Numerical and analytical solutions for the dynamic stability of edge cooled superconducting tapes using two dimensional variational principles

The dynamic stability of an edge cooled superconducting tape is a nonlinear, 3-D magnetothermal problem. In this analysis, a 2-D linearized version is solved using variational principles. To model the physical behavior of the conductor accurately, trial functions are carefully chosen subject to the exact boundary conditions and a numerical solution is obtained. This solution is compared to a recently obtained analytic solution and the 1-D solution obtained by H.R. Hart Jr. (1968). The 2-D analysis indicates that the finite thermal diffusion in the superconductor can play a significant role for w_o /d_SC<100, where w_o is the half width of the tape and d_SC is the thickness of the superconductor