等离子体平衡是托卡马克研究的基础，它与装置的概念设计、物理实验、后期的数据分析都有密切关系。本文在SUNIST/SUNIST-2装置上开展了以平衡为核心的放电设计、平衡反演算法研究。论文的第一部分是磁诊断系统的搭建，这是后续工作的实验基础。SUNIST装置的高场侧空间狭窄，本文通过扁平状的结构设计，在中心柱上安装了一个紧凑型磁探针阵列；在SUNIST-2装置上，本文搭建了一个完善的包括极向、环向磁探针阵列、等离子体电流罗科线圈、单匝环在内的磁诊断系统。标定结果显示，SUNIST/SUNIST-2装置磁诊断系统的信噪比、频率响应等关键指标均满足实验要求，平衡反演结果显示增加了高场侧磁探针的约束之后，反演残差下降了36.4%。SUNIST-2是新装置，欧姆补偿线圈的设计、零场与击穿所需的电源方案等都是亟待解决的问题。针对此需求，本文开发了基于启发式算法的零场与击穿优化算法TSU，并进行了一系列与启动相关的计算分析，包括欧姆补偿线圈的最优位置以及匝数的确定、初始磁化、动态零场与击穿的优化等。TSU的优化不要求电源可反馈控制，很好地满足了装置运行初期的需求，通过使用这套代码进行击穿与垂直场适配的实验研究，顺利完成了SUNIST-2装置的首轮欧姆放电实验。在平衡位形的设计上，本文开发了具备双环位形（包括droplet以及doublet）求解能力的FBE代码，并使用这套代码计算了双零、负三角双零、droplet以及doublet等一系列位形，计算发现对预设位形，偏滤器线圈的电流负载最大。同时，本文也实现了用于控制器设计的动态平衡演化代码FBEE，并给出了一个从限制器位形向负三角双零位形演化的实例。SU-EFIT具备等离子体平衡求解的基本模块，但无法满足SUNIST装置平衡重建常态化运行的需求，主要困难包括：涡流求解的局限性，等离子体快速变化所引发的Picard迭代垂直滑移不稳定性，以及反演权重需手动调整，代码不够鲁棒，计算速度比较慢等。针对这些问题，本文对其进行了重构与拓展，主要的升级包括响应函数方法与傅里叶分解法相结合的涡流处理方法、垂直位移的稳定、拓扑约束、磁轴处安全因子约束、逆磁约束等。升级之后的SU-EFIT代码能力得到了全面提升，实现了常态化运行。
The equilibrium of plasma torus is the basis of tokamak research, which is related to the concept design of a new device, physical experiments, and subsequent data analysis. This dissertation mainly focuses on the discharge design and equilibrium reconstruction algorithm implemented on the SUNIST (Sino UNIted Spherical Tokamak) /SUNIST-2 device.The construction of a magnetic diagnostic system is carried out first and acts as the experimental basis for subsequent research. On the SUNIST device, the space in the high field side (HFS) is narrow while the magnetic diagnostics there are required for equilibrium reconstruction. In this dissertation, a flat and compact magnetic probe array satisfying the space requirements is installed on the central column. On the SUNIST-2 device, A comprehensive magnetic diagnostic system is installed, which includes the poloidal and toroidal magnetic probe arrays, a Rogowski coil measuring plasma current, and flux loops. Based on calibration, it is confirmed that the key parameters, including signal-to-noise ratio and frequency response, meet the experimental requirements. And a decrease of 36.4% in the reconstruction residual is observed when the constraint from the HFS magnetic probe array is used in equilibrium reconstruction.SUNIST-2 is a new facility, and the design of the ohmic compensation coils, as well as the power supply solutions required for achieving zero field and breakdown, are all pressing issues that need to be addressed. Utilizing the heuristic algorithm, we have developed a TSU (Tokamak Start Up) code with the primary objective of addressing the problem mentioned above. With the code, a series of calculations have been conducted including determining the optimal position and turns for the ohmic compensation coil, assessing initial magnetization, design of dynamic zero field and breakdown. One notable characteristic of our code is its independence from power supply feedback control. This feature aligns well with the initial phase of SUNIST-2 operation, where feedback control capabilities might be limited. Finally, we investigated the synchronization between the breakdown time and the vertical field penetration and successfully completed the initial ohmic discharge experiments of the SUNIST-2 device.In the aspect of equilibrium design, a Free Boundary Equilibrium (FBE) code which is capable of equilibrium calculation of two plasma torus is developed. Four configurations including double null configurations with positive and negative triangularity, as well as doublet and droplet configurations are designed. Results show that the DF (Divertor Field) coils have the highest current load requirements, especially in the case of negative triangularity configuration. In the meanwhile, we have also developed a FBEE (Free Boundary Equilibrium Evolve) code which is dedicated to the controller design, and an example of the plasma evolution from a limiter configuration to a negative triangularity configuration is given.Equilibrium reconstruction is a crucial method for inferring plasma equilibrium parameters from discharge data. SU-EFIT(SUnist Equilibrium FITting) is an existing code in the SUNIST laboratory which has the fundamental function for plasma current profile parameter reconstruction, but it still cannot meet the needs of routine use for equilibrium reconstruction in the SUNIST device. There are some underlying issues. For example, the eddy currents and vertical position can still not be determined properly. Additionally, the fitting weights need to be adjusted manually, and the code is not robust enough, and computation is not efficient enough. To address these problems and ensure compatibility with discharges under all operating conditions of SUNIST, the code is refactored. The major updates include the combination of the response function and Fourier expansion method to solve eddy currents, improving the vertical stability of the plasma column, introducing single-point and multi-point topological constraints, and implementing constraints for the axial safety factor and diamagnetic flux. The capabilities of the new version of the SU-EFIT code have been significantly improved. Consequently, we have successfully achieved routine operation for equilibrium reconstruction and deployed it on the SU-EFIT server.
