[论文解读] Study of circular cross-section plasmas in HL-2A tokamak: MHD equilibrium, stability and operational \b{eta} limit

Shen Yong, Dong JiaQi+7 more|arXiv (Cornell University)|Jan 16, 2026

Magnetic confinement fusion research被引用 0

一句话总结

本论文在HL-2A进行圆截面托卡马克等离子体分析，研究MHD平衡、稳定性与运行beta极限，结果涉及屈 kink 不稳定性与beta标度。

ABSTRACT

Circular cross-section plasma is the most basic form of tokamak plasma and the fundamental configuration for magnetic confinement fusion experiments. Based on the HL-2A limiter discharge experiments, the magnetohydrodynamic (MHD) equilibrium and MHD instability of circular cross-section tokamak plasmas are investigated in this work. The results show that when q_0=0.95, the internal kink mode of m/n=1/1 is always unstable. The increase in plasma \b{eta} (the ratio of thermal pressure to magnetic pressure) can lead to the appearance of external kink modes. The combination of axial safety factor q_0 and edge safety factor q_a determines the equilibrium configuration of the plasma and also affects the MHD stability of the equilibrium, but its growth rate is also related to the size of \b{eta}. Under the condition of q_a>2 and q_0 slightly greater than 1, the internal kink mode and surface kink mode can be easily stabilized. However the plasma becomes unstable again and the instability intensity increases as q_0 continues to increase when q_0 exceeds 1. As the poloidal beta (\b{eta}_p) increases, the MHD instability develops, the equilibrium configuration of MHD elongates laterally, and the Shafranov displacement increases, which in turn has the effect on suppressing instability. Calculations have shown that the maximum \b{eta} value imposed by the ideal MHD mode in a plasma with free boundary in tokamak experiments is proportional to the normalized current I_N (I_N=I_p (MA)/a(m)B_0 (T)), and the achievable maximum beta \b{eta}(max) is calibrated to be 2.01I_N,i.e. \b{eta}(max)~2.01I_N. The operational \b{eta} limit of HL-2A circular cross-section plasma is approximately \b{eta}_N^c~2.0. Too high a value of q_0 is not conducive to MHD stability and leads the \b{eta} limit value to decrease. When q_0=1.3, we obtain a maximum value of \b{eta}_N of approximately 1.8.

研究动机与目标

• 研究HL-2A 限制放电中的圆截面托卡马克等离子体的MHD平衡与稳定性。
• 识别q0和qa以及beta如何影响内部和外部kink模。
• 量化可达到的最大beta(eta)及其与归一化电流I_N的关系。
• 就q0和qa如何影响HL-2A等离子体的稳定性与beta极限提供指导。

提出的方法

• 使用HL-2A 限制放电的实验数据研究圆截面等离子体。
• 分析相对于内部kink (m/n=1/1) 和外部kink模的MHD稳定性。
• 考察稳定性对q0、qa、beta，以及极化beta eta_p的依赖性。
• 计算自由边界托卡马克等离子体的最大理想MHD beta，并将其与I_N联系起来。
• 将eta(max)校准为大约2.01 I_N，并与实验eta_N^c ≈2.0进行比较。

实验结果

研究问题

• RQ1 内部kink模稳定性如何随qa、eta变化而受q0影响？
• RQ2 当beta增加时，外部kink模的稳定阈值是什么？
• RQ3 q0、qa、以及eta_p如何共同塑造HL-2A圆截面等离子体的平衡与稳定性？
• RQ4 HL-2A中的最大理想MHD beta与归一化电流I_N之间的关系是什么？
• RQ5 HL-2A圆截面等离子体的运行eta极限是多少？

主要发现

• 内部kink模(m/n=1/1)在q0=0.95时始终不稳定。
• beta增大会导致出现外部kink模。
• 轴向安全因子q0与边界安全因子qa的组合决定了平衡并影响MHD稳定性，且增长率也依赖于eta。
• 当qa>2且q0略高于1时，内部和表面kink模可以得到稳定，但进一步增大q0会降低稳定性。
• 随着eta_p增加，MHD不稳定性增强，拉长与Shafranov位移增大，这可以抑制不稳定性。
• 具有自由边界的最大理想MHD beta与归一化电流I_N成正比，eta(max)≈2.01 I_N。
• HL-2A圆截面操作beta极限大约为eta_N^c ≈2.0。
• 对于q0=1.3，观察到的最大eta_N约为1.8。