High-beta operation is a key requirement for achieving high energy gain in magnetic confinement fusion devices. In this work, the beta limit of the recently designed USTC-QI4 stellarator is systematically investigated. USTC-QI4 is a four-field-period quasi-isodynamic stellarator optimized to achieve improved neoclassical confinement and stability properties. To evaluate its high-beta capability, the equilibrium beta limits are analyzed using three widely adopted criteria: the Shafranov shift, the Mercier criterion, and ballooning mode stability. The results are compared with those of the W7-X stellarator to provide a benchmark assessment.
All calculations are done with a linear pressure profile. The beta limit predicted from the Shafranov shift is defined as the point at which the magnetic axis displacement reaches approximately half of the minor radius. The corresponding beta limit for USTC-QI4 is found to be approximately 25.9 %, which is higher than that of W7-X (20.2 %). This improvement is likely related to the higher degree of quasi-isodynamicity achieved in the USTC-QI4 configuration. The Mercier stability limit is evaluated using the VMEC equilibrium code, yielding a beta limit of about 6.1 % for USTC-QI4, which is lower than that of W7-X (14.3 %). As the Mercier criterion incorporates a broader set of equilibrium stability conditions, it provides a more stringent assessment of equilibrium stability. The ballooning stability limit is calculated using the COBRA code. The resulting beta limit for USTC-QI4 is approximately 4.3 %, slightly higher than the value of 3.1 % obtained for W7-X. Among the three criteria, ballooning mode stability provides the most restrictive limit and therefore represents the most realistic estimate of the achievable operational beta.
In summary, the practical operational beta limit of USTC-QI4 is expected to be constrained by ballooning mode instability at β≈4.3 %. These results provide a quantitative evaluation of the high-beta operational capability of the USTC-QI4 stellarator and offer useful guidance for the design and optimization of future high-performance stellarators. Future work will extend this study to include nonlinear effects and more comprehensive stability analyses.