Analysis on dynamic stability of superconducting coils in a three-coil partial torus

Based on a theoretical model of the magnetoelastic interaction of superconducting coils from the theory of curved beams and the Biot–Savart law, the dynamic behavior of the current-carrying coils disturbed by a pulse current is investigated in this paper. The initial boundary-value equations of the problem are numerically solved by applying the finite difference method for spatial part and the Wilson-θ method for time part. The numerical responses exhibit that the equilibrium position of the vibration of the deformable coil may sometimes jump from one to another, which is referred to as the magnetoelastic dynamic instability of the coil. It is found that the dynamic stability is mainly dependent upon the magnitudes of the steady working current, the peak and the duration of the pulse current. The ranges of these parameters for the magnetoelastic dynamic stability of the coils are searched in detail.