[Paper Review] 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 research0 citations

TL;DR

This paper analyzes circular cross-section tokamak plasmas on HL-2A, examining MHD equilibrium, stability, and the operational beta limit, with findings on kink instabilities and beta scaling.

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.

Motivation & Objective

• Investigate MHD equilibrium and stability of circular cross-section tokamak plasmas in HL-2A limiter discharges.
• Identify how q0 and qa, along with beta, influence internal and external kink modes.
• Quantify the maximum achievable beta (eta) and its relation to normalized current I_N.
• Provide guidance on how q0 and q_a affect stability and the beta limit in HL-2A plasmas.

Proposed method

• Use HL-2A limiter-discharge experimental data to study circular cross-section plasmas.
• Analyze MHD stability with respect to internal kink (m/n=1/1) and external kink modes.
• Examine the dependence of stability on q0, qa, beta, and poloidal beta eta_p.
• Compute the maximum ideal MHD beta for free-boundary tokamak plasmas and relate it to I_N.
• Calibrate eta(max) approximately as 2.01 I_N and compare with experimental eta_N^c ≈ 2.0.

Experimental results

Research questions

• RQ1 How does the internal kink mode stability depend on q0 when qa and eta vary?
• RQ2 What are the stability thresholds for external kink modes as beta increases?
• RQ3 How do q0, qa, and eta_p jointly shape the equilibrium and stability of circular cross-section HL-2A plasmas?
• RQ4 What is the relationship between the maximum ideal MHD beta and the normalized current I_N in HL-2A?
• RQ5 What is the HL-2A operational eta limit for circular cross-section plasmas?

Key findings

• The internal kink mode (m/n=1/1) is always unstable at q0=0.95.
• Increasing beta leads to external kink modes.
• The combination of axial safety factor q0 and edge safety factor qa determines the equilibrium and affects MHD stability, with growth rate also depending on eta.
• When qa>2 and q0 slightly above 1, the internal and surface kink modes can be stabilized, but further increasing q0 reduces stability.
• As eta_p increases, MHD instabilities grow, elongation and Shafranov displacement increase, which can suppress instability.
• The maximum ideal MHD beta with a free boundary is proportional to the normalized current I_N, with eta(max) ≈ 2.01 I_N.
• The HL-2A circular-cross-section operational beta limit is approximately eta_N^c ≈ 2.0.
• For q0=1.3, the maximum eta_N observed is about 1.8.