magnets (MBH). The modified dipole circuits will contain 153 Nb-Ti magnets and two MBH magnets. The latter will be connected to an additional trim power converter to compensate for the differences in the magnetic transfer functions. These modifications imply a number of challenges from the point of view of the circuit integrity, operation, and quench protection. In order to assess the circuit performance under different scenarios and to validate the circuit quench protection strategy, reliable and accurate numerical transient simulations have to be performed. We present the field/circuit coupling simulation of the reconfigured main dipole magnet chain following the introduction of the MBH magnets. 2-D distributed LEDET models of the MBHs have been created to simulate the electrothermal transient occurring during a quench event, whereas the full electrical circuit of the main dipole chain, containing the 11 T magnets and their trim circuit, is simulated in PSpice. These two models are coupled through the STEAM cosimulation framework, calculating the electromagnetic and thermal transients in the magnets and circuit. The field/circuit coupling simulations performed with STEAM evaluate how the complex circuit affects the quenching magnet and vice versa. The results show a safe fast power abort of the system in the event of a quench in one of the MBH magnets, and support the validation of the correct functioning of the reconfigured main dipole circuit.

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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 multiphysics, multirate, and multiscale problem requires a consistent formulation and a dedicated framework to tackle the challenging transient effects occurring at both the 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 nonlinear 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.

Sn dipole magnets

In recent years, the superconducting Nb3Sn cable material became the privileged mature candidate for the high-field magnets in new projects like high-luminosity LHC (HL-LHC) accelerator at CERN, Geneva, Switzerland. The technology in 2017–2021 needs to be deployed through an unprecedented magnet series production with dedicated online quality control. The key fabrication stage of the vacuum pressure impregnation (VPI) after the heat treatment reaction of Nb3Sn coils, as on the new 11-T dispersion region dipole, enhances both the structural integrity and the dielectric strength of the winding packs. The global vacuum impregnation pressure method exhibits various merits in insulation performance and high dielectric strength reliability, which is strongly dependent on the success of the resin filling cycle. This online capacitive measurement method enables one to derive comparative master trend curves of various impregnated coils and possibly optimize the curing cycle. Ultimately, a combination of the above methods with a dielectric frequency response can bring insights on the impregnation process, the impacts from the resin choice and insulation material quality on the degree of curing, and the coil assembly geometry. The frequency impedance measurement of the first short dipole models DP101-102 provides the distributed lumped circuit fitting electrical parameters for the transient characterization of produced magnets.