Deformation of a superconducting cylindrical tube in a perpendicular magnetic field

Stresses and displacements are obtained for an elastic superconductor in the form of an infinitely long, circular cylindrical tube subjected to an initially uniform magnetic field perpendicular to the tube's axis. The effect of the magnetic field penetration on the stressed State is assessed by solving the problem, firstly taking into account this penetration and, secondly, neglecting it. The problem involves the solution of a non-homogeneous biharmonic equation in two dimensions for the stress function. The special case of a circular cylinder is also given. Numerical calculations estimate the variation between the two cases for some quantities of practical interest. It is shown, in particular, that neglecting the penetration of the magnetic field in the elastic superconductor may induce a non-negligible error in the evaluation of the stressed state.