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 $ \beta $ (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}_{{\mathrm{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 $ \beta $. Under the condition of $ {q}_{{\mathrm{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 $. As the poloidal specific pressure ($ {\beta }_{{\mathrm{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 $ \beta $ value imposed by the ideal MHD mode in a plasma with free boundary in tokamak experiments is proportional to the normalized current $ {I}_{{\mathrm{N}}} $ ($ {I}_{{\mathrm{N}}}={I}_{{\mathrm{p}}}\left({\mathrm{M}}{\mathrm{A}}\right)/a\left({\mathrm{m}}\right){B}_{0}\left({\mathrm{T}}\right) $), and the maximum specific pressure $ \beta \left({\mathrm{m}}{\mathrm{a}}{\mathrm{x}}\right) $ is calibrated to be $ ~2.01{I}_{{\mathrm{N}}},{\mathrm{ }}{\mathrm{i}}. {\mathrm{e}}. $ $ \beta \left({\mathrm{m}}{\mathrm{a}}{\mathrm{x}}\right)\sim 2.01{I}_{{\mathrm{N}}} $. The operational $ \beta $ limit of HL-2A circular cross-section plasma is approximately $ {\beta }_{{\mathrm{N}}}^{{\mathrm{c}}}\approx 2.0 $. Too high a value of $ {q}_{0} $ is not conducive to MHD stability and leads the $ \beta $ limit value to decrease. When $ {q}_{0}=1.3 $, we obtain a maximum value of $ {\beta }_{{\mathrm{N}}} $ of approximately $ 1.8 $. Finally, based on the existing circular cross-section plasma, some key factors affecting the operational $ \beta $ and the relationship between the achievable high $ \beta $ limit and the calculated ideal $ \beta $ limit are discussed.
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