Modelling of high temperature superconductor magnetic systems to enable low carbon advancements in science and technology

本项目将通过建立新的电磁和热耦合模型来探索高温超导体（HTS）线圈中的失超起始和传播。为了在4.2开尔文的操作温度下实现超过约20特斯拉的磁场，必须使用HTS。通常，这些被用作低温超导（LTS）“外套”内的插入物。已经探索了在LTS线圈中准确地建模失超行为的能力，然而，由于HTS材料的行为差异，这些技术不直接适用于HTS插入线圈。这一领域的精确建模能力将有助于设计紧凑的高场磁体、量子材料分析、高分辨率NMR和聚变等能源应用。模型必须耦合材料的电磁和热行为，及其与环境的相互作用，包括LTS磁体。超导线圈内的热传递由偏微分方程控制，该偏微分方程具有表示热扩散的第一项和表示热生成机制的其他项，该热生成机制包括响应于电流密度和磁场的变化的电阻加热和AC损耗。HTS插入线圈中的电流由线圈的电感器-电阻器（LR）电路和保护电路控制，其中线圈之间具有互感，并且HTS线圈中的电阻由EM和热效应引起。磁场由线圈电流的二维Biot-Savart积分确定。在高温超导体失超开始之前，问题是轴对称的。在失超的瞬间，轴对称性被破坏，失超传播的模拟必须切换到三维。需要考虑材料特性的随机变化在确定淬火起始位置中的作用。在这个项目中，将创建新的模型来探索这种行为。将创建一个二维轴对称模型来预测高温超导线圈在失超前的行为。超导体在临界状态下的最小失超能的概念将被用来确定失超开始传播的时间。失超在圆周方向上的传播将通过傅立叶级数的应用在三维空间中求解，并行处理应用于独立求解每个傅立叶系数。该项目将集中在HTS测试线圈在~ 10 T的LTS背景场中运行的情况下。这将使实验能够进行，以测试模型的预测。这些实验是对这个项目的补充，而不是它的一部分。

This project will explore Quench initiation and propagation in a high temperature superconductor (HTS) coil by creating new coupled electromagnetic and thermal models. In order to achieve magnetic fields in excess of approximately 20 Tesla at an operating temperature of 4.2 Kelvin, HTS must be utilised. Typically, these are used as inserts within low temperature superconducting (LTS) 'outserts'. The ability to model quench behaviour accurately in LTS coils has been explored, however due to the differences in behaviour of HTS materials these techniques are not directly applicable to HTS insert coils. Accurate modelling capability in this area will aid the design of compact, high field magnets quantum materials analysis, high-resolution NMR and energy applications such as fusion. Models must couple Electromagnetic and thermal behaviour of the material, and its interaction with its environment, including with LTS magnets. Heat transfer within a superconducting coil is governed by a partial differential equation with a first term representing heat diffusion and other terms representing mechanisms of heat generation including resistive heating and AC losses in response to changes in current density and magnetic field. Current in the HTS insert coil is governed by an inductor-resistor (LR) circuit of coils and protection circuit with mutual inductance with between the coils and resistance in the HTS coils arising from EM and thermal effects. The magnetic field is determined by two-dimensional Biot-Savart integration of the coil currents. Before the instant of quench initiation in the HTS the problem is axisymmetric. At the instant of quench, the axial symmetry is broken and the simulation of quench propagation must then be switched to three dimensions. The role of random variations in the material properties in determining the location of the quench initiation will need to be considered. In this project new models will be created to explore this behaviour. A two-dimensional axisymmetric model will be created to predict the behaviour of the HTS coil in the lead up to the quench. The concept of Minimum Quench Energy for a superconductor at critical state will be exploited to determine the time at which the quench begins to propagate. The propagation of the quench in the circumferential direction will then be solved in three dimensions by application of a Fourier series, with parallel processing applied to solve for each Fourier coefficient independently.The project will focus on the case of a HTS test coil operating in a LTS background field of ~10T. This will enable experiments to be carried out to test the predictions of the model. These experiments are in addition to this project, not part of it.