托卡马克聚变堆中环向磁场超导线圈的磁弹性弯曲与稳定性

本文针对托卡马克装置中超导载流磁体的磁弹性弯曲与稳定性问题，运用Ｂｉｏｔ－Ｓａｖａｒｔ定律和曲梁弯曲理论，给出了其环向磁场的超导载流线圈结构在自身电流产生的磁力作用下的磁弹性力学模型。所得到的控制方程反映了磁场与线圈变形之间的非线性耦合作用，全面描述了结构的轴向拉伸、绕轴扭转、面内弯曲和面外弯曲等各种变形模式。本文采用半解析半数值方法对控制方程进行了定量求解，获得了有关线圈形变和内力分布的定量结果。通过其面外弯曲变形与外加电流的非线性关系，应用Ｓｏｕｔｈｗｅｌ图，给出了线圈在磁弹性相互作用下发生磁弹性失稳的临界电流值，并讨论了临界电流随环向磁场线圈个数变化的规律

MAGNETOELASTIC BENDING AND STABILITY OF SUPERCONDUCTING TOROIDAL FIELD COILS IN A TOKAMAK REACTOR

A new theoretical model is applied to study magnetoelastic bending and stability of toroidal superconducting magnetic field coils which are subjected to strong magnetic force in a tokamak reactor according to the Biot Savart law and the curved beam theory. The governing equations of the model characterize the coupled behavior of nonlinear interaction between magnetic fields and deformation of the coils. They describe overall deformations of the coil: axial extention, torson about the centerline, in plane bending and out of plane bending. A semi analytical and seminumerical method is used for solving the governing equations to get quantitative results of the deformations and internal forces. Based on the nonlinear relation between the out of plane bending and the applied current, the critical current of magnetoelastic instability of a superconducting coil is obtained with the Southwell plot method. After that, the dependence of the critical current on the number of the superconducting coils in a full tokamak torus is discussed quantitatively.