###### Abstract  
The Institute of Plasma Physics Chinese Academy of Sciences (ASIPP) is currently engaged in the design of a compact fusion device with a fusion power gain (Q) exceeding one. Due to space limitation for the device, the conductor jacket of the central solenoid (CS) magnet experiences significant electromagnetic stress. Therefore, a higher strength stainless steel known as modified N50 (CHSN01) is utilized for manufacturing the jacket. To effectively heat the plasma, the CS magnet within the device requires operation with alternating current. It is crucial to monitor fatigue crack growth caused by stress cycles in the CS jacket and assess its severity in order to ensure the safety and reliability of the fusion device. In this study, a finite element method is applied to establish a functional relationship between the stress intensity factor range \(\Delta K\) and the jacket defect depth \(a\) precisely based on actual cyclic loads experienced by CS magnet operation. Experimental investigations are conducted to determine fatigue crack growth rates (FCGRs) at 4.2 Kelvin (K) for the CHSN01 jacket. The maximum likelihood estimation method is employed to calculate the probability equations of FCGRs with a random variable description. Consequently, it is possible to determine the maximum allowable initial defect size for a jacket to withstand 60,000 plasma pulses, which will serve as an input parameter for non-destructive testing of jackets. CS magnet; CHSN01; jacket; FCGR 2025  
30 April 2025 3 May 2025 30 April 2025 3 May 202 the construction and operation of the Experimental Advanced Superconducting Tokamak (EAST) [10] will significantly contribute to the successful implementation of this project. The large magnetic field generated by the CS magnet will impose high stress on the jacket of the conductor for the magnet. To address this challenge, a specialized high-strength jacket named CHSN01 has been developed for the device, featuring a yield strength of up to 1500 MPa. Further details regarding this development will be presented subsequently. One cycle of alternating current operation in the CS magnet can excite the plasma to discharge electricity once. The current variation in the CS magnet results in stress fluctuations in the CS magnet jacket. The device is designed to discharge plasma 60,000 times, thereby requiring the CS magnet jacket to endure the same number of stress cycles. Cracks that form during the manufacturing of the jacket are prone to grow under such stress cycles, leading to deterioration in mechanical properties and even fractures, posing significant risks for its safe operation. Fracture mechanics suggests that cracks [11; 12] of a certain size can exist safely in any structure and grow during load cycles up to a critical size where structural strength is compromised. This approach which is applied to engineering design can reduce the costs related to the components of enormous size without affecting safety by providing information such as the maximum allowable crack size or the maximum number of sustainable loading cycles. The fatigue crack growth rate (FCGR), \(da/dN\)[13], which is the change rate of crack length \(a\) with cycle times \(N\) under the action of a fatigue load, reflects the speed of crack growth and plays an important role in estimating the fatigue life of cracked bodies. Therefore, the maximum allowable defect area should be obtained based on the required number of cycles experienced and FCGR. When conducting non-destructive testing on the jacket, the crack area must not exceed this value. The simulation of FCGR can employ various techniques, including the finite element method (FEM), the extended finite element method (XFEM), cohesive zone modeling (CZM), and the virtual crack closure technique (VCCT). Compared to the traditional FEM, the XFEM eliminates the need for mesh repartitioning and does not require a higher density mesh in regions of high stress concentration. [PERSON] et al.