Induced current state in a hollow superconducting cylinder

The problem of the destruction of the state with induced current (or, which is the same, with trapped magnetic flux) in a thin-walled superconducting cylinder is treated within the framework of the Ginzburg--Landau theory. Two problems are solved, namely, for a uniform specimen and a specimen with weak coupling along the cylinder generatrix. It is shown that in the case of the nonuniform cylinder the effective value of the trapped flux may be smaller than a flux quantum (n/sub asterisk/<1). Therefore, it turns out that the induced current state in a cylinder with weak coupling persists to higher temperatures than the n = 1 state in a uniform cylinder. This indicates that the nonuniform state may be an important factor in the destruction of superconductivity of cylindrical specimens with trapped magnetic flux