A backward computation method has been developed to accelerate modelling of the critical state magnetization current in a staggered-array bulk high-temperature superconducting (HTS) undulator. The key concept is as follows: i) a large magnetization current is first generated on the surface of the HTS bulks after rapid field-cooling (FC) magnetization; ii) the magnetization current then relaxes inwards step-by-step obeying the critical state model; iii) after tens of backward iterations the magnetization current reaches a steady state. The simulation results show excellent agreement with the H-formulation method for both the electromagnetic and electromagnetic-mechanical coupled analyses, but with significantly faster computation speed. Solving the FEA model with 1.8 million degrees of freedom (DOFs), the backward computation method takes less than 1.4 hours, an order of magnitude or higher faster than other state-of-the-art numerical methods. Finally, the models are used to investigate the influence of the mechanical stress on the distribution of the critical state magnetization current and the undulator field along the central axis.

中文翻译：

---

使用反向计算方法快速有效地对场冷块状高温超导体进行临界状态建模

已经开发了一种反向计算方法来加速交错阵列体高温超导 (HTS) 波荡器中临界状态磁化​​电流的建模。关键概念如下：i）在快速场冷却（FC）磁化后，首先在 HTS 块体表面产生大的磁化电流；ii) 然后磁化电流按照临界状态模型逐步向内松弛；iii) 经过数十次反向迭代后，磁化电流达到稳定状态。仿真结果表明，对于电磁和电磁-机械耦合分析，与 H 公式方法非常吻合，但计算速度明显加快。求解具有 180 万个自由度 (DOF) 的 FEA 模型，后向计算方法只需不到 1.4 小时，比其他最先进的数值方法快一个数量级或更高。最后，利用模型研究了机械应力对临界状态磁化​​电流和波场沿中心轴分布的影响。