Mechanical Property Evaluation of CSMC Armour and Helium Inlet under Steady-State Operation

Mechanical Property Evaluation of CSMC Armour and Helium Inlet under Steady-State Operation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Mechanical Property Evaluation of CSMC Armour and Helium Inlet under Steady-State Operation Xianwei Wang, Wenlong Xu, Haikuo Zhao, Aihua Xu, Wentao Xie This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8274653/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 28 Apr, 2026 Read the published version in Journal of Fusion Energy → Version 1 posted 10 You are reading this latest preprint version Abstract To verify the mechanical safety of the armour and helium inlet of the China Fusion Engineering Test Reactor (CFETR) Central Solenoid Model Coil (CSMC) under multi-physics coupling fields during steady-state operation, this study adopted the electromagnetic-structural indirect coupling method, complying with ASME analytical design criteria and ITER magnet design specifications. A simplified electromagnetic model of CSMC was established via ANSYS Maxwell, and a current filament mapping approach was employed to achieve complete and accurate transfer of electromagnetic forces to the structural model. Static structural analysis using ANSYS was conducted to obtain the stress distribution of key components under multi-field coupling. Evaluation based on stress linearization results and ITER stress thresholds demonstrated that the Nb₃Sn armour and helium inlet fully meet safety requirements, while the NbTi armour complies with design criteria after cold working hardening treatment. This study confirms that the existing design of CSMC armour and racetrack-shaped helium inlet can withstand the strength demands of cryogenic multi-coupling fields, providing critical technical support for the engineering application of CFETR CSMC and a valuable reference for the cooling interface design of Cable-in-Conduit Conductors (CICC) in large-scale superconducting magnets. CFETR CSMC Jacket Helium inlet CICC Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1 Introduction The Cable-in-Conduit Conductor (CICC) is an integrated current-carrying component fabricated by first twisting multiple superconducting strands into a cable, then encapsulating the cable within a metallic conduit, and finally filling the conduit with supercritical helium to achieve both cooling and insulation. Endowed with efficient cooling capacity, excellent mechanical stability, favorable reliability and maintainability, as well as high current-carrying capability, CICC has been widely applied in large-scale superconducting magnet devices [1] . The Central Solenoid (CS) coil of the China Fusion Engineering Test Reactor (CFETR) [2–3] is the core component for plasma confinement, and its performance directly determines the operational reliability of the reactor. To simulate the full-operating-condition characteristics of the CFETR CS coil while balancing R&D economy and design objectives, the CFETR Central Solenoid Model Coil (CSMC) adopts a hybrid conductor design: Nb₃Sn superconducting conductors are selected for the high-magnetic-field-region coils to meet the demand for strong magnetic fields [4] , while NbTi conductors are used for the low-magnetic-field-region coils to balance cost and performance [5] . The CICC conductor of the CSMC features a four-layer "outer-to-inner" composite structure, consisting of an insulation layer, an armour layer, a cable, and a central cooling tube. Specifically, the insulation layer is made of glass fiber-reinforced resin (G10) to realize electrical insulation between the conductor and external structures. The armour layer is composed of austenitic stainless steel (316 LN for Nb₃Sn coils and 316 L for NbTi coils) and undertakes the functions of structural support and supercritical helium sealing; The cable is formed by twisting Nb₃Sn/NbTi superconducting strands with pure copper in a designed proportion, which balances current-carrying and thermal conductivity performances. A through-hole is reserved at the center of the cable for the insertion of the central cooling tube, so as to realize supercritical helium circulation. The cross-sectional dimension parameters of the two types of conductors are shown in Fig. 1 [6] . The manufacturing process of CICC conductors follows four key procedures: five-stage cabling of superconducting strands, welding and forming of stainless steel armour, insertion of the cable into the conduit, and overall rolling and diameter reduction to the designed dimensions. Since the CICC conductors of CSMC rely on forced-flow cooling with supercritical helium (to maintain the coil at a cryogenic temperature of 4.5 K), helium inlets and outlets must be opened on the inner and outer armours of the coil to enable the transportation of supercritical helium. As an integral part of the armour structure, the helium inlets and outlets are connected to the armour via welding to ensure sealing performance; a total of 10 helium inlets and outlets are arranged on the CSMC, distributed uniformly on the armours of the five sub-coils to guarantee uniform cooling. Key parameters of the racetrack-shaped helium inlet designed in this study are as follows: total height of 40 mm, boss diameter of 28.4 mm, and weld arc radius of 6.3 mm; corresponding racetrack-shaped holes are drilled on the armour, with a diameter of 12 mm and a flow area of 215 mm² to reduce flow resistance. The 3D model and detailed dimensions of a single helium inlet are shown in Fig. 2 . Previous studies on the JT-60SA CSMC [7–8] , ITER CSMC [9–12 ], and ITER PF6 coil [13] have focused on armour material selection, geometric design of helium inlet, optimization of welding processes, and thermal stability. Earlier research on the CFETR CSMC [14] has also covered similar directions, but none have systematically analyzed the mechanical behavior of the armour and helium inlet under the multi-field coupling of preload, thermal, electromagnetic, and supercritical helium pressure. However, this coupled load environment is the core factor determining the structural safety of CSMC during steady-state operation. To address this gap, the present study focuses on the following core objectives: First locating the high electromagnetic load regions of CSMC through 3D electromagnetic simulation. Second calculating the stress distribution of the armour and helium inlet under multi-coupling fields. Then evaluating their safety margins in accordance with ASME and ITER standards. Finally verifying the effectiveness of the existing design to provide data support for the engineering application of CFETR CSMC. 2 The load cases During the steady-state operation of the CFETR CSMC, the armour and helium inlet are subjected to four types of mutually coupled loads, with specific characteristics as follows: Ⅰ) Preload: To prevent separation of coil modules under electromagnetic loads, a total preload of 75 MN needs to be applied via the inner and outer pre-tightening rods of the CSMC. This load is gradually transferred to the armour of the CICC conductor through the load beams, compression plates, and buffer zones, ultimately achieving tight bonding of the coil windings and avoiding relative displacement during the excitation process. Ⅱ) Thermal load: Before the CSMC is excited, it must be cooled from room temperature to an ultra-low temperature of 4.5 K. Due to the significant difference in thermal expansion coefficients between the armour and the outer insulation layer (the thermos-physical properties of each material at 4.5 K are shown in Table 1 ), significant thermal stress is generated at their contact interface after cooling due to inconsistent deformation. Ⅲ) Electromagnetic load: After excitation, the high-field Nb₃Sn coils generate a magnetic field of approximately 12 T, while the low-field NbTi coils produce a magnetic field of about 6 T. The electromagnetic force generated by the interaction between the magnetic field and the conductor current exerts concentrated impact loads on the armour and helium inlet, serving as the dominant factor driving structural stress. Ⅳ) Supercritical helium pressure load: When supercritical helium flows through the CICC conductor via the cooling pipeline, it acts indirectly on the inner wall of the armour through the superconducting cable, generating a uniform pressure of approximately 5 bar. This pressure is further superimposed on the internal stress field of the armour. 3 Electromagnetic calculation of CSMC 3.1 1/15 simplified electromagnetic model and 3D static magnetic field solution Considering the circumferential symmetry of the CSMC structure and loads, the coil windings were equivalent to a homogeneous block structure to reduce computational complexity, and a 1/15 simplified 3D electromagnetic model was established using ANSYS Maxwell. The key parameters of the model are as follows: For the Nb₃Sn inner coils, with the radius of 748.7 mm and height of 1651.2 mm. For the NbTi outer coils, with the radius of 1773.7 mm. With regard to the solution domain, a 1/15 spherical domain, whose size is 30 times that of the coil model, which can effectively avoid the interference of boundary effects on magnetic field calculation. For the boundary conditions, the two side faces of the spherical domain were set as master-slave boundaries to simulate circumferential symmetry, and the spherical surface was set as a far-field boundary to simulate the magnetic field attenuation characteristic in infinite space. According to the CSMC design current parameters, an excitation current of 47.65 kA×128 was applied to the two Nb₃Sn coils, and an excitation current of 47.65 kA×80 was applied to the three NbTi coils. A 3D static magnetic field solver based on the magnetic vector potential finite element method was invoked to calculate the magnetic density and electromagnetic force density distributions of the coils shown in Fig. 3 . The simulation results indicate that the maximum magnetic density of the coils is 11.97 T, concentrated at the inner mid-plane of the Nb₃Sn inner coils, which is close to the design target of 12 T. The maximum electromagnetic force density is 2.38×10⁸ N/m³, coinciding with the maximum magnetic field region and also located at the mid-plane of the Nb₃Sn inner coils. The maximum electromagnetic force of the NbTi coils is concentrated at the inner top ends of the upper and lower coils, and this distribution is directly related to the magnetic field gradient generated by the Nb₃Sn coils. 3.2 Refined verification of electromagnetic-structural load transfer To ensure the consistency of electromagnetic load transfer to the structural model in the subsequent magnetic-structural coupling analysis of the armour and helium inlet, an electromagnetic model incorporating discrete current filaments was further established based on the high-load regions identified in Section 3.1 . The calculation method of this model is consistent with that in Section 3.1 , but the current application strategy was optimized to match the actual cable arrangement. For the electromagnetic model of helium inlet, one cable was separated from the inner Nb₃Sn windings to simulate the cable adjacent to the helium inlet, and a current of 47.65 kA was applied individually. The remaining windings were equivalent to a block structure, with a current of 47.65 kA×127 applied shown in Fig. 4 . For the electromagnetic model of the armour, six cables were separated from the inner Nb₃Sn windings (covering the high-stress region of the armour), with a current of 47.65 kA applied to each cable. the remaining Nb₃Sn winding block was applied with a current of 47.65 kA×122. Meanwhile, four cables were separated from the upper NbTi windings, with a current of 47.65 kA applied to each. The remaining upper NbTi winding block was applied with a current of 47.65 kA×76 shown in Fig. 4 . The calculation results show that the electromagnetic force transfer ratio between the electromagnetic model and the structural model is close to 1, indicating that the electromagnetic force has been completely and accurately transferred to the structural model, laying a foundation for subsequent mechanical analysis. 4 Multi-coupling field analysis of armour and helium inlet 4.1 Analysis model and boundary conditions The armour and helium inlet are key components of the CSMC that directly bear multi-coupling loads, and also high-risk regions for strength failure. In this study, a local refined finite element model was established based on the ANSYS static structural solver to analyze their mechanical behavior. Based on the high-load regions identified in Section 3.2 , a local refined model was selected to balance calculation accuracy and efficiency. For the Nb₃Sn armour model, heat-treated 316 LN stainless steel was used, and 6 single-cell structures on the inner side of the mid-plane corresponding to 6 equivalent current filaments were selected, focusing on the high electromagnetic load region. For the NbTi armour model, heat-treated 316 L stainless steel was used, and 4 single-cell structures at the upper-left part of the NbTi upper coil corresponding to 4 equivalent current filaments were selected. For the helium inlet model, heat-treated 316 LN stainless steel was used, and 1 complete helium inlet structure at the mid-plane of the Nb₃Sn inner coil was selected to capture the stress concentration effect of holes and welds. To simulate the tight fitting state achieved through preloading and welding in actual assembly, the interfaces between armour and insulation layer, armour and cable, and helium inlet and armour were all set as bonded contact. Since the CSMC restricts displacement and rotation in all directions via anchor bolts, the support plate under the load beam was set as fixed constraint in the finite element model. In addition, the upper and lower boundaries of the 1/15 model were set as cyclic symmetry constraint to match the circumferential symmetry of the structure and loads, avoiding false stress concentration at the model boundaries. The load application sequence followed the actual operation process of the CSMC to ensure the accuracy of the load coupling effect. For the preload, preload elements were created on the inner and outer pre-tightening rods, and a total preload of 75 MN was applied to simulate the bolt preloading process. For the thermal load, a reference temperature of 293 K was set, and the thermal expansion coefficients of each material at 4.5 K (as shown in Table 1 ) were input to simulate the cooling process from room temperature to cryogenic temperature and generate interface thermal stress. For the electromagnetic load, the electromagnetic calculation result file from Section 3.2 was imported, and the electromagnetic force was loaded onto the structural model in the form of nodal forces to match the actual force distribution. For the supercritical helium pressure load, a uniform pressure of 5 bar was applied to the inner wall of the armour to simulate the effect of supercritical helium forced flow. Table 1 Material properties of different CSMC components at 4.5 K 316 L 316 LN Cable G10 ρ (Kgm - ³) 8040 7900 8900 - E (GPa) 206 207 4 15 µ (-) 0.3 0.3 0.3 0.3 CTE (×10 − 6 K -1 ) 10.24 10.2 2.4e-3 17.3 4.2 Stress distribution under multi-coupling field The stress states of the armour and helium inlet under multi-field coupling were obtained through calculation (as shown in Figs. 6 and 7 ). The maximum stress of the Nb₃Sn armour is 587 MPa, concentrated on the inner wall of the inner armour. This stress concentration stems from two factors. One is that the inner armour has no stacked structure for support (unlike the outer armour, which is supported by adjacent coils), making it more prone to deformation under electromagnetic forces. The other is because the bonded contact between the cable and the armour restricts the radial deformation of the armour, leading to a local increase in stress. The maximum stress of the NbTi armour is 403 MPa, concentrated on the inner wall of the upper armour. This distribution fully corresponds to the high electromagnetic load region of the NbTi coil identified in Section 3.1 (the inner top end of the upper coil), confirming that electromagnetic force is the dominant driving factor for the stress in the NbTi armour. There are two key stress concentration regions in the helium inlet. The maximum stress at the edge of the helium hole in the armour reaches 739 MPa, which is caused by geometric discontinuity (the transition from the armour plane to the hole), under the superposition of electromagnetic force and supercritical helium pressure, the local stress is significantly amplified. The maximum stress at the weld toe of the weld joint is 671 MPa, resulting from the superposition of electromagnetic force and welding residual stress. 5 Mechanical performance evaluation 5.1 Stress classification and linearization method To rigorously verify the structural safety of the armour and helium inlet, this study adopted the ASME Analytical Design Code (for stress classification) and the ITER Magnet Design Specification (for stress thresholds) to conduct a systematic stress evaluation. According to the stress generation mechanism, action range, and failure risk, the stresses were classified into primary stress, secondary stress, and peak stress. The stress extraction adopted the stress linearization method recommended by the ASME Code, and the path selection was based on the location of maximum stress. For the Nb₃Sn and NbTi armours, the maximum stress is located on the inner wall, so the linearization path was set along the thickness direction of the armour to capture the stress distribution law along the wall thickness (as shown in Fig. 8 ). For the helium inlet, the maximum stress is located at the edge of the racetrack-shaped hole, so the linearization path was set along the width direction of the hole (traversing the edge of the hole) to quantify the stress concentration caused by geometric discontinuity (as shown in Fig. 9 ). 5.2 Stress thresholds and safety evaluation The design stress intensity (Sₘ) of the material is determined by its yield strength (σ γ ) and ultimate tensile strength (σ u ) at 4.5 K, taking the smaller value between 2/3σ γ and 1/2σ u . For the safety criticality level of the CSMC armour and helium inlet, more stringent stress thresholds from the ITER Specification were adopted, local membrane stress should be less than1.3Sₘ. Membrane and bending plus secondary stress should be less than 2.0Sₘ. The specific thresholds for 316 L and 316 LN stainless steels are shown in Table 2 . For the Nb₃Sn armour, the stress linearization results indicate that the maximum values of global membrane stress, local membrane stress, local membrane plus bending stress, membrane and bending plus secondary stress are 429 MPa, 512 MPa, 564 MPa, and 587 MPa, respectively. All stress types are below their corresponding thresholds, showing sufficient safety margin. For the Helium inlet, considering that welding residual stress (ranging from 50 to 200 MPa) remains in the welded area after welding, the upper limit of 200 MPa was adopted for superposition. The superposed local membrane stress is 670 MPa, and the maximum value of membrane and bending plus secondary stress is 739 MPa. Based on the respective stress thresholds, the helium inlet still meets the safety requirements even under extreme residual stress, confirming reliable structural stability. For the NbTi armour, the global membrane stress and local membrane plus bending stress are 279 MPa and 372 MPa, respectively, both close to their corresponding thresholds. To improve the safety margin, a cold working hardening process optimization scheme was proposed. Experimental data from ASIPP [15–16] show that after cold working hardening of 316 L stainless steel, its yield strength at 4.5 K increases from the initial 480 MPa to 789 MPa. At this point, Sₘ is updated to 526 MPa, and the NbTi armour can fully meet the safety requirements after cold working hardening, verifying the effectiveness of this process. Table 2 Stress thresholds of 316 L &316 LN at 4.5 K (MPa) Stress Type Threshold 316 L 316 LN P m S m 288 600 P L 1.3S m 374 780 P L +P b 1.3S m 374 780 P L +P b +Q 2.0S m 576 1200 6 Conclusion Ⅰ) A 1/15 simplified electromagnetic model of the CSMC was established and the 3D static magnetic field simulation results show that during steady-state excitation, the maximum magnetic density and electromagnetic force density at the inner mid-plane of the Nb₃Sn inner coil are 11.97 T and 2.38×10⁸ N/m³, respectively. the maximum electromagnetic force of the NbTi coils is concentrated at the inner top ends of the upper and lower coils. Through a mapping model with current filaments, complete transfer of electromagnetic force to the structural model was achieved, and the high-load regions of the armour and helium inlet were accurately identified. Ⅱ) Under the coupling effect of preload, thermal load, electromagnetic load, and supercritical helium pressure, the maximum stress of the Nb₃Sn armour is 587 MPa located on the inner wall of the inner armour, the maximum stress of the NbTi armour is 403 MPa located on the inner wall of the upper armour, the maximum stress of the helium inlets is 739 MPa at the edge of the hole, the stress at the weld toe of the weld joint is 671 MPa. All high-stress regions are consistent with the locations of load concentration or geometric discontinuity, which conforms to mechanical principles. In accordance with ASME and ITER standards, the Nb₃Sn armour has sufficient safety margin, the helium inlet still meet safety requirements after superimposing 200 MPa residual stress, the NbTi armour meets the standards after cold working hardening, verifying the necessity of process optimization. Ⅲ) The material matching schemes for the CSMC armour, the racetrack-shaped design of helium inlet, combined with the cold working hardening process for the NbTi armour, can meet the strength requirements under cryogenic multi-coupling fields. This provides structural assurance for the steady-state operation of the CFETR CSMC and also offers a reference for the design of CICC conductor cooling interfaces in large-scale superconducting magnets. Declarations Author Contribution Xianwei Wang conceived the research, developed the coupling simulation method, led data analysis, and drafted the manuscript. Wenlong Xu built the CSMC electromagnetic model and optimized force transfer. Haikuo Zhao established the finite element model and conducted multi-coupling stress analysis. Aihua Xu performed safety evaluation and proposed NbTi armour optimization.Wentao Xie revised the manuscript. All authors read and approved the final manuscript. References Jiang H., Wu S.T., Cheng J. Optimization model of a structural simulation design for a CICC. Chinese Science Bulletin, 2011, Vol. 56, No. 27, pp. 2978-2983. Shi N., Chan V.S., Wan Y.X., Li J.G., Gao X., Ye M.Y. Evaluation of CFETR key parameters with different scenarios using system analysis code. Fusion Engineering and Design, 2016, Vol. 112, pp. 47-52. Zhuang G., et al. Progress of the CFETR design. Nuclear Fusion, 2019, Vol. 59, No. 11, Art. No.: 112010. Wu Y., et al. Basic design and progress of central solenoid model coil for CFETR. IEEE Transactions on Applied Superconductivity, 2018, Vol. 28, No. 3, Art. No.: 4200205. Wang X., Han P., Xu X., Xie F., et al. The preload analyses of CFETR CSMC pre-compression structure. IEEE Transactions on Applied Superconductivity, 2022, Vol. 32, No. 6, Art. No.: 4202005. Ma G., Wu Y., Shi Y., et al. Manufacture and Test of a Prototype Nb₃Sn-NbTi Joint Sample for the CFETR Central Solenoid Model Coil. IEEE Transactions on Applied Superconductivity, 2020, Vol. 30, No. 4, pp. 1-5. Obana T., Takahata K., Hamaguchi S., et al. Magnetic Field Measurements of JT-60SA CS Model Coil. Fusion Engineering and Design, 2015, Vol. 90, pp. 55-61. De Marzi G., FiamozzI Zignani C., et al. JT-60SA NbTi Wire Characterization After Thermal Shock Due to Helium Inlet Welding. IEEE Transactions on Applied Superconductivity, 2014, Vol. 24, No. 3, pp. 1-4. Decool P., Cloez H., Nicollet S., et al. Design and Qualification of ITER CS and TF Cooling Inlets. IEEE Transactions on Applied Superconductivity, 2006, Vol. 16, No. 2, pp. 876-879. Myatt r.L., Martovetsky N.N., Barbier C., et al. ITER CS Conductor Helium Inlet Design Optimization and Evaluation. Fusion Science and Technology, 2013, Vol. 64, No. 2, pp. 161-167. Aviles Santillana I., Sgobba S., Castillo Rivero S., et al. Post-Mortem Analysis of ITER CS Helium Inlets Fatigue Tested at Cryogenic Temperature. Fusion Engineering and Design, 2019, Vol. 146, pp. 642-646. Li X.B., Jin H., Qin J.G., et al. Mechanical Properties of ITER CICC Jacket in China. IEEE Transactions on Applied Superconductivity, 2018, Vol. 28, No. 3, pp. 1-5. Zhang Z., Song Y., Wu H., et al. Fatigue Tests on ITER PF6 Coil Helium Inlet at 77 K. IEEE Transactions on Applied Superconductivity, 2018, Vol. 28, No. 5, pp. 1-7. Xu A., Wu Y., Jin J., et al. Development of the Helium Inlet and Outlet for the CFETR Central Solenoid Model Coil. IEEE Transactions on Applied Superconductivity, 2018, Vol. 28, No. 4, pp. 1-5. Hua J.L., Yu W., Qi Y.H., et al. Low temperature mechanical test of ITER PF conductor jacket (in Chinese). Superconductivity, 2009, Vol. 37, No. 9, pp. 31-33. Xin H.Z., Jing S., Hui J., et al. Study on the mechanical properties of 316 LN jacket for fusion under different conditions (in Chinese). Superconductivity, 2016, Vol. 45, No. 3, pp. 38-42. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 28 Apr, 2026 Read the published version in Journal of Fusion Energy → Version 1 posted Editorial decision: Revision requested 02 Mar, 2026 Reviews received at journal 17 Feb, 2026 Reviews received at journal 10 Feb, 2026 Reviewers agreed at journal 26 Jan, 2026 Reviewers agreed at journal 25 Jan, 2026 Reviewers agreed at journal 20 Jan, 2026 Reviewers invited by journal 09 Dec, 2025 Editor assigned by journal 04 Dec, 2025 Submission checks completed at journal 04 Dec, 2025 First submitted to journal 03 Dec, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8274653","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":557890415,"identity":"733c7b70-5b99-4995-8426-03fa66779333","order_by":0,"name":"Xianwei Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYPACG2YIzUa8ljSgFmbStBxmIF6LwfGzh1/ztp1nl5+Rf4DhQ9lhBv7ZDQS0nMlLs5zZdpvZ4EYyA+OMc4cZJO4cwK/F7ECOmcHHbUAtEskMzLxthxkMJBIIaDn/xswgcds5ZvkZQC1/idJyI8f4wcdtB5gZgA5jZiRGi/2NN2aMM/8lMxuceWxwsOdcOo/EDQJaJPtzjD/znLFLlm9PfPjgR5m1HP8MAlqAgE0CSCSDWAeAmIegeiBg/gAk7IhROQpGwSgYBSMUAABWRkI8Fh3aHgAAAABJRU5ErkJggg==","orcid":"","institution":"Jiangsu University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Xianwei","middleName":"","lastName":"Wang","suffix":""},{"id":557890417,"identity":"b480eb7c-ce49-47d6-9c9f-8656025023bb","order_by":1,"name":"Wenlong Xu","email":"","orcid":"","institution":"Jiangsu University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Wenlong","middleName":"","lastName":"Xu","suffix":""},{"id":557890420,"identity":"0ef41c38-de9d-4ac5-b5e2-c447291f9bfd","order_by":2,"name":"Haikuo Zhao","email":"","orcid":"","institution":"Jiangsu University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Haikuo","middleName":"","lastName":"Zhao","suffix":""},{"id":557890422,"identity":"025376de-d690-4c19-b658-6af74e9e87e0","order_by":3,"name":"Aihua Xu","email":"","orcid":"","institution":"Changzhou Vocational Institute of Mechatronic Technology","correspondingAuthor":false,"prefix":"","firstName":"Aihua","middleName":"","lastName":"Xu","suffix":""},{"id":557890424,"identity":"40c5f836-1ed9-4182-a43f-6fbf05d86104","order_by":4,"name":"Wentao Xie","email":"","orcid":"","institution":"Jiangsu University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Wentao","middleName":"","lastName":"Xie","suffix":""}],"badges":[],"createdAt":"2025-12-04 02:38:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8274653/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8274653/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10894-026-00576-w","type":"published","date":"2026-04-28T15:57:24+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":98433369,"identity":"2826bf30-b44d-46bf-bc2a-e8f52c9dd707","added_by":"auto","created_at":"2025-12-17 16:50:41","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2853977,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.docx","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/3685d4691c793831e96cd2e4.docx"},{"id":98433043,"identity":"37add1c0-aaa7-4bd6-952c-b5a889d9c1d8","added_by":"auto","created_at":"2025-12-17 16:50:12","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":6457,"visible":true,"origin":"","legend":"","description":"","filename":"c0ab76f7c5f04f71925ac09ddabf2cf5.json","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/1f3c92f725a266df98c660c4.json"},{"id":98237511,"identity":"cc9de920-6cb2-498b-8e36-8868682d3b65","added_by":"auto","created_at":"2025-12-15 14:48:27","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":58994,"visible":true,"origin":"","legend":"","description":"","filename":"c0ab76f7c5f04f71925ac09ddabf2cf51enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/5c2ec61e80d1d0973929aad6.xml"},{"id":98433256,"identity":"52a4bf36-732e-4d43-9e51-9b75828dc676","added_by":"auto","created_at":"2025-12-17 16:50:31","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":105216,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/cbad289ff0ae6968a7ce7ff3.png"},{"id":98237519,"identity":"ba41c31f-9612-41bc-a503-dbd9232aa12e","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"png","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":96253,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/c1032147f18409631c36b278.png"},{"id":98434619,"identity":"8bdb1dfd-14d8-4e4d-80a7-453842e14c8b","added_by":"auto","created_at":"2025-12-17 16:52:23","extension":"png","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":722113,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/9cb9da89dc85a3cd1c89a0c9.png"},{"id":98433019,"identity":"8634b9b8-7081-47e4-92b5-d2bfbe7237dc","added_by":"auto","created_at":"2025-12-17 16:50:11","extension":"png","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":121752,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/83f21a3d494b1e5a1482467f.png"},{"id":98434408,"identity":"6672f8e1-9c76-427d-8ab1-ec24c90e1c6d","added_by":"auto","created_at":"2025-12-17 16:52:04","extension":"png","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":514222,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/bc4c28dccdd35fa263e16158.png"},{"id":98433393,"identity":"581e1586-14ab-43ed-814d-55af1af462ee","added_by":"auto","created_at":"2025-12-17 16:50:42","extension":"png","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":503745,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/ce5ad8260b170e2788a52a8a.png"},{"id":98237527,"identity":"60ae562c-7a77-4d0c-abd4-f83e38e677ae","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":280884,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/80e0b8082903c462a6e36747.png"},{"id":98432797,"identity":"50734227-f818-4b37-b4f8-d148f0f09a57","added_by":"auto","created_at":"2025-12-17 16:49:58","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":261408,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/d682c0d1d2a07705535256dc.png"},{"id":98237539,"identity":"7cc7cb24-e084-4794-a8d6-74dc09c36c45","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"png","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":198553,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/6afb241e68ac9e64d8af9abf.png"},{"id":98237518,"identity":"a276ff09-de2b-4312-a254-0c3b62652ab8","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":23241,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/347a6dd81e5b79ca6a8afc47.png"},{"id":98237522,"identity":"4176484d-3928-49b7-8317-a4d12fed3a9c","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"png","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":19066,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/24b7c4633d8279fb7f743129.png"},{"id":98237528,"identity":"33be435a-e993-4a87-b48b-1e33ba0bce86","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"png","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":119698,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/f5da31ad7843cd39ef441ab1.png"},{"id":98434472,"identity":"c8d6092b-a250-4e82-9c5e-199c8a8a82c5","added_by":"auto","created_at":"2025-12-17 16:52:09","extension":"png","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":20507,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/ea18ef8e09b78bfc8cabdf13.png"},{"id":98434344,"identity":"1d1aeac4-f1fe-49c6-ae03-c780e2bd1e16","added_by":"auto","created_at":"2025-12-17 16:51:58","extension":"png","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":57141,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/8179fded61a3d4bac2a65e93.png"},{"id":98434186,"identity":"09d6b27a-1a6d-40de-a9c9-185e70a39e0d","added_by":"auto","created_at":"2025-12-17 16:51:39","extension":"png","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":45759,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/65986adf7556d1bf93633a24.png"},{"id":98237531,"identity":"7b5177af-c058-4d94-a640-bba38cd9fe7e","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"png","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":29536,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/d2f21ea7f97d6d32a5d6800c.png"},{"id":98434557,"identity":"60acd230-f847-477b-9273-adf9fe93f611","added_by":"auto","created_at":"2025-12-17 16:52:19","extension":"png","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":27241,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/619dcc1a692140a8e023d9f1.png"},{"id":98237535,"identity":"d4085d43-2205-4bf9-a846-c404a3e7b618","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"png","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":23512,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/215bb3b38f0697d52b4e6f01.png"},{"id":98237534,"identity":"d63b1163-44e5-44ad-a0ad-258463e470cc","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"xml","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":55641,"visible":true,"origin":"","legend":"","description":"","filename":"c0ab76f7c5f04f71925ac09ddabf2cf51structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/872222e4bfbf8d03d5ce8a56.xml"},{"id":98237530,"identity":"6d95208a-08a2-4d6d-9534-61b1dee2ac69","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"html","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":63346,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/1bb2b3e89d18ea47d098b2a9.html"},{"id":98237508,"identity":"53875d8e-22fa-48db-8ba5-6ebc4ab74480","added_by":"auto","created_at":"2025-12-15 14:48:27","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":65889,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of cross-section and dimensions of Nb₃Sn and NbTi single-cell conductor\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/97059311b74fde626a439968.png"},{"id":98432759,"identity":"594efc25-e055-4779-b92c-239da63dd9b8","added_by":"auto","created_at":"2025-12-17 16:49:54","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":94829,"visible":true,"origin":"","legend":"\u003cp\u003eModel of helium inlet at the armour and cross-sectional view of helium inlet structure\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/7ba9b0e8c86cdcd3604e07a5.png"},{"id":98433232,"identity":"60b8f6d8-86fb-4d04-af81-b0053d71686e","added_by":"auto","created_at":"2025-12-17 16:50:29","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":378823,"visible":true,"origin":"","legend":"\u003cp\u003eMagnetic density and electromagnetic force density of CSMC coil windings\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/0710d4291c50193d02e420f7.png"},{"id":98434372,"identity":"edb6898b-a0b3-460a-aaf4-64ddb387f980","added_by":"auto","created_at":"2025-12-17 16:52:01","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":73958,"visible":true,"origin":"","legend":"\u003cp\u003eElectromagnetic analysis models of helium inlet and armour. (A) Electromagnetic analysis model of helium inlet. (B) Electromagnetic analysis model of armour.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/d8f42594956582be2974d8e8.png"},{"id":98237514,"identity":"6b56766e-1920-4787-8c48-e052826f5f5e","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":259501,"visible":true,"origin":"","legend":"\u003cp\u003eFinite element models of armour and helium inlet\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/39b4d8d3c7c929b884392340.png"},{"id":98432548,"identity":"e6544612-0716-4ff9-9e7d-58ce8f6f11db","added_by":"auto","created_at":"2025-12-17 16:49:40","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":228254,"visible":true,"origin":"","legend":"\u003cp\u003eTreca stress on Nb₃Sn and NbTi armours\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/f27c64e1ab4e0185164b87b2.png"},{"id":98237532,"identity":"178dd1ab-718c-49d5-8ac1-715585c9fe55","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":163200,"visible":true,"origin":"","legend":"\u003cp\u003eTresca stress on helium inlet armour and welded joints\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/10c117de4d9792b902ea9f16.png"},{"id":98237525,"identity":"3b351568-209a-49ca-9e35-bc43da491224","added_by":"auto","created_at":"2025-12-15 14:48:28","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":178773,"visible":true,"origin":"","legend":"\u003cp\u003eStress linearization of Nb₃Sn and NbTi armours. (A) Stress linearization of Nb₃Sn armour.\u003cbr\u003e\n(B) Stress linearization of NbTi armour.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/8895041a11bee39ded01bfd8.png"},{"id":98434493,"identity":"869d43f3-21b3-421c-9814-eae32fb107ad","added_by":"auto","created_at":"2025-12-17 16:52:11","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":122820,"visible":true,"origin":"","legend":"\u003cp\u003eStress linearization results of helium inlet\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/fc64330c5e6e8e98e1fb5ec4.png"},{"id":108440229,"identity":"24c32613-9d49-40b2-85c4-f02e464aad41","added_by":"auto","created_at":"2026-05-04 16:33:47","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1668889,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8274653/v1/00338819-23d1-4c56-8a39-f54d9e87b064.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mechanical Property Evaluation of CSMC Armour and Helium Inlet under Steady-State Operation","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe Cable-in-Conduit Conductor (CICC) is an integrated current-carrying component fabricated by first twisting multiple superconducting strands into a cable, then encapsulating the cable within a metallic conduit, and finally filling the conduit with supercritical helium to achieve both cooling and insulation. Endowed with efficient cooling capacity, excellent mechanical stability, favorable reliability and maintainability, as well as high current-carrying capability, CICC has been widely applied in large-scale superconducting magnet devices \u003csup\u003e[1]\u003c/sup\u003e. The Central Solenoid (CS) coil of the China Fusion Engineering Test Reactor (CFETR) \u003csup\u003e[2\u0026ndash;3]\u003c/sup\u003e is the core component for plasma confinement, and its performance directly determines the operational reliability of the reactor. To simulate the full-operating-condition characteristics of the CFETR CS coil while balancing R\u0026amp;D economy and design objectives, the CFETR Central Solenoid Model Coil (CSMC) adopts a hybrid conductor design: Nb₃Sn superconducting conductors are selected for the high-magnetic-field-region coils to meet the demand for strong magnetic fields \u003csup\u003e[4]\u003c/sup\u003e, while NbTi conductors are used for the low-magnetic-field-region coils to balance cost and performance \u003csup\u003e[5]\u003c/sup\u003e. The CICC conductor of the CSMC features a four-layer \"outer-to-inner\" composite structure, consisting of an insulation layer, an armour layer, a cable, and a central cooling tube. Specifically, the insulation layer is made of glass fiber-reinforced resin (G10) to realize electrical insulation between the conductor and external structures. The armour layer is composed of austenitic stainless steel (316 LN for Nb₃Sn coils and 316 L for NbTi coils) and undertakes the functions of structural support and supercritical helium sealing; The cable is formed by twisting Nb₃Sn/NbTi superconducting strands with pure copper in a designed proportion, which balances current-carrying and thermal conductivity performances. A through-hole is reserved at the center of the cable for the insertion of the central cooling tube, so as to realize supercritical helium circulation. The cross-sectional dimension parameters of the two types of conductors are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e \u003csup\u003e[6]\u003c/sup\u003e. The manufacturing process of CICC conductors follows four key procedures: five-stage cabling of superconducting strands, welding and forming of stainless steel armour, insertion of the cable into the conduit, and overall rolling and diameter reduction to the designed dimensions. Since the CICC conductors of CSMC rely on forced-flow cooling with supercritical helium (to maintain the coil at a cryogenic temperature of 4.5 K), helium inlets and outlets must be opened on the inner and outer armours of the coil to enable the transportation of supercritical helium.\u003c/p\u003e\u003cp\u003eAs an integral part of the armour structure, the helium inlets and outlets are connected to the armour via welding to ensure sealing performance; a total of 10 helium inlets and outlets are arranged on the CSMC, distributed uniformly on the armours of the five sub-coils to guarantee uniform cooling. Key parameters of the racetrack-shaped helium inlet designed in this study are as follows: total height of 40 mm, boss diameter of 28.4 mm, and weld arc radius of 6.3 mm; corresponding racetrack-shaped holes are drilled on the armour, with a diameter of 12 mm and a flow area of 215 mm\u0026sup2; to reduce flow resistance. The 3D model and detailed dimensions of a single helium inlet are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Previous studies on the JT-60SA CSMC \u003csup\u003e[7\u0026ndash;8]\u003c/sup\u003e, ITER CSMC \u003csup\u003e[9\u0026ndash;12\u003c/sup\u003e], and ITER PF6 coil \u003csup\u003e[13]\u003c/sup\u003e have focused on armour material selection, geometric design of helium inlet, optimization of welding processes, and thermal stability. Earlier research on the CFETR CSMC \u003csup\u003e[14]\u003c/sup\u003e has also covered similar directions, but none have systematically analyzed the mechanical behavior of the armour and helium inlet under the multi-field coupling of preload, thermal, electromagnetic, and supercritical helium pressure. However, this coupled load environment is the core factor determining the structural safety of CSMC during steady-state operation. To address this gap, the present study focuses on the following core objectives: First locating the high electromagnetic load regions of CSMC through 3D electromagnetic simulation. Second calculating the stress distribution of the armour and helium inlet under multi-coupling fields. Then evaluating their safety margins in accordance with ASME and ITER standards. Finally verifying the effectiveness of the existing design to provide data support for the engineering application of CFETR CSMC.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"2 The load cases","content":"\u003cp\u003eDuring the steady-state operation of the CFETR CSMC, the armour and helium inlet are subjected to four types of mutually coupled loads, with specific characteristics as follows: Ⅰ) Preload: To prevent separation of coil modules under electromagnetic loads, a total preload of 75 MN needs to be applied via the inner and outer pre-tightening rods of the CSMC. This load is gradually transferred to the armour of the CICC conductor through the load beams, compression plates, and buffer zones, ultimately achieving tight bonding of the coil windings and avoiding relative displacement during the excitation process. Ⅱ) Thermal load: Before the CSMC is excited, it must be cooled from room temperature to an ultra-low temperature of 4.5 K. Due to the significant difference in thermal expansion coefficients between the armour and the outer insulation layer (the thermos-physical properties of each material at 4.5 K are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), significant thermal stress is generated at their contact interface after cooling due to inconsistent deformation. Ⅲ) Electromagnetic load: After excitation, the high-field Nb₃Sn coils generate a magnetic field of approximately 12 T, while the low-field NbTi coils produce a magnetic field of about 6 T. The electromagnetic force generated by the interaction between the magnetic field and the conductor current exerts concentrated impact loads on the armour and helium inlet, serving as the dominant factor driving structural stress. Ⅳ) Supercritical helium pressure load: When supercritical helium flows through the CICC conductor via the cooling pipeline, it acts indirectly on the inner wall of the armour through the superconducting cable, generating a uniform pressure of approximately 5 bar. This pressure is further superimposed on the internal stress field of the armour.\u003c/p\u003e"},{"header":"3 Electromagnetic calculation of CSMC","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e3.1 1/15 simplified electromagnetic model and 3D static magnetic field solution\u003c/h2\u003e\u003cp\u003eConsidering the circumferential symmetry of the CSMC structure and loads, the coil windings were equivalent to a homogeneous block structure to reduce computational complexity, and a 1/15 simplified 3D electromagnetic model was established using ANSYS Maxwell. The key parameters of the model are as follows: For the Nb₃Sn inner coils, with the radius of 748.7 mm and height of 1651.2 mm. For the NbTi outer coils, with the radius of 1773.7 mm. With regard to the solution domain, a 1/15 spherical domain, whose size is 30 times that of the coil model, which can effectively avoid the interference of boundary effects on magnetic field calculation. For the boundary conditions, the two side faces of the spherical domain were set as master-slave boundaries to simulate circumferential symmetry, and the spherical surface was set as a far-field boundary to simulate the magnetic field attenuation characteristic in infinite space. According to the CSMC design current parameters, an excitation current of 47.65 kA\u0026times;128 was applied to the two Nb₃Sn coils, and an excitation current of 47.65 kA\u0026times;80 was applied to the three NbTi coils. A 3D static magnetic field solver based on the magnetic vector potential finite element method was invoked to calculate the magnetic density and electromagnetic force density distributions of the coils shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The simulation results indicate that the maximum magnetic density of the coils is 11.97 T, concentrated at the inner mid-plane of the Nb₃Sn inner coils, which is close to the design target of 12 T. The maximum electromagnetic force density is 2.38\u0026times;10⁸ N/m\u0026sup3;, coinciding with the maximum magnetic field region and also located at the mid-plane of the Nb₃Sn inner coils. The maximum electromagnetic force of the NbTi coils is concentrated at the inner top ends of the upper and lower coils, and this distribution is directly related to the magnetic field gradient generated by the Nb₃Sn coils.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Refined verification of electromagnetic-structural load transfer\u003c/h2\u003e\u003cp\u003eTo ensure the consistency of electromagnetic load transfer to the structural model in the subsequent magnetic-structural coupling analysis of the armour and helium inlet, an electromagnetic model incorporating discrete current filaments was further established based on the high-load regions identified in Section \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e. The calculation method of this model is consistent with that in Section \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e, but the current application strategy was optimized to match the actual cable arrangement. For the electromagnetic model of helium inlet, one cable was separated from the inner Nb₃Sn windings to simulate the cable adjacent to the helium inlet, and a current of 47.65 kA was applied individually. The remaining windings were equivalent to a block structure, with a current of 47.65 kA\u0026times;127 applied shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. For the electromagnetic model of the armour, six cables were separated from the inner Nb₃Sn windings (covering the high-stress region of the armour), with a current of 47.65 kA applied to each cable. the remaining Nb₃Sn winding block was applied with a current of 47.65 kA\u0026times;122. Meanwhile, four cables were separated from the upper NbTi windings, with a current of 47.65 kA applied to each. The remaining upper NbTi winding block was applied with a current of 47.65 kA\u0026times;76 shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The calculation results show that the electromagnetic force transfer ratio between the electromagnetic model and the structural model is close to 1, indicating that the electromagnetic force has been completely and accurately transferred to the structural model, laying a foundation for subsequent mechanical analysis.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4 Multi-coupling field analysis of armour and helium inlet","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Analysis model and boundary conditions\u003c/h2\u003e\u003cp\u003eThe armour and helium inlet are key components of the CSMC that directly bear multi-coupling loads, and also high-risk regions for strength failure. In this study, a local refined finite element model was established based on the ANSYS static structural solver to analyze their mechanical behavior. Based on the high-load regions identified in Section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e, a local refined model was selected to balance calculation accuracy and efficiency. For the Nb₃Sn armour model, heat-treated 316 LN stainless steel was used, and 6 single-cell structures on the inner side of the mid-plane corresponding to 6 equivalent current filaments were selected, focusing on the high electromagnetic load region. For the NbTi armour model, heat-treated 316 L stainless steel was used, and 4 single-cell structures at the upper-left part of the NbTi upper coil corresponding to 4 equivalent current filaments were selected. For the helium inlet model, heat-treated 316 LN stainless steel was used, and 1 complete helium inlet structure at the mid-plane of the Nb₃Sn inner coil was selected to capture the stress concentration effect of holes and welds. To simulate the tight fitting state achieved through preloading and welding in actual assembly, the interfaces between armour and insulation layer, armour and cable, and helium inlet and armour were all set as bonded contact. Since the CSMC restricts displacement and rotation in all directions via anchor bolts, the support plate under the load beam was set as fixed constraint in the finite element model. In addition, the upper and lower boundaries of the 1/15 model were set as cyclic symmetry constraint to match the circumferential symmetry of the structure and loads, avoiding false stress concentration at the model boundaries. The load application sequence followed the actual operation process of the CSMC to ensure the accuracy of the load coupling effect. For the preload, preload elements were created on the inner and outer pre-tightening rods, and a total preload of 75 MN was applied to simulate the bolt preloading process. For the thermal load, a reference temperature of 293 K was set, and the thermal expansion coefficients of each material at 4.5 K (as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) were input to simulate the cooling process from room temperature to cryogenic temperature and generate interface thermal stress. For the electromagnetic load, the electromagnetic calculation result file from Section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e was imported, and the electromagnetic force was loaded onto the structural model in the form of nodal forces to match the actual force distribution. For the supercritical helium pressure load, a uniform pressure of 5 bar was applied to the inner wall of the armour to simulate the effect of supercritical helium forced flow.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eMaterial properties of different CSMC components at 4.5 K\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e316 L\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e316 LN\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eCable\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eG10\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eρ (Kgm\u003csup\u003e-\u003c/sup\u003e\u0026sup3;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8040\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e7900\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e8900\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eE (GPa)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e206\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e207\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u0026micro; (-)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCTE (\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e K\u003csup\u003e-1\u003c/sup\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e10.24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e10.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.4e-3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e17.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e4.2 Stress distribution under multi-coupling field\u003c/h2\u003e\u003cp\u003eThe stress states of the armour and helium inlet under multi-field coupling were obtained through calculation (as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e and \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). The maximum stress of the Nb₃Sn armour is 587 MPa, concentrated on the inner wall of the inner armour. This stress concentration stems from two factors. One is that the inner armour has no stacked structure for support (unlike the outer armour, which is supported by adjacent coils), making it more prone to deformation under electromagnetic forces. The other is because the bonded contact between the cable and the armour restricts the radial deformation of the armour, leading to a local increase in stress. The maximum stress of the NbTi armour is 403 MPa, concentrated on the inner wall of the upper armour. This distribution fully corresponds to the high electromagnetic load region of the NbTi coil identified in Section \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e (the inner top end of the upper coil), confirming that electromagnetic force is the dominant driving factor for the stress in the NbTi armour. There are two key stress concentration regions in the helium inlet. The maximum stress at the edge of the helium hole in the armour reaches 739 MPa, which is caused by geometric discontinuity (the transition from the armour plane to the hole), under the superposition of electromagnetic force and supercritical helium pressure, the local stress is significantly amplified. The maximum stress at the weld toe of the weld joint is 671 MPa, resulting from the superposition of electromagnetic force and welding residual stress.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"5 Mechanical performance evaluation","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e5.1 Stress classification and linearization method\u003c/h2\u003e\n \u003cp\u003eTo rigorously verify the structural safety of the armour and helium inlet, this study adopted the ASME Analytical Design Code (for stress classification) and the ITER Magnet Design Specification (for stress thresholds) to conduct a systematic stress evaluation. According to the stress generation mechanism, action range, and failure risk, the stresses were classified into primary stress, secondary stress, and peak stress. The stress extraction adopted the stress linearization method recommended by the ASME Code, and the path selection was based on the location of maximum stress. For the Nb₃Sn and NbTi armours, the maximum stress is located on the inner wall, so the linearization path was set along the thickness direction of the armour to capture the stress distribution law along the wall thickness (as shown in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e). For the helium inlet, the maximum stress is located at the edge of the racetrack-shaped hole, so the linearization path was set along the width direction of the hole (traversing the edge of the hole) to quantify the stress concentration caused by geometric discontinuity (as shown in Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003e5.2 Stress thresholds and safety evaluation\u003c/h2\u003e\n \u003cp\u003eThe design stress intensity (Sₘ) of the material is determined by its yield strength (\u0026sigma;\u003csub\u003e\u0026gamma;\u003c/sub\u003e) and ultimate tensile strength (\u0026sigma;\u003csub\u003eu\u003c/sub\u003e) at 4.5 K, taking the smaller value between 2/3\u0026sigma;\u003csub\u003e\u0026gamma;\u003c/sub\u003e and 1/2\u0026sigma;\u003csub\u003eu\u003c/sub\u003e. For the safety criticality level of the CSMC armour and helium inlet, more stringent stress thresholds from the ITER Specification were adopted, local membrane stress should be less than1.3Sₘ. Membrane and bending plus secondary stress should be less than 2.0Sₘ. The specific thresholds for 316 L and 316 LN stainless steels are shown in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. For the Nb₃Sn armour, the stress linearization results indicate that the maximum values of global membrane stress, local membrane stress, local membrane plus bending stress, membrane and bending plus secondary stress are 429 MPa, 512 MPa, 564 MPa, and 587 MPa, respectively. All stress types are below their corresponding thresholds, showing sufficient safety margin. For the Helium inlet, considering that welding residual stress (ranging from 50 to 200 MPa) remains in the welded area after welding, the upper limit of 200 MPa was adopted for superposition. The superposed local membrane stress is 670 MPa, and the maximum value of membrane and bending plus secondary stress is 739 MPa. Based on the respective stress thresholds, the helium inlet still meets the safety requirements even under extreme residual stress, confirming reliable structural stability. For the NbTi armour, the global membrane stress and local membrane plus bending stress are 279 MPa and 372 MPa, respectively, both close to their corresponding thresholds. To improve the safety margin, a cold working hardening process optimization scheme was proposed. Experimental data from ASIPP \u003csup\u003e[15\u0026ndash;16]\u003c/sup\u003e show that after cold working hardening of 316 L stainless steel, its yield strength at 4.5 K increases from the initial 480 MPa to 789 MPa. At this point, Sₘ is updated to 526 MPa, and the NbTi armour can fully meet the safety requirements after cold working hardening, verifying the effectiveness of this process.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eStress thresholds of 316 L \u0026amp;316 LN at 4.5 K (MPa)\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eStress Type\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eThreshold\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e316 L\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e316 LN\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eP\u003csub\u003em\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS\u003csub\u003em\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e288\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e600\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eP\u003csub\u003eL\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.3S\u003csub\u003em\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e374\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e780\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eP\u003csub\u003eL\u003c/sub\u003e+P\u003csub\u003eb\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.3S\u003csub\u003em\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e374\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e780\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eP\u003csub\u003eL\u003c/sub\u003e+P\u003csub\u003eb\u003c/sub\u003e+Q\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.0S\u003csub\u003em\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e576\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1200\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"6 Conclusion","content":"\u003cp\u003eⅠ) A 1/15 simplified electromagnetic model of the CSMC was established and the 3D static magnetic field simulation results show that during steady-state excitation, the maximum magnetic density and electromagnetic force density at the inner mid-plane of the Nb₃Sn inner coil are 11.97 T and 2.38\u0026times;10⁸ N/m\u0026sup3;, respectively. the maximum electromagnetic force of the NbTi coils is concentrated at the inner top ends of the upper and lower coils. Through a mapping model with current filaments, complete transfer of electromagnetic force to the structural model was achieved, and the high-load regions of the armour and helium inlet were accurately identified.\u003c/p\u003e\u003cp\u003eⅡ) Under the coupling effect of preload, thermal load, electromagnetic load, and supercritical helium pressure, the maximum stress of the Nb₃Sn armour is 587 MPa located on the inner wall of the inner armour, the maximum stress of the NbTi armour is 403 MPa located on the inner wall of the upper armour, the maximum stress of the helium inlets is 739 MPa at the edge of the hole, the stress at the weld toe of the weld joint is 671 MPa. All high-stress regions are consistent with the locations of load concentration or geometric discontinuity, which conforms to mechanical principles. In accordance with ASME and ITER standards, the Nb₃Sn armour has sufficient safety margin, the helium inlet still meet safety requirements after superimposing 200 MPa residual stress, the NbTi armour meets the standards after cold working hardening, verifying the necessity of process optimization.\u003c/p\u003e\u003cp\u003eⅢ) The material matching schemes for the CSMC armour, the racetrack-shaped design of helium inlet, combined with the cold working hardening process for the NbTi armour, can meet the strength requirements under cryogenic multi-coupling fields. This provides structural assurance for the steady-state operation of the CFETR CSMC and also offers a reference for the design of CICC conductor cooling interfaces in large-scale superconducting magnets.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eXianwei Wang conceived the research, developed the coupling simulation method, led data analysis, and drafted the manuscript. Wenlong Xu built the CSMC electromagnetic model and optimized force transfer. Haikuo Zhao established the finite element model and conducted multi-coupling stress analysis. Aihua Xu performed safety evaluation and proposed NbTi armour optimization.Wentao Xie revised the manuscript. All authors read and approved the final manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eJiang H., Wu S.T., Cheng J. Optimization model of a structural simulation design for a CICC. Chinese Science Bulletin, 2011, Vol. 56, No. 27, pp. 2978-2983.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eShi N., Chan V.S., Wan Y.X., Li J.G., Gao X., Ye M.Y. Evaluation of CFETR key parameters with different scenarios using system analysis code. Fusion Engineering and Design, 2016, Vol. 112, pp. 47-52.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eZhuang G., et al. Progress of the CFETR design. Nuclear Fusion, 2019, Vol. 59, No. 11, Art. No.: \u0026nbsp;112010.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eWu Y., et al. Basic design and progress of central solenoid model coil for CFETR. IEEE Transactions on Applied Superconductivity, 2018, Vol. 28, No. 3, Art. No.: 4200205.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eWang X., Han P., Xu X., Xie F., et al. The preload analyses of CFETR CSMC pre-compression structure. IEEE Transactions on Applied Superconductivity, 2022, Vol. 32, No. 6, Art. No.: 4202005.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eMa G., Wu Y., Shi Y., et al. Manufacture and Test of a Prototype Nb₃Sn-NbTi Joint Sample for the CFETR Central Solenoid Model Coil. IEEE Transactions on Applied Superconductivity, 2020, Vol. 30, No. 4, pp. 1-5.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eObana T., Takahata K., Hamaguchi S., et al. Magnetic Field Measurements of JT-60SA CS Model Coil. Fusion Engineering and Design, 2015, Vol. 90, pp. 55-61.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eDe Marzi G., FiamozzI Zignani C., et al. JT-60SA NbTi Wire Characterization After Thermal Shock Due to Helium Inlet Welding. IEEE Transactions on Applied Superconductivity, 2014, Vol. 24, No. 3, pp. 1-4.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eDecool P., Cloez H., Nicollet S., et al. Design and Qualification of ITER CS and TF Cooling Inlets. IEEE Transactions on Applied Superconductivity, 2006, Vol. 16, No. 2, pp. 876-879.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eMyatt r.L., Martovetsky N.N., Barbier C., et al. ITER CS Conductor Helium Inlet Design Optimization and Evaluation. Fusion Science and Technology, 2013, Vol. 64, No. 2, pp. 161-167.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eAviles Santillana I., Sgobba S., Castillo Rivero S., et al. Post-Mortem Analysis of ITER CS Helium Inlets Fatigue Tested at Cryogenic Temperature. Fusion Engineering and Design, 2019, Vol. 146, pp. 642-646.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eLi X.B., Jin H., Qin J.G., et al. Mechanical Properties of ITER CICC Jacket in China. IEEE Transactions on Applied Superconductivity, 2018, Vol. 28, No. 3, pp. 1-5.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eZhang Z., Song Y., Wu H., et al. Fatigue Tests on ITER PF6 Coil Helium Inlet at 77 K. IEEE Transactions on Applied Superconductivity, 2018, Vol. 28, No. 5, pp. 1-7.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eXu A., Wu Y., Jin J., et al. Development of the Helium Inlet and Outlet for the CFETR Central Solenoid Model Coil. IEEE Transactions on Applied Superconductivity, 2018, Vol. 28, No. 4, pp. 1-5.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eHua J.L., Yu W., Qi Y.H., et al. Low temperature mechanical test of ITER PF conductor jacket (in Chinese). Superconductivity, 2009, Vol. 37, No. 9, pp. 31-33.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eXin H.Z., Jing S., Hui J., et al. Study on the mechanical properties of 316 LN jacket for fusion under different conditions (in Chinese). Superconductivity, 2016, Vol. 45, No. 3, pp. 38-42. \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-fusion-energy","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jofe","sideBox":"Learn more about [Journal of Fusion Energy](http://link.springer.com/journal/10894)","snPcode":"10894","submissionUrl":"https://submission.nature.com/new-submission/10894/3","title":"Journal of Fusion Energy","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"CFETR, CSMC, Jacket, Helium inlet, CICC","lastPublishedDoi":"10.21203/rs.3.rs-8274653/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8274653/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTo verify the mechanical safety of the armour and helium inlet of the China Fusion Engineering Test Reactor (CFETR) Central Solenoid Model Coil (CSMC) under multi-physics coupling fields during steady-state operation, this study adopted the electromagnetic-structural indirect coupling method, complying with ASME analytical design criteria and ITER magnet design specifications. A simplified electromagnetic model of CSMC was established via ANSYS Maxwell, and a current filament mapping approach was employed to achieve complete and accurate transfer of electromagnetic forces to the structural model. Static structural analysis using ANSYS was conducted to obtain the stress distribution of key components under multi-field coupling. Evaluation based on stress linearization results and ITER stress thresholds demonstrated that the Nb₃Sn armour and helium inlet fully meet safety requirements, while the NbTi armour complies with design criteria after cold working hardening treatment. This study confirms that the existing design of CSMC armour and racetrack-shaped helium inlet can withstand the strength demands of cryogenic multi-coupling fields, providing critical technical support for the engineering application of CFETR CSMC and a valuable reference for the cooling interface design of Cable-in-Conduit Conductors (CICC) in large-scale superconducting magnets.\u003c/p\u003e","manuscriptTitle":"Mechanical Property Evaluation of CSMC Armour and Helium Inlet under Steady-State Operation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-15 14:48:23","doi":"10.21203/rs.3.rs-8274653/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-02T08:51:34+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-18T02:01:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-11T03:17:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"185275312027537089725866943870350187125","date":"2026-01-26T16:01:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"18598420256532206272332900297028457031","date":"2026-01-26T00:08:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"336847720251679023922025996945301874905","date":"2026-01-21T02:55:53+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-09T23:31:41+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-04T05:45:51+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-04T05:44:24+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Fusion Energy","date":"2025-12-04T02:30:22+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-fusion-energy","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jofe","sideBox":"Learn more about [Journal of Fusion Energy](http://link.springer.com/journal/10894)","snPcode":"10894","submissionUrl":"https://submission.nature.com/new-submission/10894/3","title":"Journal of Fusion Energy","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"ba032487-8fbd-43f3-b483-07c20181c4ab","owner":[],"postedDate":"December 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-05-04T16:33:42+00:00","versionOfRecord":{"articleIdentity":"rs-8274653","link":"https://doi.org/10.1007/s10894-026-00576-w","journal":{"identity":"journal-of-fusion-energy","isVorOnly":false,"title":"Journal of Fusion Energy"},"publishedOn":"2026-04-28 15:57:24","publishedOnDateReadable":"April 28th, 2026"},"versionCreatedAt":"2025-12-15 14:48:23","video":"","vorDoi":"10.1007/s10894-026-00576-w","vorDoiUrl":"https://doi.org/10.1007/s10894-026-00576-w","workflowStages":[]},"version":"v1","identity":"rs-8274653","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8274653","identity":"rs-8274653","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}