Critical fields of a superconducting cylinder

The self-consistent solutions of the nonlinear Ginzburg-Landau equations, which describe the behavior of a superconducting mesoscopic cylinder in an axial magnetic field H (provided there are no vortices inside the cylinder), are studied. Different, vortex-free states (M-, e-, d-, p-), which exist in a superconducting cylinder, are described. The critical fields (H ₁, H ₂, H _p , H _i , H _r ), at which the first or second order phase transitions between different states of the cylinder occur, are found as functions of the cylinder radius R and the GL-parameter . The boundary , which divides the regions of the first and second order (s, n)-transitions in the icreasing field, is found. It is found that at R→∞ the critical value, is . The hysteresis phenomena, which appear when the cylinder passes from the normal to superconducting state in the decreasing field, are described. The connection between the self-consistent results and the linearized theory is discussed. It is shown that in the limiting case and R ≫ λ (λ is the London penetration length) the self-consistent solution (which correponds to the socalled metastable p-state) coincides with the analitic solution found from the degenerate Bogomolnyi equations. The reason for the existence of two critical GL-parameters and in, bulk superconductors is discussed. An erratum to this article is available at.