非圆Tokamak载流线圈的磁弹性分析

Analysis of Magnetoelastic Interaction of Non circular Current carrying Coils in Tokamak Device

基于曲梁理论和Ｂｉｏｔ－Ｓａｖａｒｔ定律描述超导载流线圈全部形变的理论模型，采用边值问题的齐次微分方程封闭形式解析通解和非齐次微分方程数值特解相叠加的半解析半数值方法，对非圆Ｄ型Ｔｏｋａｍａｋ载流线圈弯曲，失稳的磁弹性相互作用进行了研究；并且就线圈初始扰动位移对失稳临界电流的影响也进行了定量分析．数值模拟结果表明：线圈失稳的临界电流随线圈曲率半径的增大而增大，随线圈非完全对称排列这一初始缺陷的增大而减小．

By means of curved beam theory and the Biot Savart law, the mechanical characteristics such as bending and buckling of magnetoelastic interaction for non circular D shaped coils of superconducting magnets in Tokamak device is studied. In the theoretical analysis,overall deformations of the coils are considered. A semi analytical and semi numerical method, which is combined by the exact solution with closed form to the homogeneous differential equations and a set of numerical particular solutions to the inhomogeneous differential equations, is employed to solve the boundary value problem in which the nonlinearity is solved by iteration. It is found that this method can simulate the deformation process of the coils from magnetoelastic bending to instability. At the same time, the effect of initial deformation on the critical current of the magnetoelastic instability is also discussed quantitatively. The numerical results show that the critical current increases with the curvature radius of the coils, and decreases with an imperfection of initial misalignments to axisymmetric alignment of the magnets.